Youtube comments of Fhf Fhf (@fhffhff).

  1. Вы что, с ума сошли смотреть 8 часов видео?
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  2. Церковь похоже на цирк,что в переводе означает круг.
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  3. А смотрящие программу "Давай поженимся" должны уже про нее забыть.
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  4. 3⁴*5/3⁵=5/3
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  5. Вообще-то,глаза зеркало души,но для неё всё правильно.
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  6. Никогда бы до этого не додумался.
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  7. Это ритуальная жертва как начало большой игры.
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  8. 7:24 это не парабола, а нормальное распределение.
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  9. BA²-4BABC+BC²=0 BA=(2±√3)BC BM²=(2+√3)BC² BC=BM(√1,5-+√0,5) Строим отрезок длиной BM(√1,5-√0,5), под прямым углом отрезок длиной BM(√1,5+√0,5), соединяем концы и получаем треугольник.
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  10. Наибольший общий делитель—НОД.
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  11. а,21а-¹ 8-а,3-а а=2,1✓
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  12. Про цикличную историю:закон мироздания- я альфа, я омега.
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  13. Уважаемый главред! Почему у Вас имя Сигизмунд?
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  14. "Лошарик" стал лошарой...
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  15. 36√3/(36+√3*π)=1,502
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  16. xy+xz+yz+1/x+2/y+5/z y+z-x-²=0 x=±1/(y+ z)⁰,⁵ +*+>x min=y/(y+z)⁰,⁵+z/(y+z)⁰,⁵+yz+(y+z)⁰,⁵+2/y+5/z ..'=((y+z)⁰,⁵-y*0,5(y+z)-⁰,⁵)/(y+z)+z*0,5(y+z)-⁰,⁵+z+0,5(y+z)-⁰,⁵-2y-²=0 {y≤√(2/z),y≥-√(2/z),[0=(z²+3z³)y⁷+(-1-z-0,2 5z²)y⁶+(-7z-2,5z²-0,5z³+3z⁴)y⁵+(-14,25z²-1, 5z³-0,25z⁴+z⁵)y⁴+(4-12z³)y³+(12z-4z⁴)y²+1 2z²y+4z³;+*z^-0,5->y z^-0,25(1+z¹,⁵)-⁰,⁵+z ¹,²⁵(1+z¹,⁵)-⁰,⁵+z^0,5+z^-0,25(1+z¹,⁵)⁰,⁵+2z⁰,⁵+5z-¹ ...'=-0,25z^-1,25(1+z¹,⁵)-⁰,⁵+z^-0,25-0,5(1+z¹,⁵)-¹,⁵*1,5z⁰,⁵+1,25z^0,25(1+z¹,⁵)-⁰,⁵+z^1,25*-0,5(1+z¹,⁵)-¹,⁵*1,5z⁰,⁵+z-⁰,⁵-5z-²=0, {(-0,25z^0,75+0,25z^2,25+0,875z^3,75)²/(1+z¹,⁵)³=(-z¹,⁵+5)², z⁰,⁷⁵(1/343z⁰,⁵-393/98 ²+(z+1/7z⁰,⁵-1/98)²)/(z¹,⁵-5)≤0*0+°5^(2/3) *(14 1/28)²+>z; 395/9604+√3/4802<0,(-1/14)-1571/2401/4²<0 z=(14 1/28)² {(-0,25z^0,75+0,25z^2,25+0,875z^3,75)²=(1+3z¹,⁵+3z³+z⁴,⁵)(z³-10z¹,⁵+25),z{0}U(5^(2/3);(14 1/28)²];{[z¹,⁵=-1,29,z¹,⁵=3,10, z¹,⁵=31,74;z{0}U(5^(2/3);(14 1/28)²]; z=31,74^(2/3)=10,1124<197,..*+>z min= 22 19/36
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  17. (x+28)¹/³(x-28)¹/³=8 x=±36
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  18. a+9,2a-3 4,a-2,a-1 A+5,a+1,a a+9+a+5=2a-3+a-1+a -2a=-16 a=8. ?=17² =289.
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  19. Лукашенко на картине больше похож на Гитлера.🤔
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  20. Жизненный опыт—ж.опы.
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  21. r/tga+r/tg(90°-a)+2r=c, r=c/(2+ctga+tga),
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  22. Не восторжествует. По крайней мере, в нашей жизни.
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  23. х,у=(n²+1;n³+n)
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  24. А может это количество лунных месяцев, начиная от 1117г.,т.к. если прибавить 7208 лунных месяцев, то выйдет 1.01.1700г. И тогда на монете 1569г..
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  25. 4/1,5=2 2/3 ч
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  26. 112/3=37 1/3
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  27. (2x+cosy)/dy=(-x²tgy-cos²y)/dx -siny=-2xtgy -siny(1-2x/cosy)=0[y= πn,y=±arccos(2x)+2πn.
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  28. Это 9,248~9,25 рубля,а не 9248!
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  29. a^(1+1/m+1/m²+..)=a^(m/(m-1))
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  30. А у нас звонки перенесли всего лишь на 10мин.
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  31. ((a+b)²+ab)/a/b/(a+b)=((a+b)²+2000/(a+b))/2000 1/2000(2(a+b)+2000•-(a+b) ^-2)=0,(a+b)³-1000=0,a+b=10,-*+>a+b mi n=(10²+2000/10)/2000=0,15
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  32. S=2,5(√3+1)/2*2,5(√3-1)=6,25
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  33. (3a+2b)²-(5c-3)²=(3a+2b-5c+3)(3a+2b+5c -3)
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  34. Что, серьезно он сидел за барабанами?!
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  35. Посмотри Юрия Абарина про потоп 1536 г.
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  36. 2⁵*5!=1920
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  37. (b+a-2c)²=0 b+a-2c=0 (b-c)/(c-a)=1
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  38. (41/6-a)*6=17 a=4(cm)
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  39. (x²+1)y''+xy'-xy=0, (x²+1)(u''+u'²)+xu'-x=0, (u'+0,5x/(x²+1))'+(u'+0,5x/(x²+1))²=(x³-0,2 5x²+x+0,5)/(x²+1)² u'+0,5x/(x²+1)=z,z'+z² =0,z-1/-1+x=c,z=1/(x-c),n-1≤2n,n=-0,5≥-1 z=a(-0,5)x-⁰,⁵+...+a0 0,5a(-0,5)x-¹,⁵+...+a ²(-0,5)x-¹+...+2a(-0,5)a(-1,5)x-²+...=(x³-0,2 5x²+x+0,5)/(x²+1)²=0,5+x-x³-0,5x²+... {a1=-a0²+0,5,a2=a0³-0,5a0+0,5,a3=-a0⁴+1/3a0²-1/4, a4=a0⁵-2/3a0³+0,25a0²+0,25a0 0,375,..;z=a0+(-a0²+0,5)x+(a0³-0,5a0+0,5) x²+(-a0⁴+1/3a0²-1/4)x³+...[u'=-0,5x/(x²+1) +1/(x-c),u'=-0,5/(x²+1)+a0+(-a0²+0,5)x+(a0³-0,5a0+0,5)x²+(-a0⁴+1/3a0²-1/4)x³+...;[u=c1-0,25ln|x²+1|+ln|x-c|,u=c1-0,25ln|x²+ 1|+a0x+(-0,5a0²+0,25)x²+(a0³/3-1/6a0+ 1/6)x³+(-a0⁴/4+1/12a0²-1/16)x⁴+...;[y=c1 (x²+1)-⁰,²⁵(x-c),y=c1(x²+1)-⁰,²⁵e^(a0x+(-0,5 a0²+0,25)x²+(a0³/3-1/6a0+1/6)x³+(-a0⁴/4+1/12a0²-1/16)x⁴+...).
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  40. Рудой,''крепостное право'' давно отменили.
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  41. √(13+12cosa) √(5-4cosa),arcsin(1/√(5-4cosa)*sina) /_1=arrcos((2+3 cosa)/√(13+12cosa)) AF=√(13+12cosa)sin(arcsin(1/√(5- 4cosa)*sina)+arrcos((2+3cosa)/√ (13+12cosa)))=8sina/√(5-4cosa) AF=√(16+64sin²a/(5-4cosa)-64sin ²a/(5-4cosa))=4
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  42. у=log(9)15*x 5^log5(3³)=27
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  43. Мой комментарий под номером 1.
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  44. an=$(√3;2√2)(x^(2n-3)√(x²+1)-x^(2n-5)√(x ²+1)+..+(-1)^(n-2)*x√(x²+1)-(-1)^(n-2)x/√(x² +1))dx=(x²+1)^(n+0,5)/(n+0,5)/2-(n-1)(x²+ 1)^(n-0,5)/(n-0,5)/2+((n-1)(n-2)/2-1)(x²+1) ^(n-1,5)/(n-1,5)/2+(-n²+3n+4)(n-3)/6(x²+1) ^(n-2,5)/(n-2,5)/2+...(x²+1)^2,5/5+(-1)^(n- 2)(x²+1)¹,⁵/3-(-1)^(n-2)(x²+1)⁰,⁵|(√3;2√2)= 3^(2n+1)/(n+0,5)/2-(n-1)3^(2n-1)/(n-0,5)/2+((n-1)(n-2)/2-1)3^(2n-3)/(n-1,5)/2+(-n²+ 3n+4)(n-3)/4*9^(n-2)/(n-2,5)+...211/5+(-1) ^(n-2)*5 1/3-2^(2n)/(n+0,5)+(n-1)2^(2n-2)/(n-0,5)+((n-1)(n-2)/2-1)*2^(2n-4)/(n-1,5)-(- n²+3n+4)(n-3)/6*4^(n-2)/(n-2,5) a1=1,a2= 30 1/5
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  45. 32/25√(625-R²),7/25R 24/25R=32/25√(625-R²),R=20 S∆=0,5*20*15=150✓
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  46. 4cos²(x/2)+4cos(x/2)-1=0 cos(x/2)=(-1± √2)/2 cos(x/2)=(-1+√2)/2 x=±2arccos((-1+ √2)/2)+4πn
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  47. 1:50(?) налодов. Р не выговаривает.
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  48. [x=20°+60°n,x=18°+72°n,x=90°+36 0°n;M=5sin(2x+1°)-2tg⁴(3x-9°)=5sin(41°+120°n)-2tg⁴51°;5sin(37°+144° n)-2tg⁴(45°+36°n);5sin1°-2tg⁴9°A)
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  49. √(a²+24a-36)-3 S=72+27=99
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  50. Прощай, Единая Россия, С страны рабов,с страны господ.(Лермонтов)
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  51. 12*144³=12mod13×
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  52. e^(ilni)=e^(-π/2-2πn)
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  53. (a+(m-1)d/2)*m=(2l+1)nd
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  54. Y=ctg-²(x/2)+tg⁵0,5x/5+2tg³0,5x/3+2tg0,5x+x
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  55. (2sinx-√3(cosx=0[sinx=√3/2,cosx=0;[x=π/3+2πn,x=2/3π+2πn,x=π/2+πn.
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  56. 601+2/3+1/3=602
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  57. √(3x+10)+√(x+2)=2 {x[-2;2],[x=-2,√(x+2)=-2;{-2}
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  58. {Z=2(x+y)/x/y,[x=0,y=0;x≠0, y=(-3+x²±√(9 -12x²+x⁴))/x;[x=0,±√(120/7)=x;(0;0;z)(±2√ 210/7;[±61/140√210,±3/28√210;[±101/10 980√210,±7/610√210;±11/90√210,-+1/18√210;
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  59. 2/3(x³+6x²+7)¹/²+c
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  60. √(R²-6,5²)=6+√(R²-11,5²) R≥11,5 152,5⁰,⁵=R✓
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  61. 2√3^ncos(30n°),2√3^ncos(30°n)
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  62. (x-2)(x+3)(x+4)(x-6)=16x² x⁴-x³-42x²-18 x+144=0 (x²-0,5x-21,125)²-39,125x-302 17/64=0 (x²-0,5x+12)²-66,25(x²+24/26 5x)=0 x=-1,624;3,207 x²+0,583x-35,6689 43=0 x=5,688;-6,271|x²-1,583x-5,208168
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  63. Tg(x/2)=t,x=2arctgt,dx=2/(1+t²)dt 6(Tg(x/2)+(√2-2/3√3)ln|Tg(x/2)+ √2-√3|+(√2+2/3√3)ln|Tg(x/2)+√2+ √3|)+c
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  64.  @АккаХайко ,а Вы чулi,што дау́но ёсць майкi з таблiцай для праверкi зроку:Ш О С—штоб он сдох?
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  65. (√7+2)/√3=√(7/3)+2/3√3
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  66. 0,4х+0,7у=0,5(х+у) х=2у✓
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  67. $(√2/2;1)√(1-x²)x-³arcsinxdx/(1-x²)⁰,⁵=(1 -x²)⁰,⁵x-³arcsin²x/2-(-3+2x²)x-⁴arcsin³x/6...(√2/2;1)=-π²/16...
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  68. (4-r)²+4²=(4+r)² 16=4*4*r r=1{π}
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  69. Я по этому произведению смотрел постановку в театре.
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  70. (х-у)(х+у)=55, х-у=1,х+у=55; х=28,у=27, (±28;±27)х-у=5,х+у=11;х=8,у=3, (±8;±3)
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  71. 2√3/2cos15°/-cos15°=-√3
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  72. (97-x)¹/⁴x¹/⁴=44;6[(97-x)x=44⁴,(97-x)x=6⁴;[-x²+97x-44⁴=0, -x²+97x-1296=0;[0/,x=(97±65)/2.{81;16}
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  73. -sin(2π/7)/2/sin(2π/7)=-1/2
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  74. √135+2√(3*5)/2=4√15
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  75. (X-1)⁴-10(x-1)²+24(x-1)-27=0, (z-1)(z²-4z+9)=0 z=1;2±√5i x=±√10✓
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  76. 70-rctg/_A=50-rctg/_B cos/_A=5/6 sin/_A=√11/6 cos/_B=19/30 sin/_B=7√11/30 r=35/4√11
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  77. b<c<1 a>c>b 35.A) x¹,² C)
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  78. 2log(3)tgx=log(2)sinx,{tgx>0,sinx>0;{xє(πn;π/2+πn),xє(2πn;π+2πn);xє(2πn;π/2+2πn) log(3)tg²x=log(2)sinx,tg²x=3^log (2)sinx,≤1,xє(2πn;π/4+2πn),3^log(2)(√2/2)=3^-0,5,tgx=3^-0,25,x=arctg3^-0,25+πn, π/4>arctg3^-0,25>33°..x=π/6,3/9=3^log(2)0,5=3^-1=1/3,✓ x=π/6+2πn,2tgx*1/cos²x-3^l0g(2)sinx*ln3*1/sinx/ln2*cosx=0, />,2*√3/3/(3/4)-3^lo g(2)0,5ln3/0,5/ln2*√3/2=8√3/9-1/3*log (2)3*√3/2=√3/3(8/3-log(2)3/2)<0,a значит функция убывает и при хє(2π n;π/6+2πn) решений нет.
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  79. 507/2,5=202,8 маш.2,5+1,5+0,5*201=4+100,5=104,5т, 104,5/3=34,8(3)т
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  80. Сигизмунд 1 Старый похож на типа моего двоюродного брата.
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  81. 1/(√x-4)/(√x-5)=1/(√x-6)/(√x-7) x-9√x+20=x-13√x+42 x=121/4
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  82. {√x+y=7,x+√y=11;{y=7-√x,x+√(7-√x)=11; √(7-√x)=-x+11,7-√x=x²-22x+121,x≤11,x=(-x²+22x-114)²,x²-22x+114≤0,(x-(22+√(484- 4*114))/2)(x-(11-√(484-456)/2))≤0+*11- √7-11+√7+>x xє[11-√7;11+√7],хє[11-√7; 11]*/> 11-√7>0,11<49,11+√7>0,-(11+√ 7)/((11+√7+38)/√7)+11+√7=-(11√7+7)/(49+√7)+11+√7=-(11√7*49-77+7*49-7√7)/(49²-7)+11+√7=-(532√7+266)/2394+11 +√7=7√7/9+10 8/9,х=12,9..х=7,9..х⁴-44х³ +672х²-5017х+114²|х-12,9..=х³-21,1х²+39 9,81х+140,549,х³-21,1х²+398,81х-140,549|х-7,9=х²-13,2х+294,53 х=(13,2±√(13,2²- 4*294,53))/2,х=6,6±√-1003,88/2 0/х=12,9>11,х=7,9.. у=7-√7,9..=7-(3-0,18)= 4,18..
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  83. i^(1/2+1/4+1/8+..)=i
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  84. |p²-2q²|≥1 [p≥√(2q²+1),p≤-√(2q²+1); p≤√(2 q²-1),p≥-√(2q²-1);p(-∞;-√(2q²+1)]U[-√(2q²-1);√(2q²-1)]U[√(2q²+1);∞),|p/q-√2|<1 |p/q-√2|>1/(2√2+1)/q
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  85. {F2=1962sin50°/cos(a-50°) H, F1=1962cosa/cos(a-50°) H.
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  86. 3/5R=6cm l=√(10²-6²)=8 QR=16cm
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  87. (x-1)⁴-10(x-1)²+32(x-1)-7=0 (z-5/3)³-1/3(z-5/3)-11 25/27=0 z=5/3+(161+72√5)¹/³/3+(..-..)..; 5/3-(161+72√5)¹/³/6-(..-..)..±√(3/4 ((161+72√5)¹/³/3+(..-..)..)²-1/3)i x=-1±√5
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  88. x⁴+y⁴=((x+y)²-2xy)²-2(xy)²=47
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  89. (1/x-2)(1/x⁴+4/x²+16)=0 x=0,5✓,x-²=-2±√12i×
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  90. {x+y=a,xy=b;{a³-15a+18=0,b=0,5a²-2,5; a=(-9+√(81-5³))¹/³+(..-..)..=2√5cos (1/3arccos(-9/5/√5)+2/3πn) b=10cos²(1/3arccos(-9/5/√5)+2/3 πn)-2,5 {y=√5cos(1/3arccos(-9/5/√5)+2/3πn)-+√(-2,5cos(2/3arccos (-9/5/√5)+4/3πn)),x=√5cos(1/3arc cos(-9/5/√5)+2/3πn)±√(-2,5cos (2/3arccos(-9/5/√5)+4/3πn)).n=0;2 x⁷+y⁷=129;(√5cos(1/3arccos(-9/5/√5)+4/3π)+√(-2,5cos(2/3arccos(- 9/5/√5)+8/3π)))⁷+(√5cos(1/3arcco s(-9/5/√5)+4/3π)-√(-2,5cos(2/3arc cos(-9/5/√5)+8/3π)))⁷
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  91. 30^(1/log2(30))=2
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  92. 484/49=9,88>9,81
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  93. S=1/3*1*1/2=1/6
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  94. 1012*2023/9999=204 7480/9999
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  95. lgx=±2 x=100;1/100
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  96. f(x)+xf(-x)=x 1/xf(-x)-f(x)=-1 (x+1/x)f(-x)= x-1 f(-x)=(x²-x)/(x²+1) f(x)=(x²+x)/(x²+1)
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  97. 1*68/13,6=5(cm)E)
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  98. AB/sin(140°-x)sin40° /_C=70°-x AB/sin(140°-x)sin40°/sin(70°-x)= AB/sin70° ±150°+360°n=210°-2x [x=30°-180°n,x=180°-180°n;x(0;70°) x=30°B)
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  99. a/(a+b)*c,/_1/2,/_1/2+/_2 (c²+2ab (1+cos/_1))/2/(a+b)/cos0,5/_1-r(1/sin0,5/_1-1)≠a/(a+b)*c/sin/_3*sin(/_1/2+/_2)
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  100. {a=1,125,0=b;R=3
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  101. 9/4а-а=5/4а 5/4а=3 а=12/5 S=0,5*12/5*24/5+0,5*4,4*4,8+4,8*2,4=27,84
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  102. {a⁴-24a²-1225=0,b=35/a; a=±7,b=±5
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  103. 256*π²*10-³=2,54(Тл)Е)
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  104. 60*5*cos40°=300cos40°
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  105. 0,5(2+x)-⁰,⁵-0,5(6-x-y)-⁰,⁵+0,5(x+y)-⁰,⁵-0,5(4-x)-⁰,⁵=0 +*4/3->x max=√30+2√6
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  106. 1/(1+x-¹)=5/3 x=-2,5
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  107. 410*2,54=1041,4руб.
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  108. √(R²-5²)+R=12,√(R²-25)=12-R,{R²-25= (12-R)²,12-R≥0;{R²-25-R²+24R-144=0, R≤12;{R=169/24,R≤12;R=7 1/24
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  109. (x²)²-3x²+1=0,x²=(3±√(9-4*1))/2[x²=1,5 +√5/2,x²=1,5-√5/2;[x=±(√5+1)/2,x=±(√5- 1)/2; x⁵-x^-5=(√5+1)⁵/2⁵-(√5+1)^-5/2^-5= (176+80√5)/32-32/(176+80√5)=5,5+2,5 √5-1/(5,5+2,5√5)=5,5+2,5√5-(5,5-2,5√5)/(5,5²-2,5²*5)=11,=-11,=((√5-1)/2)⁵-1/(√5/ 2-1/2)⁵=(80√5-176)/32-32/(80√5-176)= 2,5√5-5,5-2(5√5+11)/4=-11,=11
    2
  110. X(0;40/3°) AC=2ABsin6x,/_CAD= 15x-90° 2ABsin6x/sin(6x)=AB/sin(90°-6x) 10^;-10°-π/3n=x x=10°C)
    2
  111. X≤1 0=x⁴+6x²-40 x²=-3±7=4;-10 x=±2{-2}
    2
  112. 2^(х/2-1)=1 х/2-1=0 х=2
    2
  113. [x=1,x=e^±3¹,⁵.
    2
  114. $(0;π/3)do/cos^no=√3*2^(n-2)/(n-1)+(n-2)/(n-1)√3*2^(n-3)/(n-2) +..+(n-2)!!/(n-1)!!√3*2^2{n/2}/(2{n/2}+1)+(n-2)!!/(n-1)!![n:2,π/3;n:/2,-ln|2-√3|;
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  115. Иностранцы. Де-факто фальшивые друзья.
    2
  116. x=(103±√(103²-2c))/2,c≤5304,5 x1x2=c/2>0,c≥8 103²-2c=(2n+1)² c=(51-n)(104+2n),n=44 c=7*192 n=38,c=13*180 n=8,c=43*120 n=15,c=36*134 n=27,c=24*158 n=45,c=6*194,n=51;-52,c=0
    2
  117. (1 1 1|14) (0 5/2 -1|11/2) (0 0 1|96/13){Y=67/13,x=6/13.{(6/13;67/13;96/13)}
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  118. {25x²+(-100a-26)x+130a²-77a+1=0, y=(a+1-4x)/3; x=(50a+13±√(-750a²+3325a+171))/25 a[(665-√462745)/300;(665+√462'745)/300]
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  119. {-4=c,2=a,3=b;y=25a-5b+c=31
    2
  120. √(6-2x)=2x≥0,±5/4=x+1/4 x=✓1;-1,5×
    2
  121. {f(x)+f(1/(1-x))=1/x,f(1/(1-x))+f((-1+x)/x)= 1-x,f((-1+x)/x)+f(x)=x/(-1+x);f(x)+f(1/(1-x))+f((-1+x)/x)=0,5/x-0,5x+1+0,5/(-1+x) f(x)= 0,5/x+0,5x+0,5/(x-1)
    2
  122. 17/82>3/38
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  123. х+1=±1 х=0;-2 (5х²+10х+4)/(7х²+6х+1)= 4/17×{0}
    2
  124. 60/11=√х,х[0;120] х=3600/121
    2
  125. (4-r)2+4²=(4+r)² 16=4*4*r,r=1{π/2}
    2
  126. $(0;1)cosx-²dx+$(0;1)cosx²*x-²dx не сходится
    2
  127. 1373=26²+693 0/
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  128. {z=1-x-y,(3-y)x²+x(-y²+4y-3)+3y²-3y-12=0;x=(y²-4y+3±√((y-3)(y+3)(y+2-√21)(y+2+ √21)))/-2/(y-3) y(-≠;-7]U[-3;∞) (y²+2y-15)²+24y-72 0≥(y-5)²-3,5 y[4;6] y=4,7*15× y=5,2*8*28× y=6,3*9*43×0/
    2
  129. f(x)=(x²-4x+7)/(x²+2x+5) f'(x)=((2x-4)(x²+2x+5)-(x²-4x+7)(2x+2))/(x²+2x+5)²=0, x³+2x²+5x-2x²-4x-10-x³-x²+4x²+4x-7x-7=0, 3x²-2x-17=0, x=(2±√(4-4*3(-17))/2/3, x=1/3+√52/3,x=1/3-√52/3,+-*--*+->x max f(1/3+√52/3)=(1/9+52/9+2√52/9-4/3-4√52/3+7)/(1/9+52/9+2√52/9+2/3+2 √52/3+5)=(104-10√52)/(104+8√52)=(104-10√52)(13-√52)/8/(13²-52)=(26*13-26√52-5√13*13+5√13*√52)/2/117=(468-13√13)/234=2-√13/18 26 13 78 26 338 +130 468
    2
  130. $(x-1)/(-x-1)log((1+x)/(1-x))*(-x-1)(x-1)^ 1dx=(x-1)/(-x-1)log²((1+x)/(1-x))/2 (x-1)/(x+1)log³((1+x)/(1-x))/6+...+c=1-(x-1)/(-x- 1)-(x-1)/(-x-1)log((1+x)/(1-x))+c -2/(x+1)/(x-1)
    2
  131. А причем здесь чистописание?
    2
  132. log3(x²)<log1,5(0,5){x²<3^log1,5(0,5), x²>0;{x<3^(0,5log1,5(0,5)),x>-3^(0,5log 1,5(0,5)),x≠0;x(-3^(0,5log1,5(0,5));0)U(0;3 ^(0,5log1,5(0,5)))
    2
  133. R(1+1/√2)=1 R=2-√2 S=2(3-2√2)-(3-2√2)²= -1+8√2
    2
  134. Александр Пыко, ишь ты, разбежался!
    2
  135. Молитва - это вредное, а вот молва да. И он умрёт также,как Жириновский.
    2
  136. y'-4y=e^5xcos3x k-4=0 k=4,y0=c1e^4x y=e^5x(c2sin3x+c3cos3x) e^5x*5(c2sin3 x+c3cos3x)+e^5x(3c2cos3x-3c3sin3x)-4 e^5x(c2sin3x+c3cos3x)=e^5xcos3x {5c2 -3c3-4c2=0,5c3+3c2-4c3=1;{c2-3c3=0, -3 1/3c3=-1/3;{c2=-0,3,c3=-0,1.yp=e^5x(-0,3 sin3x-0,1cos3x) y=c1e^4x+e^5x(-0,3sin3 x-0,1cos3x)
    2
  137. Ei=0;n-1 2(π²(i+1)²-2)/n³=(π²(n+1)(2n+1)/3-(n-1))/n²=2/3π²
    2
  138. En=1;16log2(√(sin²(kπ/8)+1)-sin(kπ/8))= log2(√(sin²(π/8)+1)-sin(π/8))+log2(√(sin ²(2k/8)+1)-sin(2π/8))+...+log2(√(sin²(16 k/8)+1)-sin(16π/8))=log2((√(1,5-√2/4)- √(0,5-√2/4))(√1,5-√2/2)...1)
    2
  139. 380'000³/R³=29,53²/7² R=141'000 км
    2
  140. {cosx≥0,(2^sin²x)²-3*2^sin²x+2=0;2^sin²x =(3±1)/2=2;1 sin²x=1;0 cos2x=-1;1 x=π/2+ πn;πn x=πn/2 x[-π/2+2πm;π/2+2πm] x=±π/2+2πm;2πm
    2
  141. log3(x)=(-x+2±(x-6))/2=-2;-x+4 [x=1/9,x=3 (1=1✓);{1/9;3}
    2
  142. √2r=(√(2r²-2r²cosa-9)+√(2r²-2r²sina-36))²+3², √2r=2r²-2r²cosa-9+2√(2r²-2r²cosa-9)(2r²-2r²sina-36)+2r²-2r²sina-36+9, 2√(2r²-2r²cosa-9)(2r²-2r²sina-36)=(-4+2co sa+2sina)r²+√2r+36,4(2r²-2r²cosa-9)(2r²-2r²sina-36)=((-4+2cosa+2sina)r²+√2r+36)², (16-16sina-16cosa+16sinacosa)r ⁴+(-(8-4cosa)36-(8-8sina)9)r²+36*36=(- 4+2cosa+2sina)²r⁴+2√2(-4+2cisa+2sina)r³+72(-4+2cosa+2sina)r²+2r²+72√2r+36²,(16-16sina-16cosa+16sinacosa-(-4+2cosa+2sina)²)r⁴+(-8*36+144cosa-72+72sina+288-144cosa-144sina-2)r²-2√2(-4+2cisa+2sina)r³-72√2r=0,r=0,(16-16sina-16cosa+16sinacosa 16-4cos²a-4sin²a+16cosa+16sina-8sinacosa)r³+(-74-72sina)r-2√2(-4+2c0sa+2sin a)r²-72√2=0, (-4cos²a+8sinacosa-4sin²a) r³+(8√2-4√2cosa-4√2sina)r²-(74+72sina)r-72√2=0, (r+(-2√2+√2cosa+√2sina)/(cosa-sina)²/3)³+((74+72sina)/(cosa-sin a)²-(-2√2+√2cosa+√2sina)²/(cosa-sina)⁴/3)(r+(-2√2+√2cosa+√2sina)/(cosa-sina)²/3)-(-2√2+√2cosa+√2sina)³/(cosa-sina)⁶/27-(74+72sina)/(cosa-sina)²-(-2√2+√2c osa+√2sina)²/(cosa-sina)⁴/3)(-2√2+√2c osa+√2sina)/(cosa-sina)²/3+18√2/(cosa sina)²=0,r+(-2√2+√2cosa+√2sina)/(cosa-sina)²/3=((-2√2+√2cosa+√2sina)³/(cosa-sina)⁶/54+(37+36sina)/(cosa-sina)²+2(-√2+√2/2*cosa+√2/2*sina)²/(cosa-sina)⁴/3)(-2√2+√2c osa+√2sina)/(cosa-sina)²/3-9√2/(cosa- sina)²+√((-(-2√2+√2cosa+√2sina)³/(cosa-sina)⁶/27-(74+72sina)/(cosa-sina)²-(-2√2+√2cosa+√2sina)²/(cosa-sina)⁴/3)(-2√2+√2c osa+√2sina)/(cosa-sina)²/3+18√2/(cosa- sina)²)²/4+((74+72sina)/(cosa-sin a)²-(-2√2+√2cosa +√2sina)²/(cosa-sina)⁴/3)³/27))^(1/3)+(-(-2√2+√2cosa+√2sina)³/(cosa-sina)⁶/27-(74+72sina)/(cosa-sina)²-(-2√2+√2c osa+√2sina)²/(cosa-sina)⁴/3)(-2√2+√2c osa+√2sina)/(cosa-sina)²/3+18√2/(cosa- sina)²-√((-(-2√2+√2cosa+√2sina)³/(cosa-sina)⁶/27-(74+72sina)/(cosa-sina)²-(-2√2+√2c osa+√2sina)²/(cosa-sina)⁴/3)(-2√2+√2c osa+√2sina)/(cosa-sina)²/3+18√2/(cosa- sina)²)²/4+((74+72sina)/(cosa-sina)²-(-2√2+√2co sa+√2sina)²/(cosa-sina)⁴/3)³/27))^(1/3) r=-(-(-2√2+√2c osa+√2sina)/(cosa-sina)²/3+((-2√2+√2cosa+√2sina)³/(cosa-sina)⁶/54+(37+36sina)/(cosa-sina)²+2(-√2+√2/2*cosa+√2/2*sina)²/(cosa-sina)⁴/3)(-2√2+√2c osa+√2sina)/(cosa-sina)²/3-9√2/(cosa- sina)²+√((-(-2√2+√2cosa+√2sina)³/(cosa-sina)⁶/27-(74+72sina)/(cosa-sina)²-(-2√2+√2c osa+√2sina)²/(cosa-sina)⁴/3)(-2√2+√2c osa+√2sina)/(cosa-sina)²/3+18√2/(cosa- sina)²)²/4+((74+72sina)/(cosa-sin a)²-(-2√2+√2cosa +√2sina)²/(cosa-sina)⁴/3)³/27))^(1/3)+(-(-2√2+√2cosa+√2sina)³/(cosa-sina)⁶/27-(74+72sina)/(cosa-sina)²-(-2√2+√2c osa+√2sina)²/(cosa-sina)⁴/3)(-2√2+√2c osa+√2sina)/(cosa-sina)²/3+18√2/(cosa- sina)²-√((-(-2√2+√2cosa+√2sina)³/(cosa-sina)⁶/27-(74+72sina)/(cosa-sina)²-(-2√2+√2c osa+√2sina)²/(cosa-sina)⁴/3)(-2√2+√2c osa+√2sina)/(cosa-sina)²/3+18√2/(cosa- sina)²)²/4+((74+72sina)/(cosa-sina)²-(-2√2+√2co sa+√2sina)²/(cosa-sina)⁴/3)³/27))^(1/3)
    2
  143. Почему у тебя везде рабские условия?..
    2
  144. 512^x+256^x+2*128^x-4*64^x+120*32^x-8*16^x+72*8^x-112*4^x-448=0 512+256+2*128+98*32>0, 107/512-464<0{0,4}
    2
  145. 10³*9,81*0,1=981Па
    2
  146. Z=±√(a²-ax),y=±√(-x²+ax) $(0;a)0,5√a√((x+a)/x/(a-x))dx=1,6 (a=1)
    2
  147. x=±√(35log5(7))
    2
  148. (x+1)(x²-x-6)=(x+1)(x-3)(x+2)
    2
  149. an=2^ka1+k*2^k=(k+1)*2^k
    2
  150. e^(lnlnx)=lnx
    2
  151. e^W(3ln(7+5√2))=x
    2
  152. S=π•7²-π•3,5²=36,75π
    2
  153. $(0;π)π/2(-1-3/4/(cosx-2)+3/4/(cos x+2))dcosx=π/2(-cosx-3/4ln|cosx-2|+3/4ln|cosx+2|)(0;π/2)=π/2(1-3/4ln 3)
    2
  154. {y=10-x,[x=8,x=2;{(2;8)(8;2)}
    2
  155. En=1;∞(-1)^(n-1)/(2n-1)=π/4
    2
  156. 10! N=20
    2
  157. X=(√13-√5)/4 (-11'207'141+1'390'142√65)/64✓
    2
  158. |(0;1)En=0;∞(-1)^n/(2n)!(ln^(2n-1)x (x-x²/2)-(2n-1)ln^(2n-2)x(x-x²/4)+.. -(2n-1)!(X-x²/2^(2n)))=0,5ln0,4
    2
  159. 0=0
    2
  160. c=ab/(ab-a-b) 1+(-1)/a+1/a=1
    2
  161. √5*a=10 a=2√5 S=20
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  162. $(0;∞)sin(2ln²x)/(1+x)/ln²xdx=$(- ∞;∞)En=1;∞(-1)^(n-1)/(2n-1)!2^(2 n-2)u^(4n-4)du=En=1;∞(-1)^(n-1)/(2n-1)!*2^(-0,5)(2u²)^(2n-1,5)/(2n-1, 5)|∞ сходится
    2
  163. i+1+i+..+i=4+5i
    2
  164. X=(20*36¹/³-16)^(1/3)
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  165. -х³+(х-1)²-17=0,-х³+х²-2х-16=0,(х-1/3) ³+1/3(х-1/3)+16 4/27=0,х-1/3=(-8 2/27 +√((8 2/27)²+(1/3)³/27))^(1/3)+(-8 2/27 -√47525/27)^(1/3),х=1/3+(-8 2/27+√475 25/27)^(1/3+)(-8 2/27-√47525/27)^(1/3)
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  166. Я думал, что он будет себя вести как лжеученый или любитель теории заговора.
    2
  167. x¹,⁵-5x⁰,⁵-2√3=0 x⁰,⁵=(√3+2/9√(-33))¹/³+(√3-2/9√(-33))¹/³=2√(5/3)cos(arccos(9/ 5/√5)/3+2πn/3)≥0 n=0, x=20/3cos²(arcc os(9/5/√5)/3) x-√(3x)=20/3cos²(arcc os(9/5/√5)/3)-√20cos(arccos(9/5/√5)/3)=2
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  168. 5783:19=304ост.7 10,8822д. 10,8822*7= 76,1754=17,5854д. 20.09 131-4*29,5=13
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  169. X²-2,5xy+y²=0 x=(2,5±√2,25)/2*y= 2y;0,5y y=1;y=2{(2;1)(1;2)}
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  170. 164=(2a+21)/2*8 a=10
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  171. √((x2+2+x)/2)+√((x2+2-x)/2)
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  172. y=-0,5ln(e-1)/x
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  173. {F1=500/(sin50°+√3/3cos50°) H, F2=1000/(√3tg50°+1) H.
    2
  174. 1/2+π²/12-1/2=π²/12
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  175. 🩴🩴🩴
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  176. Я второй, кто смотрит и 1-ым оставляет комментарий!😀
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  177. S1=(1,5+1,5√3)/2*(1,5√3-1,5)+4,5(π/6-0,5)=0,75π S=1,5π(cm²)
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  178. (1-tg15°)cos15°=cos15°-sin15°=√2cos60°=√2*0,5
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  179. √(2х²+2)/4/х=(х-1)/√(2х²+2) -х²+2х+1=0 х=1+√2✓
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  180. х=(-1/2+√(1/4+3^3/27))^(1/3)+(-1/2-√(1/4+3^3/27))^(1/3)=(-0,5+√5/2)^(1/3)+(-0,5-√5/2)^(1/3), Д>0=>1 корень
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  181. ​a(1,5+√3)=1 a=4√3/3-2
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  182. Min=32log2(e/32ln2)<0 x=1/32;8
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  183. 4xcos-²ysiny=0[x=0,y=πn.✓
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  184. 180-144cos/_1=a²+64+16acos/_1 cos/_1=(a²-116)/(-144+16a) arcsin(4/3/√(5-4cos/_1)*sin/_1)+ arcsin(2/√(5-4cos/_1)*sin/_1)=180 °-arcsin(a/6/√(5-4cos/_1)*sin/_1)- arcsin(1/√(5-4cos/_1)*sin/_1) 16|(-a²+7a+44)/(-9+a)|-√(140(a-9)² +(a²-18a+56)²)*4/|a-9|=a(-a²+32a- 172)/(-9+a)+√(-512a²+(a³-244a+32 *36)²)/|a-9| a=2,938
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  185. (2x²-19x+42)(x²-7x+11)/(x-2)/(x-5)/(x-3)/(x-4)=0 [x=5,5,x=4,x=(7±√5)/2.
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  186. 13:20 это совет от Льва Толстого.
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  187. х^х=2¹⁶⁰ 1 решение.х=32
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  188. (BM²-8)/2/MB=-(MC²-3)/2/MC BM²+(MC²-3)/MCMB-8=0 BM=(-MC²+3+√(MC⁴+MC²*26+9))/2/MC (MC²+3+√(MC⁴+MC²*26+9))/2/MC,MC(1;3) (MC²+3MC-3+(MC⁴+ MC²*26+9)-⁰,⁵(MC⁴-9))/MC²/2=0 MC⁶+29/6MC⁵+23MC⁴+6MC³-56MC²+87/2MC-27=0-*1,057+>MC min=4,94 C)
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  189. {z=(x³+16)/x/y,y=(x³+19)¹/³, [x=-8/3,x=2;{(2;3;4)(-8/3;1/3;-7 1/3)}
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  190. Квантовая механика какая-то!
    2
  191. 8^9^(1/3)=64*1,1875=76,0000<81
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  192. 10⁶/600=1,(6)*10³=1667 лет!
    2
  193. z=W(-π/2-2πn)/(-π/2-2πn)
    2
  194. y,2c 18-2y,27-3y,-6+3y,-2+y,8-y 8=x
    2
  195. -4(sinx-1/8)²+3 1/16≤3 1/16;≥-2 D)
    2
  196. Ln((3x²+8)(2x²+6)/(x²+2)²/a)/lna>0 (6-a)x⁴+(34-4a)x²+48-4a=0 x=±√((-17+2a±√(1+4a))/(6-a)) [×,a(6;12].{((6;12];±√(-17+2a-√(1+4 a))/(6-a))}
    2
  197. (x²-1/2x)(x-1)=2025
    2
  198. 3/2+√7/2 3
    2
  199. (х+х-¹)³-3(х+х-¹)=±3√6 9*6=54
    2
  200. x⁹+x³+x²+x+1=0 {2/3cos(1/3arccos (11/16)+2/3πn)-73/27+8cos²(1/3arccos(11/16)+2/3πn)-4(2/9cos(1/3 arccos(11/16)+2/3πn)-35/54+16/9cos²(1/3arccos(11/16)+2/3πn))³= 0,cosf=2/3cos(1/3arccos(11/16)+ 2/3πn)-1/3;(x²-(4/3cos(1/3arccos(11/16))-2/3)x+1)(x²-(4/3cos(1/3arccos(11/16)+ 2/3π)-2/3)x+1)(x²-(4/3cos(1/3arcc os(11/16)+4/3π)-2/3)x+1)(x²-x+1)(x-1)?
    2
  201. √(10²-2²)=√96,√(6²-(6-AB)²)=√(36-36+12AB-AB²)=√(12AB-AB²) √(8AB-AB²),√(12AB -AB²)+AB+√(8AB-AB²)=√96,AB≥0,≤4 12AB-AB²+2AB√(12AB-AB²)+AB²=96-2√ 96√(8AB-AB²)+8AB-AB²,2AB√(12AB-AB²) =-AB²-4AB+96-8√6√(8AB-AB²),48AB³-4AB ⁴=AB⁴+16AB²+96²+8²*6(AB-AB²)+8AB³ -192AB²+16√6AB²(√8AB-AB²)-768AB+64√6AB√(8AB-AB²)-192*8√6√(8AB-AB²),-5AB⁴+40AB³+560AB²+384AB-9216=(16AB²+64AB-1536)√6√(8AB-AB²),(-5AB⁴+40AB³+ 560AB²+384AB-9216)²=(256AB⁴-64*704AB²+1536²+32*64AB³-128*1536AB)*6(8AB-AB²),25AB⁸+1600AB⁶+560²AB⁴+384² AB²+9216²-400AB⁷-5600AB⁶-3840AB⁵+92160AB⁴+80*5600AB⁵+80*384AB⁴-8*9216AB³+2*569*384AB³-1120*9216AB²-2*384*9216AB=256*48AB⁵-256*6AB⁶-64*704*48AB³+64*4224AB⁴+1536²*48AB-1536²*6AB²+32*64*48AB⁴-32*384AB⁵-128*1536*48AB²+128*9216AB³,25AB⁸-400AB⁷-2464AB⁶+444'160AB⁵+67'840AB⁴+1'346'304AB³+13'418'496AB²-120'324'096AB+84'934'656=0,
    2
  202. Sin80°/sin40°=2cos40° √(2-2cos40°)=2sin20° 2=1/sinx x=30°;150°(0;110°) x=30°✓
    2
  203. 2√((4x²+1)(9x²-1))=13x² -25/4x⁴+5x²-1=0 x=±√(2/5)
    2
  204. 2sin²(0,5x)/2/sin(x/2)²=1
    2
  205. f(x)=1/2*f(3x),f(1-x)=1-f(x);f(1/13)=? f(x)=1-f(1-x), f(1/2)=1/2,f(0)=0, f(12/13)=1-f(1/13),f(1/13)=0,5f(3/13), f(3/13)=0,5f(9/13)=2f(1/13),f(4/13)=0,5f(12/13),f(9/13)=1-f(4/13),4f(1/13)=1-0,5(1-f(1/13))=0,5+0,5f(1/13), f(1/13)=0,5/3,5=1/7,
    2
  206. x=e^log(10/e²)0,01
    2
  207. 35*365*24/74650=70*730*6/74650=30660/7465=4,11 ч! 29860 8000 7465 6350
    2
  208. [x=-1,4=x,x=±2.
    2
  209. 6*1,5²-5*1,5+4=10
    2
  210. ​​ @СеваПадалка  {b=2/a,c=3-2/a, d=4a/(3a-2),3a²-13a+10=0;[a=1,a=10/3;[b=2,b= 0,6;[c=1,c=2,4;[d=4,d=5/3;{(1;2;1;4)(10/3 ;0,6;2,4;5/3)}
    2
  211. limn->∞2(n+0,5-n)=1
    2
  212. f(x)=64x⁵-40x³+5x✓
    2
  213. X=π/2+πn;±π/3+2πn 4cos²x-2|a-1|cosx+a-2=0,x=π\2+πn cosx=(|a-1|±(a-3))/4={a[1;∞),1/2;a{3}
    2
  214. dy/dx=4sinx/(3y²) 3y²dy=4sinxdx 3y³/3=-4cosx+c, y=(-4cosx+c)^(1/3) 2=(-4 +c)^(1/3) 8=-4+c, c=12 y=(-4cosx+ 12)^(1/3)
    2
  215. х/1=(х+1)/...,..=(х+1)/х (х+1)²+(х+1)²/х²= 4²,х²+2х+1+(х2+2х+1)/х²-16=0,х⁴+2х³-1 4х²+2х+1=0,(х²+х-7,5)²+17х-55,25=0,\*/*\*/17(-0,5-√(1-4*-7,5)/2)-55,25=-63,75 -17√31/2<0,х<-0,5-√31/2✓,(0,5^2+1*-0,5 -7,5)²+17*-0,5-55,25=7,25²-63,75=-10 3/ 16<0 -63,75+17√31/2<0,х>-0,5+√31/✓х =-4 1/4-√31,х=-3 1/4+√31,хє(0;4){-3 1/4+ √31}
    2
  216. √(25-n)+2√n 0,5(25-n)^-0,5*-1+n^-0,5=0, -n⁰,⁵+2(25-n)⁰,⁵=0,4(25-n)=n,n=20 +*->n max=√5+2√20=5√5
    2
  217. y'+ycos-²x=sinx/cos³x y=ce^-tgx+e^tgx*tgx-e^tgx
    2
  218. √72√2/3=4см 16см²
    2
  219. N=(10⁶¹-1)/9:31 10³⁰=1(mod31),..=0 (mod31)
    2
  220. {х²+20х+у²-20у+75=|х²+у²-25|,х-у=а;[{хє(-∞;-5]U[0;∞),у=х+5,-5=а;{хє(-5;0) у=5-√(25-(x+5)²),х-5+√(25-(х+5)²)=а;1+0,5(25-(х+5)²)^-0,5*-2(х+5)=0,(х+5)/(25-(х+5)²)=1,(х+5)²/(25-(х+5)²)=1,(х+5)² =25-(х+5)²,(х+5)²=12,5 х+5=±√12,5,х=-5± √12,5≥-5,х=-5+√12,5+*->х максимум-5+ √12,5-5+√(25-(-5+√12,5+5)²)=-10+√12,5+√(25-12,5)=-10+√12,5+√12,5=2√12,5-10,-10+√(25-0²)=-10+5=-5,0-5+√(25-5²)=-5,ає(-5;2√12,5-10);ає[-5;2√12,5-10).
    2
  221.  @tube.idi.naher.  , ему 47 лет в этом году. И он сам пошел в Ютуб.
    2
  222. ((6+√35)^x-1/3)³-1/3((6+√35)^x-1/3)-4 2/27=0 21/4,12√21 (6+√35)^x-1/3=5/3 x=log(6+√35)2
    2
  223. e^(e^(0,5x¹/³lnx)lnx)e^(0,5x¹/³lnx)(x¹/³(lnx+3)lnx+6)x-¹/6=0 x(e-³;1), 1/3x-²/³(ln²x+9lnx+9)=0 x=e^(-4,5±3√5/2)°0+*-*+>x min=e^(-1,5+√5/2)(18-9√5)+6~-62 65/127/113+5>0/> x=2^n n*2^(n/2*2^(n/3))=16,58*2^(8,29*2⁵,⁵²(⁶))/> x=2^16,58✓
    2
  224. {x+4=(x+2)²,x+2≥0;{-x²-3x=0,x≥-2;{[x=0,x= -3;x≥-2;x=0.
    2
  225. Y'y''/(y'²-1)=x/(1+x²) 0,5ln|y'²-1|=0,5 ln(x²+1)+c y'=±√(1+(x²+1)c)[{c=0,y=±x+c1;{c>0,y=±√c(0,5x√(x² +1+1/c)+0,5(1+1/c)ln|x+√(x²+1+1/c)|)+c1;{c<0,y=±√-c(0,5x√(-x²-1-1/c)+0,5(-1-1/c)arcsin(x/√(-1-1/c)))+c1.
    2
  226. {1/(x+y)=a,1/(x-y)=b;{a=0,2,b=1; {X=3,y=2.
    2
  227. f(n)=f(n-1)+2f(n-2)=f(2)(2n-5)+(2N- 4)f(1)=2n-5 f(34)-f(32)=4 A)
    2
  228. √(4-2y)+√y -(4-2y)-⁰,⁵+0,5y-⁰,⁵=0 2/3=y+*->y max=3√(2/3)
    2
  229. 60/(a-5)/5=(b-60/(a-5))/(a-5) b=12+60/(a-5) x=√(25+12²)=13
    2
  230. x=-a;(5-a)/2 (x-2a)²-(4a²-5a)≥0,D≥0,a(-∞;0] U[5/4;∞) x(-∞;2a-√(4a²-5a)]U[2a+√(4a²-5 a);∞) 5a²+5a=5a(@+1)≥0 a(-°;-1]U[0;∞)
    2
  231. x'+x=t,x(0)=C x=ce^-t+te^t-e^t C=c-1 c=C+1 x=(C+1)e^-t+e^t(t-1)
    2
  232. 9,16 S∆=0,5*9*12+0,5*12*16=150
    2
  233. Ei=1;∞(1/(i-3)!+3/(i-2)!+1/(i-1)!)=e +3e+e=5e
    2
  234. {(9а²-49а)х+36у=9а²-58а+44,у=(90а²+45а+220)/(81а²-441а+180);
    2
  235. {х=4(у-2х),у-х=10;{9х-4у=0,-х+у=10;*-9{9х -4у=0,5у=90;{х=8,у=18;
    2
  236. 192 их зомбаки.
    2
  237. √(1+4sin²20°-2²sin²20°)=1 40°✓
    2
  238. (±1;0)(±1;-1) k=3k1±1 4p(p+1)=(3k1±2)k1 p=1,k1=-+2 k=-+5 p=-2 (1;-5)(-2;5)
    2
  239. 8cos(a/2),8sin(a/2) h=4sina H=6sina h1=2sina 1/2*8=4
    2
  240. ​X(t)=e^(At)c
    2
  241. 73*10-³Н/м т=mg/S=p(н)/l, где l - продольная длина h=mg/p(н)=67 *9,81/(73*10-³)=9,01(км)
    2
  242. a=3-3/b,c=1/(1-b) abc=-3✓
    2
  243. √3/4а²/(3а)=√3/12а √3/2а=6 а=4√3 √3/12*4√3=1
    2
  244. х=1/2;±√2/2°-1+°-√2/2+*0,5-°√ 2/2-°2> x(-1;-√2/2)U(-√2/2;0,5]
    2
  245. X=±√log(40)4
    2
  246. a(n+1)=2^na1-(2^n-1) an=2^(n-1)+1 n>1+log2(-0,5+√(10¹⁵+0,25))=1+log2(-0,5+2²⁴+2²³+2²²+2²¹-2¹⁵+2¹⁴-2¹²-2⁹-2⁷)=25,.. n=26
    2
  247. 2013/7=286 1/7 286+√2sin(π/28)/|sin(2π/7)-cos(2π/7)|=287
    2
  248. 38:10 аналогичная логика и для Беларуси в целом и в 1939г.
    2
  249. S1=50ctg²40°(2/9π-sin40°) S2=50(5/18π-sin50°) S3=50cos40°*(1-tg20°) S=100ctg²40°/9π+125/9π-50tg50°
    2
  250. n≠1,x^(x-n)=n×
    2
  251. 100/4=25
    2
  252. {b=(a²-14)/a,a⁴-51a²+98=0; a²=(51±47)/2=49;2 a=±7;±√2 b=±5;-+6√2{(7;5)(-7;-5)(√2;-6√2)(-√2;6√2)}
    2
  253. Вообще-то,школы для дебилов нет, есть только классы для УО.
    2
  254. A²(((a²-ab+2b²)√(-a²b²+144a²+144b²)+2a³ b-144a²-5ab³+3b⁴-144b²)²+(a⁴+2a³b-144a² -2ab³+b⁴-144b²)²b²=64(2a⁴+4a³b-288a²-4 ab³+2b⁴-288b²)² -112a⁸+4a⁸b²+8a⁷b³-2176a⁷b+328*288a⁶-21a⁶b⁴-448a⁶b²+12a⁵b⁵+160a⁵b³+255*576a⁵b-6a⁴b⁶+1680a⁴b⁴+184*288a⁴b²-246*144²a⁴-26a³b⁷+21a³b⁶-272a³b⁵+256*112a³b³+13a²b⁸-1580a²b⁶-511*144²a²b²+400*288a²b⁴+576ab⁷-256*576ab⁵+b¹⁰-544b⁸+328*288b⁶-256*144²b⁴=(288a⁴+288a²b²-6a²b⁴ -4ba⁵+10a³b³)(144a²+144b²-a²b²)⁰,⁵(a²+2 b²-ab)
    2
  255. {(x+1)²+(y+2)²=25,z²+(w-1)²=144,xw+yz-x +w+2z-61≥0,x≥(-yz-w-2z+61)/(w-1),w-1≥0, w≥1 x=±√(25-(y+2)²)-1,z=±√(144-(w-1)²), ±√(25-(y+2)²)-1≥(-y*±√(144-(w-1)²)-w+61)/(w-1),±√(25-(y+2)²)(w-1)≥-+y√(144-(w- 1)²)-w+61,[{(-y²-4y+21)(w-1)²≥(-y√(-w²+2w +143)-w+61)²,-y√(-w²+2w+143)-w+61≥0, y√(-w²+2w+143)-w+61<0;[{-yw²+2wy-y² 4yw²+8yw-4y+21w²-42w+21≥y²(-w²+2w+143)+w²+3721+2yw√(-w²+2w+143)-122y√(-w²+2w+143)-122w,y√(-w²+2w+143)≤-w+61;[{-y²w²+2y²w+143y²≤w²-122w+37 21,y≥0;{y<0,✓;[{-5yw²-2wy²+w²y²+10wy-144y²+ -4y+20w²+80w-3700≥(2yw-122y)√(-w²+2w+143),y≤-w+6/√(-w²+2w+143);[{-y²w²+2y²w+143y²≤w²-122w+3721,y≥0;{y<0,✓;[{(y-(5w²-10w+4+2(w-61)√(-w²+2w+143)+√((5w²-10w+4+2(w-61)√(-w²+2w+143))²-4+w²-2w-144)(20w²+60w-3700)))/2/(w²-2w-144))(y(-5w²-10w+4+2(w-61)√(-w²+2w+143)-√((5w²-10w+4)²+4(5w²-10w+4)(w-61)√(-w²+2w+143)+4(w-61)²(-w²+2w+143)-80w⁴-80w³+26800w²+5760w-2131200))/2/(w²-2w-144))≤0, ,y≤(-w+61)/√(-w²+2w+143);[{-y²w²+2y²w+143y²≤w²-122w+3721,y≥0;{y<0,✓;
    2
  256. $х^(2/lnx)/√(e^x)*dx=$e^2*e^(-x/2)*dx=e²*e^(-x/2)/(-0,5)+c=-2e²*e^(-x/2)+c
    2
  257. ​F(y/x-1)-F(a)=F(y-1)-F(x-1) F(x)=ln(x+1): ln(y/x)-ln(a+1)=lny-lnx✓ a=0. f(t)=1/(x+1)
    2
  258. Слишком далеко перевозить производства.😜
    2
  259. {x>-5,[x=-6,x=±2;{±2}
    2
  260. V<300Гц,л>10^6 м=1000км
    2
  261. √(a²/4-(a-x)²)+a/2=√(a²-x²),x[a/2;a] 0=5x²-8xa+3a²,x≤0,75a x=a;0,6a✓ S1=(0,5arccos0,6-0,4)a² S2=(π/8- 1/8arccos0,6-0,1)a² S=S1+S2=(0,375arccos0,6-0,5+π/8)a²
    2
  262. √(2021*6063/3)=2021
    2
  263. a=√20 √20*√2=√40,S=40✓
    2
  264. (х-1)³-7(х-1)+k-6=0 x-1=(-k/2+3+ √((-k/2+3)²-343/27))¹/³+(..-..).. (k-6-14/3√(7/3))(k-6+14/3√(7/3))< 0 k(6-14/3√(7/3);6+14/3√(7/3)) k[-1;13] x=1+2√(7/3)cos(1/3arccos ((-3k/14+9/7)√(3/7))+2/3πn) k=0;12
    2
  265. На 40-й день после его смерти вышло.
    2
  266. CD=12√14 /_BAD=arccos(1/15){√(R²-1,5²)*4√14/15+R/15=.., |√(R ²-1,5²)/15-R*4√15/15|=..; √(R²-2,25)/1,7=0,8/R R=1,7
    2
  267. ((x-127,5)²+5/12)³-1/3((x-127,5)²+5/12)-18 2/27=0 x=127,5±√(-5/12+(244+63√15)¹/³/3+(..-..)..)✓
    2
  268. 0,5(1/(1²-1+1)-1/(1²+1+1)+1/(2²- 2+1)-1/(2²+2+1)+..+1/(50²-50+1)-1/(50²+50+1))=1275/2551
    2
  269. 0,5*8*3sina/(0,5sina*12*11)=2/11, 11/2*S-S=36, S=36/(9/2)=4*2=8
    2
  270. log3(x)²-4=0 log3(x)=±2 x=9;1/9D)
    2
  271. ±0,5arccos0,9+πn=a(0;30°) a=0,5arccos0,9 x=10sin(3a)-8sina=22sina-40sin³a=2√5
    2
  272. А как мне кажется, в Беларуси с этим значительно лучше.
    2
  273. Федя Сюткин, всё по Джанни Радари "Приключения Чиполлино".
    2
  274. {(а+2)х
    2
  275. log2¹/¹²(3/2)=7 log2¹/¹²(√5/2)=1 83/92~ 2 log2¹/¹²(5¹/⁴)=6 175/184~7
    2
  276. (S+45)/(S+105),(S+35)/(S+105),S/(S+105) (S+45)(S+35)/(S+105)²=S/(S+10 5) S²+80S+45*35=S²+105S -25S=-45*35 S=9*7=63 ?=63+15=78.
    2
  277. {x≥-2a+1,x≥a;-2a+1≥a,a≤1/3 [{a[0;1/3], 2,25a²-2a+1=x;{a(1/3;√2],0,5a²+a=x.
    2
  278. X=1/9 x=2/3 2/3-1/9+(9-2/3)*2=17 2/9 155✓
    2
  279. (2025-909)/144=7,75 7 периодов и просеки между ними 909-1053,1201-1345,1257-1401 - 3-й,1413-1557 - 4-й,1569-1713 - 5-й,1725-1869 - 6-й,1881-2025 - 7-й
    2
  280. V=1/3π(b²+ba+a²)h-2/3πr³ H=bh/(b-a)
    2
  281. h²+144=(h-h1)²+16² 0=112-2hh1+h1² h1=h-√(h²-112), h≥√112 h=8/3√14~10 S∆=0,5*√(h1²+16)√(140+0,75h²)=0,5√((h²-48-h√(h²-112))(1,5h²+280))= 8/3√(161(29-14√(-2))/6)~41,9 Sk=(7952-4032√(-2))/27~83,96 A)
    2
  282. √4(+√7)=√(7/2)+√(1/2)
    2
  283. $(sin²x/(xcosx-sinx)²-2x-²ln|xcosx-s inx|-2sinx(xcosx-sinx)-¹)dx-x+x²cosx(xcosx-sinx)-¹-2/xln|xcosx-sinx|+c похоже, что не берется
    2
  284. Поздравлять надо в день рождения, а не 2 дня спустя.
    2
  285. (2x²-5x-3)(2x²-3x-5)=0 x=(5±7)/4;(3±7)/4{3;-0,5;2,5;-1}
    2
  286. (1,01³-1)/1=1,030301-1=0,030301=3, 0301%
    2
  287. 0,96/8,93=0,108см³ 125см³,h=0,108/6/ 5²=0,00072см уменьшились на 0,00144 см.
    2
  288. Ольга Иванова, референдум.
    1
  289. 2√2=x/sina=y/sin(150°-a) {x=2√2sina,y=2√2sin(150°-a);√2/sin45°=x/2/sin(a-15°) sin(a-π/4)=0 a=π/4+πn(15°;150°)a=π/4 x=2√2* √2/2=2
    1
  290. y''>0 вогнута функция
    1
  291. S=11 5/9*18=198+5*2=208(cm²)
    1
  292. x²/4+y²≤1,y≤1-(1+√3/2)x x²/4+(1-(1+√ 3/2)x)²≤1,x(-1+x)≤0+*0-*1+>x x[0;1], [{x[- 2;0],y[-√(1-x²/4);√(1-x²/4)];{x[0;1],[-√(1-x²/4);1-(1+√3/2)x]. S=π+1/2-√3/4+|(0;1)arcs in(x/2)+√(4-x²)x/4=1 1/6π-1/2
    1
  293. e^x=(1±7)/2=4;-3 x=ln4
    1
  294. (x³+5x²-4x-20)/(x²+3x-10)=x+2
    1
  295. $(0;l)|u|²dx≤0
    1
  296. (x-2010)P(x+67)=xP(x), x=2010, P(2010)=0, (67m-2010)P(67m+67)=67mP(67m), (m-30)P(67(m+1))=mP(67m), P(67(m+1))=m/(m-30)*P(67m), a0(67(m+1))^n+a1(67(m+1))^(n-1)+...+an=m/(m-30)*(a0(67m)^n+a1(67m)^(n-1)+...+an), -30a0/(m-30)*(67m)^n+a0C(n;1)(67m)^(n-1)+...+a0-30a1/(m-30)*(67m)^(n-1)+a0C(n-1;1)(67m)^(n-2)+...+a1+...-30an/(m-30)=0, -30a0*2010^n-30a1n2010^(n-1)-..-30an=0, 2010^n+a1/a0*2010^(n-1)+...+an/a0=0, a0=0, n:/2=>a(2k-1)=-a0,a2k=a0, n:2=>a(2k-1)=-a0,a(2k)=a0,an=0,
    1
  297. 0,037⁰,⁶=0,022..
    1
  298. (2cos²x-5cosx+2)log11(-sinx)=0,{-sinx>0, sinx<0,хє(-π+2πn;2πn),[2cos²x-5cosx+2 =0,-sinx=1;[cosx=(5±√(25-4*2*2))/4,sinx =-1;[cosx=2,cosx=1/2,x=-π/2+2πn;[x=±π/3+2πn,x=-π/2+2πn;[x=-π/3+2πn,x=-π/2+ 2πn;
    1
  299. а(n+1)=an²-2an-3 an²-3an-3=0 an=(3±√(9 -4*-3))/2=1,5±√21/2≤10,an(-∞;1,5-√21/2] U[1,5+√21/2;∞) an²-2an-3≥an,(an-1-√14)(an-1+√14)≤0,an[1-√14;1+√14].
    1
  300. R,√(R²-4),R-√(R²-4),R+√(R²-4),(R+√(R²-4))² +(2R-2)²=4R²,R²+2R√(R²-4)+R²-4+4R²-8R+4-4R²=0,2R²-8R+2R√(R²-4)=0,R-4+√(R²-4)=0,√(R²-4)=-R+4,{R²-4=R²-8R+16,-R+4≥0;{8R-20=0,R≤4;R=2,5✓ S=(2*2,5)²=25
    1
  301. (2^x-257)(2^x+1)≤0-log2(257)+>x x≤log2(257) log(x+7)((x-8)/(x+7)/x)≤0 °-7-°-6+-4-*-2+°0°8->x 0=x²+6x+8,x=-2;-4 x(-7;-6)U[-4;-2]U(8;∞) x(-7;-6)U[-4;-2]U(8;log 2(257)]
    1
  302. :19*35✓.
    1
  303. a⁵-a⁴-12a³+12a²+16a=16
    1
  304. 10!
    1
  305. 5((4x)^log2(4x))²-9(4x)^log2(4x)-2≤0 ((4x)^log2(4x)-2)((4x)^log2(4x)+0,2)≤0+*-* +>.. (4x)^log2(4x)[-0,2;2]{x≤0,5,x≥0,125;
    1
  306. M(P+∆P)/R/T/р(в)=m/m(в)
    1
  307. У=2/х у=5(х-2)+1 0=5х²-9х-2 х=(9±11)/10=2;-0,2 у=1;-10✓
    1
  308. y'/(ln|y-1|+c)=1 ln|y-1|=u y=±e^u+1 y'=±e^uu' En=1;∞e^-c*(ln|y-1|+c)^n/n/n!+ln|ln|y-1|+c|=±x+c1
    1
  309. Gorbachev и никак иначе.
    1
  310. 1007²/505=1014049/505=2008 9/505
    1
  311. 101 - простое, 10101 - 10101:3 - составное, 1010101/:2,:/3,:/5,:7=144300 (ост.1) :11=91827(ост.4),:13=77700(ост.1) :17=59417(ост.12):19=53163(ост.4)(10⁷-1)/9-(10⁵-1)/9+(10³-1)/9-(10²-1)/9+1 =(10⁷-10⁵+10³-10²)/9+1=10²(10⁵-10³+10- 1) /9+1:р=ост.0 10⁵-10³+10-1:р=ост.9(р-1) р=73, 27²*10-27*10+10-1=7290- 270+9=-10-51+9=-52=21=9*72=648=64 составное, 3n:3, то и всё число кратно 3, а так как оно всегда больше 3, то оно составн ое. А простые будут те, которые не делятся на все простые числа, меньших или равных корню из этого числа. А 101 однозначно входит в них.
    1
  312. BE=BD√(2-0,5√3) x=arccos(1/√(2-0,5√3))
    1
  313. [0=x³⁴-140x³⁰+8400x²⁶-280'000x²²+5600'000x¹⁸-21*32*10⁵*x¹⁴+(448*10⁶-1)*x¹⁰-100x⁸-160004*10³x⁶-80000x⁴-8*10⁵x²-20⁵,x=0;x=-0,59;-0,29;0,643{0;±0,802}
    1
  314. 0=x⁴+5x³+x²-18x-24 x=2;-4
    1
  315. X=(√17-√5)/6 (517-56√85)/27 (517+56√85)/27 1034/27✓
    1
  316. f(x+1/3/x)=3((x+1/3/x)⁵-5/3(x+1/3/x)³+5/9(x+1/3x-¹)) f(x)=3x⁵-5x³+5/3x f(2)=59 1/3
    1
  317. (√X+1,5)⁴-22,5(√x+1,5)²+90 9/16=0 (√x+1,5)²=(22,5±12)/2=17,25;5,25 x=(47-3√85)/2;(15-3√21)/2
    1
  318. (2+√3)(√1,5+√0,5)=1,5√6+2,5√2 1,5√6-2,5√2 3√6✓
    1
  319. (X+0,5)⁴-15,5(x+0,5)²+37(x+0,5)-68 11/16=0
    1
  320. c=√(h²+(b-a)²) h²+(b+a)²=2500,24/h=(25²+a²-(h²+(b-a)²)/4)/50/a {[h=30,h=40;[a+b=40,a+b=30. S=(a+b)/2*h=30*40/2=600
    1
  321. x=(-5y±√(9y²+76))/2 y[-12;12] y=±6✓ x=(-30±20)/2=-5;-25;25;5
    1
  322. En=0;∞c(-1)/(2n)!π/2u^(2n-1)+π/2/uchu=0
    1
  323. E^(√2*(π/3-2πn)),nєZ
    1
  324. Вам лучше бы дописать название канала!
    1
  325. Х=(-а±√((а-2116)(а-1936)))/2+ 1012 а(-=;1936]U[2116;°) (a-2026)²-90²=n²,[{a=4052,n=2024;{a=2704,n=672;{a=2436,n=400;{a=2260,n=216;{a=2166,n=110;{a=2128,n=56;{a=2128,n=48;{a=2116,n=0;{a=2128,n=48;{a=2132,n=-56;{a=2166,n=-110;{a=2260,n=-216;{a=2436,n=-400;{a=2704,n=-672;{a=4052,n=-2024; 9×2=18
    1
  326. x=e^$dty'/(y'-y)*c
    1
  327. Миллиарда,а не триллиона.
    1
  328. (√(R²-2)-√8)²+2=(√(R²-9)-6)²+3² 9/4+√2/3√(R²-2)=√(R²-9) 12 1/16+3√2/2√(R²-2)-7/9(R²-2)=0 R=√(9(9√2+√1513)²/28²+2) S=π(16643+162√3026)/28²(cm²)
    1
  329. $-1/2sin4xdx=1/8cos4x+c
    1
  330. x²+(3x)²-2x*3xcos3a=x²*8,704 √8,704x arccos(1,1/√85) h=x/(ctg arccos(1,1/√85)+ctgarccos0,9)=x* 21√19/200 y=h/sinarccos0,9=x*2 1/20 h1=x√(83,79/85)sin(2arccos 0,9)/sin(arccos(1,1/√85)+2arccos 0,9)=63√19x/250 z=63√19x/250/sin(2arccos0,9)=7x/5✓ y/z=21/20 x/(7/5x)=3/4
    1
  331. 2022²⁰²¹*337+1:/2,:/3,:5 {5}.
    1
  332. {(11/5;0)(1;-6)}
    1
  333. 4(-2+log2(log2(x))(3/4log2log2(x))-1)=1 3/4log²2log2(x))-log2log2(x))-1,5log2log2(x))+2=1/4,3/4log²2log2(x))-2,5log2log 2(x))+1,75=0 log2log2(x)=(2,5±√(2,5²-4 *3/4*1,75))/1,5[log2log2(x)=7/3, log2log2(x)=1;[log2(x)=2^(7/3),log2(x)=4;[x=2^2^(7/3),x=16; xN=>{16}
    1
  334. у²[√х;0,5+√(0,25+х)] (0;0),×
    1
  335. ​​ @ИгорьБогун-н2й  sinx=u cosxdx=du $du/√(1,5-u²)/√2=√(1/3)arcsin(u/√1,5)+c=√(1/ 3)arcsin(sinx/√1,5)+c
    1
  336. $(4x³-12x5+9x⁷)dx=x⁴-2x⁶+9x⁸/8+c
    1
  337. h=v0sinat-gt²/2=v0²sin²a/2/g=3186 m
    1
  338. √(x³+17)=3x-5+√(x³+8),{x³+17=(3x-5)² +2(3x-5)√(x³+8)+x³+8,3x-5+√(x³+8)≥0;{(6x-10)√(x³+8)=-9x²+30x-16,√(x³+8)≥-3x+5;{36x⁵-201x⁴+640x³-900x²+544=0,(x-2/3)(х-8/3)/(х-5/3)≤0-*2/3+*5/3-*8/3 +>х; [{x≥3+(-9/2+√85/2)^(1/3)+(-4,5-√85/ 2)^(1/3), x≤5/3;x>5/3; 0,425✓{[х=1,26.., х=2,х=-0,625..,хє(-∞;2/3]U(5/3;8/ 3];хє[3+(-9/2+√85 /2)^(1/3)+(-4,5-√85/2)^ (1/3);∞);{[х=2,0/,0/,хє(5/3;8/3];{2}
    1
  339. a²-8a-15=0 a=4±√31>0 a=4+√31 x=(7+√31)(7-√31)/18*5=5
    1
  340. 4/9(10^2n-1)=4..4,m=n
    1
  341. N¹⁰≥n!/(N-10)!≥(n-1)(n-2)..(n-10) {N⁹≥(n-9)(n-8)..(n-1),n≥10;[n/2][n/3]*..*[n/10]=(n-9)..(n-1)/10!(?×)
    1
  342. (15-5√5)/(3-√5)=5
    1
  343. 2(135°-b)-180°-a+2b=180° a=-90° R=5/sin(a/2) (2Rcosb+20√2sin(-45°+0,5a+b))* 20√2sin(-45°+0,5a+b)=(2Rcos(135 °-b)+20√2sin(0,5a+b))*20√2sin(0, 5a+b) b=-0,5arccos((sin1,5a-sin0,5a+cos0,5a(1-2cosa))/√(-2cosa+3-4sin0,5a cosa))-arcsin(-√2cos(a/2+π/4)/√(- 2cosa+3-4sin0,5acosa))+π/2,(0;π/2) b=3/4π,a=3/4π R=5/sin67,5° S=25(2+√2)π
    1
  344. sin(π[n/2+1/2]/n)/sin(π/n)/2^([n/2 +1/2]+(n-1)/2)
    1
  345. S=π/2-2o
    1
  346. 21+2(a/b+b/a)+4(a/c+c/a)+8(b/c +c/b)≥21+2*2+4*2+8*2=49
    1
  347. Потому что нынешние телефоны значительно сложнее 10-летней давности.
    1
  348. 2cos15°,1,√2/2/sin15° l=1 x=arccos((√3+1)/4)=15°
    1
  349. {2x+y+z=1,x+2y+3z=2,3x-y+2z=3;{2x+y+z=1,-3y-5z=-3,-5 3/5z=-4 4/5;{x=2/7,y=-3/7,z=6/7;
    1
  350. (√(R²-6,5²)-6)²+11,5²=R² 126-12√(R²-42,25)=0 R=√152,5
    1
  351. (1-у)/sin100°=y/sin20° 1/4/cos²10° =y x/sin100°=(1-y)/sin40° x=1/(-1+ 2cos20°)✓
    1
  352. ∆=(1,01¹/³-1)*100=0,33%
    1
  353. X²/2+1/2x(0;3)+X²/2+1/2x(1;3)+X²/2+1/2x(2;3)+X²/2+1/2x(4;3)+X²/2 +1/2x(5;3)=6+6-1+6-3+6-10+6-15=1
    1
  354. -6cos²x+5cosx+4=0 cosx=(5±11)/12=4/3; -0,5 x=±2/3π+2πn
    1
  355. {x≥2,[x=0,x=8;{8}
    1
  356. 0=x²+9x+15 x=(-9±√21)/2
    1
  357. e^x(e²-1)=e2 x=2-ln(e²-1)
    1
  358. 55/3k=-95 x=-57/11
    1
  359. x³=(-1±√3i)³=8
    1
  360. (2⁵,²⁵(^4=2²¹
    1
  361. 2/(1-tg²a)/>°/>(0;π/6) max=3
    1
  362. an=8/9-25/9/(9an+2)
    1
  363. S∆1=0,5*0,5a*1/3h=1/12ah=3 ah=36 5h/a*h2=0,5h h2=0,1a S∆2=0,5*0,5h*0,1a=0, 025ah=0,9
    1
  364. 1/(kcos(f/2)cosf-√(1-k²cos²(f/2))sinf) 1/(kcos(f/2)) 1/(kcos(f/2)cosf+√(1-k²cos²(f/2))sinf)
    1
  365. {w=x^24,x=y¹,⁵,y^0,5=z; logz(w)=log(y⁰,⁵)(y³⁶)=72
    1
  366. 5080/5207 117,49,19,11,1 3007/3201 194,97,0 31/33 10'003/12
    1
  367. 8√2+16√2=24√2
    1
  368. (1/2)^ncos(π/6n) n=12m,Em=0;∞(1/2)^ 12m+Em=0;∞(1/2)^(12m+1)√3/2+Em=0;∞(1/2)^(12m+2)/2+Em=0;∞(1/2)^(12m +3)*0+Em=0;∞-(1/2)^(12m+4)/2+Em=0; ∞-(1/2)^(12m+5)√3/2+Em=0;∞-(1/2)^(12m+6)+Em=0;∞-(1/2)^(12m+7)√3/2+Em=0;∞-(1/2)^(12m+8)/2+Em=0;∞(1/2)^ (12m+9)*0+Em=0;∞(1/2)^(12m+10)/2+ Em=0;∞(1/2)^(12m+11)√3/2=(1+4017/2¹²√3+157/2¹¹)/(1-0,5^12)
    1
  369. (1-3r/²+(1-r)²=(1+r)² 1-10r+9r²=0 r=(10±√64)/18=×1;2/9✓{4/27π}
    1
  370. m=1+n,n≠0;-1,nZ
    1
  371. х=1/1500+1/3000log10(2)
    1
  372. √(π√0,5)e⁴Ф((x+1)²/√0,125)(-1;∞)= √(π√0,5)е⁴*0,5
    1
  373. √((2¹⁰+1)2⁸/(1+2¹⁰))=2⁴
    1
  374. 18*4000=72'000
    1
  375. m=±√(√(1+80n)+n²)>n,n≥-1/80,n≥0 m=√ (√(1+80n)+n²)>n,n=0:m=1, n=1:m=√10,√ (1+80n)≥2n+1,1+80n≥4n²+4n+1,-4n²+76n≥0,n(n-19)≤0+*0-*19+>n,nє[0;19] n=2:m= √(√161+4), n=3:m=√(√241+9), n=4:m= √(√1281+16),n=19:m=20(1;0)(20;19)
    1
  376. -5(0,5+8cos⁴20°-8cos²20°+2,5cos 20°)/(0,125-cos²20°-0,5cos20°)-9= -1(?)
    1
  377. f=x²-y²+i(2xy-1) (x²-y²;2xy-1)
    1
  378. z-*|z|(z+i)=(x²+y(y+1))√(x²+y²)+x√(x²+y²)i
    1
  379. (z+i)/(i-z-)=(-x²+(y+1)²-2x(y+1)i)/(x²+(y+1) ²)
    1
  380. 2+1,5-1=2,5 √(4-h²)+√(2,25-h²)=2,5 4-h² =6,25-5√(2,25-h²)+2,25-h²,√(2,25-h²)=0,9 2,25-h²=0,81 h=√1,44=1,2 √(4-1,2²)=1,6 tg/_1=0,4/1,2=1/3,tg/_2=0,6/1,2=0,5 tg(/_1+/_2)=(1/3+1/2)/(1-1/3*1/2)=5/6/(5/ 6)=1 /_1+/_2=45°
    1
  381. x=(d-b)/(a-c) 5/6 B)
    1
  382. -ce^(-(p-a)b)/(p-a)=e^(-2s)/(p+2) a=-2,c=-e⁴,b=2 b=4,c=3e⁸ y={(-e⁴+3e⁸)e^(-2t),t≥4, -e⁴e^(-2t),t[2;4), 0,t[0;2).
    1
  383. {x1²(1+x²/4/a²)+(a-1,5x²/a)x1+5x²/4=0,x(x1+a)/(2a)=y;x1=(-a²+1,5x²±√ (a⁴-8a²x²+x⁴))/(2a+x²/2/a) ?=√(((-a² +1,5x²±√(a⁴-8a²x²+x⁴))/(2a+x²/2/a)) ²+x²((2a²+2x²±√(a⁴-8a²x²+x⁴))/(4a²+ x²))²) arcsin(√(((-a²+1,5x²±√(a⁴-8a²x²+x⁴))/(2a+x²/2/a))²+x²((2a²+2x²±√(a⁴-8 a²x²+x⁴))/(4a²+x²))²)/2/√(x²+a²/4))
    1
  384. a/b=S/4,5 c/d=S/3,5 ac/(a+b)/(c+d)=S/(S+10,5) 4/63S²+2/3S=4/63S²+32/63S +1 S=63/11 S1=63/11+1,5=7 5/22
    1
  385. y'/√(y²+4)=±√-1 ln|y+√(y²+4)|=±√-1x+c y+√(y²+4)=(sinx+c1cosx)c, {-2/(sinx+co sxc1)/c+0,5(sinx +c1cosx)c=y,(sinx+c1 cosx)c≥y;y=-2/(sinx+cosxc1)/c+0,5(sinx +c1cosx)c sin(x+arccos(1/√(1+c1²)))c>0
    1
  386. F(x)=ax³+bx²+cx+d 6ax²+(12a+4b)x+8a+4b+2c[2x-8;4x²+14x]{a>0,-a+(b-1/2)²/3/a-3≤c, x(-=;-2]U[-1;=),a<2/3,(a²+13/3a-1/3b²+b-49/12)/(-a+2/3) ≥c;(a+(b-3)/6-√(5b²-10b+10)/6)(a+(b -3)/6+√(5b²-10b+10)/6)≥0
    1
  387. |sin(2018x)|/sin(2018x)*-cos(2018 x)/2018|(0;2018π)=-1/2018+1/2018 =0
    1
  388. DE=1,5BP (25+BP²-169)/10/BP= -(100+BP²-196)/20/BP BP=8√2 DE=12√2
    1
  389. k=0,n=1;2;3;4;.. k=1,n⁵+n⁴+1 n=1;.. ..
    1
  390. y=(2|x|-1)/(|x|-2x²),[{x≥0,y=2(x-1/2)/-2/x(x-1/2)=-1/x,x≠1/2;{x<0,y=(-2x-1)/-2/x/(x+1/2)=1/x,x≠-1/2;
    1
  391. у'(х)=1,5(1+t) y''(x)=-0,75t/(t-1) y'''(x)= -0,375/(t-1)³
    1
  392. cos-²osino'=2cos-³o*sin²o+cos-¹o
    1
  393. ​tlnt'=lnt+1 t-¹✓
    1
  394. ​$(0;4)dz$(0;√z)dy$(0;√y)x³ydx=$(0;4)dzy⁴/16(0;√z)=z³/48(0;4)=4/3
    1
  395. 2x+√(x²+y²)=13 x≤6,5, y=±√(169-52x+3x²) z=x±√(169-52x+3x²)i x(-∞;13/3]U[13;∞)
    1
  396. CD=√3/2+√3/3*4,5=2√3(cm) DA=3√3(cm)
    1
  397. X=tg²u,dx=2tgucos-²udu $(0;1)x√((1-x)/(1+x))dx=$(0;π/4)2 √(2Cos²u-1)(cos-³u-cos-⁵u)dcosu= (-π+4)/4
    1
  398. У меня, похоже,ОКР.
    1
  399. 3(√6-√2),3(√6+√2) S∆=0,5*9*4=18
    1
  400. y=2y1+1 x:2 2x1²=5y1²+5y1+3×
    1
  401. A1=1,a2=2,a3=24,an=(6a(n-1)²a(n-3)-8a(n-1)a(n-2)²)/a(n-2)/a/(n-3) q=0
    1
  402. |sinx|=sinxcosx,{sinx≥0,[x=πn,2πn=x; {πn}
    1
  403. (2а)²+(0,5√(25-а²))²=25 а=√5 S=3*√5*√20=30
    1
  404. |х-3|^(х2-х)=(х-3)²,{х-3≥0,(х-3)^(х²-х-2)=1,х-3=0,{х≥3,х-3=1,х2-х-2=0, {х=3;{х<3,(х-3)^(х²-х-2)(-1)^(х2-х)=1;[{х≥3,х=3,х=4,х=(1±√(1-4*-2))/2,{х<3, х=3,х=4,[х=2, х=-1,х-3=-1,х2-х-2:2;[{х=3,х=4;х=2,х=1,х=2,4-2-2=0:2✓;{3;4;2;1}
    1
  405. f(xy+1)=xf(y)-f(x)+6,f(1)=-f(0)+6,f(1)=xf (0)-f(x)+6,-f(0)=xf(0)-f(x),f(x)=xf0+f0,f0= f0,✓,f(1)=1f0+f0,-f0+6=2f0,f0=2 fx=2x+2
    1
  406. T->=к$N->ds B->=-т$N->ds T->=-к В->/т dN->/ds=N->
    1
  407. 4x⁶-250x³+1/128=0 x=(125/4±√999'998/32)¹/³ 128x⁵+1/256/x⁵=128((125/4±√ 999'998/32)⁵/³+(125/4-+√999'9 98/32)⁵/³)=125992
    1
  408. 1/4Sпр,0,5*0,5a*b=0,25Sпр,0,5*3/8b*a=3/16Sпр,0,5*3/8a*0,5b=3/32Sпр ?=7/32Sпр=7
    1
  409. -у²+у+х=0, у=(-1±√(1-4(-1)х))/(&2)=0,5+√(0,25+х)=1
    1
  410. (36-3)/90=11/30
    1
  411. Ei=1;≠$(i;i+1)1/0dx=∞
    1
  412. x^x=2,x=1 1/3
    1
  413. (x+2)²=-45+√1215×,x=-2✓
    1
  414. {√у=3,√х=6;{(36;9)}45✓
    1
  415. ..=13,83..
    1
  416. {(cosy-sinx+1)(tg²(x-π/3)+tg²(y+π/6))=0,(sinx-cosy)(2-sin2y+siny)=0;{[cosy=sinx-1;tg(x-π/3)=0,tg(y+π/6)=0,[sinx=cosy,{sin2y=1,siny=-1;{[y=±arccos(sinx-1)+2πr,x-π/3=πl,y+π/6=πp,[x=(π/2-y)(-1)^k+2k,π/2-y≥-π/2,≤π/2 {2y=π/2+2πn,y=-π/2+2πm,{[y=±arccos(sinx-1)+2πr,x=π/3+πl,y=-π/6+πp,[x=π/2-y+2πk,x=π/2+y+2πk,yє[0;π]{у=π/4+πn,y=-π/2+2πm;1+4n=-2+8πm,0/ {[-π/6+πp=±arccos(sin(π/3+πl)-1)+2πr, x=π/3+πl π/3+πl=π/2-y+2πk,yє[0;π],y=-π/6+πp,{-π/6=±arccos(√3/2-1)+π(2r-p), y=-π/6+π(l-2k),x=π/2+y+2πk,yє[0;π]; [{0/, x=π/3+2πk, π/6=y,0/,{0/, y=5π/6,x=8π/6+2πk;{π/3+2πk;π/6}{4π/3+2πk;5π/6}
    1
  417. AD=√(30-30/121AC²) 27+AE²-12AEcos/_BAE=0 BE=6cis/_ABE+√(36cos²/_ABE- 27) (6;6/11AC;√(30-30/121AC²)) 5/11A C/√(30-30/121AC²) (30/11AC/√(30-30/1 21AC²);30/121AC²/√(30-30/121AC²);5/1 1AC) 6-30/11AC/√(30-30/121AC²) AC²-1 1=√((31-AC²)(121-AC²)),{AC²=3*121/13, AC²≥11;AC=11√(3/13) CE/sin/_ABE=AE/sin/_ACE sin/_ABE=√(35/156) cos/_AB C=2/√39 sin/_ACE=1/6*√35 CE/√(35/1 56)=√39/(√35/6) CE=3 39√35/43,6-39/4 3√35
    1
  418. 2√(x+a)=a√(x-a) a≥0,{x+a≥0,x-a≥0;{x≥-a,x≥ a;x≥a 4(x+a)=a²(x-a),x(4-a²)=-4a-a³,x=a (a²+4)/(a²-4) ((3a²+4)(a²-4)-(a³+4a)*2a)/(a²-4)²=0 3a⁴-12a²+4a²-16-2a⁴-8a²=0,a⁴-1 6a²-16=0 a²=(16±√(16²-4*-16))/2=8±4√5 a=√(8+4√5) -*+>a (3+√5)√(8+4√5)/(1+√ 5) хє[(0,5√5+0,5)√(8+4√5);+∞)
    1
  419. 27⁰,⁵✓
    1
  420. 1+1/(2+1/(7n+1)) несократимо Следовательно, исходная дробь не сократима.
    1
  421. 2tga=ctga tga=1/√2
    1
  422. f(t)=tsint
    1
  423. $(0;∞)(x^(n-1)-x^(n-2)+..)dx=x^n/n-x^(n-1)/(n-1)+..(0;∞)=-∞+∞-..=∞
    1
  424. 5+2+3+6=1+4+5+6
    1
  425. C(n-1;m)p^(n-1-m)(1-p)^m - C(n-1;m)(1-p)^(n-1-m)p^m (2/3)²+1(/3)²=5/9(A)
    1
  426. $dx*(2(2-x²)-⁰,⁵x-√(2-x²)x)=-2(2-x²)⁰,⁵+(2-x²)¹,⁵/3+c
    1
  427. 8((x+0,5(y+1))³-0,75(x+0,5(y+1))(y+ 1)²-0,25y³+0,75y²+0,75y+7/8)/(x+y+ 1)²=0 x=-0,5(y+1)+(y³-3y²-3y-7/2+√ ((-12y²-12y-9)(y³-5/4)))¹/³/2+(..-..).. *+>y min=(-3(y+1)((y³-3y²-3y-7/2+√ ((-12y²-12y-9)(y³-5/4)))¹/³+(..-..)..)²+ 9y³-9y²-9y+2+6(y+1)²((y³-3y²-3y-7/2+√((-12y²-12y-9)(y³-5/4)))¹/³+(.. -..)..))/(y+1+(y³-3y²-3y-7/2+√((-12y² 12y-9)(y³-5/4)))¹/³+(..-..)..)>=3 32((y+1/4)3-3/16(y+1/4)-9/32)/(2y +1)²=0 y=0,5-*+>y
    1
  428. (10t⁹f(x)-x¹⁰f'(t))/(9t⁸)=10/9xf(x)-1/ 9x²f'(x)=1 f(x)-0,1xf'(x)=0,9x-¹ f(x)=ce^(0,05x²)+0,45E(-0,05x²) (2-0,45E(-0,05))e-⁰,⁰⁵=c f(x)=(2-0,45E(-0,05))e-⁰,⁰⁵e^(0,05x²)+0,45E(-0,05x²)
    1
  429. 1,25*6=7,50 7,5-6=1,5cm
    1
  430. (1,5cos2t-3sin2t)e^t✓
    1
  431. (x+1)((X+5/6)³-21 7/12(x+5/6)+26 11/27)=0 x=-1,x+5/6=(-713/2+√ (713²*4²-259³)/8)¹/³/3+(..-..)..=2/3 (259/2)¹/²cos(1/3arccos(-713/259 √(2/259))+2/3πn) x=-5/6+2/3(25 9/2)¹/²cos(1/3arccos(-713/259√ (2/259))+2/3πn){-1;-5/6+2/3(259/ 2)¹/²cos(1/3arccos(-713/259√(2/ 259))+2/3πn)} 1426<259*6 3/32+2590
    1
  432. 0,5ln(x²+1)(0;3)=0,5ln10
    1
  433. 86400*0,005=432с
    1
  434. 365,2422/(12 7/19)=29,53018
    1
  435. Ek=1;n2^(k-1)xk=8-5n x1=3,x1+2x2=-2, x2=-2,5 xk=(8-5n)/2^(n-1)-2^(-n+1)x1-.. -2^-1x(n-1)=-5/2^(n-1) En=1∞xnsin(πn/2)=En=1;∞-5*0,5^(n-1)*sin(πn/2) абсолютно сходится,Em=1;∞-5*0,5^ (2m-1)*0+Em=1;∞-5*0,5^(4m)+Em=1;∞ 5*0,5^(4m-2)=-5/16/(1-1/16)+5/4/(1-1/ 16)=-5/15+20/15=1
    1
  436. $(0;π)(1+1/cosx)ln((cos2x+2cosx +2)/(cos2x-2cosx+2))dx=$(0;π)(-1+ 1/cosx)ln((cos2x+2cosx+2)/(cos2x -2cosx+2))dx=$(0;π)1/cosxln((cos 2x+2cosx+2)/(cos2x-2cosx+2))dx= 10,566 4sinxcos2x/((cos2x)²+2cos2x+2)
    1
  437. у=3х⁴-5х³+2х,у'=12х³-15х²+2,у"=36х²-30х
    1
  438. (x+2)^(1/3),1/3(x+2)^(-2/3),-2/9(x+2)^(-1 2/3),y""=-80/81(x+2)^(-3 2/3)
    1
  439. y=cos(4x+1),y'=-sin(4x+1)*4,y^(3)=cos(4x+1+π/2*3)*4³=64*sin(4x+1)
    1
  440. [{24≥b,24=c,a=24;{c≥12,a≥c,c<24,a=b;{a≥b,a<24,c=24; {c>a≥b,c≥12,c<24; {a≥b,c<12,a<c; {a<24,a≥c≥24,b=24;{c≥12,b>a≥c,c<24;∞ решений
    1
  441. a=(√3+1)/(√3-1) a²,⁵=(9√3+45+30√3+30+5√3+1)√2/8 11√6
    1
  442. x=(1±√5)/2 x⁵-5x=3;6/2=3
    1
  443. 6⁸²-6⁸¹*8+..+8⁸²=1+1+..+1=83=6 35✓
    1
  444. S1=π/2+π/3=5/6π
    1
  445. $(0;π)(cos²(nx)+cos²((n+1)x)-(1+(-1)^n)*1,5cos(nx)-(1-(-1)^n)*1,5co s((n+1)x)-(1-(-1)^n)*0,5cos((n-1)x)-(1+(-1)^n)*0,5cos((n+2)x))/4/(1-cos ²x)dx-π/4=π/2(для n=1)
    1
  446. -(х+2)/(х-2)³
    1
  447. √(-x²-14x-24)=y y²-15+8y≤0 4±1=5;3 (y-3)(y-5)≥0+*3-5*+>y y(-∞;3]U[5;∞) [{(x+3)(x+11)≥0+*-113+>x,x²+14x+24≤0+-12*-2+>x,x=-7;[x[-12;-11]U[-3;-2];x=-7;x[-12;-11] U{-7}U[-3;-2]
    1
  448. X2+2x≥3 (x-1)(x+3)≥0+*-3-*1+>x x(-∞;-3]U[1;∞)
    1
  449. |3^(3x²-29)-42|≤39 [x²≤11,x²≥10;[+*-√11-√11+>x,+-√10-*√10+>x;[x[-√11; √11],x(-∞;-√10]U[√10;∞);x[-√11;-√10]U[√01;√11]
    1
  450. -°6+°1-*2+>xx(6;1)U[2;∞)
    1
  451. (X-2)(x+2)(4^x-4)<0-°-2+°1-°2+>x x(-∞;-2)U(1;2)
    1
  452. (5^(2x²+2x-20)-5^(-x2+2x+7))/(2^2x-8)≤0 x=±3-*-3+°1,5-3*+>x x(-∞;-3]U(1,5;3]
    1
  453. $(0;√2-1)2/3(t²+6t-1)/(1235/1296 +2/27(t-1/6)+11/6(t-1/6)²+(t-1/6)⁴) dt=√2/20 (Z+11/36)³-799/81/32(z+11/36)+11443/729/128=0, 42 771/799>√(1598/3) z=-11/36+(-22886+√(22886²-799³/3³*8))¹/³/72+(..-..)..;-11/36-(-22886+√(22886²-799³/3³*8))¹/³/144-(..-..)..±√(3/4((-22886+√(22886²-799³/3³*8))¹/³/72+(..-..)..)²-799/81/32)i t=1/6-√(-11/36+(-22886+√(22886²-799³/3³*8))¹/³/72+(..-..)..)±2√(0,5√(-557/81/32+11/36((-22886+√(22886²-799³/3³*8))¹/³/72+(..-..)..)+((-22886+√(22886²-799³/3³ *8))¹/³/72+(..-..)..)²)-11/72-(-22886+√(22886²-799³/3³*8))¹/³/288-(..-..)..);1/6+√(-11/36+(-22886+√(22886²-799³/3³*8))¹/³/72+(..-..)..)±2√(0,5√(-557/81/32+11/36((-22886+√(22886²-799³/3³*8))¹/³/72+(..-..)..)+((-22886+√(22886²-799³/3³ *8))¹/³/72+(..-..)..)²)+11/72+(-22886+√(22886²-799³/3³*8))¹/³/288+(..-..)..)i
    1
  454. ±√(AP²-l1²+((l2²-l1²)/BC-BC)²/4)-0, 5(l2²-l1²-BC²)/BC=x coso=(-+√(AP²-l1²+((l2²-l1²-BC²)/B C)²/4)(l2²-l1²-BC²)+0,5BC(l2²-l1²-BC ²)²+BC²(2AP²-2l1²))(±√((4AP²-4l1²)B C²+(l2²-l1²-BC²)²)+l2²-l1²-BC²)/AP/((4AP²-4l1²)BC)$(-+√(AP²-l1²+((l2²-l1 ²-BC²)/BC)²/4)(l2²-l1²-BC²)+0,5BC(l2 ²-l1²-BC²)²+BC²(2AP²-2l1²))(√((4AP ²-4l1²)BC²+(l2²-l1²-BC²)²)±(l2²-l1²-BC ²))/((4AP²-4l1²)BC)*(AP²-l1²+((l2²-l1 ²)/BC-BC)²/4)-⁰,⁵dAP(0;BC)=l2-l1
    1
  455. 2^2(a+b+c+1)/64-2^(a+b+c+1)+2^(2a+2b -1)+2^(2a+2c-3)+2^(2a)+2^(2b+2c-4)+2^ (2b-1)+2^(2c-3)+1=0,2^(a+b+c+1)=32±32√(15/16-1/16*2^(2a+2b-1)-1/16•2^(2a+2c-3)-1/16*2^(2a)-1/16*2^(2b+2c-4)-1/16* 2^(2b-1)-1/16*2^(2c-3)) 2a=0,2b-1=0, 2c-3=0,{0;0,5;1,5}
    1
  456. Arccos(2/R) √(36-R²) 2/R=√(36-R²)/6 √15±√3=R S=18±6√5
    1
  457. Х[2;8],у(х;8] y≥(4+102x)/(98-x) (x+2)²≥0 x≤78/11 $(2;78/11)(-1000 0/(x-98)-102-x)dx+$(78/11;8)(8-x) dx=-10000ln|x-98|-102x-x²/2(2;78/ 11)+8x-x²(78/11;8)=10'000ln(132/125)-543 29/121
    1
  458. (25³⁰⁰⁹-25³⁰⁰⁸)/(5⁶⁰¹⁷-5⁶⁰¹⁶)=25³⁰⁰⁸(25-1)/5⁶⁰¹⁶/(5-1)=5^(6016-6016)*24/4=6
    1
  459. √(1,4²+9,8²)=1,4√(1+7²)=7√2
    1
  460. 1/32(17+14cos4x+(cos4x)²)=17/32 cos4x(cos4x+14)=0 x=π/8+πn/4✓
    1
  461. (log2|4-x|-4)(log2|4-x|+1)≤0 log2|4-x|[-1;4] |4-x|[0,5;16] x[-12;3,5]U[4,5;20]
    1
  462. X³=sin²u x=sin²/³u dx=2/3sin-¹/³u cosudu $(0;1)√(x(1-x³))dx=$(0;π/2)2/3cos²udu=1/3(u+sin2u/2)(0;π/2)=π/6
    1
  463. u(n+1)=un-n+3,u0=5,u(n+1)/un=1-n/un +3/un=1,
    1
  464. х/(у+2)-(х-2)/(у+2)=2/(у+2)
    1
  465. (z³)²-2z³-8=0 z³=(2±6)/2=4;-2 z=4¹/³;-2¹/³. x=4¹/³-2/4¹/³=2²/³-2¹/³;-2¹/³+2²/³{2²/³-2¹/³}
    1
  466. А Вы тут полностью согласны с Выход есть.
    1
  467. 8/sina=12/sin2a,a=arccos(3/4) x=4√(13-27/4)=10
    1
  468. (X+1/63)³-316/63/21(x+1/63)-10960/63³=0 x=-1/63+(5480+8√(685²-79²*79))¹/³/63+(..-..)..=-1/63+4/63√79*cos (1/3arccos(2740/79/√158)+2/3πn) 53<56/9+64
    1
  469. А ещё идей в тему: капитализм заработал именно так, как в "Капитале" только после развала СССР.
    1
  470. (1-1/512)¹/⁵>0,875
    1
  471. Sсин=-0,5d²+da+(b²-2bd+d²)/2=b²/2+da -bd Sб=ab-b²/2-da+bd [b=a,b=2d;
    1
  472. {5±√24;3;1/3}
    1
  473. 0<1/log(1/2)-x<1/log(1/7)-x,{1/log0,5 -x(1-log2(7))<0,0<log0,5-x;{log0,5-x>0,1 >-x;{-x<1,-1<x,-x>0;{x>-1,x<0;xє(-1;0)
    1
  474. 386/2019=0,1911..<a/b<35/183=0,1912.. b=13652: b>2610 222/2019,<2611 17/ 183 (16)3 13/2019;3 11/183
    1
  475. f(x)=x3-x2-2x=(x-2)x(x+1), $(-1;0)(x³-x²-2x)dx-$(0;2)(x³-x²-2x)dx=x⁴/4-x³/3-2x²/2|(-1;0)-(x⁴/4-x³/3-x²)|(0;2)=-1/4-1/3+1-4+8/3+4+0=-7/12+2 2/3\4+1=3 1/12
    1
  476. [√n+√(n+1)+√(n+2)]=[√(9n+8)] {√n+√(n+1)+√(n+2)+1≥√(9n+8),√n+√(n+1)+√(n+2)-1≤√(9n+8); √n(√(n+1)+√(n+2)+1)≤-√((n+1)(n+ 2))-√(n+1)-√(n+2)+3n+2× n=-0,778;-0,258;-0,888× n[m²/9-8/9;(m+1)²/9-8/9),√n+√(n+1)+√(n+2)[(√(m²-8)+√(m²+1)+√(m²+10))/3; (√((m+1)²-8)+√((m+1)²+1)+√((m+1)²+10))/3),m=3,75.. m=1,6*10²⁷;1,9*10²⁹;3,2*10²⁷ m=3,√n+√(n+1)+√(n+2)[2,8..;4,03..) n[0,16..;0,88..)U[(m²-8)/9~;(m+1)²/9 -8/9~)m≥4 √n+√(n+1)+√(n+2)[4,03..; 5 17/360)
    1
  477. {[×,x=1±√3;x+y=2;{(1±√3;-1+√3)}
    1
  478. (√3/2+1/2)⁹=153√3/32+265/32
    1
  479. x=8|x-1|(1-|x-1|)[{x≥1,0=-8x²+23x-16;{x<1,[x=0,x=7/8;[{x≥1,x=(-23±√(23²-4*8*-16))/ -16;x=0,x=7/8;[x=23/16+√17/16,x=23/16 √17/16,x=0,x=7/8.4решения
    1
  480. 14x<x²,-x²+14x<0,x(x-14)>0+0°-°14+>x хє(-∞;0)U(14;∞)
    1
  481. L=aR a=16/7(rad) /_1=π/2-8/7(rad) S1=24,5(16/7-sin(16/7)) S2=24,5(π-16/7-sin(16/7)) S1-S2=24,5(32/7-π)~35(cm²)
    1
  482. a,180°-a 180°-b=120°-2/3a b=60°+2/3a 180°-c=60°-a/3 c=120°+a/3 b+c=180°+a=253° a=73°
    1
  483. {2x+y=-3,x-y=-6;{2x+y=-3,y=5;{x=-4,y=5.
    1
  484. x=1,4x=-0,5/x x¹/²=-1/2×{1}
    1
  485. $(0;∞)lnx*2e^x/(e^x+1)²dx=-2lnx*(e ^x+1)-¹+$dxx-¹*2(e^x+1)-¹(0;∞)=2Ei =2;∞(-1)^iEj=1;∞(1-i)^jx^j/j/j!|≠-∞=- ∞ e^x=u,x=lnu,dx=du/u 2Ei=1;∞(-1)^i ((1-i)lnx+Ej=1;∞(1-i)^jx^j/j/j!)(0;∞)+2lnx(0;≠)
    1
  486. x-a=5+a x=5+2a S=2(5+2a-2a)²=50
    1
  487. $(1-(lnx-e^x)/(xlnx-x-e^x))dx=x-ln|x lnx-x-e^x|+c lnx-e^x✓
    1
  488. 3/7,2/5 (29/35)/(29/35)=1 a=6 S∆=(6+14+15)*6=210
    1
  489. (cosx-log(6)b)(cosx-3+3b)=0,xє[0;2π] 4 разл.корня b>0,[cosx=log6(b),cosx=3-3b;4 разл.корня log6(b)≤1,≥-1,[b≤6,b≥1/6;3- 3b≤1,≥-1,{b≥2/3,b≤4/3;bє[2/3;4/3] [х=±arc coslog6(b)+2πn,x=±arccos(3-3b)+2πn;{arccoslog6(2/3);2π-arccoslog6(2/3);0; 2π}{arccoslog6(4/3);2π-arccoslog6(4/3); π}bє[2/3;4/3),log(6)b=3-3b,/>\>b=1:0=0 bє[2/3;1)U(1;4/3)
    1
  490. 3a+11b=31, a>0,b>0 a=11a1+...,b=3b1+... a=3,b=2 {a=11a1+3,b=-3a1+2; a1≥1,b≤-1 a1≤-1,b≥5 5✓
    1
  491. {x⁴-1/4x²-1/16=0,y=1/4/x; x=±√(2+2√5)/4,y=±√(-2+2√5)/4 {(√(2+2√5)/4;√(-2+2√5)/4)(-√(2+2√5)/4;-√(-2+2√5)/4)}
    1
  492. acosasina=3,a=4 A)
    1
  493. 9,(99-10+1)2=180,9n*10^(n-1) 9+180+ 2700=2889,2021-189=1842,1842:3=614, 99+614=713
    1
  494. √2cos2°sin4°cos6°sin8°*..sin44°/2⁶⁷=√2/2⁹⁹
    1
  495. S=15/32√3
    1
  496. (lnx+0,557)/(ln400000+0,557)=0,8, x=e^(-0,557+(ln400000+0,557)0,8)=4*⁰,⁸*10⁴*e^(0,557*(-0,2))=3+13/5/3⁴)*10⁴*e^(-0,1114)=3,03 *10⁴ 2,6|81 243 0,03
    1
  497. Sin⁴x(1/a+1/b)-2sin²x/b+1/b-1/(a+b)=0 sin²x=a/(a+b) tg⁴x/a⁴+ctg ⁴x/b⁴=1/a²/b²+1/b²/a²=2/(ab)²
    1
  498. |i j k| i(sino√(1-sino))-j(coso√(1-sin0 |Coso sino 0|=))+k(cososin2o-sinoc |Cos2o sin2o √(1-sino)|os2o) 0,5√(sin²o(1-sino)+cos²o(1-sino)+(sino)²)=0,5√(1-sino+sin²o)
    1
  499. En=1;∞(-a/b)^n/n*Ei=1;∞(-1)^i/i^n~ln(1+a/b)
    1
  500. y=XT,Y'=t+xt' -1/x=(1/t+√(1+t²)/t)t' -ln|x|+c=ln|t|+√(t²+1)+ln|t+√(t²+1)-1| -ln|t+√(t²+1)+1| c=ye^√(y²/x²+1)(y/x +√(y²/x²+1)-1)/(y/x+√(y²/x²+1)+1) c=e^(√145/12)(-12+√145)/4 e^(√145/12)(-12+√145)/4=ye^√(y²/x²+1)(y/x +√(y²/x²+1)-1)/(y/x+√(y²/x²+1)+1)
    1
  501. 27/15+1/5=2
    1
  502. {2=a+b,-12=a-b;{(-5;7)}
    1
  503. {x≥-1,8,x≤-0,8;x[-1,8;-0,8]
    1
  504. 1/x(333/ln10-100x¹⁰⁰)=0 x=±(3,33/ln10)⁰,⁰¹°0+*->x max=3,33lg(3,33/ln10/e)=-3,33*0,..>-6,67 x=10^(n/100) 3,33n-10^n?-6,67 n=1;-2 x=10⁰,⁰¹;10-⁰,⁰²
    1
  505. X≠0,y≠0 (1+y)x²-xy²-y²-11=0 y=-1,x=-12 x=(y²±√((y²+2y)²+4y+44))/2/(1+y) (y²+2y)*2+1≥4y+44 y[-4;4] y=-2,36 y=-5,15²+24× x=(4±6)/2/-1=-5;1 {(-5;-2)(1;-2)(-12;-1)}
    1
  506. |(0;3)-54(3-x)⁰,⁵+18(3-x)¹,⁵-18/5(3- x)²,⁵+2/7(3-x)³,⁵=(24 24/35)√3
    1
  507. UT->(-6;7),UR->(2;9),TS->(2;9),RS->(-6;7) 36+49=85,4+81=85✓
    1
  508. log2(x)√((0,5log2(x)-1)/log2(x))≤1,[{log2(x)≥0,log²2(x)(0,5log2(x)-1)/log2(x) ≤1;{log2(x)<0,(0,5log2(x)-1)/log2(x)≥0;[{log2(x)≥0,(log2(x)+2)/log2(x)≥0+•-2 -°0+>log2(x){x<1,x>0,x≥4;[{log2(x)≥0,log 2(x)є(-∞;-2]U(0;∞);0/;{x≥1,x(0;1/4]U (1;∞);x(1;∞)
    1
  509. S=4*2-2²π/4-0,5*1²π=8-1,5π A)
    1
  510. X=-y±√(5-y²) 2x+y=-y±2√(5-y²)≤5,≥-5 -1±(5-y²)-⁰,⁵*-2y=0 -+1=y+-1*->y-1*+>y
    1
  511. √(2+0,5a²),√(23+0,5a²) 4/9(2+0,5a²)+4/9(23+0,5a²)=a² 20⁰,⁵=a 4√6✓
    1
  512. 41285/3950=10 357/790(лет) 2013г.(!!) (17*10⁶-41285)/3950= 4293 273/790(г.) 2024+4293=63 15г.
    1
  513. (sinx+1)²+π-1[π-1;π+3]B)
    1
  514. EC=1,5BE S∆BEM=2S∆BEC S∆BCM=5S∆BEC S∆ABC=10S∆BEC=80A)
    1
  515. (2x-15)/(x-8)/(x-7)+(x-7)³-4(x-7)²+6(x-7)-4+(x-8)¹⁰+11(x-8)⁹+..+11 A)
    1
  516. N⁴-n³+2n=n(n+1)(n²-2n+2) n=2 2*3*2=12 n=3 3*4*5=60 B)
    1
  517. 12/(2a)=√(169-a2)/13 169/2±65/2=a²[a=3√13,a=2√13.S=6√(4a²-144)-0,5a√(169-a²)=69;9
    1
  518. {√35=c,a=√7,b=2√7.√35+3√7cm
    1
  519. y'(x)=e^(xy),xy=z,y+xy'=z',y'=z'/x-z/x² z'/x-z/x²=e^z,(e^-z)'+ze^-z/x=-x,-z'/z+1/x =0,-ln|z|+ln|x|=C,z=±x/e^C=cx,z=-1/x,z=cx -1/x,y=c-1/x²
    1
  520. X[0;3+√14),(x-1,5)⁴-18,5(x-1,5)²+76 9/16=0 (x-1,5)²=(18,5±6)/2=12,25; 6,25 x-1,5=±3,5;±2,5 x=5;-2;4;-1{5;4}
    1
  521. x⁷+1/x⁷=(x+1/x)⁷-7(x+1/x)⁵+14(x+1/x)³-7(X+1/x) f(x)=x⁷-7x⁵+14x³-7x
    1
  522. π-1=lnz+coslnz+sinlnz z=p(cosf+isinf) π-1=lnp+(coslnp+sin lnp)*chf+((coslnp-sinlnp)shf+1)i {π-1-lnp=(coslnp+sinlnp)√(1/(cos lnp-sinlnp)²+1),-1/(coslnp-sinlnp)= shf;(π-1-lnp)²(1-sin(2lnp))=(1+sin(2lnp))(2-2sin(2lnp)) lnp=-8,75;-5,5;-2,5;0,25;0,52,4;2,5;3,75;7;.. p=e^-8,75;e^-5,5;e^-2,5;e^0,25;e^0,5;e^2,4;e^2,5;e^3,75;e^7;.. f=-1/(cos 8,75+sin8,75);-1/(cos5,5+sin5,5);.. z=e^-8,75(cos(1/(cos8,75+sin8,7 5))+isin(-1/(cos8,75+sin8,75))); e^-5,5(cos(1/(cos5,5+sin5,5))+ isin(-1/(cos5,5+sin5,5));e^-2,5(..);..
    1
  523. C/√3cisx=ccos2x 0=2cos²x-√3/3cosx-1 cosx=(√3±5√3)/12≥0 x=30° S∆=0,5*c√3/2*c/2=c²√3/8
    1
  524. S∆=0,5*5*3√2*sin(135°-arcsin(4/5))=10,5(cm²)
    1
  525. Дорогой автор! В вашей команде только 2 человека?
    1
  526. S=(2+3)/2*1+0,5*3*5-0,5*2*7=3
    1
  527. En=1;≠(-1)^(n-1)(n-1)!e-¹=-∞
    1
  528. 8126*2=16252 5 цифр Д=1,Р≠0 А:2
    1
  529. a=7/cos/_A b=6cos/_A ab=42
    1
  530. Ei=0;n-1|(i/n;(i+1)/n)(e^(nx-i)/nx²-e^ (nx-i)/n²*2x+e^(nx-i)/n³*2)=Ei=0;n-1 e/n³*2i+(e-2)n-²=en-¹-2n-² 0✓
    1
  531. l²+3+l√3=9 l=√3 S=(9-3√3)/4+4,5 arcsin((3√2-√6)/12)-(3√2-√6)/8
    1
  532. Время последнее 1:07:20.
    1
  533. 2a²/(6a²)=1/3 D)
    1
  534. Cos(π(cos²x-1))*π=π
    1
  535. limx->∞(x+a/2-(x+b/2))=a/2-b/2
    1
  536. x'(y)-x/y=-2y²e^y² x=cy-e^y²✓
    1
  537. 2=(1,5-1)B Г=4,В=4,Р=6 Пирамида правильная треугольная с ребром √2.
    1
  538. f4(z)=4+3z+2z²+z³,(z+2/3)³+1 2/3(z+2/3)-8/27-10/9+4=0, z+2/3=(-2 16/27/2+√((1 8/27)²+(5/3)³/27))^(1/3)+(-35/27-√(1225/729+125/729))^(1/3),z=-2/3+(-35+15*2,45)^(1/3)/3+(-35-15*2,45)^(1/3)/3=-2/3+1,25/3-4,16/3=-0,75/3-1,38..=-1,63..<-1, (z+2/3)²+((-35+√1350)^(1/3)/3+(-35-√1350)^(1/3)/3)(z+2/3)+((-35+15√6)^(1/3/3)+(-35-15√6)^(1/3)/3)²=0,z+2/3=(-(-35+15√6)^(1/3)/3-(-35-15√6)^(1/3)/3±√(((-35+15√6)^(1/3)/3+(-35-15√6)^(1/3)/3)²-4((-35+15√6)^(1/3)/3+(-35-15√6)^(1/3)/3)²))/2
    1
  539. a+b-h=c (b-a)²+h²=(a+b-h)² 2ba/(a +b)=h{21=a,28=b;S=(21+28)ba/(a+ b)=588
    1
  540. 1/sinx=√3/sin(90°-y)=2cosy/sin(90 °-x+y){x=arcsin(cosy/√3),[y=90°,πn/2-22,5°=y.y=67,5° x=arcsin(cos67,5°/√3),z=112,5°-arcsin(cos67,5°/√3) 180°B)
    1
  541. 12,5sin(2x-2arccos(3/5))[-12,5;12,5]{12,5}
    1
  542. 1+1/(1+√2)=1+√2-1=√2 2⁴=16 C)
    1
  543. a(n+1)=-1/2^n(n+1,5)+2
    1
  544. a(n+1)=(9+17an)/(23-an)=(9+7a(n-1))/(13-a(n-1))=(9+(-9+b*17)/(c+b)a1)/((c*23-9)/(c+b)-a1) (9+11/3a(n-2))/(18/5-a(n-2)) bn=17(n-1)-7,45-...- (-9-17c(n-1))/(c(n-1)+b(n-1)) cn=23+(-23b(n-1)-9)/(c(n-1)+b(n-1)) -a²+6a-9=0 a=3
    1
  545. √(3/2-x²)/(x-2)² (3/2-x²)-⁰,⁵(x²+2x-3)/(x-2)³=0 x=-1±2=1+*1->x max=√0,5 min=-√0,5
    1
  546. $(0;π/2)4√((a²-b²)cos²o+b²)do
    1
  547. 2|(0;2)x³/3+4=28/3
    1
  548. 5х+1=3х+2,5 х=0,75 S=6x²+(2x+1)²+(2x+ 2)²+2(x+1,5)²=40
    1
  549. X=15°✓
    1
  550. 1+(3/2)^х=(3/2)^3х (3/2)^х=у,у³-у-1=0 у= (1/2+√(1/4+(-1)³/27))^(1/3)+(1/2-√(23 /3)/6)^(1/3) х=log1,5((0,5+√(23/3)/6)^(1/ 3)+(0,5-√(23/3)/6)^(1/3))~0
    1
  551. 1-11 ложны,12 истинно,13 ложны
    1
  552. $E^x(1/(1-x)¹,⁵/√(1+x)+√((1+x)/(1- x)))dx=e^x√((1+x)/(1-x))+c (1+x)-⁰,⁵/(1-x)¹,⁵
    1
  553. $(-1;1)dx$(-1;1)dy(2xy+x²y'-2y'-y²y' -x(2yy'²+y²y''))=4/3-8=-20/3
    1
  554. 1/((1-cos36°)/2)+1/((1-cos108°)/2)=2/(0,25+0,25√5)+2/(1+2(0,25+0,25√5)²+1)=2(√5-1)+2/(2+6/8+2/8*√5)=2√5-2+2(2,75-0,25*√5)/(2,75²-0,25²*5)=2√5-2+4,5/116*16-0,5/116*16√5=-1 11/29+1 27/29√5 121/16-5/16=116/16
    1
  555. (1-cosa)/sina arctg(sin²0,5a/sin²(π/4-a/2)) ?=90°-arctg(sin²0,5a/sin²(π/4-a/2))
    1
  556. log2(x)=±√2 x=2^±√2
    1
  557. -log2(6)*-log6(2)=1
    1
  558. {x<-1,x(-1;0);×
    1
  559. {a+b=5,b+2c=-3,c=-2;(4;1;-2) 4³+1³+(-2)³=57
    1
  560. C=-2b,[{y=3(x-2)+1,x≥2;{x<2,y=-(x-2) +1; y=(a+b)x-2b+d;(a-b)x+2b+d {b=2,d=-1,a=1,4-1=3✓;y=x+|2x-4|-1
    1
  561. (0,25;-0,5)(0,23;0,49)
    1
  562. 2r+2√r√3=6,√r=-√3/2+√15/2 r=(9-3√5)/2
    1
  563. z³=1 z=1;-0,5±√3/2i
    1
  564. 2^n*sin(1/x/3^(n+1))(-1+4sin²(1/x/3^(n+1)))<0\>
    1
  565. log2((2*2^(2x)-4*2^x+2)/2^x)/|x- 1/2|≤0 2*(2^x)²-5*2^x+2=0 2^x=(5±√9)/4=2;1/2 x=1;-1+*-1-°1/2-*1+>x x[-1;1/2)U(1/2;1]
    1
  566. √(8х+13)+√(2х-3)=5,{8х+13≥0,2х-3≥0;{х≥- 13/8,х≥1,5;х≥1,5. √(8*1,5+13)=5≥5,х=1,5.
    1
  567. S=9/2+1,5π-4,5=1,5π
    1
  568. x²sin(nx)/n-2xcos(nx)/n²+2sin(nx)/n³(-π;π)=-4π(-1)^n/n²
    1
  569. (2r)²+1,75²=6,25² r=±3{3}
    1
  570. R²-8R+16+R2-4R+4=2R²-12R+20 R=6±4=10✓;2× A1=25π-48 25π/48-1✓
    1
  571. 146+247+348+449+550+651+752+853+954=1100+1100+1100+1100+550=4950 4950/9=550
    1
  572. {xy=a,x+y=b;{a⁴b=90/a⁴,a³b(b²-3a)=42;
    1
  573. 60sin(90°-arctg(3/4)*2)=84/5(cm) 12*3*8/5=288/5(cm) FG=869 1441/3136
    1
  574. (m²-1)/m=√n/>×
    1
  575. [x⁶+3,99x⁴+6,01x³+213,92x²-186,01x+859,94=0,x=1,3..,x=-2,3,x=1;{1;2,3;-1,3}
    1
  576. S1=6π+9-9√3 S=4S1=24π+36-36√3
    1
  577. (R-r)²=(2r)²+r² R=(1+√5)r✓
    1
  578. а=g(x)/f(x)^(1/n) g(x)f(x)^-n-¹≤f(x)^(1-n-¹) (2n+1)!/6/n!²=(2n⁰,⁷⁵+n-⁰,²⁵)/3*4^(n-1)≥4 ^(n-1)
    1
  579. (24-((17,5^2-R^2)(-2,5^2+R^2))^0,5/R)/R x=2(-432+R^2+24((17,5^2-R^2)(-2,5^2+R^2))^0,5/R)^0,5,R[2,5;17,5]
    1
  580. Символ троицы и белого,черного и золотого папы.
    1
  581. 1/x+1/√(13-x²)=5/6,xєIR, x≠0, 13-x²>0, (x-√13)(x+√13)<0, +_-√13*-_√13*+_>x xє(-√13;√13),x≠0,xє(-√13;0)U(0;√13) √(13-x²)+x=5/6*x√(13-x²), x²=(5/6*x-1)²(13-x²), x²-25/36*x²*13+25/36*x⁴+10/6*x*13-5/3*x³-13+x²=0,x⁴-12/5*x³-253*25*x²+13/5*12*x-468/25=0,(x²-1,39x-78,34*80,73)(x²-0,004x+0,000490)=0,x=80,73, x=-78,34,т.к.xє(-√13;0)U(0;√13), то 0/. (6/5)²=36/25,-253*25-36/25=-6326,44 1265 506 6325+1,44=6326,44⁰,⁵=80-73,56/160=80-0,46=79,54 18/5/79,54=3,6/79,54=0,05, 0,05²=0,0025
    1
  582. {√х-√у=4,√х+√у=20;{√х=12,√у=8;{(144;64)}
    1
  583. 2cos15°/sina=1/sin(135°-a) -75°+1 80°n=a,a=105°✓
    1
  584. ДЕ'Д¹50+Б0'Б50+РЕ'П50=150'З50 9 цифр С=1 А=0;5 3К+0;1=..К К=5;× 2Е+2=..0 Е=4;9 Д+Б+П=2З 6;7;8;9 З=2;3(6;7;8,9)-Р+П=7 Д,Б=(6;7)(7;6) 6;7¹4²'6;7¹50+7;60'7;650+24'950=150'350
    1
  585. y'''+y''-6y'+4y=0 k³+k²-6k+4=0 (k-1)(k²+2k -4)=0[k=1,k=(-2±√(2²-4*-4))/2;y=c1e^x+c 2e^((-1+√5)x)+c3e^((-1-√5)x)
    1
  586. y'/(1-y)=x³,y(0)=3 -ln|y-1|=x⁴/4+c y=ce^ (-x⁴/4)+1 3=c+1,c=2 y=2e^(-x⁴/4)+1
    1
  587. c=d±4,b=c±3=d±4±3 a=b±2=d±4±3±2 |a-d|=9;5;3;1 18✓
    1
  588. f(x)={cx²+2x,x<2,x³-cx,x≥2; 4c+4=8-2c,c= 2/3 И тогда разрыва не будет.
    1
  589. {a[0,975+0,5b;1,025+0,5b),a[19,95-2b;20,05-2b);{b<7,63,7,57>b;b<7,57 a[4,77;4,83) a+b[19,95-b;1,025+1,5b)=[12,36;12,44) (a+b)/(2a-b)(6,05;6,36]
    1
  590. 11/(2√5-3)=2√5+3
    1
  591. 97^32:100=01
    1
  592. √((17+10+9)/2*(18-17)(18-10)(18- 9))=36
    1
  593. {0=a³+ba+c,[a=b,-a²/(a+1)=b; a+b+c=a+b-a³-ba=2a-a³-a²=-a³+a²-a+2-2/(a+1)
    1
  594. E^e(e^m-ex^(m-1)+..+m!(-1)^m)- $dxe^x(x^(m-1)-mx^(m-2)+..+(m-1)!(-1)^(m-1))*nln^(n-1)x-$dx*e^x*m!(-1)^m*nln^(n-1)xx-¹(1;e)=>0(n=≠)
    1
  595. {x>-1,x=2±√3;{2<√3}
    1
  596. x(-∞;-3)U[1;3],0=(x+1)⁴-8(x+1)²+x+1+12 (z-4/3)³-13/3(z-4/3)-5935/64/27=0 z-4/3=(5935/128+√(5935²/128²-13 ³))¹/³/3+(..-..)..=2/3√13cos(1/3arcc os(5935/128/13/√13)+2/3πn) z=4/3+2/3√13cos(1/3arccos(593 5/128/13/√13)+2/3πn) x=-1-√(4/3+2/3√13cos(1/3arccos (5935/128/13/√13)))+√(4/3+2/3√ 13cos(1/3arccos(5935/128/13/√ 13)+2/3π))+√(4/3+2/3√13cos(1/3 arccos(5935/128/13/√13)+4/3π)) ×;-1+√..-√..+√..✓;-1+√..+√..-√..×;-1- √..-√...-√..✓ 47/128<0,8
    1
  597. {R-r=8,R²=r²+16²;
    1
  598. (5-4/3а)*3/4=15/4-а S∆=0,5*5*15/4=75/8(cm²)
    1
  599. √x=y x=y² [y=2,y⁵+2y⁴+4y³+8y²+16y+31=0;x=4
    1
  600. √(3√3+√15)=√(5√3/2)+√(√3/2)
    1
  601. По-моему,пример с ценой не корректен.
    1
  602. 1000/150=6 2/3
    1
  603. y'=xy²++y+1/x²,y1=-1/x
    1
  604. S=(4√3)²*√3/2=24√3
    1
  605. sin¹/³(x/8)=u x=8arcsinu³ dx=24u²/√(1-u⁶)du $(48u⁷cos(2/3arcsinu³)- 24u⁴(2√(1-u⁶)-1/√(1-u⁶))sin(2/3arcsi nu³))du
    1
  606. y=0,5x²-6x+8lnx+7, y'=x-6+8/x=0,x²-6x+ 8=0,x=(6±√(36-4*8))/2[x=4,x=2. +*2-* 4+>x минимум х=4,
    1
  607. ±13 56=4*14 (9;5) ±5{±13;±5}
    1
  608. {x=5,y=-3.
    1
  609. f(x+1)=f(x)²/f(1)=f(1) f(x)=f(1)
    1
  610. √(m/k/p/S/g)+m/v0/k/p/S=∞
    1
  611. (2х-1)/(х+1)=у,х=(у+1)/(-у+2) f(y)=(y+1)/2,f(x)=(x+1)/2
    1
  612. √3cos5°/(√2sin85°)=√1,5
    1
  613. S∆=R²x³/4,3✓,S=R²(sin(x/2)+tg(x/2))(1-cos0,5x),3✓,S=R²/2(x-sinx),3✓
    1
  614. 11/x=4/(8-x) 88-11x=4x x=88/15 11*17/15+4*17/15=17{88/15}
    1
  615. y=±√(3(1-x²/16)) S(AB)=(yA+yB)/2*(xB-xA) S=(√(3(1-xA²/16))xB-+√(3 (1-xB²/16))xA-+√(3(1-xC²/16))xB±√ (3(1-xB²/16))xC-√(3(1-xA²/16))xC±√ (3(1-xC²/16))xA)/2,xB≥0,yB≥0,xA≤xC S'(xA)=((1-xA²/16)-⁰,⁵xA/16(-xB+xC) ±√(1-xC²/16)-+√(1-xB²/16))√3/2=0 [xB=xC,xA=±√(8+0,5xBxC-+*±0,5√((16-xC²)(16-xB²)));+(-)*+(-)*-(+)>xA √(4+0,25xBxC+xB+xC)-+*±√(4+0,25xBxC-xB-xC) S=√3√(1-xB²/16)(|xB|+|xA|);√3(√(1- xA²/16)xB-+√(1-xB²/16)xA-+√(1-xC ²/16)xB±√(1-xB²/16)xC-√(1-xA²/16) xC±√(1-xC²/16)xA)/2 √3/8(1-xB²/16)-⁰,⁵(8-xB/2*xA-xB²)=0 xB=-xA/4+√(xA²+128)/4+*->xB max=√3√(8-xA²/8+xA√(xA²+128)/8)(3xA+√(xA²+128))/16 64-4xA²× S'=√3/32(8-xA²/8+xA√(xA²+128)/8)- ⁰,⁵(-xA²+64+(xA²+128)⁰,⁵xA)=0 xA=±4-*+>xA max=9✓ S=-(6√3,5+3√6-2√21-18)/8~1,08
    1
  616. πg*8=136π g=17 h=15 V=1/3π*8²*15=320π B) S=4π+2πl≥8π S=16π D)?
    1
  617. S∆=120sin53° m²
    1
  618. En=-2023;2022(-arcsin(n/2023)+arc sin((n+1)/2023)*2n=(π/2-0)*-2=-π
    1
  619. 1/b-1/a+1/c-1/b=(-c+a)/a/c
    1
  620. a+b=c+d E=7¹=7
    1
  621. 1,44*10^6/(5+27/30.5+12-9-19/30.5)=1440000/(8+16/61)=1440000*61/494=177611 144 864 8784|494 494 17,7611 3844 3458 3860 3458 3020 2964 560 494 660 494 166
    1
  622. 0,0015*4,55=0,006'825
    1
  623. 0,0015*4,55=0,006'825
    1
  624. 24*32=768
    1
  625. FG=7tg(45°+arctg(3/7))-3=14,5(cm)
    1
  626. 2+861/148'953,172 261/861,3+ 78/261,27/78,24/27 3✓ 173/347✓
    1
  627. Sin24°/sin(x+24°)/sin30°=1/sin(-x+126°) x=arctg(sin24°(-1+√ 5)/(4cos18°cos6°-1))
    1
  628. (4x³+4x²-29x+21)/(2x-3)=2x²-x-16-27/(2x- 3)
    1
  629. n≤-2-log(5)4-m+mlog(5)4
    1
  630. 14+75=89 89-30=59,59-31=28.01
    1
  631. a/sinA*sinB=b A=B;π/2-B У нас треугольник либо равнобедренный с AC=CB, либо прямоугольный с /_С=90°.
    1
  632. (√(a²/4-x²)+a/2)²+(a/2-x)²=a² 0=2x²+xa/2-3a²/16 x=(-1+√7)/8*a a√2/2=4 a=4√2 R=2√2✓
    1
  633. {z=√(xy),√((-y/2±√(b²-3/4y²))y)=a- y/2-+√(b²-3/4y²),x=-y/2±√(b²-3/4y²); 0=4a²y²-2ay(a²+b²)+(a²-b²)²,a-y/2≥±√(b²-3/4y²),+=>(a²+b²)/a≥y Y=(a²+b²±√(-3a⁴+10a²b²-3b⁴))/4/a ±√(-3a⁴+10a²b²-3b⁴)/a≤(3A²+3b²)/a 7a-(b²±√(-3a⁴+10a²b²-3b⁴))/a≥√(6a⁴ +28a²b²+6b⁴-+6(a²+b²)√(-3a⁴+10a²b²-3b⁴))/|a| a[-√3|b|;-√3/3|b|]U[√3/3|b|;√3|b|] a[-√3|b|;-|b|]U[|b|;√3|b|]
    1
  634. 365/29,53=12(ост.10,64) 360-6+0,36=354,36
    1
  635. 0-3;3-5 6!/(6-5)!*2=120*6*2=720*2=1440 0,1,2,3,4,5:5!=120 1,2,3,3,4,5:3!*С(5;2)= 6*5!/2!/3!=6*20/2=60 1,2,3,4,5,0:5!=120 300
    1
  636. х=2+3(2+3х³)³/>/> 81(х³+2/3)³+х-2=0, 81*(х³+2/3)²*9х²+1=0,(х³+2/3)²х²=1/729,(х³+2/3)х=±1/27,[х⁴+2/3х-1/27=0,х⁴+2 /3х+1/27=0;[х=1/44,(х+1/132)³+1/2904 (х+1/132)+383'333/21296/27=0,х+1/132=(-383'333/21296/54+√(383'333²/2129 6²/54²+(1/2904)³/27))^(1/3)+(-383'333/21296/54-√(383'333²/26737² +1/2/121³)/432)^(1/3),х=-1/132+(-383'333/21296/54+√(383'333²/26737² +1/2/121³)/432)^(1/3)+(-383'333/21296/54-√(383'333²/26737² +1/2/121³)/432)^(1/3),-4/9(2/9)^(1/3) +1/27<0,х=-1/12,(х-1/36)³+1/216(Х-1/3 6)+7771/9/36²=0,х-1/36=(-7771/18/36²+√(7771²/18²/36⁴+(1/216)³/27))^(1/3)+(-7771/4-√60388443/4)^(1/3)/18, х=1/36+(-7771/4-√60388443/4)^(1/3)/18+(-7771/4+√60388443/4)^(1/3)/18 --1/32+...+*1/36+..--1/12+*1/44->х минимум=-81((-1/132+(-383'333/21296/54+√(383'333²/26737² +1/2/121³)/432)^(1/3)+(-383'333/21296/54-√(383'333²/26737² +1/2/121³)/432)^(1/3))³+2/3)³-1/132+(-383'333/21296/54+√(383'333²/26737² +1/2/121³)/432)^(1/3)+(-383'333/21296/54-√(383'333²/26737² +1/2/121³)/432)^(1/3)-2=663,..>0, максимум=-81((1/36+(-7771/4-√60388 443/4)^(1/3)/18+(-7771/4+√60388443/ 4)^(1/3)/18)³+2/3)³+1/36+(-7771/4-√60 388443/4)^(1/3)/18+(-7771/4+√60388 443/4)^(1/3)/18-2=-2,87..<0 минимум =-81(-1/12³+2/3)³-1/12-2=-26,...<0 макс имум=-81(1/44³+2/3)³+1/44-2=-25,97..<0,х=-0,84-2,87/665,87*0,55=-0,842..
    1
  637. 99a-99c=600+-bc-,a≥c -bc-:3,b+c:3 -bc-≤291×,a-c[6+2/33;7+6/99] a-c=7 a=c+7,c[0;2] -bc-=93{b=9,c=3;a=10 100+81+9=190E)
    1
  638. 10!/3!/2!/2!=151200
    1
  639. $(0;π/2)(lncosx*ctgx*lnlnsinx-lnlnc osx*lncosx*ctgx)dx=lncosx(lnsinxlnsimx-lnsinx)+$tgx(lnsinxlnsimx-lnsi nx)dx(0;π/2)+lnu*u²/2-u²/4(0;-∞)= ∞+$(0;π/2)tgx(ln²sinx-lnsinx)dx=∞
    1
  640. M1M2(8;0;7)M1M3(7;-5;1)M1M4(9;2;1) |8 0 7|=-40+0+98-(-35*9)-0-16=357 |7 -5 1| |9 2 1| V=1/6*357=59,5
    1
  641. x=√(65+4²-2√65*4*7/√65)=5
    1
  642. S1=π(3√2)²/2-(6²π/4-6²/2)=18
    1
  643. (b+c+a+c)/(a+c)/(b+c)=3/(a+b+c), (a+b+2c)(a+b+c)=3(a+c)(b+c), a²+ab+ac+ab+b²+bc+2ac+2bc+2c²-3ab-3ac-3bc-3c²=0, a²-ab+b²-c²=0, cos/_a=0,5, /_a=60°,
    1
  644. 3x¹/³/(x¹/²-1)/(x¹/⁶+1)=∞
    1
  645. МУХА*2=СЛОН А≠0 М[1;4],С[2;9] 4531*2=9062 и другие варианты
    1
  646. (1/x+4)(1/x³-5*1/x+20)=0 x=-1/4
    1
  647. 8:00 Вы это только Лукашенко скажите.
    1
  648. (1 0|3) (0 1|7/2)✓
    1
  649. 2х²-х-55>0,(х-(1+√(1-4*2*-55))/4)(х-(1-√ 441)/4)>0,(х-5,5)(х+5)>0+-5°-°5,5+>х хє(-∞;-5)U(5,5;∞)
    1
  650. $((e^x-1)-²⁰²³+(e^x-1)-²⁰²⁴)de^x=-(e^x -1)-²⁰²²/2022-(e^x-1)-²⁰²³/2023+c
    1
  651. $(0;1)arcsin√((1+x)/2)/√(1-x²)dx+1 =3π²/16+1 1/√(1-x²)*0,5
    1
  652. К,У,Б,Л,И К*98=99Б+ЛИ0 Б≤7,Л≤7 К≥3 К=3,294=99Б+ЛИ0× К=4, 392=99Б+ЛИ0× К=5, 490=99Б+ЛИ0× К=6,Б=2 39=ЛИ, У=0,1,4,5,7,8✓ К=7,Б=4, 29=ЛИ У=0,1,3,5,6,8✓ К=8,Б=6,19=ЛИ У=0,2,3,4,5,7✓ К=9,Б=8 9=ЛИ× 396:6=66✓297:7=77× 198:8=88×
    1
  653. 30²+50²-2*30*50*-3/5=5200 20√13Н М=-470 Н*м
    1
  654. 4/0,889=4,5(ч)
    1
  655. А Вы знаете,как выяснить из-за чего кто-то умер? Спросить у карт Таро!
    1
  656. 2√(2/3),1/2,√3 h=2S∆/a=√(83/3)/12
    1
  657. 6arcsin(2/R)+6arcsin(1/R)=360°,arcsin (2/R)+arcsin(1/R)=60° 2/R*√(1-1/R²)+√(1 4/R²)*1/R=√3/2,4/R²(1-1/R²)+4/R²√(1-1/R²)√(1-4/R²)+(1-4/R²)/R²=3/4,√(1-1/R²) √(1-4/R²)=3/16R²-5/4+5/4/R² {R⁸-40/3R⁶ +86/3R⁴+160/3R²-656/9=0,(R²-(10+2√1 0)/3)(R²-(10-2√10)/3)≥0+**+>R² {[R²=4,0 17,R²=1,04,R²=10,00,R²=-1,737;-43 2/9?40 R²є(-∞;(10-2√10(/3]U[(10+2√10(/3;∞);[R²=10,R²=1,04,R²=-1,737;[R=√10,R=1,04, 0/;R>2,R=√10 S=0,5*4*√6*3+0,5*2√9*3=6√6+9~24
    1
  658. (x/y)^(pq)✓ 2sinAsimB=2sinAsinB✓
    1
  659. AAAA+AAAB=CCCCC C=1,A=5,5555+ 5556=11'111,B=6 E=12
    1
  660. ГОРА+ОГОНЬ=ВУЛКАН 10 цифр В=1,¹6¹947+96925=103872 мин=9246 9 Макс=106173 20*Г=89;88+10Л, Гє[6; 7] Г=4,Оэ́[3;4]Кэ́[7;8] 47+25=72 2;4;5;7 Н=2;4;5 А=6;7(5;2)
    1
  661. (Xy-1)(x+1)(y+1)✓
    1
  662. {(1-12/(y+3x))√x=2
    1
  663. 6²,¹²⁵(0,5-Ф(2,5ln⁰,⁵6))
    1
  664. P(x)=Ei=0;naix^i ai²+2a0a(2i)+..+2a (i-1)a(i+1)=ai,a1=0,..,a(n-1)an=0 P(x)=Ei=0;[n/2]a(2i)x^(2i) ost.=a0+a2+..+a[n/2] ost.=a0+a2+..+a[n/2]-1
    1
  665. S=0,5*4√5*√20=20
    1
  666. 17^x=17⁴ x=4✓
    1
  667. {[{a=-6,b=9;{a=2,b=1;[x=3,x=-1.✓
    1
  668. 25-0,5*5*15/4=15 5/8
    1
  669. $(0;r)dR$(-√(r²-R²);√(r²-R²))h/r*Rdy= 2hr²/3✓
    1
  670. х=0 2^xln2(1-(1/3)^xlog2(1,5)-(3/8)^xlog2(4/3))=0 x=0(0=0)-*+>x{0}
    1
  671. log5((3-x)(x²+2))≥log5(x²-7x+12)+log 5(5-x),{(3-x)(x²+2)>0,(x²-7x+12)>0,5-x>0;{x-3<0,(x-(7+√(49-4"12))/2)(x-(7-√1)/2)>0, +°3-°4+>x x<5;{x<3,хє(-∞;3)U(4;∞),x<5;х є(-∞;3).(-х+3)(х²+2)≥(х²-7х+12)*(х-5),-(х -3)(х²+2-(х-4)(х-5))≥0,(х-3)(х²+2-х²+5х+ 4х-20)≤0,(х-3)(9х-18)≤0,(х-3)(х-2)≤0 +*2*3+>х хє[2;3],хє[2;3)
    1
  672. √(2x²-98)=l [x=7,x=√63.x>7{√63}
    1
  673. (x²-4x+a²+2a+3)¹²=0,x²-4x+a²+2a+3=0,D=16-4(a²+2a+3)=16-4a²-8a-12=-4a²-8a+4=0 a=(8±√(64-4*-4*4))/-8[a=-1-√2,a=-1+√2.
    1
  674. En=0;∞(-1)^nC(-0,5;n)/(4n+1): En=0;∞C(-0,5;n)/(4n+1)
    1
  675. x=3+1/(4+1/x),x>0 x=±√12{√12}
    1
  676. S=1/(2,5×0,5^2×1,5)^0.5=4/15×15^0,5
    1
  677. Специально всех запугивают, чтобы боялись его.
    1
  678. x=log3(y),y=3^x=3⁴⁹
    1
  679. e^-x(c1sinx+c2cosx)'=e^-x((c1-c2)cosx+(-c1-c2)sinx){c1=0,5,c2=-0,5; -c2=0,5✓
    1
  680. 135000 000₽!500*65=32500₽—средняя зарплата.8000/0,43=18605 пенсия,(135*10^6-32500)/18605=7254!
    1
  681. Она вроде как исчезла в феврале 2020.
    1
  682. BC=2√(AB²-25) sin(2/_1)=6/AB √(AB²-25)=3/5AB AB=25/4 BC=10√(9/16)=7,5{7,5}
    1
  683. (хе)^(хе-2)=1 х=1/е;2/е
    1
  684. {b=a&1/a,c=b-1/b,a≠±1,a≠(±1±√5)/2 0=(a²-1)³-(a²-1)-1/3;a²-1=(1/6+√(1/4-1/3)/3)¹/³+(..-..)..=2/√3cos(10°+2/3 πn) a=±√(1+2/√3cos(10°+120°n)) -3✓
    1
  685. {a=9,b=3;9✓
    1
  686. 1-16/15(5/3)^x-((5/3)^x)²=0 (5/3)^x=3/5{-1}
    1
  687. 4/3+(14/9+4/9)/(2+1)=2
    1
  688. 2023 окурка,674 сигареты и 1 окурок,675 окурков,225 сигарет, 225 окурков,75 сигарет,75 окурков,25 сигарет,25 окурков,8 сиг. и 1 оку.,9 оку.,3 сиг.,3 оку.,1 сиг., 1 оку. 674+225+75+25+8+3+ 1=1011✓
    1
  689. [a=0,a=9,5+√9,25.0×;√9=3
    1
  690. $r²dm=4πp$r⁴dr=4πpr⁵/5(0;R)=3mR²/5 1/3pπh/(b-a)$(a;b)3r⁴dr=πph(b⁴+b³a +..+a⁴)/5=3m/5(b²+(a³b+a⁴)/(a²+ab+b²)) I=1/5πp(h(b⁵+b3a+b²a²+a³b+a⁴)-4R⁵) 1/3π(a²+ab+b²)h
    1
  691. 1990≥(c+3)³-18(c+3)+27 (c+3)³-18(c+3)-1963≤0 c≤-3+(1963/2+√(1963²-864)/2)¹/³+(...-..)..=9,.. a³+9b²+9c=1990 a³:9=1,a:3=ost.1✓ a³+9b²=1909× c≤8,a³=-9b²+1990-9c≤-9b²+1990,≥-9b²+1918(1765¹/³..1793¹/³;5)×0/
    1
  692. Ek=1;n k³-k²(2n+3)+k(n+1)(n+2)=n²(n+ 1)²/4-n(n+1)(2n+1)/6*(2n+3)+1/2*n(n+ 1)²(n+2)
    1
  693. h1=h/2 V1=13/72h√3a² V=2√3a²h/3 V1/V=13/48
    1
  694. z=i(π/2+2πm)+ln(π/2+2πn),m,nZ
    1
  695. {3x²y+y³+c(y)=v(y),-3x²y+c1(x)=v(x);×
    1
  696. $(cos-²x+sinx/cos³x)dx=tgx+cos-² x/2+c
    1
  697. 100/21*3=14 2/7
    1
  698. {y=±√(xz),±√(xz)z=1-x²,±√(xz)x=1-z²; z=(1-x²)²/³/x¹/³,±√0,5=x, (x²-5/8)⁴-3/32(x²-5/8)²-9/64(x²-5/8)-323/8⁴=0 ((..-1/64)²+5/256)(..-1/64)=0 ..=1/64;1/64±√5/16i x=±(√2,5±√0,5)/2 z=±(4√2,5-+4√2)¹/³/2 y=±(1-+√5)/2/(4√2,5-+4√2)¹/³
    1
  699. Беда в России не в том,что бедные не богатеют,а в том, что богатые не могут нажраться (Задорнов).
    1
  700. 2044²+1956²+4022²+3978²=4000'000+176'000+1936+4'000'000-176'000+1936+16'000'000+176'000+484+16'000'000-176'000+484=30'004'840
    1
  701. {z=x²-y,y=x,[x=0,x=2;{3;1}
    1
  702. {1/2=a,b=-1.
    1
  703. {x=y+5/(y-3),z=x-y+3;y-3=1;-1;5;-5 y=4;2;8;-2 x=4+5/1=9;2+5/-1=-3;8+ 5/5=9;-2+5/-5=-3 z=8;-2;4;2{(9;4;8)(-3;2;&-2)(9;8;4)(-3;-2;2)}
    1
  704. y/(yw-1)=x
    1
  705. R-r,√((R-r)²-r²)+R√2/2 (√(R²-2Rr)+R√ 2/2)²+r²=(R√2/2+r)² R²-2Rr=(-√2/2R +(√2+1)r)²,r≥(1-√2/2)R 0=-0,5R²-√2R r+(3+2√2)r² r=(1,5√2-2±(3-2√2)√(2+ √2))R≥(1-√2/2)R 0,433≥0,29✓{(1,5√ 2-2+(3-2√2)√(2+√2))R}
    1
  706. -10/[x]{x}²-11{x}+8[x]=0 {x}=(11±21)/(-20)[x]=-1,6[x];0,5[x],[x]≠0 [x]=1,{x}=0,5 x=1,5
    1
  707. {x=-y/2±√(39-3/4y²),z=-y/2±√(49 3/4y²),-+1,5y√(49-3/4y²)±*±√((39 3/4y²)(49-3/4y²))-+1,5y√(39-3/4y²)= 3/4y²-69,y[-2√13;2√13];27/8y⁴-160,5y²-2850-+3y(3/4y²-69)√(39-3/4y²)=±(±4,5y²√(39-3/4y²)+3y(3/4y²-69)) √(49-3/4y²) y=±5;±19√7/7;±7,2;±1,29 +;+=>(-7,5*11/2-7,5*9/2+99/4=-20 1/4)
    1
  708. L=L0*10^(-2/5m)=cπD²/4,где с - солнечная постоянная 187,5(mkm)=D1{76,8m}
    1
  709. e^(2iz)=i z=π/4+πn
    1
  710. 3/(r-1)=3/(r-1),b=2r-1,a=r+3 r²=9+(r-1)² r=5,S=9*8=72
    1
  711. 8*5+7*5+..1*5=9/2*8*5=180
    1
  712. у=е^u y''=e^u(u'²+u'') u'²+u''=4x²+2 2n≥n-1,n≥-1 n=1 u'=kx+b k²x²+2kx+b²+k=4x2+2{k=±2,b=0;4;× u=√2(e^-x²ln|Ф(√2х)+С/2/√π|+2x√π (Ф(√2х)+С/2/√π)(ln|Ф(√2х)+С/2/√ π|-1)-$2√πdx(Ф(√2х)+С/2/√π)(ln|Ф(√2x)+C/2/√π|-1))+x²+c у=се^х²(Ф(√2х)+С/2/√π)^(√2е^-х²+ 2√(2π)х(Ф(√2х)+С/2/√π))е^(-2х√(2 π)(Ф(√2х)+С/2/√π))е^-$2√(2π)dx (Ф(√2х)+С/2/√π)(ln|Ф(√2x)+C/2/√π|-1))
    1
  713. 16=(16-x)²,[16-x=4,16-x=-4;[x=12,x=20.x ≤16 x=12.
    1
  714. 4x√(-5/4X²+45+9a²/4)/√(64x²-(x²+ 16-a²)²)
    1
  715. {x[1;∞),x<-3/5,(x+433/720)³-14689/ 720/240(x+433/720)-80'963'71/72²/10 =0;x+433/720=10,76 x=10,16
    1
  716. (x⁰,⁵)²/6-5/6x⁰,⁵+1=0 x⁰,⁵=3;2 x=9;4 y=4;9 E=13
    1
  717. a/R=x/r x=a/Rr b=(R+r)√(R2-a²)/R (R+r)[R=a,R/(4(R+r)²+1)⁰,⁵=a; b=2(R+r)²/√(4(R+ r)²+1)
    1
  718. V¹/³/S⁰,⁵≤2-¹/³/3¹/³π-¹/⁶
    1
  719. S=π(6-4√2)
    1
  720. {z=77-x-y,[x=-y,x=77,77=y;1/77⁹⁹✓
    1
  721. e^limx->0(-1/lnx*x)=e⁰=1
    1
  722. 2(log2(x)-1/2)²+1/2≥1/2 [x(0;1),x=2,x=1.x(0;1]U{2}
    1
  723. 0,5/n-1/(n+1)+0,5/(n+2) 0,5+0,5/(n+2)✓
    1
  724. a(x-2)²+3,-a(x-4)²-4 2|a((x-3)²+1)+ 3,5|≥2|a+3,5|=9 B)
    1
  725. z=(-iln√2+π/4+2πm)/(π/2+2πn)
    1
  726. $(x-2x^-0,5+x^-3)dx=x²/2-2/1,5x¹,⁵+x^-2/-2 +c
    1
  727. 4004-1196√10✓
    1
  728. n(a/n)²=a²/n✓
    1
  729. 0=x^log2(5)-x²-1,log2(5)(x^(log2(5)- 2)-2log5(2))x=0,x=0;(2log5(2))^(log(5/4)2)*-*+>x,min=(2log5(2))^log(5/4)5-(2log5(2))^(log(5/4)4)-1=-1,05..<0{2}
    1
  730. {c(x)=±√s'(x),En=0;∞C(-2/3;n)(-1)^n s(x)^(3n+1)/(3n+1)=x.
    1
  731. l=4√7 a=3√21 arccos(3/√21) R=4√7/2/√(4/7)=7
    1
  732. P(x)=a(x-1)(x³+bx²+cx+d){3/a-8- 4b-2c=d,-1,5/a-19-5b=c; P'(x)=4a(x³+(3b-3)/4x²+(-0,75/a- 9,5-3b)x+15/8/a+49/4+11/4b)=4 a(x-2)(x-3)(x-f) +*2-*f+*3->x,a<0,{-9=b,a=-3/4;(x-2)(x-3)(x-2,5)✓ P(x)=-3/4(x-1)(x³-9x²+28x-32) P(6)=-3*5(7)=-105
    1
  733. $tg^mxdx=En=0;m/2 Cn;m/2(-1)^n*Ek=0; 0,5m+n C(-0,5m+n;k)0,5^(-0,5m+n)*...cos 2^[log2(m)]x+c,m:2;En=0;m/2-0,5 Cm/2 0,5;n*(-1)^(m/2+0,5)(cosx)^(2n-m)+c,m:/2
    1
  734. n≥2,(2n)!/n!³/((2n-2)!/(n-1)!³)=(2n-1)2n/n³=2(2n-1)/n²?1,(n-(2-√2))(n-(2+√2))¿0 +2-√2*-*2+√2+>n,<,n[4;∞)
    1
  735. a(n+1)=(an²-1)/(n+2),a1=4, a(n+1)>an на1,(а(n+1)-an)²=3(a(n+1)+an),(n+4-n-3) ²=3(n+4+n+3),n=-3 1/3 0/
    1
  736. $lnxx-²dx=-lnx*x-¹-x-¹+c
    1
  737. 0,25(56/45)=14/45
    1
  738. [x=1,x=-1±√2.
    1
  739. [x=0,x=log(5/13)2.
    1
  740. -1/4+ln8+1-ln2=3/4+ln4
    1
  741. 2sin(x/2)/0,5|(0;π)=4*1-0=4
    1
  742. x"+x=1,k²+1=0,k=±√-1 x0=c1sint+c2cost, xp=b,0+b=1,b=1 x=c1sint+c2cost+1 x(0) =2,x'(0)=-1 2=c2+1,c2=1 x'=c1cost-sint, -1=c1,x=-sint+cost+1
    1
  743. (-√5+3)/8+(√5-2)/24=(-2√5+7)/24
    1
  744. {ф1-ф2=6I1,ф1-ф3=6(I1+I2),I=-15I2,ф1-ф4=-66I2,I1=-8I2;R=4,4Ом
    1
  745. U:I1*10,10I2,20(I1-I2),50(I-I1),50(I-I2). 4I1-2,5I=I2 I2=1/4I1+5/8I 5/6I=I1 R=16 2/3 Om 29 29/30 Om, I=3000/899A
    1
  746. х=(-√5+√15)/5 -568√5+328√15✓
    1
  747. r*2√2,2+√2r √2r-2 ((2+√2r)²+(7-r)²-r*4)/2/(2+√2r)/(7-r)=-((-2+√2r)²+(7-r)²-r*4)/2/(-2+ √2r)/(7-r) 45-14r-r²=0 r=-7+√94 S=π(143-14√94)✓
    1
  748. (-5ab+2b(-a))(-a)=7a²b {a²+ab+b²=-a,ab*(a+b)=b;
    1
  749. Алиса это пудинг, пудинг это Алиса.
    1
  750. r(√2+1)=5√2-5 r=15-10√2
    1
  751. -3+2√2sin(4x)+2sin²(4x)=0 son(4x)=(-√2±2√2)/2=√2/2;-3√2/2× x=π/16+1/2πn;3/16π+1/2πn n[0;1],n[0;1],x=π/16;9/16π;3/16π; 11/16π S=1,5πD
    1
  752. x=-10(a+3/20)/(a-7,5)
    1
  753. Z=1+i±(-√2-√2i)✓
    1
  754. X=4;-6 5x+7y=24 y=4/7;54/7 B)
    1
  755. π^((86x-323)/(343x-433))=u π²-(π²+1)u+u²=0 u=(π²+1±(π²-1))/2=π²;1[x=0,905,x=323/86.
    1
  756. Хє[-√5;√5],[х²+х-5=0,0=х²-х-4;[х=(-1±√21)/2,х=(1±√17)/2;{(-1+√21)/2;(1-√17)/2}
    1
  757. En=1;∞(-1)/(2n-1)!π+πsh1=0
    1
  758. h√(v²+c²)/c²>h/c,v≠0
    1
  759. 1/999!(999+n)!*(n-1)!/(2n-1)!*2^(n-1) ~√π/999!*(999+n)^999,5*(e²/2)^n q=e²/2>1 расходится
    1
  760. X≥0,(x+1/x)²-13(x+1/x)+40=0 x+1/x=(13±3)/2=8;5 [x²-8x+1=0, x²-5x+1=0;x=4±√15;(5±√21)/2 {4±√15;(5±√21)/2}
    1
  761. {а5=2,а4=3,А1=5,а2=6,А3=9;а1а2а3а4а5=56932
    1
  762. cos3°?coa1°,?=<
    1
  763. √х^log(2)√x≥2,√x>0,x>0.x^(0,25log(2)x)≥2,[{xє(0;1),0,25log(2)x≤log(x)2;(1){x>1,0,25log(2)≥log(x)2;(1):0,25log(2)x-1/log(2)x≤0,(log²(2)x-4)/log(2)x≤0,(log(2)x 2)(log(2)x+2)/log(2)x≤0*-2+ 0°-*+2>log (2)x log(2)xє(-∞;-2]U(0;2],хє(0;1/4]U(1;4][xє(0;1/4],{x>1,хє[1/4;1)U[4;+∞);[xє(0;1/4],хє[4;+∞);xє(0;1/4]U[4;+∞)
    1
  764. X[0;=),(x²⁰-1025)¹/⁵=x²-5 0=(x²-2,5)⁴+25/2(x²-2,5)²-33 3/16 (x²-2,5)²=9/4 x²-2,5=±1,5 x=±1;±2{1;2}
    1
  765. ∆t=1,853*34,7/58,5=1,099K
    1
  766. X=cosu,u[0;π],dx=-sinudu $(-1-cosu)du=-u-sinu+c=-arccosx-√(1-x²)+c
    1
  767. $(0;π/2)dx/cos³x=tgx/cosx+$dx/cosx (0;π/2)=tgx/cosx+ln|tg(π/4-x/2)|(0;π/2)= ∞-0-∞-0=ln|tg(π/4-x/2)|(-1/cos²x+1)|π/2 =∞
    1
  768. S∆=0,5*26cos15°*8sin15°=26
    1
  769. limn->∞n-³Ek=1;n-1sin((2k-1)π/2/n)/cos²((k-1)π/2/n)/xos²(kπ/n)=limn->∞n-²π =0
    1
  770. limx->1(sin(πx/2)*π*x⁰,⁵)=π
    1
  771. CD/DB=1/2 CD=0,5DB S∆ABC=666, S∆DEC=0,5*DB*h1/2*0,5=0,5*666=333
    1
  772. y'+9y=0,k+9=0,k=-9,y=c1e^(-9x)
    1
  773. √-lnx=y,x=e^-y²,dx=e^-y²*-2ydy $(0;∞)e^-0,5y²*2dy=√(2π)
    1
  774. 3^8,5n=3^(6n+10) n=4
    1
  775. S=(3√3-π)/36L²=25/9(3√3-π) L=10m S=25/3π(m²)
    1
  776. -abc-/(a+b+c)=19 a+b+c[6;27] -abc-=114;5 13 -abc-=114;133;152;171;190;209;228; 247;266;285;399
    1
  777. (x-2)!=(x²+1)/10 x=3✓;
    1
  778. x1=x2/(x2-1) 1/x1+1/x2=1
    1
  779. f(n)=kn+b (2k²-5k+2)n+(2k-3)b=0 k=(5±√9)/4=2;1/2 b=0 f(n)=2x;1/2x
    1
  780. (√(R²-((a+b)/2)²)+a)²+(b/2-a/2)²=R² (b²+a²)/2=R²,a≥b b²+a²=32
    1
  781. 0,5(ln|e^x-1|-2x+ln|e^x+1|)+c
    1
  782. а(2/27)=54 а=729
    1
  783. $(1-x²)/2ln((1+x)/(1-x))/(1+x)*2/(1-x)dx= (1-x²)/2ln²((1+x)/(1-x))/2+(x-x³)/2ln³((1+ x)/(1-x))/6+..+c
    1
  784. $lnx/(x+1)³dx=lnx(x+3)-²/-2+$1/x/(x+3)²/ 2dx=-lnx(x+3)-²/2+1/18ln|x|-1/18ln|x+3|+ 1/6(x+3)-¹+c 1/2=A(x+3)²+Bx(x+3)+Cx {B=-1/18,C=-1/ 6,A=1/18;
    1
  785. 21/х 7,25(7,25-х),43х/21 х=2 5/8 S=(7,25-2 5/8)*8=37
    1
  786. h+h/2=6,h=4 /_A=45°+arctg0,5 /_B=90°-a rctg0,5 AB=4√2+3√2+√2=8√2 AC=4√1,25 +√20+√5+√5=5√5 S=8√2*5√5sin(45°+arc tg0,5)=40√10(√2/2*2/√5+√2/2*1/√5)=40 √10(√10/5+√10/10)=40*0,3*10=120
    1
  787. (x+y)/y*x l=(y+x)√((y-x)/y) -y²(2cos100°+1)+2xy+x²=0 y=(1±2cos50°)/(-2cos80°+1)x>x cos50°<cos80°×,+✓ y=(1+2cos50°)/(-2cos80°+1)x a=arccos(√(1/(sin10°-cos10°)(0,5 +cos10°-sin20°)+√2*sin5°+2)/2)= 65°
    1
  788. x=4(±1±i)
    1
  789. 2(5√2-7)¹/³=2(√2-1) 193-132√2 193²-132²*2=2401 √((193+49)/2) -√((193-49)/2)=11-6√2 3-√2✓
    1
  790. √(x-√(1-x))=1-x⁰,⁵{x[1/4;1],[x=0,16/25=x;{16/25}
    1
  791. En=2;≠(-1)^(n-1)n!Ei=0;n(-1)^i/i!/(n-i)+E(-t)(0;=)+1+e^-tln²t|0=∞
    1
  792. A=1,3/4=c 3/4+(sin2x*2x-1+cos(2 x))/4/x²=1 1/4=b{(1;1,25;0,75)}
    1
  793. (x-y-z)(x-y+z)
    1
  794. √x=u,x=u²,dx=2udu $2ud/(1+(u+2) ²)=ln|(u+2)²+1|-4arctg(u+2)+c=ln|(√ x+2)²+1|-4arctg(√x+2)+c
    1
  795. 7a²xy³(x-2y)(x-4y)✓
    1
  796. 3R(1+√2)=6√2 R=2(2-√2)m S=36-20π(6-4√2)m²
    1
  797. √(25^х-2^(3-х))≤7*2^(-х/2)-2*5^х,{25^х- 8/2^х≤49*2^-х-28*2^(-х/2)*5^х+4*25^х,(50^х-8)/2^х≥0-*log(50)8+>х;{-3*25^х-57/2^х+28*(5/√2)^х≤0,хє[log(5 0)8;+∞);{(5√2)^2x-28/3*(5√2)^x+19≥0,х є[log(50)8;+∞);{((5√2)^x-(28/3+√(28²/9-4*19))/2)((5√2)^x-(14/3-√(196-171)/3))≥0,+*log(5√2)3-*log(5√2)19/3+>xхє[log(5 0)8;+∞);{хє(-∞;log(5√2)3]U[log(5√2)(19/3);+∞),хє[log(5√2)2√2;+∞);хє[log (5√2)2√2;log(5√2)3]U[log(5√2)(19/3);+ ∞)
    1
  798. √(12,5²-25r)/(12,5-r)=7/25 0=-5,76+576/625r+49/125²r² r=12/(49/25)=300/49 b=arccos(4/5)+arcsin(24/175)=arcsin(3√(151*199)/875+96/875)
    1
  799. 4a²+9/a²+13≥25
    1
  800. х²-2ix+1=0 x=(1±√2)i
    1
  801. limx->π/2-3/7=3/7
    1
  802. х^3+у³=7х²+у² х³=7х²,х2(х-7)=0,{0;7} у³=у²,у²(у-1)=0,{0;1} (х-7/3)³-49/3(х-7 /3)-686/27+у³-у²=0 х-7/3=(343/27-у³/2+у ²/2+√((343/27-у³/2+у²/2)²+(-49/3)³/27))^ (1/3)+(343/27-у³/2+у²/2-у√(0,25(у+1)(-1372/27+у³-у²))^(1/3) -686/27<0,х=7/ 3+2√7/3*397^(1/6)cos(1/3arccos(49/√(7*397))+2πn/3)
    1
  803. 49^х+(2а²-а+6)*7^х+2а²+а-6=0 D=4a⁴-4a³+17a²-16a+60≥0 (2a²-a+4)²-8a+ 44≥0 7^x=-a²+0,5@-3±√((a²-a/2+2)²-2a+1 1){√((a²-a/2+2)²-2a+11)>a²-0,5a+3,-a ²+0,5a-3<√((a²-a/2+1(²-2a+11); 2a²+a-6<0 +°(-2)-°1,5+>a a(-2;1,5)
    1
  804. x≥-1,x≤48,8=x;{8}
    1
  805. -3(2-3y)=y+2 y=1
    1
  806. logx=log(2){2}
    1
  807. lnx*lnx*lnx=1 lnx=1,x=e
    1
  808. То, что раньше, поставлено позже события, которое позже.
    1
  809. 2((x²-10)/10/x)²+1/50=1/10 x²-+2x-10=0 x=±1±√11
    1
  810. a>(3+x²)/2/(x-6) 0,5(x²-12x-3)/(x-6)² =0 x=6±√39+*-*+>x max=-1/4 a>-1/4
    1
  811. En=0;=(-a/(bn+1))^n/(bn+1)
    1
  812. o=-2πn;2πn/5 o=2/5π coso=(-1+√5)/4
    1
  813. (2x-13-31/(2x-3))²=4 2x-13-31/(2x- 3)=±2,[4x²-36x+14=0,4x²-28x+2=0; [x=(9±√67)/2,x=(7±√47)/2.
    1
  814. x/a=(10-a)/(10-x) (x-a)(-x-a+10)=0 x=a,a=10-x 2*x²=20,x²+(10-x)²=20 x=√10,2x²-20x+80=0 x=5±√-15× {√10cm}
    1
  815. (√2/2-0,5)(√2-1)=1,5-√2
    1
  816. Z=1+i/(π+2πn) |z|=√(1+1/(π+2πn) ²)>1 0/
    1
  817. (1 -200 100;-200 199 0;-200 200 1)
    1
  818. {9^x*7^2y=27,5^y*4^(x+1)=32;{x+2ylog9(7) =1,5,xlog(5)4+y=log5(8);{x=1,5, y=0;
    1
  819. $(0;1)lnxdx/√x=lnx*2x⁰,⁵-4x⁰,⁵(0;1)= -4
    1
  820. А скажите честно, это настоящая деревня на заднем фоне?
    1
  821. ±2√889/3=a arccos(17/27) S=24√110-288π/(2,7+√4,4)
    1
  822. 175/2-160/9-12-175/18=48
    1
  823. 33-207x-168x²=0 x=(69±85)/(2*- 56){-7/8;1/7}
    1
  824. xlnx-x(1;e)=e*1-1*0-e+1=e-e+1=1
    1
  825. sin(6x²/(x²-1))+sin((2x²-6x-2)/(x²-1))≥0,2 sin((4x²-3x-1)/(x-1)/(x+1))cos((2x²+3x+ 1)/(x-1)/(x+1))≥0,[{sin(4x²-3x-1)/(x-1)/(x+1))≥0,cos((2x²+3x+1)/(x-1)/(x+1))≥0;{sin(4x²-3x-1)/(x-1)/(x+1))≤0,cos((2x²+3x +1)/(x-1)/(x+1))≤0;[{n≥1,хє[(-4πn-2 π+2)/(4πn+2π-8);-1-1,5/(πn-2)],(2x²+3x+1)/(x-1)/(x+1)≥-π/2+2πn,(2x²+3x+1)/(x-1)/(x+1)≤π/2+2πn;{(4x²-3x-1)/(x-1)/(x+1)≥π+2πn,(4x²-3x-1)/(x-1)/(x+1)≤2π+2πn,(2x²+3x+1)/(x-1)/(x+1)≤1,5π+2πn,[n≤0 хє(-∞;-1) U(-1;1)U[(-4πn-π-2)/(-4πn-π+4);∞);n>0,х є(1;(-4πn-π-2)/(-4πn-π+4)]
    1
  826. 2sin(x⁰,⁵)(0;8)=2sin√8
    1
  827. En=0∞4^n(n!)^2/(n+1)/(2n+1)! limn->∞ 4^(n+1)((n+1)!)^2/(n+2)/(2n+3)!/(4^n(n!) ^2/(n+1)/(2n+1)!)=limn->∞4(n+1)²/(2n+ 2)/(2n+3)=1 limn->∞(4^n(n!)^2/(n+1)/(2n+1)!)^(1/n)=4limn->∞e/4/n=0✓
    1
  828. PQ=2/3√3
    1
  829. 6=(a+b)c c=6/(a+b) 16=(a+?)c ?=16/c-a -1/3(b+a)(a+4b)-3=-3 b=8/3(a+b)-a -b=a
    1
  830. Могли бы хотя бы маты запикать?
    1
  831. lg(2π)/2+3001,5-lge*1000=2567,6.. {2568}
    1
  832. √(R²-(R-1)²)+2=R,√(2R-1)=R-2,{2R=R²-4R+ 4,R-2»0;{-R²+6R-4=0,R»2;{R=(-6±√(36-4*-1 *-4))/-2,R≥2;{[R=3+√5,R=3-√5;R≥2;R=3+ √5.
    1
  833. 7x√(625-x²)=7500-24x² x=15
    1
  834. -(4i-2)=2-4i
    1
  835. x²+17x+71=±(x²-17x+71)[x=0,x²=-71;{0}
    1
  836. 1/(x-1)=2/(3-x) 3-x=2x-2,x=5/3✓
    1
  837. (1+х!)(1+у!)=(х+у)!≥4, х+у≥3, (1,2)(2,1) 0+2≠3, (х+у)!>>левой части, то больше корней не существует.
    1
  838. 2f(x)-f((x+7)/(2x-1))=x,f((x+7)/(2x-1))-0,5f(x-2/5)=0,5(x+7)/(2x-1) f(x)=0,25f(x-2/5)+0,5x+0,125+15/8/(2x-1)=(1/4)^(5/2x)f(0)+7/90/4^ (5/2x)+7/90+2/3x+15/16(1/4^(5/2 x)/(2/5-1/2)+..+1/4/(x-2/5-1/2)+1/(x-1/2))~(1/4)^(5/2x)f(0)+7/90/4^ (5/2x)+7/90+2/3x+75/128/√2(E(ln (1/4)(5/2x-5/4))-E(5/2ln2))
    1
  839. (R-1)²+2²=R² -2R+5=0,R=2,5
    1
  840. S1+S2+S4+S5+20+14++=
    1
  841. 6/y=x/(y+6) 6+36/y=x x+y=6+36/y +y≥6+2*6=18
    1
  842. (√(5-x)-2)/(√(2-x)-1)=0,5(5-x)^-0,5*-1/(0,5 (2-x)^-0,5*-1)=4-⁰,⁵/1-⁰,⁵=1/2/1=0,5
    1
  843. 1/(1+1/(4+1/3/n))/2 дробь 1/3/n несократима Следовательно,и исходная дробь несократима. Ч.т.д.
    1
  844. 105°-а=2а,а=35° х=180°-2*70°=40°
    1
  845. БРИКС,ОАЭ,СА,Е,Ир,Э=>БРИКСОАЭСАЕИрЭ
    1
  846. 0=42-х¹/⁴-14√х+х (z-7/3)³-175/12(z-7/3)-36'875/64/27=0 z-7/3=(295/2+√(295²-7³*128*2)/2)¹/³*5/12+(..-..)..=5/3*7⁰,⁵cos(1/3 arccos(295/112/√7)+2/3πn) 3,8/112<0,04 z=7/3+5/3*7⁰,⁵cos(1/3arccos (295/112/√7)+2/3πn) x¹/⁴=√(7/3+ 5/3*7⁰,⁵cos(1/3arccos(295/112/√7)))+√(7/3+5/3*7⁰,⁵cos(1/3arcco s(295/112/√7)+2/3π))+√(7/3+5/3* 7⁰,⁵cos(1/3arccos(295/112/√7)+4/ 3π))✓;-√-√+√×;-√+√-√×;√-√-√✓ x=(√(7/3+ 5/3*7⁰,⁵cos(1/3arccos(295/112/√7)))-√(7/3+5/3*7⁰,⁵cos(1/3arcco s(295/112/√7)+2/3π))-√(7/3+5/3* 7⁰,⁵cos(1/3arccos(295/112/√7)+4/ 3π)))⁴✓
    1
  847. 10^2+39^2+28^2=100+1521+784=2405 224 56
    1
  848. a=0,5±√2405/2,b=0,5±√2405/2 b=a²-601,0=(a²-a-601)(a²+a-600) a=-1/2±49/2=24;-25 b=-25;24{(0,5+√2405/2;0,5+√2405/2)(0,5-√2405/2;0,5-√2405/2)(24; -25)(-25;24)}
    1
  849. y=arctge^x-x-0,5ln(e^2x+1) y'=1/(e ^(2x)+1)e^x-1-1/(e^2x+1)e^2x
    1
  850. E^-xsinx=(e^-x(c1sinx+c2cosx))'=e^-x((c1-c2)cosx+(-c1-c2)sinx) {c1=-0,5,c2=-0,5;e^-πn(-0,5)+0,5=0,5
    1
  851. |2х-1 х+1| |Х+2 х-1|=-6,(2х-1)(х-1)-(х+1)(х+2)=-6,2х²- 3х+1-(х²+3х+2)+6=0,х²-6х+5=0,х=(6±√(36-4*5))/2[х=5,х=1.
    1
  852. 5((z+a/5)⁴+(3/5b-6/25a²)(z+a/5)²+ (2/5c-6/25ba+8/125a³)(z+a/5)+d/5+9/125ba²-2/25ca-3/625a⁴)=0 (Z+b/10-a²/25)³+(-3/400b²-d/20- 9/500ba²+1/50ca)(Z+1/10b-1/25 a²)+(-1/400b²+d/20+13/500ba²-1/ 50ca-a⁴/625)(b/10-a²/25)-(1/20c- 3/100ba+1/125a³)²=0+*a/5-..-..* -a/5-..+..+>z max?0,min?0 действительных решений Максимум 3,b>2/5a² не все значения действительные
    1
  853. (x-1)(x²+1-4x)(x²+3x+1)=0 [x=1,x=2±√3,x=(-3±√5)/2.
    1
  854. 1/(1+√x)/(1+x¹/³+x²/³)/../(1+x^(1/n)+..+x^((n-1)/n))=1/2/3/../n=1/n!
    1
  855. 20-W(5²⁰ln5)/ln5=x
    1
  856. 8,9,2,7,4,3,4,7,2,9,
    1
  857. X²+8x+7,5=±8,5[x²+8x-1=0,x²+8x+16=0;[x=-4±√17,x=-4.
    1
  858. 6059/1241=73✓ 6205,146,73
    1
  859. (2^(х²-2х)-1)²=0 2^(х²-2х)-1=0 х²-2х=0[х=0, х=2.
    1
  860. a,ctg22,5° a/sin22,5°=6 a=6sin22,5° S=18-7,5√2
    1
  861. Tg³x*sin²0,5x(6)/x⁵=1,5
    1
  862. {cosa=31/112,x=14;{14}
    1
  863. 10^7,826+10^7,5376=11,23..*10⁷. 0,4711*16=7,5376
    1
  864. 2021ab:41,11+-ab-:41,ab=30;71
    1
  865. CO=(a+b)/√2
    1
  866. f(x)+2f(1-x)=x²+1,f(1-x)+2f(x)=(1-x)²+1,*2 -3f(x)=x²+1-2+4x-2x²-2=-x²+4x-3,f(x)=x²/3-4/3x+1,
    1
  867. (ln2500+0,557)/(ln15*10⁴+0,557)=log(15*10⁴*e⁰,⁵⁵⁷)(2500*e⁰,⁵⁵⁷)=0,67
    1
  868. (a√3+y)/2=b y=2b-a√3 S=ba-0,25a²√3
    1
  869. x=1-10/a
    1
  870. (2^x-1/3)³-1/3*(2^x-1/3)-2/27-48=0 x=log2(1/3+(649+180√13)¹/³/3+(..-..)..){2}
    1
  871. √143'641=379
    1
  872. a²f'(x)-2xf(a)=a²f'(a)-2af(a)
    1
  873. х=2(2+15√2)¹/³ (2+15√2)¹/³+(2-15√2)¹/³~2/27 a=1/27,b=18-1/3⁷ (18+8/3⁷)√(9-1/2/3⁷)?15×
    1
  874. Вообще-то, мадам Помпадур.
    1
  875. Х'=2х-3у,у'=у-2х{у=2/3х-1/3х',-4х-3х'+х"=0.k²-3k-4=0 k=(3±√25)/2=4;-1 x=c1e^(4t)+c2e^-t y=-2/3c1e^(4t)+c2e^-t 8-c1=c2,3=8-5/3c1 c1=3,c2=5{x=3e^(4t)+5e^-t, y=-2e^(4t)+5e^-t.
    1
  876. $(0;1)de^x(1/e^x-1/(e^x+1))=lne^x- ln(e^x+1)(0;1)=1-ln(e+1)+ln2
    1
  877. 5/3!×,5/4!×
    1
  878. B=a/3 S=5/12√3a² a=2*3¹/⁴,S=18
    1
  879. (x-1)(y-1)(z-1)<0---<0✓.
    1
  880. lpg2(x)*1/2-3/2/log2(x)=1 log²2(x)/2-lpg2(x)-3/2=0 log2(x)=1±2=3;-1 x=8;1/2
    1
  881. А из Беларуси только БНТУ (1000+).
    1
  882. 34/(38/(47*9/28-9)-35/9)-9(cm) ?=39(cm²)
    1
  883. a=0,5arcsin0,6(-1)^n+πn/2 b=a-30°;150°-2πm=0,5arcsin0,6-π/6 +π(n-2m);0,5arcsin0,6-5/6π+π(n-2m);π/3-0,5arcsin0,6+π(n-2m);-π/3-0,5 arcsin0,6+π(n-2m) sin(a+b)=0,6;-0,3√3-0,4;0,4±0,3√3
    1
  884. ma=-2Gxb, где b - поперечная длина струны T=2π√(plb/2/G)
    1
  885. (AB+CQ)/2*BQ=25*50=1250
    1
  886. Xlny+y²/2/x(1;2)=xln2+3/2/x x²/2ln2+1,5lnx(1;4/=7,5ln2+1,5ln4
    1
  887. u"(x)-u²(x)+u⁵(x)=0 u(x)=e^y y'²+y''-e^y +e^(4y)=0, y=0, u(x)=1;0
    1
  888. -√3/3(0,5x(1/3-x²)¹/²-1/6arcsin(x√3))+c
    1
  889. 1-cisx=√(1-√(cos²x(4-7cis²x))),2cosx-cos²x=√(cos²x(4-7cos²x)){cosx≥0,cos²x(-4cosx+8cos²x)=0;[cosx=0, cosx=0,5;[x=2πn,x=±π/3+2πn.
    1
  890. {x+y=a,xy=b;{b=a²-96,√(a²-96)=16-a; {A≤16,11=a;b=25 {y=11-x, x(11-x)=25;-x²+11x-25=0 x=(11±√21)/2,y=(11-+√21)/2 {(11/2±√21/2;11/2-+√21/2)}
    1
  891. AB,y=-x+2x0+5 AC,y=2x-2,5x1 -3=x0,1,2=x1 y=x+5,y=-x/2 x=-10/3,y=5/3,R=√170/3=√2|x-1|= √(5x²-6x+2) x=1±√85/3,y=-2-+√85/3 C,x=38/15; -4/3,y=2x-3=28/16;-17/3 BC=(-3418,75-+1585/4√85)/1596 (x-1-+√85/3)-2-+√85/3
    1
  892. I+J=π/2-1/2 I=J I=π/4-1/4
    1
  893. 50/1600=0,03125 доля зарплаты должен состоять подарок деньгами.
    1
  894. А Вы серьезно носите эти очки?
    1
  895. √(9+2√3-2√5-2√15)=a+b√3+c√5=1+√3-√5 1+√3-√5-1-√3+√5=0 {c=±1,b=-+1,a=-+1;
    1
  896. y/x=z y=xz y'=z+xz' (π/2z-zarctgz+0,5ln|1+z²|)'+1/x(π/2z-zarctgz+0,5ln(1+z²)) =2lnx/x $-arctgxdx=-xarctgx+0,5ln(1+x²) π/2z-z arctgz+0,5ln|1+z²|=w w=x-¹c+2xlnx-2x π/2y/x-y/xarctg(y/x)+0,5ln|1+y²/x²|=cx-¹+ 2xlnx-2x
    1
  897. ШЛИ+БОЛЕЕ=ДЕНЬГИ 10 цифр БГДЕИЛНОШЬ ШЛИ+9О'Л00=10Н'ЬГИ×
    1
  898. у=√(1-х²) 4ху-8ху³=4х√(1-х²)-8х(1-х²)¹,⁵ ...' =(-32х⁴+32х²-4)(1-х²)-⁰,⁵=0 х²=1±√2/2≥0 х=±√(1±√2/2) +*--√(1+√2/2)+*+-√(1-√2/ 2)*√(1-√2/2)-*√(1+√2/2)+>х Макс=√(1-√2/2)(2^1,75-2^2,25)
    1
  899. ​1+2х+3х²..+3х⁴+2х⁵+х⁶=1+3х²+3х⁴+х⁶+2х +4х³+2х⁵, -х³=0,х=0.
    1
  900. 27/4x¹⁸y-²z¹²✓
    1
  901. $dx/sin³x/cos³x=$2/(t²+1)dt/(2t/(1+t²))³/((1-t²)/(1+t²))³=$2/8/t³/(1-t²)³(1+t²)⁵dt= $(1/4(-t+(-1-5t²+9t⁴-7t⁶+2t⁸)/t³/(t-1)³/(t+1)³)dt=1/4(-t²/2+$(A/t+B/t²+C/t³+D/(t-1)+E/(t-1)²+F/(t-1)³+G/(t+1)+H/(t+1)² +I/(t+1)³)dt=-t²/8+1/4(8lnt+t^-2/-2-5 15/16ln|t-1|+2 5/8(t-1)^-1/-1-5 13/24(t-1)^-2/-2-1/16ln|t+1|+3,25(t+1)^-1/-1-2 19/24(t+1)^-2/2)+C= -tg²0,5x/8+2ln|tg0,5x|-tg^-2 0,5x/8-95/64 ln|tg0,5x-1|-21/32(tg0,5x-1)^-1+133/24 (tg0,5x-1)^-2-1/64ln|tg0,5x+1|-0,8125 (tg0,5x+1)^-1-67/192(tg0,5x+1)^-2+C -1-5t²+9t⁴-7t⁶+2t⁸=At²(t-1)³(t+1)³+Bt(t-1)³(t+1)³+C(t-1)³(t+1)³+Dt³(t-1)²(t+1)³+Et³(t-1)(t+1)³+Ft³(t+1)³+Gt³(t-1)³(t+1)²+Ht³(t -1)³(t+1)+It³(t-1)³=At⁸-2At⁶-At⁵+3At⁴-At²+Bt⁷-2Bt⁵-Bt⁴+3Bt³-Bt+Ct⁶-2Ct⁴-Ct³+3Ct²-C+Dt⁸+Dt⁷-2Dt⁶-2Dt⁵+Dt⁴+Dt³+Et⁷+2Et⁶-2Et⁴-Et³+Ft⁶+3Ft⁵+3Ft⁴+Ft³+Gt⁸-Gt⁷-2Gt⁶+2Gt⁵+Gt⁴-Gt³+Ht⁷-2Ht⁶+2Ht⁴-Ht³+It⁶-3It⁵+3It⁴-It³,{A+D+G=2,B+D+E-G+H=0,-2A+C-2D+2E+F-2G-2H+I=-7,-2B-A-2D+3F+2G-3I=0,3A-B-2C+D-2E+3F+G+2H+3I=9,3B-C+D-E-F-G-H-I=0,-A+3C=-5,-B=0,-C=-1;{A=8,B=0,C=1,D+ G=-6,D+E-G+H=0,-2D+2E+F-2G-2H+I=8,3F+2G-3I=8,D-2E+3F+G+2H+3I=-13,D-E-F-G-H-I=1;{A=8,B=0,C=1,D+ G=-6,-E+2G-H=-6,E+0,5F-H+0,5I=-2,3F+2G-3I=8,2E-3F-2H-3I=7,E+F+2G+H+I=-7;{A=8,B=0,C=1,D+G=-6,-E+2G-H=-6,0,5F+ 2G-2H+0,5I=-8,3F+2G-3I=8,-1,5F+2G-2H-1,5I=-2,5,F+4G+I=-13;{A=8,B=0,C=1,D+G=-6,-E+2G-H=-6,0,5F+ 2G-2H+0,5I=-8,1 2/3G-2H+I=-9 1/3, 2 2/3G-2 2/3H=-8 5/6,-2H=-6,5;{A=8,B=0,C=1,D=-5 15/16,E=-(-6+3,25-2 -1/16)=2,75-1/8=2 5/8,F=(-8-2-1/16+ 2*3,25+0,5*-2 19/24)/0,5=(-8+1/8+6 1/2-1 19/48)*2=(-7 7/8+5 5/48)2=-2 37/48*2=-4 37/24=-5 13/24, G=(-8 5/6+2 2/3*3,25)/2 2/3=(-53/6+8*13/12)/8*3=(-106+104)/12/8*3=-2/4/8=-1/16,H=3,25,I=-9 1/3-2/3 *-1/16+2*3,25=-9 1/3+1/24+6 1/2=-2 19/24; (1/2sin2x)³=1/8(1-cos4x)/2*sin2x=(sin 2x-cos4xsin2x)/16
    1
  902. 2x+0,5≥x⁶/2,2x-1,5≤0,5x⁶;{(x+0,25)(x-1,36) ≤0,(x-1)(x-0,83)≥0;{x[-0,25;1,36]x(-≠;0,83]U [1;≠);x[-0,25;0,83]U[1;1,36] x[-0,5;0):&1=1/2x⁶ 0/,x[0;0,5),1=1/2x⁶,x= ±2¹/⁶ 0/ x[0,5;1)1+1/2x6,0/ x[1;1,5) 2=1/2 x⁶ x=±2¹/³ {2¹/³}
    1
  903. V=396π
    1
  904. а=5sin/_1,b=5sin(180°-/_1-/_a) x=8-8sin/_1,y=8-8sin(180°-/_1-/_a) xy=64(1,3-1,6sin/_1-cos/_1*4/5-3/ 10*cos2/_1+sin2/_1*2/5);64(0,7- 2/5sin/_1-cos/_1*4/5+3/10cos2/_ 1+sin2/_1*2/5)[0;19,5584]
    1
  905. S∆=5,5²/2-3,5²/2-8=1
    1
  906. Y³/3(-3;3)=3²*2=18 9ln|x²+1|(0;1/=9ln2
    1
  907. 1/3,10/21/(1-1/21)=10,131/3
    1
  908. f(x)+2f(1-x)=x2+2,2f(1-x)+4f(x)=2x ²-4x+6 f(x)=1/3x²-4/3x+4/3
    1
  909. (5+5i)/(2+i)+(11-7i)/(4-i)=6
    1
  910. 1|8|@0|10 13|7|3|6 5|4|9|11 10|10|7|2
    1
  911. {√(a²+a1²-aa1√2)=b,AH=(√2a1²±√(-2a1⁴+4√2a1³a+256/225a1²a²+(-256/225√2-4)a³a1+256/225a⁴))/√(a²+a1²-aa1√2)/2, 180=(20-√(a²-aa1√2-a1√(2a²+a1²-2aa1√2)))(20-8/15a)(20-√(a²+a1²-aa1√2+(√2a1²±√(-2a1⁴+4√2a1³a+256/225a1²a²+(-256/225√2-4)a³a1+256/225a⁴))²/(a²+a1²-aa1√2)/4-√(a²+a1²-aa1√2)(a1²±√(-a1⁴+2√2a1³a+128/225a1²a²+(-128/225√2-2)a³a1+128/225a⁴))/√(a²+a1²-aa1√2))),60=√(a²-aa1√2-a1√(2a²+a1²-2aa1√2))+8/15a+√(a²+a1²-aa1√2+(√2a1²±√(-2a1⁴+4√2a1³a+256/225a1²a²+(-256/225√2-4)a³a1+256/225a⁴))²/(a²+a1²-aa1√2)/4-√(a²+a1²-aa1√2)(a1²±√(-a1⁴+2√2a1³a+128/225a1²a²+(-128/225√2-2)a³a1+128/225a⁴))/√(a²+a1²-aa1√2));{37,5cm²}
    1
  912. 36 8/45/47=0,8(см)
    1
  913. S=100-12,5π-25√2(m²)
    1
  914. X²+y²/a²=1,y=2ax-3a (2x-3)²+x⅔=1 5x²-12x+8=0 x=(12±4i)/10× y=-0,5/a(x-x0)+2ax0-3a (1+0,25/a⁴)x²-1/a² x((0,5/a²+2)x0-3)+(0,5a-²+2)²x0²-6 (0,5/a²+2)x0+8=0 x=x0+a²(-3±√(-(1+4a²)²x0²+4(3a²+12a⁴)x0-32a⁴+1))/(2a⁴+0,5) min=|a|√ (a²+0,25)|-3+√(-(1+4a²)²(x0-6a²/(1+ 4a²))²+4a⁴+1)|/2/(a⁴+0,25) x0[-1;1] -1,5/(1+4a²)+1,5≤1,5,≥0 x0[0;1] ±√(-1/4-3/8/(x0-1,5))=a≤√2/2 √(a⁴+0,25a²)(1,5/(a⁴+0,25)-(a⁴+0,2 5)-⁰,⁵) (a⁴+0,25a²)-⁰,⁵(-3a⁶-1,125a⁴+ 0,75a²+3/32+(-0,5a²+0,25a⁴-1/16)(a⁴+0,25)⁰,⁵)(a⁴+0,25)-²a=0 [a=0,{|a|≤√(-1/8+1/4√(19/3)cos(1/3arccos(-√(27/19³)))),(11a⁶+6,5a⁴-2,75a²-3/8)(13a⁶+2,5a⁴-3,25a²-3/8)=(0,5a⁴-a²-1/8)²;a=±√0,32*0+*√0,32->a min=0
    1
  915. F=1000 N My=1600N*m x=1,6m Mx=&800N*m y=0,8m (1,6m;0,8m)
    1
  916. И у меня тоже: например, про моего двоюродного деда: и скал на кладбище его могилу, но так и не нашел, но моя семья сказала, что мы ее нашли.
    1
  917. (R-6)²+12²=R²,-12R+180=0 R=15✓
    1
  918. (7²+8²-9²)/2/7/8=2/7 7/(√3/2)=а/(√45/7) а=2√15 sin(120°-arccos(2/7))=√3/7+√45/14 2+√15 19/3-4/9√15=AF AF/AC=19/ 27-4/81√15
    1
  919. 18√3 S=18*18√3-1/3π*18²=324√3-108π=221,892(cm²)
    1
  920. X-0,5x√(1-x²)-0,5arcsinx(0;1)=1-π/4
    1
  921. $dx*0,25(-2x/(x²-1)+2x/(x²-3))=0,25 (-ln|x²-1|+ln|x²-3|)+c
    1
  922. r⁰,⁵=2√2(√2-1) r=8(3-2√2)
    1
  923. -a+5x/4=0,x=4/5a,tg/_AEF=tg(-arcs in(4/5)-arctg(10/7))=58/19
    1
  924. f(x)=2x²+ax¹,⁵/1,5+bx+c (4;3) (0;-5) {c=-5,-6-4/3a=b;f(x)=2x²+ax¹,⁵/1,5+(-6-4/3a)x-5 -15=a f(x)=2x²-10x¹,⁵+14x-5
    1
  925. -5b*5b+(3c-4a)²=(3c-4a-5b)(3c-4a+ 5b)
    1
  926. (2x+1)⁰,⁷⁵=8 2x+1=2⁴ x=7,5✓
    1
  927. {lnx=a-⁷/³b²c²/³,a-¹/³b¹/³c²/³=lny,a²/³b²/³c-¹/³=lnz;{(e^(a-⁷/³b²c²/³);e^(a-¹/³b¹/³c²/³);e^(a²/³b²/³c-¹/³))}
    1
  928. {(xy-1,5)³-3,75(xy-1,5)+393 3/4=0, x+y=1;xy=1,5+(-1575+110√205)¹/³/2+(..-..)..{y=1-x,x²-x+1,5+(-1575+110√205)¹/³/2+(..-..)..=0; x=0,5±√(-1,25+(1575-110√205)¹/³/2+(..+..)..),y=0,5-+√(-1,25+(1575-110 √205)¹/³/2+(..+..)..)
    1
  929. 0,5/_1+82°+2(85°-/_1)=180° /_1= 48° ?=180°-24°-37°=119°
    1
  930. 4x=6(10-x) 10x=60,x=6(N)
    1
  931. 176/981=0,200kg
    1
  932. {x≤20/3,[x=4,x=-100/7;{-100/7;4}
    1
  933. 28=1/4a²-9/4 a=11(cm) CD=8(cm) (16/3-4)/4=1/3 4-7/3=5/3(cm) S=(5/3+4)/2*7-0,5*4*4=71/6(cm²)
    1
  934. 210•2/2119¹/⁴*2119¹/⁴=420
    1
  935. 9²+9*25+25²=931
    1
  936. 17л|3|3|8|8|13✓ 5л|0|5|0|5|0
    1
  937. 15X³(x-4/3)=0 x=0;4/3+->x min=0 max=256/81>1 Е 3 решения x=f 5(3f+2)-3(5f+3)=1✓ (x-f)(x⁴+(-7+3√5)/6x³+(2-√5)/3x²+ (-3+√5)/6x+(1-√5)/6)=0 5(3-√5)/2 -3√f(√5-2)=0,91125<1 x=2/9+20¹/³ (41-9√21)¹/³/18+20¹/³(41+9√21)¹/³/18;-√5/2+1/2✓{(√5+1)/2;2/9+20 ¹/³ (41-9√21)¹/³/18+20¹/³(41+9√2 1)¹/³/18;-√5/2+1/2}
    1
  938. (3/2 -2/3|20) (0 1|24){Х=24,У=24.
    1
  939. -8+8√2 S1=-32+32√2-4π S=-128+128√2-16π(m²)
    1
  940. 360°-5o=140° o=44°
    1
  941. (7-i)/2-1/4*i=3,5-3/4i=2 i=2 C(7;2)*/,5²=21/4
    1
  942. y=±arccos(1/(1+x²)⁰,⁵)+2πn
    1
  943. (4(xy)¹⁰⁰-2)²+16x²⁰⁰+y²⁰⁰-3=0≥(4(xy)¹⁰⁰-1)² y=±1/2¹/⁵⁰/x
    1
  944. {[z=0,x=0; y=0,x=-1,x=2;[y=0,z=-1-x; [x=0,z=0, x=0,y=-(1+x)/9;{(0;0;z)(x;0;0)(2;-1/3;-3)}
    1
  945. Mare el Madonna, era el consante Sale el ciano, senpriano. Donna bele mare, Credere contare Dame in momento Kene qyache pyu. Uno, uno, un momento, Uno,uno,uno sentimento, Uno,uno,uno secremento.
    1
  946. 3^(x²+2x+3)log5(x²+2x+3)=3^(2|x-a|+2)log5(2|x-a|+2) 3^u(ulnu+log3 (e))/u*ln3/ln5=0+>u/> x²+2x+3=2|x-a|+2,[{a≤-0,5,x=±√(-1-2a);{a≥-1,5, x=-2±√(3+2a).
    1
  947. |(0;∞)2ln(a/b)x+En=1;∞(-1)^(n-1)/nx^(2n+1)/(2n+1)(1/a^2n-1/b^2n))= ∞,a>b;0,a=b;-∞,a<b
    1
  948. {y=2-+√(-4+√85),x=2±√(-4+√85).
    1
  949. 2е^√а*/е^√а=2,f(x)=0,5
    1
  950. a(n+1)=7n/(n+2(an=7n/(n+2)*7(n-1)/(n+1)...7/3a1=7^n*n!/(n+2)!*2*3,5=7^(n +1)n!/(n+2)! an=7^n/n/(n+1)
    1
  951. (1/44)²?>0
    1
  952. x^x¹⁶=2¹/² e^(x¹⁶lnx)(16lmx+1)x¹⁵=0 x=e-¹/¹⁶-*+>x min=e^(-1/16e-¹)<1 x=2^n n*2^16n=0,5/> n=0,125 (0,5= 0,5✓){2⁰,¹²⁵}
    1
  953. R°2/0,4=5 S=25π
    1
  954. X^k(1-x)^(k+1)/-(k+1)-kx^(k-1)(1-x)^ (k+2)/(k+1)/(k+2)-..-k!(1-x)^(2k+1) *k!/(2k+1)!(0;1/2)=(-1/k!/(k+1)!-1/(k- 1)!/(K+2)!-..-1/(2k+1)!+1)k!²/(2k+1)!
    1
  955. 525/16✓
    1
  956. A/2+70°+360°-a=360° 140°=a✓
    1
  957.  @РоманВоронец , решение уравнения в геометрии.
    1
  958. 3-2(cosx+cos²x)=3-2*1=1
    1
  959. 2⁶⁴=16¹⁶ a=16,b¹⁶=2^2⁷ b=±4
    1
  960. Fp=5e^-p/(p+2),ft=e^e^at $(0;∞)e^(e^at+(-p-a)t)*(e^at-p-a)adt=1/ae^(e^at+(-p-a)t)(0;∞)=∞-1/ae,a>0,=0-1/ae,a<0 ft=5e^(-2t *e^t)
    1
  961. 0=(8^x)³-8*8^x-32 x=1/3+log8((2+10√3/9)¹/³+(..-..)..)= 2/3 1,58+0,43=2,01 1/3, 10/9√3✓
    1
  962. S=0,5*4*8+0,5*4*2=20(cm²)
    1
  963. (√(x+2)-2√(x+1)+√x)/x-¹,⁵=(0,5(x+2) -⁰,⁵x²,⁵-x²,⁵(x+1)-⁰,⁵+0,5x²)/(-1,5)=(-1 -1/2-0,25)/3=-7/12
    1
  964. ((a+b)²/2)²+()b-a)/2)²=(a²+b²)/2=64 a²+b²=128
    1
  965. {ax²=lnx,2ax=1/x;{e^(1/2)=x,a=1/e/2.
    1
  966. (e^y+6x)dx+xe^ydy=0,e^y+6x+x(e^y)'=0,3x²+xe^y=c,y=ln(-3x+c/x)
    1
  967. X²+xy+y²=1,y=-x/2±√(1-3/4x²) 1+4x²-13x⁴+4x⁶+3x⁸±(-6x⁷+12x⁵+ 2x³-4x)√(1-3/4x²) 8x-52x³+24x⁵+24x⁷±(36x⁸-96x⁶+54x⁴+12x²-4)(1-3/4x²)-⁰,⁵=0 (2/3x-13/3x³+2x⁵+2x⁷)²(1-3/4x²)=(3x⁸-8x⁶+4,5x⁴+x²-1/3)²
    1
  968. [{a[58 2/13;72),x=-9/5+a/15;{a(-24;108/13],-a/17+27/17=x;{a[-27/8;10,8],x=27/7+a/7; {a[-21,6;-27/8],x=-1/9a+3;{a[10,8;18],x=9-a/3;{a[-24;-21,6],x=27+a;aU[27/13;3,375)U{5,4}
    1
  969. 3/4=3/4AP/(8-AP) AP=4 S∆=0,5*3*4=6(cm²)
    1
  970. √(1-x)=x+1,{1-x=(x+1)²,x+1≥0;{-x²-3x=0,x≥ -1;{[x=0,x=-3;x≥-1;{0}
    1
  971. y=(x-8)^-1,x=(y-8)^-1 y=1/x+8 D(y)=R\{0} Ey=R{8}
    1
  972. log²2|2x|-5log2|2x|+2|x|log2|2x|-4|x|+6≥0,{|2x|>0,x≠0.(log2|2x|-2,5+|x|)²-(|x|-0,5)²≤0,(log2|2x|-2)(log2|2x|-3+2|x|)≤0,+*-2-*-1+ *1 -2*+>x log2|2x|-3+2|x|=0,-∞/> 1-3+2=0,log2(-2x) -3-2x=0,\>1-3+2=0,хє[-2;-1]U[1;2],x≠0,хє[-2;-1]U[1;2]
    1
  973. e^(-π/2-2πn)(π/2+2πm)=o
    1
  974. $(1/3;3)arctgx/(x²-x+1)dx=$(1/3;3)(π/2-arctgx)/(1-x+x²)dx=$(1/3;3)π/4/(x²-x+1)dx=π/2arctg((x-0,5)/√3* 2)/√3(1/3;3)=π/2/√3(π/3+arctg(√ 3/9))
    1
  975. 15/10=50/.. ..=100/3(cm)- высота между лампочкой и потолком
    1
  976. {(sinx-a)((sinx+a/2)²+3/4a²+1)=0, sinx+sin³x+a⁵-a=sin³y+sin⁵y,sinxsimysimz=a²;{sinx=a,a[-1;1],siny=a,sinz=1; (arcsina (-1)^n+πn;arcsina(-1)^n+πm;π/2+2πk)
    1
  977. 1112²-4*1112+4=1110² 1110✓
    1
  978. {c=±√(ab+22),b²+103=±a√(ab+22),a²-bc=?;0=(a+22/3/b)³-(a+22/3/b) *484/3/b²+2*22³/27/b³-b³-206b- 10609/b a=-22/3/b+(-22³/b³+27b³/2+2781b-27*10609/2/b+√(-2*22³/b³(27b³/2+2781b-27*10609/2/b)+ (27/2b³+2781b-27*10609/2/b)²))¹/³/3+(..-..).. (-22/3/b+(-22³/b³+27b³/2+2781b-27*10609/2/b+√(-2*22³/b³(27b³/2+2781b-27*10609/2/b)+ (27/2b³+2781b-27*10609/2/b)²))¹/³/3+(..-..)..)²-+b√((-22³+27b⁶/2+ 2781b⁴-27*10609/2b²+√(-2*22³b³(27b⁶/2+2781b⁴-27*10609/2b²)+ (27/2b⁶+2781b⁴-27*10609/2b²)²))¹/³/3+(..-..)..)
    1
  979. х¹/³=1;-3/2 х=1;-27/8
    1
  980. |8-|х-2||=7,8-|х-2|=±7,{|х-2|=1,|х-2|=15;{х-2=±1,х-2=±15;[х=3,х=1,х=17,х=-13
    1
  981. (X²-a+4x)³=0,x=-2±√(4+a),a≥-4,x(-2-√2;0],[√(4+a)≤2,√(4+a)<√2;[a[-4;0],a[-4;-2);a[-4;0)
    1
  982. y=(x-4)²-2,y(-5)=79
    1
  983. 2sin15°, 2sin²15°,sin30° tgx=2sin²15°/(1-0,5)=(1-cos30°)/0,5=2-√3 x=15°
    1
  984. z'(x)=1/(1+(xy²)²)y²=1/5 z'(y)=1/(1+(xy²)²)*2xy=4/5 gradz(A)=1/5i+4/5j (1/(1+(xy²)²)y²dx+1/(1+(xy²)²)*2xydy)/d(3i+ 4j)=1/√17+4/√17=5/√17
    1
  985. {x-y=5,x²+xy+y²=24;{5}
    1
  986. {x=y+5,3y²+15y+1=0;y=(-15±√213)/6 x=(15±√213)/6
    1
  987. 2√3 S=6*2√3=12√3
    1
  988. $arccosxdx=xarccosx&(1-x²)⁰,⁵+c
    1
  989. (14/9√15+6)¹/³+(-14/9√15+6)¹/³=2 2+4 1/36/12-0,3~2 5/3,14/9√14✓ 2⁸/8+8/2⁸=32 1/32
    1
  990. R²-9+1=64-R² R=6
    1
  991. ​ @yuriyapch-he  (2sin²x+√3cosx-2) log2(-cosx)=0,
    1
  992. f(x)²+f(x)f(1)-1=0 f(x)=(-f(1)±√(f(1)²+4))/2=±√2/2
    1
  993. {x=-+3/5,y=±8/5;{(-3/5;8/5)(3/5;-8/5)}
    1
  994. Нет то ли 5, то ли 14, то ли 23, то ли 29.89 84/3=28=23+5× 25=12+13,50=5+6+12+23+29✓ 66/3=22×,20×
    1
  995. x(-5;-√20]U{0}U[√20;5)
    1
  996. рН,нн|ррн,ррр Меняем 1 батарейку в фотоаппарате на 1 из оставшихся. рр×2✓рн;нр×2 нн|нр ×3 Если у нас не заработало,то вставляем 2 новые батарейки. В 4 раз к непоменяной батрейке вставляем оставшуюся батарейку, если 3 раза не загорелось.
    1
  997. 6*16*0,5=48✓
    1
  998. [x=-1,1=0×;{-1}
    1
  999. (3x+1)²y²+(-9x²-18x-5)y+2x²+7x+6=0 x=-1/3× y=(3x+5±(x+1))/2/(3x+1) (-18±12)/18=-1/3;-5/3 [y=(2x+3)/(3x+1),y =(x+2)/(3x+1); y=2/3+7/9/(x+1/3)\> (0;3)(2;1) y=1/3+5/9/(x+1/3)\>(0;2)(-2;0)
    1
  1000. x²=-0,5-(7(z-3)²-31)/2/(1+y²)≥0 7(z-3)²+y²≤30 z[1;5] z=1,y[-1;1],z=2,y[-4;4] z=3,y[-5;5],z=4,y[-4;4],z=5,y[-1;1] x=±1/2;±1 (±1;0;1)(±1;0;5) x=±√11,5(y=±0)× x=±√(-0,5+31/2)×
    1
  1001. 14x⁴+x²(-3y²-125)-5y⁴+82y²+51=0 x²=(3y²+125±17√((y²-6 137/289)²+2 (143 *289-137²)/289²))/28 (17n-289y²+1867)(17n+289y²-1867)=195380:4✓×
    1
  1002. X^(1+1/r)e^(ln(1+1/x)/(1-1/(1+1/x) ^(r+1)))=xe^(ln(1+1/x)(1+x)) e✓
    1
  1003. √5/2,√2/2 l=1/2+1=1,5 1+h, 2-h (2-h)/(1+ h)=1/2,-1,5h=-1,5,h=1 l1=√2,l2=1,5√2 S= 1/4+1²/2+1,5²/2+(1,5+1)/2*0,5=2,5
    1
  1004. Tgx/(3-4/(1+tg²x))/2=-5/18
    1
  1005. √((x-1)/(2-x))=y,x=2-1/(y²+1) dx=(y²+1)-²*2ydy $(y²+1)-2*2y²dy=arctgy-y/(y²+1)(1;√3)=π/12-√3/4+1/2
    1
  1006. S1=9sin30°+π•3/4=4,5+3/4π S2=9√3/4 +π3/2 2,25√3+0,75π~6,28>4,5
    1
  1007. X=3±√(-a²+4a-3) ∆x=2√(-(a-2)²+1)≤2,a=2
    1
  1008. 3*2¹/²✓
    1
  1009. ✓ √π*0,25^(n+1/2)/(n+1/2)! √πe⁰,²⁵(~✓)
    1
  1010. Я думал, что Ксения настоящая!
    1
  1011. LP=√(576-KP²) PN=(576-KP²)/KP KN=576/KP OP=√(64-KP²)/8=64/(576/KP) 72/√145=KP MO=√((576/KP)²-65²)-8=√5055-8
    1
  1012. √(R²-a²)/2 R=4/5a±√(a²+80)/5 1,5R-2,5a,2,5√(R²-a²)/2 +✓,-× a=3/2√2 R=2,5√2 S=6,25π
    1
  1013. (X+5/6)²=1/72±41/72=21/36;-20/36≥0 x=-5/6±√21/6
    1
  1014. arcsin(-xcos²u(x))=u(2x)?
    1
  1015. 3(b+c)(a+c)(a+b)
    1
  1016. (x+22,5)⁴+9*2018,5(x+22,5)²-45*123²(x+22,5)-18225*18'147/16=0 х=-42,24;29,30
    1
  1017. (x-3)(log(6)(x²+3x-4)+log0,2(20-5x)+1/log(4-x)5+x+1)≥x²-x-6,{x²+3x-4>0,20-5x>0, 4-x>0,4-x≠1;{(x+4)(x-1)>0-4+°-°+1>x,x<4, x≠3;{хє(-∞;-4)U(1;+∞),хє(-∞;3)U(3;4);хє (-∞;-4)U(1;3)U(3;4).(x-3)(log(6)(x²+3x-4) +x)-(x-3)(x+2)≥0,(x-3)(log(6)(x²+3x-4)+x- x-2)≥0,(x-3)(log(6)(x²+3x-4)-2)≥0,log(6)(x²+3x-4)-2=0,x²+3x+4=36,x²+3x-32=0,x=(-3±√(9-4*32))/2[x=-1,5+√137/2,x=-1,5 √137/2;--1,5-√137/2+*3--1,5+√137/2+>x хє[-1,5-√137/2;3]U[-1,5+√137/2;+∞) хє[-1,5-√137/2;-4)U(1;3).
    1
  1018. [x=-1,x=0,0=1+x²+x⁴;{-1;0}
    1
  1019. x²=(-3m±√(8m²+31m+5))/(2m+5) {(-3m±√(8m²+31m+5))/(2m+5)=0,(-3m-+√(8m²+31m+5))/(2m+5)>0; m²-31m-5=0 m=(31+3√109)/2 -(93+9√19)/2±√(418,5√109+4269, 5)±=>>0;-(93-9√19)/2±√(-418,5√10 9+4269,5)× m(-≠;-2,5)
    1
  1020. {(0;0;0)(3;3;3)}{z=(x²+y2)/6,×,y=-x-6.
    1
  1021. m(C6H12O11)=m(H2O)p/(100-p)
    1
  1022. 2а+2b,3b a=0,5b
    1
  1023. (x-4x-¹+2)(x-4x-¹)=0[x=±2, x²+2x-4=0;x=-1±√5{±2;-1±√5}
    1
  1024. $(1;3)dr$(0;π/2)sinr²*rdf=π(-cos9+ cos1)
    1
  1025. (3a+4;a-2) R=1,(4a+3;-3) R1=3 √(2a²+2)[2;5] a[-√11,5;-1]U[1;√11,5] {y=a-2±√(1-(x-3a-4)²),(a-1)x-4a²-a+7 =±(a+1)√(1-(x-3a-4)²); 2(a²+1)x²+(-14a³-14a²-6a-22)x+25a⁴+50a³+17a²+40a+64=0 x=(7a³+7a²+3a+11±√(-a⁶-2a⁵+7a⁴+16a³+a²-14a-7))/2/(a²+1), y=a-2+√(1-((a³-a²-3a+3±√(-a⁶-2a⁵+7a⁴+16a³+a²-14a-7))/2/(a²+1))²)
    1
  1026. 2$(0;π/2)√(1-x²)dx+2$(π;3π/2)(π- √(1-(x-π)²))dx=π/2√(1-π²/4)+1+π²- (π/2+π/2√(1-π²/4))=1-π/2+π²
    1
  1027. an=(n+1)*2^(n-2)≥2024 n≥10(11*2⁸≥2024)
    1
  1028. [x=2πn,y=2πm,y=-x+2πk.✓
    1
  1029. x=(4±√22)/3 382±82√22
    1
  1030. Sk=10,5π+4,5,Sж=7,5π-4,5
    1
  1031. 16=a²+(a+√2)² 2a²+2√2a-14=0 a=(-√2+√30)/2 S∆=0,5*2*4sin(45°-arcsin((-√2+√30)/8))=1
    1
  1032. 180-x+105+90-x/2=180°,x=130°
    1
  1033. 2^(х+3)*4^(х+2у)/8^(х+2)/16^(у-2)=2^ (х+3+2х+4у-3х-6-4у+8)=2^(5)=32
    1
  1034. (√2+1)³+(√2-1)³=10√2
    1
  1035. (18x+12y)/(x+y)=16,x=2y{1 18-каратного и 2 12-каратного золота}
    1
  1036. x=56
    1
  1037. 6+ln2/ln0,25=х{5,5}
    1
  1038. S1=10/3 BE/BA=S0/(S0+7 1/3) BD/BC=S0/(S0+8 1/3) S0/(S0+18 1/3)=S0²/(S0+7 1/3)/(S0+8 1/3) S0=275/12
    1
  1039. 5^x=3^xlog(3)5,(5/3)^x=log(3)5,x=log (5/3)log3(5)
    1
  1040. S=0,5(5/√3)²*√3/2+0,5(5/√3)²*π/3= 25/12*√3+25/18*π
    1
  1041. a[0;128²+1/2-√(1/4+128²)],0=(a-128²-1/2)⁴+(-2*128²-1/2)(a-128²-1/2)²-(a- 128²-1/2)+128⁴-1/2*128²-7/16;(z-128²/3-1/12)³+(64²+1/8-4(64²+1/ 8)²/3)(z-128²/3-1/12)+4/3(64²+1/8) ²(1-10/9(64²+1/8))-1/64=0 z=128²/3 +1/12+(-2(64²+1/8)(9-10(64²+1/8))+9/8+√((-2(64²+1/8)(9-10(64²+1/ 8))+9/8)²+(64²+1/8)³(3-4(64²+1/8)) ³))¹/³/3+(..-..)..;128²/3+1/12-(-2(64²+1/8)(9-10(64²+1/8))+9/8+√((-2(64²+1/8)(9-10(64²+1/8))+9/8)²+(64²+1/8)³(3-4(64²+1/8)) ³))¹/³/6-(..-..)..±√(3/4((-2(64²+1/8)(9-10(64²+1/8))+9/8+√((-2(64²+1/8)(9-10(64²+1/8))+9/8)²+(64²+1/8)³(3-4(64²+1/8)) ³))¹/³/3+(..-..)..)²+64²+1/8-4(64²+ 1/8)²/3)i a=128²+1/2+√(128²/3+1/12 +(-2(64²+1/8)(9-10(64²+1/8))+9/8+ √((-2(64²+1/8)(9-10(64²+1/8))+9/8)² +(64²+1/8)³(3-4(64²+1/8))³))¹/³/3+(..-..)..)±2√(0,5√((128²/3+1/12)²-(128 ²/3+1/12)(-2(64²+1/8)(9-10(64²+1/8))+9/8+√((-2(64²+1/8)(9-10(64²+1/ 8))+9/8)²+(64²+1/8)³(3-4(64²+1/8)) ³))¹/³/3+(..-..)..)+((-2(64²+1/8)(9-10(64²+1/8))+9/8+√((-2(64²+1/8)(9-10(64²+1/ 8))+9/8)²+(64²+1/8)³(3-4(64²+1/8)) ³))¹/³/3+(..-..)..)²+64²+1/8-4(64²+1/8)²/3)+2/3*64²+1/24-(-2(64²+1/8)(9-10(64²+1/8))+9/8+√((-2(64²+1/8)(9-10(64²+1/ 8))+9/8)²+(64²+1/8)³(3-4(64²+1/8)) ³))¹/³/12-(..-..)..) {[128²+1/2+√(128²/3+1/12 +(-2(64²+1/8)(9-10(64²+1/8))+9/8+ √((-2(64²+1/8)(9-10(64²+1/8))+9/8)² +(64²+1/8)³(3-4(64²+1/8))³))¹/³/3+(..-..)..)-2√(0,5√((128²/3+1/12)²-(128²/3+1/12)(-2(64²+1/8)(9-10(64²+1/8))+9/8+√((-2(64²+1/8)(9-10(64²+1/ 8))+9/8)²+(64²+1/8)³(3-4(64²+1/8)) ³))¹/³/3+(..-..)..)+((-2(64²+1/8)(9-10(64²+1/8))+9/8+√((-2(64²+1/8)(9-10(64²+1/ 8))+9/8)²+(64²+1/8)³(3-4(64²+1/8)) ³))¹/³/3+(..-..)..)²+64²+1/8-4(64²+1/8)²/3)+2/3*64²+1/24-(-2(64²+1/8)(9-10(64²+1/8))+9/8+√((-2(64²+1/8)(9-10(64²+1/ 8))+9/8)²+(64²+1/8)³(3-4(64²+1/8)) ³))¹/³/12-(..-..)..)]}
    1
  1042. {x=0,09,y=0,44;16x+10y=5,84$
    1
  1043. a=14sin20° b=7 h=(7-14sin20°) sin70° Str.=(a+b)/2*h=49/4 S1=49/12•π-49/4 S=Str.+S1=49/4+ 49/12π-49/4=49/12π
    1
  1044. a,b,45-a-b c,d,c+d-6 21-a-c,b+d-27,9-a-b+c+d a=19,5 19,5;b;25,5-b c;d;c+d-6 1,5-c;b+d-27;-10,5-b+c+d
    1
  1045. e*0,5√π✓
    1
  1046. $(2;4)dy*π(2y-4)=π(y²-4y)(2;4)=4π
    1
  1047. 16-а,а,14-а 91/(16-а),65/(14-а) а=9 S=91/(16-9)*9=117
    1
  1048. 9/√9,75*√3/3=6/√13(см)
    1
  1049. -X⁶e^-x²/2-6x⁴e^-x²/2²-..-6!!e^-x²/2⁴ (0;=)=6!!/2⁴=3
    1
  1050. |a²-16|+a²=S (a²-16)/a/6=-(a²-16)/6/a a=4 S=16✓
    1
  1051. (x²-1)³(-X²-3)x=0 x=±1;0
    1
  1052. x≥0 0=x⁰,⁵{0}
    1
  1053. √((45+1)/2)-√((45-1)/2)=√23-√22
    1
  1054. x=(3z-4)(z-1)-¹ z=(x-4)/(x-3)
    1
  1055. h=9,81*20²/2=1962 м
    1
  1056. {a²+16-b²-2a√(16-b²)cos(arccos(a/4)-arcsin(b/4))=4, b²+16-a²-2b√(16-a²)cos(arccos(b/4)-arcsin(a/4))=4; {b=√((-a²+24±a√(-3a²+48))/2), b[0;4]a[2;4],a[0;√12];a=√12;2 arcsin(b/4)+arcsin(a/4)=arcsin(((-a² -a+24)√(16-a²)+(16a+a²-a³)√3)/32)= 45°(?✓)
    1
  1057. √(2x²-15x+1998)=y y²-y-1980=0 y=(1±79)/2=40;-39[√(2x²-15x+1998)=40,√(2x²-15x+1998)=-39;[2x²-15x+398=0,0/;x=(15±√-296 9)/4
    1
  1058. x=(k²±(k²-4))/2[x=k²-2,x=2.
    1
  1059. 6(а+2b-2c)+c,1,a+2b-2c=14(mod17),a+2 b-c=15(mod17),(a+2b-c):17
    1
  1060. {y+4z=-5,x+3y+5z=-2,0=1;×
    1
  1061. 12/a,10-a-R R/(10-a-R) 2R/(10-a-R)/(1-R²/(10-a-R)²)=-12/a 6/a(a-10)²+R(120/a-22+a)+R²=0 R=(-120+22a-a²+√((a²-10a+72)² 1440a+9216))/2/a a=5 R=(-35+65)/10=3
    1
  1062. S=1/4*π•4²-0,5*2*4=4π-4 A)
    1
  1063. limn->∞(ln√2/n+ln(4/e))=ln(4/e)
    1
  1064. (1/√2-1/√3)(1/√6+1/3)=1/2/√3+1/3/√2-1/3/√2-1/3/√3=1/6/√3
    1
  1065. [х=-1,х=2.
    1
  1066. x[-3;3],{-16≤x²,±2,4=x;{±2,4}
    1
  1067. 5^x=5³(63±62)=5⁶;5³ x=6;3{(6;3)(3;6)}
    1
  1068. √(a²-b²)/a=8/(2b)=b/5 b=20⁰,⁵ 10=a S∆=√20*√80=40
    1
  1069. y"'-2y"-5y'+6y=0 y=e^(ax) a³-2a²-5a+6=0 (a-1)(a²-a+6)=0 a=1, a=(1±√(1-4*6))/2 =0,5±√-23/2 y=c1e^x+c2e^(0,5x)(cos√23/2x+c3sin√23/2x)
    1
  1070. Xy+16/(xy)+10≥2*4+10=18,xy=4
    1
  1071. 3/x=cos(2a),5/√(x²-9)=tga cos(2a)=(1-tg²a)/(1+tg²a) 3/x=(x² -14)/(x²-4) 0=(x-1)³-17(x-1)-4 x-1=(2+√(4-17³/27))¹/³+(..-..)..=2 (17/3)¹/²cos(1/3arccos(6/17√(3/ 17))+2/3πn) x=1+2(17/3)¹/²cos(1/ 3arccos(6/17√(3/17))+2/3πn)≥3 n=0 x=1+2(17/3)¹/²cos(1/3arccos (6/17√(3/17)))✓
    1
  1072. $(0,625/(0,625-0,5sin2x-0,125cos4x)- 0,5(-cos2x-0,25cos4x)/(0,625-0,5sin2x-0,125cos4x))dx
    1
  1073. S∆APC=(x+2) S∆ABP=12+3xP-1,5xP² xP+2=12+3xP-1,5xP²,1,5xP²-2xP-10=0 xP=(2±√(2²-4*1,5*-10))/3=2/3±8/3[xP= 10/3,xP=-2;xP>-2 xP=3 1/3
    1
  1074. z=0;cos(πn/5)+isin(πn/5),n=0;..;9
    1
  1075. F(p)=2/p³+1/p²-1/p✓
    1
  1076. 2^(2n-5)*e^(Ei=1;=(-1)^in/πsin(π/n)/i3^i((cos(π/n))^(2i-1)*2^(2i-2)(i-1)!²/(2i-1)!+2^(2i-4)(i-2)!²/(2i-3)!cos(π/n)^ (2i-3)+..+1/2^i/i!cos(π/n)-(N-1)π/n/2/sin(π/n))(2i-1)!!/(2i)!!+0,5ln(3cos² (π/n)+1)) n✓
    1
  1077. {z=5-x-y,(x-5)²+(y-5)²=0;{5;5;-5}
    1
  1078. π/2-arctg(2tg20°/(tg²20°+1))
    1
  1079. 2*36²/√(36²+a²)/√(12²+a²)=(432+ a²)/√(36²+a²)/√(12²+a²),12√15=a EC=36²/√(36²+12²*15)=9√6,D)
    1
  1080. X=5^(x-3),1-5^(x-3)ln5=0 x=log5(1/ln5)+3+*->x log5(1/ln5/e)+3>0 x=3,83;0✓
    1
  1081. arccosx=u x=cosu dx=-sinudu $e^u*sinu du=e^ucosu-e^usinu+$e^usinudu $e^u* sinudu=0,5e^ucosu-0,5e^usinu+c=0,5e^arccosx*x-0,5e^arccosx*√(1-x²)+c
    1
  1082. f(x²)=f(1)-2f(1/x)=-2f(x-¹) ax^3n=-2a,[a=0,x ^3n=-2;f(x)=0
    1
  1083. Pз=13066,7(Вт),Рп=3920(Вт)
    1
  1084. °-6-°-5+*3-3,5°°5-*5,5+>x x(-6;-5)U[3;3,5)U(5;5,5]
    1
  1085. (a+b)x²-2ax+a-b=(a+b)(x-1)(x-(a-b)/(a+b))
    1
  1086. 2^(x^6)+2^(x^2)=2^(x^4+1), при х≥0 обе части растут, 1+1=2- верно, при х≤0 - падают.x=±1, 2^(х^6)ln2*6x^5+2^(x^2)*ln2*2x-2^(x^4+1)*ln2*4x^3=2^(x^2)•ln2*2x(2^(x^6-x^2)3x^4+1-2^(x^4-x^2+1)*2x^2)=0, x=0; -0+
    1
  1087. a=7,5√2,B=6√5,√(a²+b²)/a=√(5/2) b=7,5√3 bA=100√10 A=40/3√(10/3) 25c²=26'075/243
    1
  1088. (log7(x+4)+1)(log7(x+4)+1/2)/log7(x+4)≤0°-4--3 6/7+-4+7-⁰,⁵-° -3+>x x(-4;-3 6/7)U[-4+7-⁰,⁵;-3)
    1
  1089. х>11/3,(2х-1)(3х-11)=(х+1)² 5х²-27х+10=0 х=(27±23)/10=5;0,4=>5 {5}
    1
  1090. $(0;1)(x²-1)/2arctgxln(-1+2/(1+x))*2/(x²-1) dx=(x²-1)/2arctgxln²(-1+2/(x+1))/2-(x(x²- 1)/2arctgx+(x²-1)/4-(x²-1)/2/(x²+1))ln²(-1 +2/(x+1))/2+..(0;1)=∞-0*∞+..-0+0+..=∞- 0-..=∞ 2/(x-1)/(x+1)
    1
  1091. (x+2)/(x-2)=y x=(2y+2)/(y-1) f(y)=y²/(y-1)/(y+1) f(x)=x²/(x-1)/(x+1)
    1
  1092. 1:59 что за хозяйство? Огород?
    1
  1093. (5A+1)(5b+3)=78{(0;15)(1;2)(5;0)(-8;-1)}
    1
  1094. [x²-4x=0,x²+4x+2=0;[x=0,x=4,x=2±√2.
    1
  1095. (15x³-34x²+9x+12)/(3x-5)=5x²-3x-2+2/(3x-5)
    1
  1096. 992=2⁵*31=2¹⁰-2⁵(10;5)
    1
  1097. Arccos(2/√5),arccos(8/√65) arccos(17/5/√13) BF=65√5/17 S∆=33 1/126(cm²)
    1
  1098. 2/a=(a²+15)/a/16 √17=a x=√(16+17-2*4√17*-2/√17)=7
    1
  1099. b/(√(a²+b²)+a)√(a²+b²)=.. S=√(a²+b²)b-ab/2=a²√3/2 b/(√(a²+b²)+a)=a/b b=√3a✓
    1
  1100. (√5-√1+√13-√5+..+√841-√761)/4=7
    1
  1101. {[{a=45,b=28;{a=28,b=45;c=53;{45;28;53}
    1
  1102. f(x)=$(0;x)arctg(1/√(t²+1))/arctg(√(t²+1)/t)*dt=-$(0;x)a/arctg(cosa/√cos2a)/√cos2a*cosa*2sin²ada=-ln|(cosa/√cos2a)|2sin²aa+$(π/4;arctg(1/√(x²+1))ln|arctg(cosa/√cos2a)|(2sinacosaa+2sin²a)da=-ln|arctg(√(x²+1)/x)|2/(x²+2)*arctg(1/√(x²+1)-ln(π/2)*π/4+(-cos2arctg(1/√(x²+1))/2*arctg(1/√(x²+1))-0,5sin2arctg(1/√(x²+1))/2+arctg(1/√(x²+1))-sin2arctg(1/√(x²+1))/2)ln|arctg(cosarctg(1/√(x²+1)/√cos2arctg(1/√(x²+1))|-(-0,25+π/4-1/2)ln|π/2|-$(π/4;arctg(1/√(x²+1))(-cos2a/2*a-0,75sin2a+a)/arctg(√(a²+1)/a)/(2a²+1)/√(a²+1)da ,tga=1/√(t²+1),t=±√(ctg²a-1),dt=±(ctg²a-1)^(-0,5)*2ctga*(-1)/sin²ada,arctg(√(t²+1)/t)=arctg(√(ctg²a-1+1)/±√(ctg²a-1))=arctg(±cosa/√cos2a)
    1
  1103. (x+2)³-64(x+2)+128=0 x+2=4(-1+√(1-64/27))¹/³+4(..-..)..= 16/3¹/²cos(1/3arccos(-3√3/8)+2/3 πn) x=-2+16/3¹/²cos(1/3arccos(-3 √3/8)+2/3πn) (-2+16/3¹/²cos(1/3 arccos(-3√3/8)))¹/³+(-2+16/3¹/²co s(1/3arccos(-3√3/8)+2/3π))¹/³+(-2 +16/3¹/²cos(1/3arccos(-3√3/8)+ 4/3π))¹/³
    1
  1104. [x=0,log(2,6)2=x.
    1
  1105. a/(a+b)=b/(2a+b) √2a=b o=a/(a +√2a)=√2-1 C)
    1
  1106. 7l/(ab)=7 l=ab a²b²+8abcos/_a=20 arcsin(b/√(1+b²+2bcos/_a)sin/_a) (a-1)/2/cos/_a=b cos/_a=±a(a-1)/√(6-a)/4. arcsin(8(6-a)/√(-3a²-a+33) *√(96-16a-a²(a-1)²)) угол ∆ справа.arcsin(√(96-16a-a²(a-1)²)/12) √(-3a²-a+33)*8(6-a)*√(96-16a -a²(a-1)²)√(48+16a+a²(a-1)²)+√(-3a ²-a+33-64(6-a)²*(96-16a-a²(a-1)²)) •√(96-16a-a²(a-1)²))=112(6-a)√(96-16a-a²(a-1)²) a=-23/9/(197/27+4√3 54/9)¹/³+5/3+(197/27+4√354/9)¹/³ l=2√(13/3+23/9/(197/27+4√354/9) ¹/³-(197/27+4√354/9)¹/³)(cm) ?=7/3-(197/27+4√354/9)¹/³+23/9/(197/27+4√354/9)¹/³(cm)
    1
  1107. log2(x²-9)(-∞;4]U[5;∞) x(-∞;-√41]U[-5;-3)U(3;5]U[√41;∞)
    1
  1108. 7√3/2*1/2=7√3/4 S=147/32π
    1
  1109. L-¹{1/(s²+2)²}=√2/2xsin√2x
    1
  1110. 12/11<y/x<11/10 x=21:22 10/11;23,1 y=23
    1
  1111. -x³/3+x|(-1;1)+x³/3-x|(1;2)(-2;-1)=-1³/3+1 -(-1/3-1)+2³/3-2-(1/3-1)-1/3+1-(-8/3+2)= 4 2/3
    1
  1112. (2xlnx-x+1/x)/ln²x=∞ 1,099~✓
    1
  1113. 5х²-30х+25=0 х=(30±√(30²-4*5*25))/10 [х=5,х=1;
    1
  1114. 3(a-2/3b)/a=3-2b/a✓ (22-√7)/9(?!)
    1
  1115. e^(-ar)*I*4πr²=P✓ убывание мощности волны с расстоянием
    1
  1116. АД'ЗІН*4=ЧАТ'ЫРЫ 9 цифр A[2;9] Н≠0 Ы:2 Н=1,Ы=4 3¹Д²'621*4=Ч¹3Т'484 0;5;7;9× 9³7²'621*4=390'484✓ 6²7¹'3²51*4=269'404✓ 6²Д¹'371*4=26Т'484× 6²Д³'8²51*4=26Т'404× 9³7³'3,8²51*4=39Т'404× 6²5³'8²71*4=263'484✓ 9³Д³'8²71*4=39Т'484×
    1
  1117. Rо=U²/P=220²/100=484Ом=√(R²+ (314L)²),I=U/R=220/R=2 R=110Ом L=1,49Гн
    1
  1118. {a=1,5,b=-1/4;a+b=1,25
    1
  1119. (2n)!/4^n/n!²=∞/∞ (2(n+1))!/4^(n+1)/(n+1)!²/((2n)!/4^n/n!²)=2n!(2n+1)(2n+2)/(n+1)²/(2n)!/4=(2n+1)(2n+2)/(n+1)²/4=(1+0,5/n)(1+1/n)/(1+1/n)²=1 может расходится √(2π•2n)(2n/e)^(2n)/4^n/(√(2πn)(n/e)^n)²=2√(πn)(4n²/e²/4/n²*e²) ^n/2/(πn)=0*1=0 $(0;∞)dx/(1+x^ф)^ф=$(0;∞)dx/(1+x)^ф (x^(ф-1)-...+1)^ф=$(0;∞)dx(A1/(1+x)+... Aф/(1+х)^ф+А(ф+1)/(х-1)...+А(2ф+1)/(х-1)^ф+А(2ф+2)/(х²+1)+..) 1=А1(1+х)^(ф-1)(х^(ф-1)-..+1)^ф+.. Аф(х^(ф-1)-..+1)^ф+А(ф+1)(1+х)^ф(х- 1)^(ф-1)(х^(ф-2)+..+1)^ф+...+А(2ф+2)(х+1)^ф(х-1)^ф(х²+1)^(ф-1)(х^(ф-3)+..+1)^ф+.. А1+..+Аф+..А(2ф+2)...=0,... А1+..+Аф+А(ф+1)+..+А(2ф+2)(-1)^ф+...=1,
    1
  1120. {х²+Ху+у²=529,х²+√3xz+z²=441,x²+y²=144;{х=-0,5y±√(-0,75у²+529), (-0,5y±√(-0,75 y²+529))²+√3(-0,5y±√(-0,75y²+529))z+z²=441, y⁴+144y²-385²=0;y=±(√(457/2)±√(3 13/2)){x=-+(0,5√228,5±0,5√156,5)±√(-+ 0,75√(457*313)+240,25),z=-0,5√3(-+(0,5 √228,5±0,5√156,5)±√(-+ 0,75√(457*313 )+240,25))±√(356,875±0,125√(457*313) +(0,25√228,5±0,25√156,5)√(-+0,75√(457*313)))
    1
  1121. x=lg80
    1
  1122. 1/e-1/4✓ $(-1;2)|x²-1/4|dx=$(-1;-1/2)(x²-1/4) dx+$(-1/2;1/2)(-x²+1/4)dx$(1/2;2)(x²-1/4)dx=1/3+1/4+9/4=2 5/6
    1
  1123. |3 10 -5| |-2 -2 -3|=-18&60+40-20-(-60)-(-36)= |2 4 3| =38≠0
    1
  1124. Tg(x/2)=t,x=arctgt*2,dx=2/(1+t²)dt $(0;∞)πdt/(1+t+t²)/2=πarctg((t+1/2)*2/√3)/√3(0;=)=π/√3*π/3
    1
  1125. log2(x)=6 x=64
    1
  1126. Нет.
    1
  1127. a,b,c,dєZ≥0 1/a+1/(a+b)+1/(a+b+c)+1/(a+b+c+d)=1≥4/(a+b+c+d),≤4/a,a+b+c +d≥4,a≤4,a≠0,a=1,1/1+1/(1+b)+1/(1+b+c)+1/(1+b+c+d)=1,1/(1+b)+1/(1+b+c)+1/(1+b+c+d)=0,0/,a=2,1/(2+b)+1/(2+b+c)+1/(2+b+c+d)=1/2,d=1/(0,5-1/(2+b)-1/(2+b+c))-2-b-c=(4+2b+2c+2b+b²+bc)/(2+b+c+0,5b²+0,5bc-2-b-c-2-b)-2-b-c=(4+4b+2c+b²+bc)/(0,5b²+0,5bc-2-b)-2-b-c,b≠ 0,c≠0,d≠0,(8+6b)/(0,5b²+0,5bc-2-b)-b-c, b=1,14/(0,5+0,5c-3)-1-c=14/(-2,5+0,5c)-1- c=28/(c-5)-1-c≥0,\>(28-c+5-c²+5c)/(c-5) =(-c²+4c+33)/(c-5)≥0,(c-(-4+√(16-4*1*3 3))/-2)(c-(2+√(16+132)/2))/(c-5)≤02-√ 37+*5-*2+√37+>c,cє(-∞;2-√37]U(5;2+√3 7) c=5,d=(-6²+4*6+33)/1=(-36+24+33)=- 12+33=21,(2;1;5;21)c=7,d=(-7²+4*7+33)/2=(-49-28 +33)/2=(-77+33)/2=-44/2=-22,c=8,d=(-8² +4*8+33)/(8-5)=(-64+32+33)/3=1/3,b=2,(8+6*2)/(0,5*2²+0,5*2c-2-2)-2-c=20/(c-2)-2-c\> (20-2c+4-c²+2c)/(c-2)≥0,(-c²+24)/(c-2)≥0,(c-√24)(c+√24)/(c-2)≤0--√24+*2-√24+ >c cє(-∞;-√24]U(2;√24] c=3,d=20/(3-2) 2-3=20-5=15,c=4,d=20/(4-2)-2-4=10-6=4 √24=4,.. (2;2;3;15)(2;2;4;4) b=3,(8+6*3)/(0,5*3²+0,5*3c-2-3)-3-c=26/(1,5c-0,5)-3-c ≥0,(26-4,5c+1,5-1,5c²+0,5c)/1,5/(c-1/3)=( 1,5c²-4c+27,5)/1,5/(c-1/3)≥0, (c-(4-√(16-4 *1,5*27,5))/-3)(c-(-4/3-√(16+6*27,5)/3)/(c-1/3)≤0,-5 64/78+*1/3-3 12/78+>c 4 38/78,cє(-∞;-5 32/39]U(1/3;3 6/39] c=1,d=26/1-3-1=22,(2;3;1;22) c=2,d=26/2, 5-3-2=52/5-5=5,4,c=3,d=26/(1,5*3-0,5)-3- 3=6,5-6є/Z b=4,(8+6*4)/(0,5*4²+0,5*4c-2- 4)-4-c=32/(2c+2)-4-c=(16-4c-4-c²-c)/(c+ 1)=(-c²-5c+12)/(c+1)≥0,(c-(5+√(25-41 12))/-2)(c-(-2,5+√(25+48)/2))/(c+1)≤0 +-2,5-√73/2+°-12,5+√73/2+>c,cє(-∞; -2,5-0,5√73]U(-1;-2,5+√73/2],cє[0;1],с=0, d=16/1-4-0=12,c=1,d=16/2-4-1=8-5=3,(2;4;0;12)(2;4;1;3) b=5,(8+6*5)/(0,5*5²+0,5*5c-2-5)-5-c=(38-12,5c-27,5-2,5c²-5,5c)/(2,5c+5,5)=(-2,5c²-18c+10,5)/2,5/(c+11/5)≥0 (c-(18+√(324-4-2,5*10, 5))/-5)(c-(-3,6+√(324+10*10,5)/5))/(c+2,2)≤0,+*-3,6-0,2√429+*-2,23,6+0,2√429+>C,cє(-∞;-3,6-0,2√429]U(-2,2;-3,6+0,2√429],cє{0},d=10,5/2,5/2,2=21/5/11*5э́/,а при b>5 решений уже нет Напоминаем, что а≤4.a=3,d=1/(2/3-1/(3+b)-1/(3+b+c))-3-b-c=(9+3b+3c+3b +b²+3c)/(2/3(3+b)(3+b+c)-3-b-c-3-b)-3 b-c=(9+6b+b²+3c)/(6+2b+2c+2b+2/3 b²+2/3bc-6-2b-c)-3-b-c=(9-1 2/3b²-5bc-2/ 3b³-2 2/3b²c-2/3bc²-c²)/(2/3b²+2/3b c+2b+c)≥0,b=0,d=(9-c²)/c≥0,(c-3)(c+3)/c≤0,--3+°0-3+>c cє(-∞;-3]U(0;3] c=1,d=8,(4;0;1;8)c=2,d=5/2є/Z,c=3,d=0,(4;0;3;0),b=1,(6 2/3-7 2/3c-1 2/3c²)/(2 2/3+1 2/3c)≥0,(c-(7 2/3+√((7 2/3)²-41 2/3*6 2/3))/2/-1 2/3)(c-(-23/10+√(529/9 +20*20/9)/2/5*3)/(c+2)≥0,-2,3-√929/ 10+-2-* 2,3+√929/10+>c cє(-∞;-2,3-√92 9/10]U(-2;-2,3+√929/10],cє[0] d=6 2/3/(2 2/3)=20/3/8*3=2,5 при b>1 промежуток для с уменьшается, а значит решений нет.a=4,d=1/(3/4-1/(4+b)-1/(4+b+c))-4-b -c=(16+4b+4c+4b+b²+4c)/(12+3b+3c+3 b+3/4b²+3/4bc-4-b-c-4-b)-4-b-c=(-18b²-8c-9bc-3/4b³-6/4b²c-4b²+4b-3/4bc²-2c²)/(3/4b²+3/4bc+4b+2c+4)≥0,b=0,(-8c-2c²)/(2c+4)=-2c(c+4)/2/(c+2)=-c(c+4)/(c+2)≥0+*-4*-2+*0->c,cє(-∞;-4]U(-2;0] c=0,d=0,(4;0;0;0) а больше решений нет.
    1
  1128. 1/5*4000*0,7=560(m)
    1
  1129. 3x²+2(a-2)x+a-2/3=0 x=(-a+2±√(a²-7a+6))/3 a(-=;1]U[6;=) +*-*+>x max=2/27((a²-7a+6)√(a²-7 a+6)+a³-10a²+23a+13)>0 a(-=;1]U[6;=) min=2/27(-(a²-7a+6)√(a²-7 a+6)+a³-10a²+23a+13)>0 a(-10/3+(-421/2+√58057/2)¹/³/3+(..-..)..;1]U [6;°) a=1;6 a(-∞;-10/3+(-421/2+√58057/2)¹/³/3+(..-..)..);a(-=;1]U[6;=);a=1;6
    1
  1130. f(x)=0,f(0)=1 f(x)²=f(2x)+x² f(2^n)=(..(f(1)²-...²-2^(2n-4))²-2^(2n-2) f(x)=(..(f(1)² -...²-x²/16)²-x²/4
    1
  1131. (7±5)/4=3;1/2 [sinx=4,sinx=√2/2; x=π/4(-1)^n+πn x=2,25π;2,75π
    1
  1132. рх-0,5х²-2х-6=-0,5(х-р+2)²+0,5р²-2р-4≤0,5р²-2р-4 мин(n)=En=1;n(0,5n²+7n+18,5)= n(1/6n²+3,75n+22 1/12)=159 (n+7,5)³-36,25(n+7,5)-1647 3/4=0 n=-7,5+(822 7/8+√(59170²-26866)/72)¹/³+(822 7/8-√(59170²-26'866)/72)¹/³~1,75
    1
  1133. y'=(3a(x²+y²)⁰,⁵x+y)/(x-3a(x²+y²)⁰,⁵y)
    1
  1134. x²-(4t-1)x+4t²-2t=0 x=(4t-1±1)/2[x=2t,x=2 t-1;
    1
  1135. y=2x0(x-x0)+x0² y=-0,5/x0(x-x0)+x0² k1k2=-1,-0,5x0-¹*-0,5x1-¹=0,25/x0/x1 =-1 x1=-0,25/x0
    1
  1136. l=(√(a²-1)ctg/_1-a²+1)/a 1+(a-l)²-2 (a-l)*1/a=((a²-1)ctg²/_1+(-2a²+3)√ (a²-1)ctg/_1+4a⁴-7a²+3)/a²=(a²-1)/sin²/_1/a² [ctg/_1=-4(a²-1)¹,⁵/(2a²-3),a=1; 3,5a⁴-7,25a²+3,5=0 a=√((29+√57)/28) x=√((-111+√57)/28)✓
    1
  1137. limx->1(1-x)/(π/2(1-x))=2/π
    1
  1138. MT²/R³=4π²/G G=4π²R³/M/T²
    1
  1139. 1,02*x=822'716,х=806'584руб. 5,5/32,5= 0,169 0,169*45'000*1251'000/1200'000= 507*150,6375=76'373,21руб.
    1
  1140. (2^sin²x-2)((2^sin²x-0,5)²-2,25)=0 [sin²x=1,sin²x=1;cos2x=-1 x=π/2+πn
    1
  1141. {x=-y/2±√(1-3/4y²),Y=±2√((5±2√3)/39),z=-y/2±√(4-3/4y²); -+(25√3±4)=14±3√3×,z≥0 x с -,±(√3*3±14)=14±3√3,z с +{(-√((5±2√3)/39)-√((8-+2√3)/39); -2√((5±2√3)/39);-√((5±2√3)/39)+√ ((47-+2√3)/13))} x+y+z=(-3√(5±2√3)+√(141-+6√3)-√(13+6√3±2))/√39 13+6√3±2,196±12√3-6√(669±232√3)×
    1
  1142. y''/y'=-y'/(y²-1) y'((y-1)/(y+1))⁰,⁵=c y=chu y'=shu*u' u'(chu-1)=c √(y²-1)-ln(y+√(y²-1))=cx+c1
    1
  1143. (1-x/2)log(13-3*2^x)4≤1,{13-3*2^x>0,1 3-3*2^x≠1;{2^x<13/3,2^x≠4;{x<log(2)(13/3),x≠2;хє(-∞;2)U(2;log(2)13/3) (-x/2+1-log(4)(13-3*2^x))/log(4)(13-3*2^x)≤0, 1/2-1/(13-3*2^x)*-3*2^x*ln2/ln4=0,-1/2 +3/(13-3*2^x)*2^x/2=0,-6,5+1,5*2^x+1,5* 2^x=0,2^x=6,5/3,x=log(2)(13/6) +*->x max=-log(2)(13/6)/2+1-log(2)(√13/√2)= log(2)(2√12/13)<0,log(4)(13-3*2^x)≥0,13 3*2^x≥1,2^x≤4,x≤2, xє(-∞;2).
    1
  1144. F(p)=(3p²+7p+10)/(p³+2p²+5o)=A/p+B *2/((p+1)²+4)+C(p+1)/((o+1)²+4) 3p²+7p +10=A((p+1)²+4)+2Bp+Cp(p+1)=Ap²+2Ap+5A+2Bp+Cp²+Cp{A+C=3,2A+2B+C=7,5A=10;{C=1,B=1, A=2;f(t)=2+e^-tsin2t+e^-tco s2t
    1
  1145. {cosx=±1,sinx=0;{x=πn,x=πn.
    1
  1146. (х-1)²/2(1;4)-(х-1)²/2(-3;1)=4,5+8= 12,5
    1
  1147. 2√2sin(x/2-π/4)(0;π/3)=-√3+3
    1
  1148. √(15*6*4*5)=30√2 R=abc/4/S=9* 10*11/4/(30√2)=33/8√2
    1
  1149. $dxsin2x/2=-cos(2x)/4+c
    1
  1150. в+2с=?, а+а+а+.в=26, в=с, а=0,4в в=26/2,2=11 9/11, в=11 9/11*3=35 5/11
    1
  1151. Пk=0;n(1+2^(-0,5*2^k)cos(45*2^k)+i2^(-2^(k-1))sin(45°*2^k))=(1+2^-0,5)(1+i1/2)3/4(1+2^(-2^(k-1))..,k≥3 2^k=4n,n=2^(k-2) 1+1/4*-1≠0,1+2^(-2^(k -1)) limk->∞ln(1+2^(-2^k))/ln(1+2^(-2^ (k-1)))=0/0=limk->∞2^(-2^k/2)*2=0 ряд сходится
    1
  1152. S=π/2-√2+√(2+√2)-2/3
    1
  1153. E=(1+7+22)/30=1
    1
  1154. ×=arcsin(0,18√10),o=arctg(3/4)
    1
  1155. (x-10/3)³+(-28/3+m)(x-10/3)+160/ 27-2/3m=0 x=10/3+(-80+9m+√((- 80+9m)²+(-28+3m)³))¹/³/3+(..-..)..= 10/3+2/3(-28+3m)¹/²cos(1/3arcco s((-80+9m)/√(-28+3m)³)+2/3πn) -3555 17/27-1281/3(m-25/3)+(m-25/3)³<0 m<25/3+(1777 22/27+ √((1777 22/17)²-427³/27))¹/³+(..-..).. m[28/3;23 1/3] (±√(16,5+2,25m)-5)/(-28+3m)¹/²= cos(1/3arccos((-80+9m)/√(-28+ 3m)³))0/
    1
  1156. (a+2)²+7²=(a+5)² 14/3=a S=70/3-4π
    1
  1157. 666 комментариев.
    1
  1158. В*с=Дж/А
    1
  1159. x≥1,f(x)=3$(x-1;x)2t(2t-1)dt=4t³/3-t²|(x-1; x)=4/3x³-x²-4/3(x-1)³+(x-1)²=4x²-6x+7/3 x[0;1):f(x)=c|(x-1;0)+4/3t³-t²|(0;x)=4/3x³-x² x(-∞;0):f(x)=0
    1
  1160. (x+1)³-3(x+1)+6=0 x+1=(-3+√(3²+(-3)³/27))^(1/3)+(-3-√(9-1))^(1/3) x=-1+(-3+√8) ^(1/3)+(-3-√8)^(1/3)
    1
  1161. Ek=1;nak=3n-2/3/(n+1)-1/3
    1
  1162. Gm1m3/r^2-Gm2m3/(R-r)^2=0, r^2=1/m2*m1*(R-r)^2, (1-m1/m2)*r^2+2m1/m2*Rr-m1/m2*R^2=0, r=(-2m1R/m2±√(4m1^2R^2/m2^2+4(1-m1/m2)m1/m2*R^2))/(2-2m1/m2)=R(-m1+√(m1^2+m1m2-m1^2m2^2))/(m2-m1)=15*10^7* (-300000+√(-300000^2+300000+300000^2))/-299999=(-300000+550)/-299999=15*10^7*299450/299999=149 726 718 (m1+0,5m2)^2>=m2^2(m1^2+0,25), m2>=m1/(-0,5+√(m1^2+0,25))=1/(-0,5+√1,25)=1/0,62=1,61
    1
  1163. 3^(4x&4)=3⁵ 4x-4=5,x=9/4
    1
  1164. a²+(a-√2)²=(3√2)² a=√2/2+√8,5 AB=(a-√2)/a*2√2+..=3√2 ..=(3√2+√34)/4
    1
  1165. tga=10/h,tg(45°-a)=3/h,1=(10/h+3/h)/(1-10/h*3/h),1-30/h²=13/h,-30(1/h)²-13/h+1=0 1/h=(13±√(13²-4*30))/-60[1/h= 0,5 1/h=1/15;h=15 arctg7,5 BD=tg(arctg7,5-45°)*3=(7,5-1)/(1+7,5*1)*3=6,5/8,5*3=39/17
    1
  1166. AB/sin70°=BD/sin30°=AD/sin80° AC=AB +0,5AB/sin70° (AB+0,5/sin70AB)/sin70°= AB/sinx,x=(-1)^narcsin(cos²20°/4/(cos1 0°-0,5)/(cos10°+0,5))+πn x=arcsin(cos ²20°/4/(cos10°-0,5)/(cos10°+0,5))
    1
  1167. lnxEk=1;∞sin^(1/n)(lnxk+π/4)√2^(1/n)/xk^(1/n)/n² сходится при xk≥√2. f(x)=sinlnx/x+coslnx/x
    1
  1168. $(0;π/4)1/40dcos(x+π/4)(1/(cos(x+ π/4)-5/√32)-1/(cos(x+π/4)+5/√32)) =1/40(ln|cos(x+π/4)-5/√32|-ln|cos(x +π/4)+5/√32|)(0;π/4)=1/20ln3
    1
  1169. 3^35=3^2х х=17,5
    1
  1170. Это кривосудие, а не правосудие.
    1
  1171. 17/20+3/10√(2/3)+0,5(√0,5-√(1/3))ln((26√6+37+24√3-6√2)/23)(×) a=0,5ln((1+√0,5-√(1/3))/(1-√0,5+√(1/3)))
    1
  1172. √(y/x)²-3√(y/x)-1=0 y/x=(11+3√13)/2 5*11-54=1
    1
  1173. -2(x²+1)-⁰,⁵<0\>R
    1
  1174. 4||x|-1|=x+2,{x≥-2,[4(|x|-1)=x+2,4(|x|-1)=- x-2;{x≥-2,[{x≥-6,x=2,x=-1,2;{x≤2,x=2/5,x=- 2/3;{x≥-2,[x=2;-1,2;0,4;-2/3;{2;-1,2;0,4;-2/3}
    1
  1175. x=1,62;-0,62
    1
  1176. x³+(2k-1)x²-2(k-2)x-4=0 a=±2,x=1,x²+2kx +4=0 x=-k±√(k²-4) k(-∞;-2]U[2;∞)
    1
  1177. (z-4i/3)³-2/3(z-4/3i)+20/27i=0 z-4/3i=(-1 0/27i+√(-100/729+(-2/3)³/27))^(1/3)+(1 +√3)(cos(90°+120°n)+isin(90°+120°n))/3=cos(90°+120°n)*2/3+isin(90°+120°n) *2/3
    1
  1178. X=(√7+√3)/2 y=(√7-√3)/2 x¹⁰-1/x⁸= ((√7+√3)/2)¹⁰-((√7-√3)/2)⁸ (3996)/2 =1998
    1
  1179. X=ln¹/²⁰²⁴2024(cos(-arcsin((π+2π n)/√(ln²2024+(π+2πn)²))/2024+πn/1012)+sin(-arcsin((π+2πn)/√(ln²20 24+(π+2πn)²))/2024+πn/1012)i)
    1
  1180. (x-4)(2x-4)/2=48 x=3±7=10✓;-4× P=3x+x+2x=6x=60cm
    1
  1181. {{y}+[z]=0,8,{z}+[x]=1,2,z+x+y=4,7;{y}[0;1) [z](-0,2;0,8]=0,{y}=0,8,{z}=0,2,[x]=1 z=0,2, {x}+[y]=2,7,{x}=0,7,[y]=2 (1,7;2,8;0,2)
    1
  1182. 2x(1-x²)/(1+x²)²=1/4,-2x³+2x=1/4(1+x²)²,- 1/4-1/2x²-1/4x⁴-2x³+2x=0,-0,25x⁴-2x³-0,5x²+2x-0,25=0,:-0,25x² x²+8x+2-8/x+1/x²=0, x-1/x=y,y²+2+8y+2=0,y²+8y+4=0,y=(-8± √(8²-4*4))/2=-4±√12 [x-1/x=-4+√12,x-1/x=-4-√12;[x²+(4-√12)x-1=0,x²+(4+√12)x-1 =0;[x=(-4+√12±√((4-√12)²-4*-1))/2,x=(-4-√ 12±√((4+√12)²-4*-1))/2;[x=-2+√3+√6-√2, x=-2+√3-√6+√2,x=-2-√3+√6+√2,x=-2-√3-√6-√2;{-2+√3+√6-√2;-2+√3-√6+√2;-2-√3+√ 6+√2;-2-√3-√6-√2}
    1
  1183. (х-5/4)х=0 х=5/4;0
    1
  1184. x 1 цвета,222-х 2 цвета. ксск 222:4=2 (mod4) ..кскс.. на 2 разноцветных связи больше.
    1
  1185. x^(1/x)=(y^(1/y))²≤e^(1/e) e^(2lny/y)(2/y²-2lny/y2)=0 y=e+*->y 2^(1/4)=16^(1/16) (2;16)(-2;-16) 4^(1/8)=16^(1/16)(4;16)(-4;-16)
    1
  1186. x[-1;-1/2)U[1;3/2)
    1
  1187. 3/4а+а+4/3а=5 а=60/37 S=3600/1369
    1
  1188. А почему у Вас р странное?
    1
  1189. 4^(n+1)+5*4^(n-1):21✓
    1
  1190. C/a=b/(a+b)=a/(a+b+c){C=ab/(a+b),(a+b/3)³-2 1/3(a+b/3)b²-7/ 27b³=0; a+b/3=((7/2+√(49-343*4)/2)¹/³/3+(..-..)..)b=2√7cos(1/3arccos (0,5/√7))b/3 a=b(2√7cos(1/3arccos(0,5/√7))/3- 1/3) o=3/(√7cos(1/3arccos(0,5/√ 7))+1)/2~1/2 A)
    1
  1191. Па*с?Н/м*с=Па*м*с
    1
  1192. C/(c+26)BC ..=0,5BC-c/(c+26)BC {4EO/ED=OF, 2ED√((BCED±4√(4ED²+BC²-64))²+4(ED²-16)²)(BCED±4√(4ED²+BC²-6 4))/(ED²-16)²+(BCED±4√(4ED²+BC ²-64))²/4/(ED²-16)²ED²+4((BCED±4 √(4ED²+BC²-64))/(ED²-16))²+484=2 √(26c-26²c²/(c+26)²BC²)√((0,5-c/(c +26))²BC²+ED²)+26c+(0,25-c/(c+2 6)-675c²/(c+26)²)BC², EO=(BCED±4√(4ED²+BC²-64))/2/(ED²-16)ED;c=14 B)
    1
  1193. klR1$(-L/2;L/2)(R1²+h²)-¹,⁵dh √(R1²+h²)=x,h=√(x²-R1²),dh=(x²-R1²)-⁰,⁵xdx 2klR1$(R1;√(R1²+L²/4))(x²-R1 ²)-⁰,⁵x-²dx=2kl/R1
    1
  1194. a/(b+2c)+b/(c+2a)+c/(a+2b) 1/(b+ 2c)-b(c+2a)-²*2-c(a+2b)-²=0 (A+b+c/4)²-(2,5b²+bc+17c²/8)(A+b+ c/4)²+(-b³+b²c-4bc²-c³)(a+b+c/4)+ 0,5b⁴-3,5b³c+6 13/32b²c²+45/16bc³ 31/256c⁴=0*+>a min=1
    1
  1195. н=н+н+н=ч+ч+н н..нч..ч тогда 1011 чисел,нччнчч..н..нч тогда 1681 чисел✓
    1
  1196. (4 9|1) (0 1|-1/3){У-¹=-1/3,1/х=1;{(1;-3)}
    1
  1197. 30030=2*3*5*7*11*13 17+24=41
    1
  1198. (x⁴+1)⁰,⁵/2+ln|x²+√(x²+1)|/2+c
    1
  1199. P(xP;yP;zP) zP=1/3t±√(1+t²-(xP-2/3t)²- (yP-2/3t)²)
    1
  1200. 12 13/48-2 13/48=10
    1
  1201. АВ/√3*2*sin(120°-3a)/sin(180°-a -o)=AB/sino o=arctg(√3/(1+4cos (2a+60°)))
    1
  1202. 4{x}+5[x]=7,[x]≤1,4>0,6 [x]=1,{x}=0,5 x=1,5
    1
  1203. (0;2)r³/3(2-1,5√2)=16/3-4√2
    1
  1204. у=1-х, (х²+(1-х)²)²-2х²(1-х)²=7, {х⁴+(1-х)⁴=7;(х²+(1-х)²-√2х(1-х))(х²+(1-х)²+√2х(1-х))=7, ((2+√2)х^2-(2+√2)х+1)((2-√2)х²+(-2+√2)х+1)=7, 2х⁴-4х³+6х²-4х-6=0,|:2 (х²-х)²+2(х²-х)-3=0,х2-х=(-2±√(4-4*(-3)))/2=-1±2, х²-х=1, х²-х=-3, х=(1±√(1-4(-1)))/2, х=0,5±0,5√5, х=(1±√(1-4*3))/2 -11<0,у=0,5-+0,5√5,
    1
  1205. y=√(-x²+ax) y=√(-x2+2ax) [a=0,x=0; 2$(0;a)dx$(√(-x²+ax);√(-x²+2ax))(x²+y²)dy =2$(0;r)(r'cosф-rsinф)dф$(√(-r²cosф²+ar cosф);√(-r²cos²ф+2arcosф))r²(r'sinф+rcosф)dф=2$(0;a)((2x²/3+2ax/3)(-(x-a)²+a²) ⁰,⁵-(2/3x²+ax/3)√(-(x-a/2)²+a²/4))dx=-1/4 a⁴arcsin(-(x/a-1)²+1)⁰,⁵+1/3a²(-(x-a)²+a²) ⁰,⁵(x-a)-1/6(-(x-a)²+a²)⁰,⁵(x-a)³+a(-(x-a)²+ a²)¹,⁵/3-1/3a⁴arcsin((x-a)/a)-(x-a)a²(-(x-a) ²+a²)⁰,⁵/3-1/6√(-(x-0,5a)²+a²/4)(x-a/2)(2a- ¹(x-a/2)²-a/4)+3/32a³arcsin√(-(2x/a-1)²+ 1)-1/3a√(-(x-a/2)²+a²/4)(x-a/2)+1/96√(- (x-a/2)²+a²/4)³)|(0;a)*2=-1/6a⁴*π*2=-π/3a⁴ x=rcosф,у=rsinф r=аcosф r=2acosф (-(x/a-1)²+1)⁰,⁵=sinu x/a=1±cosu d(x/a)=-+sin udu √(-(2x/a-1)²+1)=sinu x=a/2(1±cosu) dx=-+a/2sinudu
    1
  1206. y=±√(1-x2) √(x²-x⁴)≤1/2,≥-1/2
    1
  1207. у=(CH²BH/BC²-AH²BH/AB²)/(AC-CH³/BC²-AH³/BA²)(x-AH³/BA²)+AH²BH/AB²,(AC/2;AC/2/tg/_ABC)
    1
  1208. x(t-u)=3u,x=3u/(t-u)
    1
  1209. -2y²=A(2y-√2)(y²+√2y+1)+B(y²+√2y+1)+C(2y+√2)(y²-√2y+1)+D(y²-√2y+1){A=-√2/4,D=-1/2,B=-1/2,C=√2/4;-√2/4ln|y²-√2y+1|-√2/2arctg((y-√2/2)√2)+√2/4ln|y²+√2y+1|-√2/2arctg((y+√2/2)√2)+c=-√2/4ln|ctgx-√2√ctgx+1|-√2/2arctg((√ctgx-√2/2)√2)+√2/4ln|ctgx+√2√ctgx+1|-√2/2arctg((√ctgx+√2/2)√2)+c
    1
  1210. Ps=бT⁴, T=3680K,Yє[380;760]нм,P's=C1*3y²e^(-C2y/T)+C1y³e^(-C2y/T)*(-C2/T)=0, 3-yC2/T=0,y=-3/(-C2)*T=c/л=cT/b,C2=3b/c=3*2,1*10-³/3/10⁸=2,1*10-¹¹K*c,+*- ,бТ⁴=$(0;∞)C1y³e^(-2,1*10-¹¹y/T)dy=C1y³e^(-2,1*10-¹¹y/T)/(-2,1*10-¹¹/T)|(0;∞)-C1*3y²e^(-2,1*10-¹¹y/T)/(-2,1*10-¹¹/T)|(0;∞)+6ye^(-2,1*10-¹¹y/T)|(0;∞)-6e^(-2,1*10-¹¹y/T)/(-2,1*10-¹¹y/T)|(0;∞)=0,
    1
  1211. 10:30 можно округлить 1,59 до 2. Так что он выполнил свои обещания.
    1
  1212. (a 1 0)²(a² 2a 1) (0 a 1)=(0 a² 2a) (0 0 a) (0 0 a²) (a³ 3a² 3a) (;;)^n=(a^n na^(n-1) n(n- 1)/2a^(n-2)) (0 a³ 3a²) (0 a^n na^(n-1)) (0 0 a³). (0 0 a^(n-1))
    1
  1213. h=8a/(3a-4) 30=8a³/(3a-4)²-8a²/(3a-4)-8a⁴/(3a-4)² (a+0,5)⁴+113/4(a+0,5)²-118,75(a+0,5)+112 1/4=0 z³+113/8z²+(113²/64 -449)/16z-118,75²/64=0 z=-113/24+√252205*sin(-atan(9√188814162840609/27352286)/3+π/6)/48;-113/24+√252205*sin(atan(9 √188814162840609/27352286)/3 +π/6)/48;-√252205*cos(atan(9√ 188814162840609/27352286)/3)/48-113/24 а+0,5=×
    1
  1214. X[-1;12] √((x+1)(12-x))=6 -24+11x-x²=0 x=(11±5)/2=8;3{8;3}
    1
  1215. (1+r)^n=-2/(nr-2) Пусть n=36. Тогда [r=0, En=0;35(19n-18)/(n+ 1)!/(36-n)!r^n+18/36!r³⁶=0;r>0 r=0,042
    1
  1216. ((x/10)³-1)³-16(x/10)-8=0 9(((x/10)³ 1)²(x/10)²-16/9)/10=0 (x/10)⁴-x/10 -+4/3=0 (4(x/10)³-1)/10=0 x=10/4¹/³ min=-3/4/4¹/⁴-4/3<0,-3/4/4¹/³+4/ 3>0 z³+1/3z-1/64=0 z=(1/128+√(1/128²+1/27²))¹/³+(.. -..)..;-(1/128+√(1/128²+1/27²))¹/³/2 +(..-..)..±√(3/4((1/128+√(1/128²+1/ 27²))¹/³+(.. -..)..)²+1/3)i x=10(√((1/ 128+√(1/128²+1/27²))¹/³+(.. -..)..)± 2√(0,5√(((1/128+√(1/128²+1/27²))¹/³+(.. -..)..)²+1/3)-(1/128+√(1/128²+1/27²))¹/³/4-(.. -..)..))+**+>x max=((√((1/ 128+√(1/128²+1/27²))¹/³+(.. -..)..)- 2√(0,5√(((1/128+√(1/128²+1/27²))¹/³+(.. -..)..)²+1/3)-(1/128+√(1/128²+1/27²))¹/³/4-(.. -..)..))³-1)³-16(√((1/128+√ (1/128²+1/27²))¹/³+(..-..)..)-2√(0,5√ (((1/128+√(1/128²+1/27²))¹/³+(.. -..)..)²+1/3)-(1/128+√(1/128²+1/27²))¹/³/4-(..-..)..))-8<0 min<0 E!,x=(1+√5)/2
    1
  1217. M=gM/(4/3R³)$(-R;R)dr$d(a(r1²-r2²) *h)=gM наверное
    1
  1218. f(x)=x³-4x2+3,xe[0;3] X⁴/4-4x³/3+3x|(0;1)-(x⁴/4-4x³/3+3x)|(1;3)=1 11/12-(20,25-36+9-1 11/12)=1 11/12+6,75+1 11/12=8 31/12=10 7/12
    1
  1219. y=6x/(2x-1) P=4x+2x-²-6/x+2√6 x¹,⁵/√(2x-1)+3/(2x-1)+17 P'(x)=4-4x-³+6x-²+2√6x⁰,⁵(2x-1,5)/(2x-1)¹,⁵-6(2x-1)-²=0 0=4x¹⁰-8x⁹+44 1/4x⁸-120 5/8x⁷+124x⁶-52x⁵+8x⁴+ (5,5x³-10x²+5,5x-1)² x=-0,073;0,8403;1,2;0,7*-0,7*-0,8403*+*1,2+>x min=25,02
    1
  1220. a(n+2)=3a(n+1)²-6a(n+1)an+3a²n+a(n+1) a1=1,a2=3,a(n+2)=3(a(n+1)-an)²+a(n+1) a3=6,a4=33,bn=3(an-a(n-1))² ±2;3;27..:/2, n≥2 a2017=2017^10^606,3
    1
  1221. (а²+5)/√(а²+4)≥2,(а²+5-2√(а²+4))/√(а²+ 4)≥0,(√(а²+4)-1)²≥0,аєR
    1
  1222. X≥-1 [{0=x⁵/³+4x⁴/³+11,5x+21,5x²/³+29x¹/³+32,x[-1;0);x=1;{1}
    1
  1223. 5^(-4-x)=5^(2)x-5)) x=2
    1
  1224. Х=5,у=4
    1
  1225. sin⁴x/2+cos⁴x/3=1/5,10cos²2x-4cos2x+ 0,4=0 cos2x=4/20=0,2 2x=±arccos0,2+2 πn x=±0,5arccos0,2+πn
    1
  1226. В учебнике нет, а на медали памятной есть.
    1
  1227. [х=а,х=1,5±√(-а²+4а+2,25);х≠±а А≠0,а≠3,5,А≠0,5,2 решения а[-0,5;0)U(0;0,5)U(0,5;3,5)U(3,5;4,5] (а-2-√2)(а-2+√2)≤0,а[2-√2;2+√2] нечётное число корней а{-0,5}U{0}U{0,5}U(2-√2;2+√2)U{3,5}U{4,5}
    1
  1228. 90°+45°-90°=45°
    1
  1229. ((3/2+√11/2)⁴-(3/2-√11/2)⁴)/12=7,5√11
    1
  1230. (x⁰,⁵)⁴-8/3(x⁰,⁵)³+22/9(x⁰,⁵)²-8/9x⁰,⁵+1/9=0 32/9?-32/9[x=1,(x⁰,⁵-5/9)³+3 5/27(x⁰,⁵-5 /9)+1334/729=0;x⁰,⁵=5/9+(-667+√(667²+8 6³))^(1/3)/9+(-667-√(22481²-13916))^(1/ 3)/9=4 1455/2523/9 x=(5/9+(-667+√(667² +86³))^(1/3)/9+(-667-√(22481²-13916))^ (1/3)/9)²
    1
  1231. -π/4ln(√2-1)-$duln|tg(u/2)|(π/4;π/2) сходится
    1
  1232. S∆=√3*10=4h h=2,5√3 S=(2+10)/2*2,5√3=15√3
    1
  1233. a=2/3¹/⁴ S=3,5a*1,5√3a=21
    1
  1234. (1/7)^x(4log(9/7)(1/7)+9^x)*7²ln(9/ 7)=0 x=log9(4log(9/7)7)-*+>x />=\> x≤log3(2√log(9/7)7) 13+24/43<20+(5 115/261)/29× Существует минимум 1 решение. Х=2(85=85) Других решений нет.
    1
  1235. 469+1564+37=2070
    1
  1236. y'-y=c y=c1e^x-ce^-x
    1
  1237. F(x,y)=x³+2yx+c(y)+c1, f(1,y)=1+2y+c(y)+c1=y+e^y c(y)=-y+e^y,c1=-1 f(x,y)=x³+2yx-y+e^y-1
    1
  1238. (2x-1)/x=1;5[x=1,-1/3=x.
    1
  1239. 1/(x-5)+4=1/x 4x²-20x+5=0 x=(5±2√5)/2 $(2,5-√5;2,5+√5)(1/(x-5)+4-1/x)dx=ln|x-5|+4x-ln|x|(2,5-√ 5;2,5+√5)=2ln(2,5-√5)+8√5-2ln(2,5+√5)
    1
  1240. А можете ли Вы сказать, был ли молодой человек Фёдор Мусиенко несколько лет назад?
    1
  1241. (x-r)²+k,(x-r)²+2k,x²+k 3x²-4xr+2r²+4k-20=0 x=(2r±√(-2r²-12k+60))/3 r(-√5;√5) A)
    1
  1242. 22,2r-22,12,10,16,2r-26,12,14 36=2r r=18
    1
  1243. y=ln((1-x²)/(1+x²)) y'=1/((1-x²)/(1+x²)) *(-2x(x²+1)-(1-x²)*2x)/(x²+1)²=4x/(x²+1)/(x²-1),y"=(4(x²+1)(x²-1)-4x((2x(x²-1)+(x²+ 1)*2x)/(x²+1)²/(x²-1)²=4(-1-3x⁴)/(x²+1)²/(x²-1)² d²y=4(-1-3x⁴)/(x²+1)²/(x²-1)²d²x y=ln((1-tg²t)/(1+tg²t))=ln(-cos2t/cos²t*c os²t)=ln-cos2t y"=-4/cos²2td²t
    1
  1244. a≥b≥c c<5 1;2;6;24 1+1+2=2² (0;0;2;2)(0;2;0;2)(2;0;0;2)(0;1;2;2)(0;2;1;2)(1;0;2;2)(1;2;0;2)(2;0;1;2)(2;1;0;2)(1;1;2;2)(1;2;1;2)(2;1;1;2) 1+1+6=8 (1;1;3;3)(1;3;1;3)(3;1;1;3)(0;0;3;3)(0;3;0;3)(3;0;0;3)(0;1;3;3)(0;3;1;3)(1;0;3;3)(1;3;0;3)(3;0;1;3)(3;1;0;3) 2+6+24 =32 (2;3;4;5)(2;4;3;5)(3;2;4;5)(3;4;2;5)(4;2;3;5)(4;3;2;5)2+6+120=128 (2;3;5;7)(2;5;3;7)(3;2;5;7)(3;5;2;7)(5;2;3;7)(5;3;2;7) c≥3 ..:3× min(a,b,c)=0;1;2
    1
  1245. 2(a+b)²+1=2a²+4ab+2b²+1×
    1
  1246. (X+y/2+1)²-y²/4=(x+1)(x+y+1)
    1
  1247. 4500/11=409 1/11 1001,9999 8998/22+1=410 0..16 0;11 1+1=1+1,1+3=1+3,1+5=1+5=3+3,1+7=1+7=3+5,1+9=1+9=3+7=5+5,3+3=3+3,3+5=3+5,3+7=3+7=5+5,3+9=3+9=5+7,5+5=5+5,5+7=5+7,5+9=5+9=7+7,7+7=7+7,7+9=7+9,9+9=9+9 85{85}
    1
  1248. p(lnp+if)=ln4+i(π/3+2πn){p=2,f=π/6+πn;z=±(√3+i)
    1
  1249. 0=(1-1/m)/(1+1/m)n²-2n-(1-1/m)/(1+m-¹) n=(m+1±√(4m))/(m-1) m=m1²,[n=(m1+ 1)/(m1-1),n=(m1-1)/(m1+1).
    1
  1250. sin106°/sin(74°-/_B)/2,sin/_B/sin (74°-/_B)/2+1/2 sin|/_B/2-18,5°| sin37°/sin(74°-/_B) arccos((sin²(/_B-18,5°)(4sin²37°cos²(0,5/_B-18,5 °)+1/sin²37°)-sin²74°/4)/(2sin(/_B-37°))/sin|/_B/2-18,5°|)=74°?
    1
  1251. АС√(4)=2AC BD=DC✓ ч.т.д.
    1
  1252. S∆,S∆/4 S∆/6 5S∆/12=5 S∆=12
    1
  1253. 0≥√(2x-3)*log|cosx|((1+2√3|sinx|)/8/- cos2x) x+1,5 16|sinx|²-2√3|sinx|-9=0 |sinx|=(√3±7√3)/16=√3/2;-3√3/8≥0 sinx=± √3/2 x=±π/3+2πn;±2/3π+2πn x=±π/3+πn *1,5°0,5π+*2/3π°π*1 1/3π+°1,5π>x x{1,5}U{2/3π+πn}U{1 1/3π+πn}
    1
  1254. y''/y'=yy'/(y²-1) ln|Y'|=ln|y²-1|/2+c y'=|y²-1|⁰,⁵c y'/(y²-1)⁰,⁵=c ln|y+(y²-1)⁰,⁵|=cx+c1 0,5e^(-cx)/c1+0,5e^(cx)c1=y
    1
  1255. 4,291?
    1
  1256. (ln|y|)'+(y-¹)'cosx/x=(x-¹+tgx)/2 -y-²(-sinx*x-cosx)/x²,0× y-²+2y-³cosx/x,(-x-²+cos-²x)/2
    1
  1257. arctg2√2~14/33π=76 4/11°
    1
  1258. (2+х)/(2-х)+√х=1+х,{х≥0,2-х≠0;{х≥0,х≠2;х є[0;2)U(2;+∞) 2+x+√x(2-x)=2-x+2x-x²,-(x- 2)√x=-x²,√x(x-2-x¹,⁵)=0,[x=0,(x⁰,⁵)³-(x⁰,⁵)²+ 2=0;(x⁰,⁵-1/3)³-1/3(x⁰,⁵-1/3)+1 25/27=0; x⁰,⁵-1/3=(-26/27+√(26²/27²+(-1/3)³/27)) ^(1/3)+(-26/27-√(676-1)/27)^(1/3)=(-26 +15√3)^(1/3)/3+(-26-15√3)^(1/3)/3= (√3-2)/3+(-√3-2)/3=-4/3,D>0=>1 корень х⁰,⁵=-1,0/{0}
    1
  1259. $sinxdx/(1-cos²x)³=$du/(u²-1)³=$(A/(u-1)+B/(u-1)²+C/(u-1)³+D/(u+1)+E/(u+ 1)²+F/(u+1)³)du=0,5(u-1)^-2/-2-0,5(u+1) ^-2/-2+C=-0,25(cosx-1)^-2+0,25(cosx+1)^-2+C cosx=u,-sinxdx=du 1=A(u-1)²(u+1)³+B(u -1)(u+1)³+C(u+1)³+D(u-1)³(u+1)²+E(u -1)³(u+1)+F(u-1)³=Au⁵+Au⁴-2Au³-2Au²+Au +A+Bu⁴+2Bu³-2Bu-B+Cu³+3Cu²+3Cu+C+Du⁵-Du⁴-2Du³+2Du²+Du-D+Eu⁴-2Eu³+2Eu-E+Fu³-3Fu²+3Fu-F,{A+D=0,A+B-D+E=0,-2 A+2B+C-2D-2E+F=0,-2A+3C+2D-3F=0,A-2B+3C+D+2E+3F=0,A-B+C-D-E-F=1;{A=-D,2A+B+E=0,2B+C-2E+F=0,-4A+3C-3F=0,*2-2B+3C+2E+3F=0,2A-B+C-E-F=1;{A=-D,2A+B+E=0,2B+C-2E+F=0,B+1,5C-1,5F+E=0,-2B+3C+2E+3F=0,2B-C+2E+F=-1;{D=0,A=0,B=0,F=-1/2,E=0,C=1/2;
    1
  1260. 2√3/3,√2 BH=cos75°*√2=√3/2-0,5
    1
  1261. F=3x²-2±4x√(1-x²) 6x+(4-8x²)(1-x²)-⁰,⁵=0 {-25/16(x²)²+25/16x²-0,25=0,x/(x-√0,5)/(x+√0,5)≥0-0,5⁰,⁵*+0*-0,5⁰,⁵*+>x;{[x²=1/5, x²=4/5; x[-0,5⁰,⁵;0]U[0,5⁰,⁵;∞);[x=-1/√5,x=2/√5;1/√5+*2/√5->x min=-3,max=2 6x-(4-8 x²)(1-x²)-⁰,⁵=0,x=1/√5;-2/√5 +-2/√5*1/√5 +>x max=2 min=-3 F[-3;2]
    1
  1262. X³/¹⁰=y y²-y-702=0 y=(1±53)/2=27;-26× x=3¹⁰✓
    1
  1263. 0=(x+1)(x²-122/11x+1) x=-1;11;1/11{-1;11;1/11}
    1
  1264. Y=x²/3 3-1/3=8/3 D)
    1
  1265. -x²⁰²²+2024=-1+2024=2023
    1
  1266. 4^(5/(x-5))=4-¹ x=0✓
    1
  1267. {(±11;±10)(±5;±2)}
    1
  1268. Arctg((√r2-√r1)/(√r1+√r2)), arctg(√(r1/r2)) (√r2+r1/√r2)/(√ r2+r1/√r2)=1,135°
    1
  1269. 2¹¹⁰*5¹⁰⁵(2³*5-1)-1=2⁵*10¹⁰⁵*39-1=728*10¹⁰⁵-1=7279..9 7*2+2+9*104=16+936=952 32 *39 288 64 728
    1
  1270. I=eSnv,где n- концентрация электронов, v - их скорость
    1
  1271. 1/2=A,B=2,C=-1,D=π/4
    1
  1272. f(x+1)=f(x)-1=f(0)-x-1 f(x)=f(0)-x
    1
  1273. √(52-2²)=√48 S∆=0,5√48*3=6√3
    1
  1274. x^x²⁰=√2^(1/√2),e^(x²⁰lnx)'=e^(x²⁰lnx)(20 x¹⁹lnx+x²⁰*1/x)=0,x¹⁹(20lnx+1)=0[x=0,x=e^ -0,05;0*-*e-⁰,⁰⁵+>x min=e^(-0,05*e^-1)<1, √2^(1/√2)>1,x=1+(2^(√2/4)-1)/(2²^20-1)= 1,11
    1
  1275. limn->∞(π/4-arctg(1/n))=π/4
    1
  1276. (380+760)/2=1140/2=570, 570*10^(-9)Т=2,1*10^(-3), Т=3,68*10^³К, 390 342 480 458 22
    1
  1277. А=2449n,nZ 70²(34!*1731-1):(2449n)=ost.0{2449}
    1
  1278. 3^(x/9)-x=0 3^(x/9)/9ln3-1=0 x=9log3(9/ln3)-*+>x min=9log3(e/9 *ln3)<0 x=27;1,16
    1
  1279. (6+√35)^х=у 0=(у-2)(у²+у+2) у=2 x=log(6+√35)2
    1
  1280. b=a√2/2+√(4-a²/2),√(11+(7a/4+ 1)√(8-a²))/2=R,(-7/2a²-a+14)(8-a²) ⁰,⁵=0,a=(-1±√197)/7+->a [√11/2;√(11+1/28(3+√197)√(134+2√197))/2]
    1
  1281. 1512=1(5+1*2)
    1
  1282. 333/5100=0,065 306 27000 25500
    1
  1283. limn->∞π²/2/n²(n+1)²=π²/2
    1
  1284. х⁴-50/(2х⁴-7)=14,у²-14у-50=0,у=(14±√(1 96-4*-50))/2[у=7+3√11,у=7-3√11<0; х=±(7+3√11)⁰,²⁵
    1
  1285. {0;π/2+2πn,n≥0}
    1
  1286. (Sinx+0,25)⁴-2 3/8(sinx+0,25)²+9/8 (sinx+0,25)+45/256=0 (z-19/48)³-3 1/192(z-19/48)-1193/3³/2¹¹=0 z-19/48=(1193+5√56377)¹/³/48+(..-√..)..;-(1193+5√56377)¹/³/96-(..- √..)±√(3/4((1193+5√56377)¹/³/48+(..-√..))²-31/192)i y=-√(19/48+(1193 +5√56377)¹/³/48+(..-√..)..)±2√(0,5 √(-11/48²-19/48((1193+5√56377)¹/³/48+(..-√..)..)+((1193+5√56377)¹/³/48+(..-√..)..)²)+19/96-(1193+5√5 6377)¹/³/192-(..-√..)..) x=arcsin(-0,25-√(19/48+(1193+5√ 56377)¹/³/48+(..-√..)..)±2√(0,5√(-1 1/48²-19/48((1193+5√56377)¹/³/48+(..-√..)..)+((1193+5√56377)¹/³/48+(..-√..)..)²)+19/96-(1193+5√56 377)¹/³/192-(..-√..)..))(-1)^n+πn
    1
  1287. (5+3cos40°)/sin40°
    1
  1288. x=(-47+80√5)¹/³=-0,5+2,5√5
    1
  1289. а, 37,5° atg37,5° 2atg37,5°/sin75° (2atg37,5°/sin75°-a)sin75°*(2(a-2atg37,5 °*ctg75°)+a(2tg37,5°/sin75°-1)cos75°)/2-arcsin((1-2tg37,5°ctg75°+2tg37,5°*ctg75°-cos75°)/(tg37,5°))a²tg²37,5°+a(1-cos75°)*√(a²tg²75°-(a-acos75°)²)/2=a²((2tg37,5°/(√2/4+√6/4)-1)(0,5*√2/2+√3/2*√2/2)*(2-4tg37,5 °*(√6/4-√2/4)/(√2/4+√6/4)+(2tg37,5°/(√2/4+√6/4)-1)(√6/4-1/4*√2)/2-5/12*πtg²37,5°+(1-√3/2*√2/2+1/2*√2/2)*√((1-cos150°)/2/(1+cos150°)*2-(1-√6/4+√2/4)²)/2)=a²((8√(15-8√3-6√6+10√2)(√6/4-√2/4)-1)(√2/4+√6/4)*(2-√(15-8√3-6√6+10√2)*(8-2√12)+(2√(15-8√3-6√6+10√2)(√6-√2)-1)(√6/8-√2/8)-5/12*π(15-8√3-6√6+10√2)+(0,5-√6/8+√2/8)*√(6,25+4,125√3+√6/4-√2/4))*(1+²)+a²...(1+²)
    1
  1290. $(2-π;2+π)f(x)sin(x/2-1)dx=$(-π;π)-f(2-x) sin(x/2)dx 2-x
    1
  1291. x≤1 0=-40+6x²+x⁴ x²=(-6+14)/2=4 x=-2
    1
  1292. 8²+3²-2*8*3cosA=AB²,3²+5²-2*3*5cos (180-A)=AB²,73-48cosA=34+30cosA,cos A=-39/-78=0,5 A=60°,
    1
  1293. √(11-√21)=√(21/2)-√(1/2)
    1
  1294. (1-tga)/sin(90°-2a)sina/sin/_BCN =tga/sin(90°+a-/_BCN) [π/4=/_BC N,×a=90°.D)
    1
  1295. 12,9,3√5+6√3 3√5.
    1
  1296. xlnlntgx+(2x-$2lntgxdx/lntgx)+$-dx ($2lntgxdx*ln-²tgx)/sinx/cosx(π/4; π/2)=∞ arctge^e^y=x $(0;∞)(π/2-arctge^e ^y)dy=∞
    1
  1297. {5/(x-√2)+2/(x+√2y)=1, 1/(x-√2)-5/(x+√2 y)=2;{5/(x-√2)+2/(x+√2y)=1, 1/(x+√2y)=- 1/3;{1/(x-√2)=1/3,1/(x+√2y)=-1/3;{x=3+ √2,y=-3√2-1.
    1
  1298. En=0;∞C(1/4;n)2^(1-4n)(-1)^nx^(4n +2)/(4n+2)|(0;2)=8En=0;∞C(1/4;n)* (-1)^n/(4n+2)=2√π*0,25!/0,75!
    1
  1299. √(49-x²),2√(49-x²)/9=2√(49-x²)/7*x/7 1/9=x/49,x=49/9
    1
  1300. 2R/(7+x)=tga 2x/(7+x)*√(4R²+ (7+x)²)√(4R²+(x+7)²)=(7+x)² 0=(7+x)³-2(x+7)+14 x=-7+(-7+√ 3945/9)¹/³+(..-..)..✓
    1
  1301. {(х-3)(х-1)≥0+•1-•3+>х,х>1;{хє(-∞;1]U[3; ∞),x>1;x[3;∞)
    1
  1302. log(1/3)(-2x²-3x+27)≥log(1/3)(-x²-x+24) {(x-1)(x+3)≥0,(x-3)(x+4,5)<0;{x(-∞!-3]U[1; ∞),x(-4,5;3);x(4,5;-3]U[1;3)
    1
  1303. log6(6(4-x))≤log6(16-x²) {(x-2)(x-4)≤0,x<4; x[2;4],x<4;x[2;4)
    1
  1304. Log3((2-x)(x²+5))≥log3(x2-5x+6)+log3(4-x) {(x-3)(x-2)>0,x<4;{x(-∞;2)U(3;∞),x<4;x(-≠; 2)U(3;4)x²-3x+2≤0+•1-•2+>x x[1;2] x[1;2)
    1
  1305. S1²/9+11=9+S1 S1²/9-S1+2=0 S1=(1±1/3)/(2/9)=6;3 S=30;24
    1
  1306. 7/9(10-0,1^(n-1)) ∞-7/9/(1-0,1)=∞
    1
  1307. 30*2/√5=12√5 24=h по горизонтали 48 30*1/√5=6√5 по горизонтали 12√5 x=6(5-√5)✓
    1
  1308. $arctgxdx=xarctgx-0,5ln(1+x²)+c
    1
  1309. a,24/a √(a²+576/a²) a=√24 135°,b²+24-2b √24cos135°=48 b²+√48b-24=0 b=-√12±6 >0 b=-√12+6 15°•2=30°,S=0,5*24*0,5=6
    1
  1310. 4^(x-3)-2^(x-3)(16-x²)-16x²≥0,(2^x)²/64- 2^x(2-x²/8)-16x²≥0,(2^x-(-2+x²/8+√(4-x²/2+x⁴/64-4/64(-16x²)))/(1/32))(2^x-(-64 +4x²-32√(4-x²/2+x⁴/64+x²)))≥0,(2^x+64 4x²-32(2+x²/8))(2^x+64-4x²+64+4x²)≥0,(2^x-8x²)(2^x+128)≥0,(2^(x/2)-2√2x)(2^(x/2)+2√2x)≥0,-0,32+*0,4-*9,..+>x 2^(x/2)*0,5ln2-2√2=0, x=2log(2)(4√2/ln2)=2log(2)(5,64/0,69)=2 *log(2)8,2=6,.. 4√2/ln2-2√2*2(2,5-log(2)ln 2)=8,2-5,64*2,5+5,640,5=8,2-14,10-2,820=-5,9-2,82=-8,72<0 16√2-18√2=-2√2<0, 2⁵-2√2*10=32-20√2>0,-2³+2√2*6=(2^(6/2)*0,5ln2-2√2)(x-6),x=(-8+12√2)/(4ln2 2√2)+6=8,8/(4*0,69-2*1,4)+6=8,8/-0,06+ 6=-140 2/3, хє[-0,32;0,4]U[9,..;+∞)
    1
  1311. [x=1,log2,6(2)=x.
    1
  1312. P(x)=a(x-1)(x-5)(x-x1) (4-x1)(1-x1)<0 x1(1;4),(4-x1)(7-x1)>0 x1(-≠;4)U(7;∞)✓ -2,5/x1=a, a(-2,5;-5/8) P(6)=-75/x1+12,5 (-62,5;-6,25) A)
    1
  1313. limx->∞(√(x²+3x-8)-√(x²+mx+7))=∞-∞=limx->∞(x+0,5+...-(x+m/2+..))=limx->∞(0,5 -m/2)=0,5-m/2
    1
  1314. arcsinx+x√(1-x²)-(1-x²)¹,⁵/3(0;1)=π/2+1/3
    1
  1315. $(0;∞)E^(-ln²x)dx=e⁰,²⁵√πФ((y-0,5)²/√0,5)(-∞;∞)=е⁰,²⁵√π
    1
  1316. 128²⁸⁵>125²⁸⁵>125²⁸⁴ ²/³
    1
  1317. (x⁴+3x²+4)/(x²+x+2)=x²-x+2
    1
  1318. n+19=(n-1)! n-1=4,n=5.
    1
  1319. Х>0 x=10 2+5=7✓
    1
  1320. 16√(1/3(1/3))=16/3=5/3h h=48/5 S=(5+5/3)/2*48/5=32
    1
  1321. arctgt-0,5ln|t²+1||(x;x+1)=arctg(x+1)-0,5l n((x+1)²+1)-arctgx+0,5ln(x²+1)
    1
  1322. $(0;π/4)tg(x-arccos√(1/3))dx=ln|cos(x-a rccos√(1/3))|(0;π/4)=ln(1/2*√2+1)
    1
  1323. l=√(6*3-2/3√45*1/3√45)=√8 a=2 S=4
    1
  1324. (sinAcosB-cosAsinB)/(sinAcosB+cosAsin B)=sin(A-B)/sin(A+B)=sin(2B)ctgC+cos2 B=sinB/sinC+1 [sinB=0,cos(B+C)=1/2;[B= πn,B+C=±π/3+2πn;=>B+C=π/3,A=2/3π.
    1
  1325. 2sinx=t x=arcsin(t/2) dx=dt/√(1-t²/4)/2 En=1;∞(-16)^(n-1)(n-1)!²*2/(2 n-1)!/(2n-1)=∞ q=limn->∞(16)=16>1
    1
  1326. {r²/CO1=DO1,sin/_DOC=(cosa√2/√(1-cos/_BOC)±√((2cos²a(1+cos/_BOC)-4cos²/_BOC)/(1-cos²/_BO C)))/4/ctg²/_BOC,r=)/CO1(√(4sin²(/_DOC)-sin²a)+cosa)./_DOC=90° \/D..=\/..A✓ч.т.д.
    1
  1327. 3/4x=1/4(24-x) x=6 11(ч)
    1
  1328. ab=2a+3,5b+0,5(a-7)(b-4)+70 ab=168
    1
  1329. Arcsin(1/√3),60°-arxsin(1/√3) x=√(13-12cos(60°+arxsin(√3/3)))= √(19-2√6)
    1
  1330. А вот в Беларуси с пенсионной реформой было все лучше.
    1
  1331. $(0;1)ln(1+x)/(1+x²)dx=ln2*π/2-En=1;∞(-1)^(n-1)/(2n-1)(1/(2n- 1)-1/(2n-2)+..+1)
    1
  1332. √(4х²-у²-6сх-су+2с²)+√(2х-у-2с)√(6-4х+3 с)+√(-8х²-4ху+(10с+12)х+(3с+6)у-3с²-6 с)=6,√((2х-2с-у)(2х-с+у))+√(-2(2х-2с-у)(2 х-1,5с-3))+√(-8(х+0,25у-5/8с-3/4)²+0,5(у ²+3с+6)²-4 3/8с²-16,5с-13,5)=6,{у≤2х-2 с,х≤3/4с+1,5;2х-с+у≥0,у≥-2х+с,4х-3с≥0,х≥ 3/4с,хє[3/4с;3/4с+1,5],уэ́[-2х+с;2х-2с]
    1
  1333. 12=2^(x³-6)+x³/> x³=8✓,x=2✓
    1
  1334. По х:2Rsin(a/2)cos(90°+0,5a-arccos (3,5/R)),2Rsin(-a/2+arccos(3,5/R)) cos(90°-a/4-0,5arccos(3,5/R)).По у: 2Rsin(a/2)sin(90°+0,5a-arccos(3,5/R)),2Rsin(-a/2+arccos(3,5/R))sin(90 °-a/4-0,5arccos(3,5/R)). (√(36-4R²sin²(a/2)cos²(-0,5a+arcc os(3,5/R)))+√(36-4R²sin²(-a/2+arc cos(3,5/R))sin²(a/4+0,5arccos(3,5/R))))²=(2Rsin(-0,5a+arccos(3,5/R))(sin(a/2)+sin(a/4+0,5arccos(3,5/R)))+7)² R[4,83;6]S=4,83²/2π..18π
    1
  1335. x=log(1/3)(1/45) 3^x=45
    1
  1336. ВАГОН*2=СОСТАВ,7 букв Вє[1;4],Сє[2;9] В=2;4 Н=1;6;2;7(2;6):2АГО¹*2=1О1ТА, С= 1,1О≤5 0/,В=8,Н=9:8¹5¹6¹7¹9*2=171358, 2Г=9+Т,Г≥4,≤9
    1
  1337. e^(-lnx*e^(xlnx))(-e^(xlnx))(x-¹+lnx (lnx+1))=0->x x=2^-2(2^(1/2)=2^0,5)
    1
  1338. 92*2 2'255/9999=204 680/909✓
    1
  1339. 6+1/x=u,(u+1)⁴-(u-1)⁴=8u(u²+1)= 240 u³+u-30=0/>,u=3 x=1/3
    1
  1340. (3/2)^(2/9)
    1
  1341. а,√(-7+а²) а[√7;3] √(9-а²) √(7-(а+√(-7+а²)-√(9-а²))²)=√(-7+а²) 99²-2412а²+148а⁴=0, а≤√(5,25+√153/4) а=3√((67±√12)/74) -✓,±6√3?4 13/16 а=3√((67-√12)/74) 3√((67-√12)/74)+√((85-9√12)/74)=а1✓
    1
  1342. F(p)=5/p⁴,f(t)=5t³/3!=5/6t³
    1
  1343. 3²/³+2*3¹/³+1 3¹/³+1,2(?✓)
    1
  1344. 20/3,2=6 1/4,x=1 y=3
    1
  1345. 4cos(2a)+√(2+18cos2a+16cos²(2 a))=BC CE=8cosa(4cos(2a)+√(2+18 cos2a+16cos²(2a)))/(4+4cos(2a)+√(2+18cos2a+16cos²(2a))) √(2+18cos2a+16cos²(2a))=9/8-4cos(2a),cos(2a)≤9/32 -47/64/27=cos(2a) BC=-47/16/27+√97'465/16/27
    1
  1346. 7^(6-x)-x=2 \> 1 корень. x=5(7-5=2) ✓{5}
    1
  1347. {37x-53y=2,17x-19y=1;{37x-53y=2, y=1/66;{x=5/66,y=1/66;x/y=5
    1
  1348. 1,27<1,61..
    1
  1349. 4+8√3-4√3*ctga=AB,4cosa/sina* ((1+2√3)sin2a-cos2a√3)=x atcsin(±(2+√3)/2/√(4+√3))/2+1/2arccos((1+2√3)/2/√(4+√3));π/2-atcsin(±(2+√3)/2/√(4+√3))/2+arccos((1+2√3)/2/√(4+√3))/2+πn=a,a=75°,x=(8-4√3)(2-√3)=28-16√3
    1
  1350. 21x²-10y²=9,x~√(10/21)y y:3,7x²-30y1²=3, x:3,21x1²-10y1²=1,0/1;2≠0
    1
  1351. ABcos3o=2/7ABcoso o=arccos(9/14)/2 AQ/QC=htg(3o)/(htgo)=(3-5/23)/(1-3*5/23)=8 B)
    1
  1352. 1/2=(3-а)/а а=2{4}
    1
  1353. A²+b²-2abcos/_a=1 arcsin(bsin/_a) 180°-arcsin(bsin/_a),/_a 2/sin/_a=a/sin(arcsin(bsin/_a)-/_a) |a²-b²+1|=b²-1,b≥1 a+b≥1,|a-b|≥1 [a²=2b²-2,a=0;a=√(2b²-2) 3/sin/_a= b/sin(arcsin(bsin/_a)-2/_a) √((1+cos2/_a)/(-1/3cos2/_a+5/9)) =b [b=1,/_a=45°+90°n,πn=/_a×;[b=1,/_a=45°;/_a=±0,5arccos(-1/3)+ πn,(0;60°) /_a=0,5arccos(-1/3){45°;0,5arccos(-1/3)}
    1
  1354. хє[2πn;π/2+2πn],neZ, {sinx-cosx≥1,xe[π/2+2πn;π+2πn]neZ, -sinx-cosx≥1,xe[π+2πn;3π/2+2πn],neZ, -sinx+cosx≥1,xe[3π/2+2πn;2π+2πn],neZ, хє[2πn;π/2+2πn],neZ, {sin(x-π/4)≥1/√2,xe[π/2+2πn;π+2πn]neZ, sin(x+π/4)≤-1/√2,xe[π+2πn;3π/2+2πn],neZ, sin(x-π/4)≤-1/√2,xe[3π/2+2πn;2π+2πn],neZ; xe[2πn;π)2+2πn],neZ, x-π/4e[π/4+2πn;3π/4+2πn],neZ, [π/2+2πn;π+2πn],neZ, x+π/4e[-3π/4+2πn;-π/4+2πn],neZ, [π+2πn;1,5π+2πn],neZ, x-π/4e[-3π/4+2πn;-π/4+2πn],neZ, [3π/2+2πn;2π+2πn],neZ, xe[2πn;π/2+2πn],neZ, xe[π/2+2πn;π+2πn],neZ, xe[π+2πn;1,5π+2πn],neZ, xe[3π/2+2πn;2π+2πn],neZ, xeIR
    1
  1355. S=4π-(2π/2+2²/2)=3π-2
    1
  1356. а*2√3/3,arctg(2-√3)=15°
    1
  1357. $(0;∞)3ch2x/ch3xdx=3ln|e^2x-√3e^x+1|(0;∞)=∞-3ln|2-√3|=∞ 3e^4x+3=A(2e^5x-2e^3x+2e^x)+B(e^4x-e^ 2x+1)+C(2e^5x+√3e^4x+e^3x-e^x-√3)+D(e^4x-√3e^3x+2e^2x-√3e^x+1)+E(2e^5x-√3e^4x+e^3x-e^x+√3)+F(e^4x-√3e^3x+2e^2x-√3e^x+1) 2u⁵+√3u⁴+u³-u-√3 u⁴-√3u³+2u²-√3u+1 (2u+√3)(u²+1)(u²-√3u+1)=2u⁵-√3u⁴+u³-u+ √3 (u²+1)(u²-√3u+1)=u⁴-√3u³+2u²-√3u+1 {A=0,B=3,C=0,D=-F,E=0;
    1
  1358. 3/√40*20=3√10(см)
    1
  1359. cos(xy)(y+xy')=-sin(x+y)(1+y'),y'=(-ycos(x y)-sin(x+y))/(xcos(xy)+sin(x+y))
    1
  1360. 2*(2n-1)!/(n-1)!/n!✓ч.т.д.
    1
  1361. 8^(4n1+3)+47:(13;43)? 5+8:13✓
    1
  1362. Он умер сам.
    1
  1363. 186,84руб.+202х≥700,х≥2,54 В 3 месяце будут деньги для ростовой куклы.
    1
  1364. Откуда они знают русский язык?
    1
  1365. S=200-50(π/2-1)=250-25π(cm²)
    1
  1366. -1/2xe^-x²+1/2√πФ(x√2)(-=;=)=0,5√ π
    1
  1367. 2sinxcos²x-sin³x,$(0,25cosx-0,25cos3x)dx =0,25sinx-1/12sin3x+c
    1
  1368. √(36-a²),√(R²-36+a²)+R=a 18=Ra✓
    1
  1369. F*15'873=ABCDE (31756;2)(47619;3)(95238;6)
    1
  1370. √sin2x=t,x=0,5arcsint² dx=t/√(1-t⁴)dt En=1;∞C(-0,5;n)*2(1/(4n-1)-1/(4n-2) +..+1)-ln2*2⁰,⁵
    1
  1371. x+z=y'(1)×
    1
  1372. [х=а,{n≥а/π+1/4,x=-π/4+πn.
    1
  1373. X-²(-4x2+1,5x²)=-2,5
    1
  1374. {21a2-3=b,a=35a2-5,c=15a2-2.
    1
  1375. a=-5+10cos42° arccos(cos42°)=42°
    1
  1376. -tg²x+3tgx-2=0 tgx=(-3±1)/-2=1;2 x=π/4+πn;arctg2+πn
    1
  1377. √3R²-0,5πR²=(√3-0,5π)R²
    1
  1378. 6=(2e/5)^x+(e/5)^x (2^x+log(2e/5)(e/5))(e/5)^xln(2e/5)=0 x=log2(log(2e/5)(5/e))-*+>x min=56/55*1,28<6 2 решения x=..;..
    1
  1379. 2√2sin75°=√3+1 (√3+1)/sino=1/sin(60°-o) 1=tgo o=π/4✓
    1
  1380. f'(x)+f(x)x-¹=2 f(x)=cx-¹+x²
    1
  1381. (52+6√43)(√43+3)+(52-6√43)(√43- 3)=140√43
    1
  1382. $dx/(x-1)^0,75/(x+2)^1,25=$±2(u⁴+2,25)^ -0,5/(1,5±√(u⁴+2,25))⁰,⁵du=±(1,5±√(u⁴+ 2,25)⁰,⁵/0,5*2+C=±4(2+x)⁰,⁵+C (x-1)⁰,²⁵(x+2)⁰,²⁵=u,x²+x-2=u⁴,x=(-1±√(1-4(-2-u⁴)))/2=-1/2±√(9+4u⁴)/2 dx=±0,5*0,5(4 u⁴+9)^-0,5*16u³du
    1
  1383. ln-i=i(-π/2+2πn)
    1
  1384. En=1;∞(2n-3)!/2^(2n-3)/(n-1)!/(2n- 1)/(n-2)!π сходится,√πS(1,5)/2
    1
  1385. X=((1/2+√(1/4-8/27))¹/³+(..-..)..)²= 8/3cos²(1/3arccos(3/4√(3/2))+2/3 πn) $(0;8/3cos²(1/3arccos(3/4√(3/ 2))))(x⁰,⁵-x²+2x)dx=x¹,⁵/1,5-x³/3+x² (0;8/3cos²(1/3arccos(3/4√(3/2))))= 32/9*2⁰,⁵/3⁰,⁵cos³(1/3arccos(3/4√ (3/2))))-512/27cos⁶(1/3arccos(3/4 √(3/2))))+64/9cos⁴(1/3arccos(3/4√(3/2))))
    1
  1386. n+(n-1)n=n² a2023≥2023*3/2-0,5= 3034(?)
    1
  1387. f(x)=0,5x⁶+7x^(2/7)-3/x+2x⁰,⁵-5lnx f'=3x⁵ +2x^(-5/7)+3x-²+x-⁰,⁵-5/x=0,(x¹/¹⁴)⁹⁸+1/3(x ¹/¹⁴)²¹+2/3(x¹/¹⁴)¹⁸-5/3(x¹/¹⁴)¹⁴+1=0,x>0,0/ />
    1
  1388. √(15^2+24²-15*24)=21 R=7√3 x=√(14√3)²-15²)=11√3
    1
  1389. Мой дед не прошел 2022.
    1
  1390. R=√(6,5²+4,5²)=2,5√10 S=62,5π
    1
  1391. {у=3-х²/3,[х=±(-3+√105)/2,х=±3,х=0;{(±(-3+√105)/2;(-13+√105)/2)(±3;0)(0;3)}
    1
  1392. (нр)(кн)(кн)(кнр)(кнр)(кн) Нет а,в,г,е,м,о,п,с,т. ЯУЮЭЫИ
    1
  1393. a=R(1-1/2√2) 20√((2+8√2)/31)=R a²=400(-6+7√2)/31
    1
  1394. x*4x²(1+27x³)+x²(1+8x³)*3x+(1+x³) *2x*9x²-(1+x³)*4x²*3x-x²*2x(1+27x³)-x(1+8x³)*9x²=x³*2+12x⁶=10 (x³+1)(6x³-5)=0 x=-1;(5/6)¹/³
    1
  1395. (у-1/у)²=-(х-2)²≥0 {у-1/у=0,х-2=0;{у=±1,х=2.{2;±1}
    1
  1396. 14х⁴+(-3у²-125)х²-5у⁴+82у²+51=0 х²=(3у²+ 125±(17у²-113))/28=(5у²+3)/7;(-у²+17)/2 0/;ує[-4;4]у=3,х=2 у=4,х=0,5⁰,⁵ (±2;±3)
    1
  1397. Вам бы только Валентину Когут слушать.
    1
  1398. a-¹b+b-¹a+13/6≥25/6,≤1/6
    1
  1399. (x³)²+(54-3a²)x³+9³=0 x³=-27+1,5a²±3a√(- 36+a²)/2 D=0,a²(-36+a²)=0,a=0;±6{±6;0}
    1
  1400. (10/3AH+2)²+(AH+2)²=(13/3AH)² -5/3AH²+13/3AH+2=0 AH=(13±17)/10=3;-4/10>0 tg(2_/1) =1/6 0=1-12tg/_1-tg²/_1 tg/_1=-6+ √37=r1/(10-2√2√r1) r1=232-38√37-4(√37-6)√(73-7√37) 0=r2+√r2√2(-1+√37)/3+(1-√37)/2 r2=(20+16√37+√2(1-√37)√(1+17√37))/9
    1
  1401. $(sin¹⁰⁰xcos(100x)+sin(100x)(sin⁹⁹ x)'/100)dx=sin⁹⁹xsin(100x)/100+c
    1
  1402. $(x+2√x+1)dx=x²/2+4/3x¹,⁵+x+c
    1
  1403. $(e^-x+2+e^x)dx=-e^-x+2x+e^x+c
    1
  1404. (х³-1):(х⁴+x³+x²+x+1)✓
    1
  1405. 5-W(32ln2)/ln2=х Е!
    1
  1406. AD=1/cosa*k=1/cosa/sina AB=1/sina (1/3+cos2a)sin²a=0 coswa=-1/3 a=0,5arccos(-1/3) S(ABCD)=0,5√((1-cos2a)/(1+cos2 a))(1+2/(1-cos2a))=5/4√2
    1
  1407. $(0;π/4)ln(√2*sin(x+π/4))/sin(x+π/4)*cos(π/4+x)dx=ln²(√2*sin(x+π/4))/2(0;π/4)=ln²2/8
    1
  1408. 4(a²+4/a²)=50+12√6
    1
  1409. у=2,х=3 А(3;2),В(хВ;14-хВ), С(хС;1,5хС-2,5) у=(1,5хС-16,5+хВ)/(хС-хВ)(х-хВ)+14-хВ хС=(-99+9,5хВ-6хВ²)/(7,5хВ-55) (хС-2)/(2-хВ)=1/2 -88+54хВ+3хВ²=0 хВ=9±√993/3 у=(-115173*3-+4145√993)/6/(-48'071-+1805√993)(х-9-+√993/3)+5-+√993/3у=х/3+2 (2)
    1
  1410. x²=a^x E✓,x-a^(x/2)=0 1-a^(x/2)lna/2=0 x=2loga(2loga(e))+*->a max=2loga(2loga(e)/e)≥0 a(0;e^(2/e)]
    1
  1411. a/√(a²+4),2/√(a²+4) a/2=((a+1)√(a²+4)-a² -a-4)/2 (a+7/6)³-1/12(a+7/6)+4 55/108=0 a+7/6=(-2 55/216+√183/6)¹/³+(-2 55/216 -√183/6)¹/³ a=-7/6+(-2 55/216+√183/6)¹/³+(-2 55/216 -√183/6)¹/³ S∆=-7/6+(-2 55/ 216+√183/6)¹/³+(-2 55/216-√183/6)¹/³
    1
  1412. √87:a:20=0,4√87:10:8,a=25 x=√40,96=6,4
    1
  1413. a²+b²=(2R-a-b)²,R-(a+b-R)=10 {100=a²+b²,R=0,5(a+b)+5; EF=2R-a-b=10(cm)
    1
  1414. log6(x).1,x>6.
    1
  1415. (-2sin²2x-1,5sin2x+1)/cos²x≥0 (-1,5±√(2, 25-4*2))/-4=3/8±√41/8 (sin2x-(3/8+√4 1/8))(sin2x-(3/8-√41/8))/cos²x≤0 x=arczi n(3/8±√41/8)/2(-1)^n+πn/2 *arcsin(3/8-√41/8)/2+πn-°π/2+πn*π/2-arcsin(3/8-√41/8)/2+πn+>x x[arcsin(3/8 -√41/8)+πn;π/2+πn)U(π/2+πn;π/2-arcsin (3/8-√41/8)/2+πn]
    1
  1416. 2^(81/85)<(1,424)³
    1
  1417. 3000=5³(5²-1)(5;3)
    1
  1418. а,a+1,b a-1,a-2 2a-3,4+b a=0,5b+2 b-a-1=4 0,5b=7,b=14,a=9.
    1
  1419. +*0->x 1+1,5^x*log2(3)-2^x*2+3^x*log2(6)-4,5^x*log2(9),x[-0,8;-0,5] -2ln2*1,5^x(-log(2)1,5*log2(3)/2+(4/ 3)^x)=0+*->x{0}
    1
  1420. b=6a/(7a-5)=6/7+30/7/(7a-5)\> a=1,b=3 a=5,b=1✓
    1
  1421. 41/2⁴/5³=41/10³/2=0,0205
    1
  1422. 10^(x/2+y)*10,1/10^(y+x/2)/101=0,1
    1
  1423. yy'=x-1,y(3)=-5,y²/2=x²/2-x+C,y=±√(x²- 2x+2C),-5=±√(3²-2*3+2C),C=11,y=-√(x²-2x+22)
    1
  1424. An=Ei=0;[n/2]C(n;2i)*2^(n-2i)*3^i bn=Ei=0;[n/2]C(n;2i+1)*2^(n-2i-1)*3^i
    1
  1425. 2^(1/2!+1/3!+1/4!..)=2^(е-2)
    1
  1426. S∆=3√3/2-1,5π S=2S∆=3√3-3π
    1
  1427. x=2√(7*21/=14√3
    1
  1428. (x-1)²+4=14+2√6+2√10+2√15
    1
  1429. log(2-x)(a^(x+2)+2a^(1-x)+x-1)+log(2+x)(a^(-x+2)+2a^(1+x)-x-1)=2{2-x>0,2-x≠1,2+x>0,2+x≠1;{x<2,x≠1,x>-2,x≠-1;хє(-2;-1)U (-1;1)U(1;2)(a^2xa²+2a)/a^x≥2a√(2a) (a² +2a*a^2x)/a^x≥2a√(2a) {2a√(2a)-3>0;2a √(2a)-3>0;(2a)¹,⁵>3,2a>3^(2/3),a>0,5*3^ (2/3) ає[0,5;1]U[e;+∞)
    1
  1430. (а+1)х²-4х+1-+а=0{а=-1,[х=0,х=0,5;{а≠-1,[х=(2±2√(1-(а+1)²))/(а+1), х=2,х=(2-2а)/(а+1);а=0,х=2× а(-∞;-2)U(0;∞)
    1
  1431. (cb+a²-ab-c²)/2/b=(c+a-b)(a-c)/b/2=(cb+a²-ab-c²)/2/b✓
    1
  1432. [х=5,х=2,{х=6;5,5≠0,1≠0;{х=4;3,4*-7:2, 3*-8:2;{5;2;6;4;3}
    1
  1433. a²*11/12=11 a=√12 S=1/12a²=1
    1
  1434. (4x-|x-6|)(log(1/3)(x+4)+1)/(2^x²-2^|x|)≥0, {x+4>0,2^x²-2^|x|≠0;{x>-4,x²≠|x|;{x>-4,|x|(|x|-1)≠0;{x>-4,x≠0,x≠1,x≠-1;xє(-4;-1)U(-1; 0)U(0;1)U(1;+∞) [{x-6<0,(4x+x-6)((log(1/3)(x+4)+1)/2^x(2^x-1)≥0;{x≥6,(4x-x+6)(log(1/3)(x+4)+1)/2^x/(2^x-1)≥0;[{x<6,(x-6/5)log(1/3)(x/3+4/3)/2^x/(2^x-1)≥0,--1 0-*1,2+>x{x≥6,(x+2)log(1/3)(x/3+4/3)/2^x/(2^x-1)≥0 +*-2*-1+°0->x;[{x<6,хє(0;1,2];{х≥6,хє(-∞; -2]U[-1;0);[хє(0;1,2],0/;хє(0;1,2]=>хє(0;1) U(1;1,2]
    1
  1435. (1/25^x)²/5+a(1/25)^x-a-2=0 (1/25)^x=-2,5 a±5√(a²+4/5a+8/5)/2≥0 x=log0,04(-2,5a±5 √(a²+4/5a+8/5)/2)[aR,a≤-2.
    1
  1436. Arcsin(√(1-cos38°+√2cos7°)/√2) +45°✓
    1
  1437. |-1/3|=1/3<1 сходится. (-1)^(n-1)/(3n+1) 3/(6m-2)/(6m+1)=1/12/m² сходится. Следовательно, и исходный ряд сходится.
    1
  1438. (2n)!/n!²=4^n/√π/√n=∞
    1
  1439. $(x²+2x+4)dx=X³/3+X²+4x+c
    1
  1440. (5⁶(1+5¹²)/(5¹²+1))^(1/3)=5²
    1
  1441. 16(12+5a)²/9cos⁴(1/3arccos(9(-4a+8)/(1 2+5a)²√((12+5a)/3))+2/3π)+(-40а-96)(12+ 5a)/3cos²(1/3arccos(9(-4a+8)/(12+5a)²√ ((12+5a)/3))+2/3π))+(64а-128)√((12+5a)/3)cos(1/3arccos(9(-4a+8)/(12+5a)²√((12 +5a)/3))+2/3π)-31а²+144a-48=0,a>0 a=2,88;2,04
    1
  1442. Z=-1+2¹/⁶(cos(π/12+2πn/3)+isin(π/12+2πn/3)),n=0;1;2
    1
  1443. x⁴-234x²+2025
    1
  1444. х+х/√(х²-1)>35/12,(х√(х²-1)+х-35/12√(х² -1))/√(х²-1)>0,{(х²-35/12х-49/12)(х²-3 5/12х+25/12)=0, хє[0;35/12);{[х=35/24 ±7√73/24,х=5/3,х=5/4;х є[0;35/12);[х= 5/3,х=5/4.°-1°1°5/4°5/3+>х
    1
  1445. Это они не по своей воле, а из-за завещания Граветта.
    1
  1446. y'lny=x ylny-y=x²/2+c.
    1
  1447. Можете хотя бы пунктуацию правильную использовать.
    1
  1448. √((х+1)²+(у-2)²)<2, √((х-2)²+(у-6)²) Макс.(х+1)²+(у-2)²<4,хє(-3;1)у<√(-х²-2х+3)+2,у>-√(-х²-2х+3)+2,√(х²-4х+3+(√(-х²-2х+3)+2-6)²), х²-4х+3-х²-2х+3+16-8√(-х²-2х+3)=-6х+22-8√(-х²-2х+3),-6-8*0,5(-х²-2х+3)^(-0,5)*(-2х-2)=0, (х+1)²/(-х²-2х+3)=(3/4)²,х≥-1,х²+2х+1=-9/16х²-9/8х+27/16, 25/16х²+3 1/8х-13/16=0, х=(-25/8±√(625/64-4*25/16(-13/16)))/(25/8)=-1±√(625+25*13)/25, х=-1±0,2√38,хє(-1;1)х=-1+0,2√38,√(-1+0,2√38-2)²+(-√(-(-1+0,2√38)²-2(-1+0,2√38)+3)+2-6)²)=√(9+0,04*38-1,2√38-(1+0,04*38-0,4√38)+2-0,4√38+3+16+8√2,48)=√(29-1,2√38+1,6√62) 25 *13 75 25 325 +625 950=2*5²*19 24 45 120 96 1,080-0,36=0,720
    1
  1449. (2 0 -1|-3) (0-10 7|-13) (0 0 2|2) {х1=-1,х2=2,х3=1.
    1
  1450. 4*2¹/³
    1
  1451. (0 1 0|-1/a;0 0 1|1+b/a;1 0 0|0){(0;-1/a;1+b/a)}
    1
  1452. (x+2√3/3)³-(x+2√3/3)+7√3/9-1=0 x=-2√3/3+2√3/3cos(1/3arccos(-7/2+3√3/2)+2/3πn) 5-3√3<0
    1
  1453. f(40y)=30/y f(x)=1200/x f(50)=24
    1
  1454. (2x³-12x)/(x²-9)=2x+6x/(x²-9)
    1
  1455. {x=coso,y=sino+(k-o)coso;o[0;π/2],k(0;π/2) y=√(1-x²)+(k-arccosx)x
    1
  1456. ​(x/3)^(x/3)=3³ x/3=3{9}
    1
  1457. $(1;e)|logx-0,5|dx=$(1;e)(logx-0,5)dx=1/ln10*(xlnx-x)-0,5x(1;e)=1/ln10(e-e)-0,5e -1/ln10(0-1)+0,5*1=-0,5e+ln10+0,5
    1
  1458. r(√3+tg(120°-/_CPO1))/2 /_COP= arctg((3+tg/_CPO1√3)/(-√3+tg(12 0°-/_CPO1)))-arctg((1+√3tg/_CPO 1)/(-√3+tg(120°-/_CPO1)))=2-√3{15°}
    1
  1459. $1/12dt(1/(t+0,2)-1/(t+5))=1/12(ln|t+0,2|-ln|t+5|)+c=1/12(ln|tg(x/2)+0,2| -ln|tg(x/2)+5|)+c
    1
  1460. $(-∞;°)2dt/(3+t²)+$(0;1)2/(3+t2)dt= 2π/√3+2/√3π/6=7/3π/√3
    1
  1461. x/3=(x+4)/5 2x/15=4/5 x=6cm S=85-25= 60cm²
    1
  1462. √(135+R²/4)=R² R=180⁰,⁵ S=90π
    1
  1463. y=4*2^x+8*2^-x≥8√2 y=(2^x+2^-x-1/2)²-4,25≥-2
    1
  1464. (0;0;0)(√2/2;√2/2;√2/2)(-√2/2;-√ 2/2;-√2/2){y=x³+z³,[z=0,z=±√2/2; [z=x,×-1-3/4z²=(x+z/2)²;✓
    1
  1465. Sinx*2sin²(x/2)/x³/cosx=1/2/cosx= 1/2
    1
  1466. 0,01,0,99*0,02,..,0,99*0,98*..*(1-(n-1)/100)*n/100,.. 99!/(100-n)!*n*0,01^n 99!(100-n)!-¹(50(n-100)-¹-nln(100-n)+ 1,5+n*ln0,01)0,01^n=0->n max=99!/90!*10-¹⁹ Ответ:10-й.
    1
  1467. PQ=√2/2PS/sin3/_R PR=√2/2PS/si n/_R √2/2PSctg3/_R+√2/2PS=QS= √2/2PSctg/_R-√2/2PS 0=(tg/_R+ 1/3)³+3 1/3(tg/_R+1/3)-4/27 tg/_R +1/3=(2+2√251)¹/³/3+(2-2√251)¹/³/3 /_R=arctg(-1/3+(2+2√251)¹/³/3 +(2-2√251)¹/³/3)✓
    1
  1468. 180°-2a+180°-2b=112°,a+b=124° x=180° -a-b=56°
    1
  1469. {a=7,5±√28,25,b=7,5-+√28,25;S∆=0,5(56,25-28,25)=14
    1
  1470. 5^(6+1+0)=5⁷ 7 0-ей
    1
  1471. (√7+√3-3,5√5+0,5√105)/2✓
    1
  1472. Кстати, мужской род главный в прилагательных и причастиях.
    1
  1473. В 2015, а не 2019.
    1
  1474. En=1;25(4n+1)=1326 общее число кругов, красных- 1+25²=626, белых - 700 Е)
    1
  1475. 16^x-3*4^x-2*2^x-2=0 (z-1/2)³+5/16(z-1/2)+7/32=0 z=1/2+(-7+2√(362/3)/3)¹/³/4+(.. ..)..;1/2-(-7+2√(362/3)/3)¹/³/8-(.. -..)..±√(3/4((-7+2√(362/3)/3)¹/³/4+(..-..)..)²+5/16)i x=log2(√(1/2+(-7+2 √(362/3)/3)¹/³/4+(..-..)..)±2√(0,5√ (9/16-1/2((-7+2√(362/3)/3)¹/³/4+(.. -..)..)+((-7+2√(362/3)/3)¹/³/4+(.. -..)..)²)-1/4-(-7+2√(362/3)/3)¹/³/16 (..-..)..))
    1
  1476. X=2shu dx=2chudu $0,5/(e^2u-1)² de^2u=-0,5(e^2u-1)-¹+c=-(x²+x√(x²+4))-¹+c
    1
  1477. mtg(πk/n)+lsin(pπ/n)=√n,k,p,n€N,m,l€Q,m,l>0,0/<πk/n,πp/n<π/2,(mtg(π(k-1)/n)+mtgπ/n+lsinpπ/n(1-tg(π(k-1)/ntgπ/n))/(1-tg(π(k-1)/n)tgπ/n)=√n,1<k<artg(√n+l)/m/π*n+1,А n наверное, может быть любое и можно подобрать другие параметры.
    1
  1478. (0;±7)(±7;0)(±2;±3)(±3;±2)
    1
  1479. {y=√10/2-+√2/2,x=√10/2±√2/2.
    1
  1480. {a=1/6,b=1/3,c=0.(A+b+c)²=1/4
    1
  1481. x+y²≤2021≤x+y²+2y {y≤√(2021-x),y≥-√(20 21-x),y≥0,(y+1)²≥2022-x;{y≤√(2021-x),y≥0, x≤2021,y≥-1+√(2022-x); {x≤2021, y[-1+√(2022-x);√(2021-x)].
    1
  1482. {b=6c=8,√50=a✓.
    1
  1483. y'=(a(y²+(x²+y²)¹,⁵)-x(x²+y²))/y/(x²+ y²+ax)
    1
  1484. log2(3/x+2)-log2(x+3)≤log2((x+4)/x²){3/x+2>0,x+3>0,(x+4)/x²>0;{(x+1,5)/x>0 +°-1,5-°+0>x,x> 3,хє(-4;0)U(0;∞);{хє(-∞; -1,5)U(0;∞),хє(-3;0)U(0;∞);хє(-3;-1,5)U(0;∞).log2((2x+3)/x/(x+3)/(x+4)*x²)≤0, (2x+3)/(x+3)/(x+4)*x≤1,(2x²+3x-(x+3)(x+4))/(x+3)/(x+4)≤0,(x²-4x-12)/(x+3)/(x+4)≤0,(x-6)(x+2)/(x+3)/(x+4)≤0 +°-4-°-3+*-2*6+>x хє(-4;-3)U[-2;6],хє [-2;-1,5)U(0;6]
    1
  1485. $cos⁴(x/2)dx=$(0,125cos2x+0,375+0,5co sx)dx=0,0625sin2x+0,375x+0,5sinx+c
    1
  1486. 1/365,2422/24/3=3,803*10-⁵
    1
  1487. 2r1-10A,20r1-100V.30r1-100V,1,5r1-5A.3,5r1-15A,30r-100V 135r1-550=100,r1=130/27(Om)
    1
  1488. 2ln|y-1|-ln|y|+c=2ln|e^x-1|-x+c
    1
  1489. 400*0,03=12(бел.руб.)
    1
  1490. 26+15√3
    1
  1491. √((m-1)/m)(√(m+1)+1)=m,m[1;=) 0=(m²-m-1)m m=0;(1±√5)/2{(1+√5(/2}
    1
  1492. x³/3lna+x3/3lnx-x³/9+c
    1
  1493. $x²e^(ax)dx=e^(ax)(a0x²+a1x+a2)+c=e^ (ax)(1/ax²-2/a²x+2/a³)+c e^(ax)(aa0x²+(aa1+2a0)x+aa2+a1)=x²e^ (ax){a0=1/a,a1=-2/a²,a2=2/a³;
    1
  1494. |i j k| |3 7 -2|=33i-17j-10k |1 -1 5| l=√(33²+17²+10²)=√1478 S=0,5√1478
    1
  1495. ln²y/2=-ln|tg(π/4-x/2)|+c y=e^±√(-2ln|tg (π/4-x/2)|+2c)
    1
  1496. Mx=36kN*m✓
    1
  1497. ​{a=55-b-¹,c=1/(55b-1),b=1/7;{b=1/7,c=7/48,a=48.c+a-¹=7/48+1/48=1/6
    1
  1498. f(x)=x³-2x²+2x-|2x²-2x|[{x(-∞;0]U[1; ∞),f(x)=x³-4x²+4x;{x(0;1),f(x)=x³;
    1
  1499. (tg²x+1)((tg²x-1/3)³+2/3(tg²x-1/3) -5 20/27)=0 tg²x=1/3+(155/2+√ (155²+32)/2)¹/³/3+(..-..)..=2 x=±arctg√2+πn (2-1)(2²+1)=5 C)
    1
  1500. Х=а+7;2-а -х²+10х-а²>0 (а+1-√11,5)(1+а+√11,5(<0 а(-1-√11,5;-1+√11,5) (а+1,5-√10,25)(3/2+а+√10,25)<0 а(-1,5-√10,25;-1,5+√10,25) 0,75¿(≤)√10,25,а(-1,5-√10,25;-1+√11,25)
    1
  1501. А=(4 -2 1) (1 6 -2) (1 0 0) (4. 1 1)|4 -2 1|. (-2 -0,5 -0,5) (-2 6 0)*|1 6 -2|=(1. -3 0) (1 -2 0). |1 0 0|. (-0,5 1 0) 4|6 -2|-(-2)|1 -2|+1|1 6|=2(2)-6=-2 |0 0|. |1 0|. |1 0|
    1
  1502. (sin8x+sin3x)cosx=0[x=π/2+πn,sin8x= sin-3x;8x=-3x+2πn,=π+3x+2πn x=2/11πn; π/5+2/5πn{π/2+πn;2/11πn; π/5+2/5πn}
    1
  1503. 47*10^9/214/10^6=0,22*10^3=220₽ на каждого.
    1
  1504. 2√3/3*(√3/2cos50°-1+0,5cos20°)/sin80°✓
    1
  1505. N/11=a²+b²+c², N=-abc-, a≠0, 100a+10b+c=11(a2+b2+c²), 11a²+100a+10b+c-11b²-11c²=0, a=(-100±√(100²-4(-11)(10b+c-11b²-11c ²)))/-22=4 6/11±√(2500+110b+11c-121b ²-121c²)/11≥1,≤9 [√(2500+110b+11c-121b ²-121c²)≥-39,≤ 49, -√(2500+110b+11c-121b ²-121c²)≥ 39,≤49, [2500+110b+11c-121b ²-121c²≤ 49²,≥0, 2500+110b+11c-121b ²-121c²≤ 39²,≥0, [{-121b²+110b+11c-121c²+99≤0, 121b²+110b+11c-121c²+2500≥0, {-121b ²+110b+11c-121c²+11*89≤0, -121b²+110 b+11c-121c²+2500≥0; [{(b-(-110+√(110²-4*(-121)(11c-121c²+ 99)))/-242)(b-(-110-√(110²+484*11c-484 11c²+484*99))/-242)≥0,++>b(b-(-110-√(110²+484*11c-484*11c²+484*2500))/-242)(b-(5/11-√(110²+5324c-532 4c²+1210000)/242))≤0,++>b {(b-(-110-√(110²+484*11c-484*11c²+484*979))/-242)(b-(5/11-√(25+11c-11c²+97 9)/11))≥0 ++>b (b-(-110-√(110²+484*11c-484*11c²+484*2500))/-242)(b-(5/11-√(25+11c-11c²+25 00)/22)≤0,+-*+>b [{bє(-∞;110/242-√(110²+484*11c-484 *11c²+484*99))/242]U[110/242+√(11 0²+484*11c-484 *11c²+484*99))/242;+ ∞),*5/11-√(25+111c-11c²+2500)/11✓*5/11-√(25+111c-11c²+99)/11*5/11+√(25+111c-11c²+99)/11 ✓*5/11+√(25+111c-11c²+2500)/11>b bє[5/11-√(110²+5324c-532 4c²+121000 0)/242;5/11+√(110²+5324c-5324c²+121 0000)/242], {bє(-∞;5/11-√(25+11c-11c²+979)/11]U[5/ 11+√(25+11c-11c²+97 9)/11;+∞),*5/11-√(25+11c-11c²+2500)/11✓*5/11-√(25+11c-11c²+979)/11*5/11+√(25+11c-11c²+979)/11 ✓*5/11+√(25+11c-11c²+2500)/11>b bє[5/11-√(25+11c-11c²+25 00)/q1;5/11+√(25+11c-11c²+25 00)/11], [bє[5/11-√(25+11c-11c²+2500)/11;5/11-√(25+11c-11c²+99)/11]U[5/11+√(25+11c-11c²+99)/11 ;5/11+√(25+11c-11c²+2500)/11], bє[5/11-√(25+11c-11c²+2500)/11;5/11-√(25+11c-11c²+979)/11]U[5/11+√(25+11c-11c²+979)/11 ;5/11+√(25+11c-11c²+2500)/11];*\/*/*/*\/ bє[5/11-√(25+11c-11c²+2500)/11;5/11-√(25+11c-11c²+99)/11]U[5/11+√(25+11c-11c²+99)/11;5/11+√(25+11c-11c²+2500)/11] с=0,bє[5/11-√2525/11;5/11-√124/11]U[5/11+√124/11;5/11+√2525/11], bє[2;5], а=4 6/11±√(10000+440*2+44*0-484*2²)/22=4 6/11±√(10880-1936)/22=4 6/11±√ 8944/22=4 6/11±2*√2236/22= 4 6/11±4 √559/22є/N, a=4 6/11±√(10000+440*3- 484*3²)/22=4 6/11±√6964/22=4 6/11± 83 75/166/22є/N, Чтобы а было натуральным числом, надо чтобы под корнем был квадрат целого числа, которое при делении на 11 даёт остаток 6, 5. a=4 6/11±√(10000+440*4- 484*4²)/22=4 6/11±√(11760-7744)/22=4 6/11±√4016/22=4 6/11±2*√1004/22є/N, a=4 6/11±√(10000+440*5-484*5²)/22=4 6/11±√(10000+2200-12100)/22=4 6/11± √0100/22, a=5,a=4 1/11, 550,-11(c-0,5)²+ 2,75+2525≤2527,75 b max=5/11+√2527 ,75/11=5,..,b min 5/11-√2527,75/11=-4,.. c=1,bє[5/11-√(25+2500)/11;5/11-√(25+99)/11]U[5/11+√(25+99)/11;5/11+√(25+2500)/11],bє[2;5],b=2, a=4 6/11±√(10000+440*2+44*1-484*2²-484*1²)/22=4 6/11±√(10000+880+44-1936- 484)/22=4 6/11±√8424/22=4 6/11±2√21 06/22=4 6/11±(45-10/90)/11є/N,b=3,a=4 6/11±√(10000+440*3+44*1-484*3²-484*1²)/22=4 6/11±√(10000+1320+44-4356- 484)/22=4 6/11±√6524/22=4 6/11±80 124/160/22є/N, b=4,a=4 6/11±√(1000 0+440*4+44*1-484*4²-484*1²)/22=4 6/11±√(10000+1760+44-7744-484)/22= 4 6/11±√3576/22=4 6/11±(60-24/120)/22є/N, b=5, a=4 6/11±√(10000+440*5+ 44*1-484*5²-484*1²)/22=4 6/11±√(100 00+2200+44-12100-484)/22=4 6/11±√ (-19660)/22є/N, c=2, bє[5/11-√(25+11*2-11*2²+2500)/11;5/11-√(25+11*2-11*2²+99)/11]U[5/11+√(25+11*2-11*2²+99)/11;5/11+√(25+11*2-11*2²+2500)/11], 5/11+√(2525+11с-11с²)/11>=5, 11с²+11с+2525≥50², -11с²+11с+25≥0, (с-(-11-√(121-4*(-11)*25))/-22)(с-(-11+√(121+1100))/-22)≤0, +*+>с сє[0,5-√1221/22;0,5+√1221/22], сє[0;2] bє[5/11-√2503/11;5/11-√102/11]U[5/11+√102/11;5/11+√2503/11],bє[2;5], b=2, a=4 6/11±√(10000+440*2+ 44*2-484*2 ²-484*2²)/22=4 6/11±√(10000+880+88 -1936-1936)/22=4 6/11±√709 6/22=4 6/11±2√1774/22=4 6/11±42 10/84/11є/N, b=3, a=4 6/11±√(1000 0+440*3+44*2-484*3²-484*2²)/22=4 6/11±√(10000+1320+88-4356-1936)/22 =4 6/11±√5116/22=4 6/11±71 75/142 /22є/N,b=4, a=4 6/11±√(10000+440*4+ 44*2-484*4²-484*2²)/22=4 6/11±√(1000 0+1760+88-7744-1936)/22=4 6/11±√21 68/22=4 6/11±(46 52/92)/22є/N,b=5,a=4 6/11±√(10000+440*5+44*2-484*5²-484 2²)/22=4 6/11±√(10000+2200+88-12100 -1936)/22=4 6/11±√-1748/22є/N, c=3, bє[5/11-√(25+11*3-11*3²+2500)/11;5/11-√(25+11*3-11*3²+99)/11]U[5/11+√(25+11*3-11*3²+99)/11;5/11+√(25+11*3-11*3²+2500)/11], bє[5/11+√48/11;5/11+√2459/11], bє[2;4], решений нет, при с≥4, решений нет. 2025+91=2116 1680+84=1764 484 *16 2904 484 7744 4356 1320
    1
  1506. $dx/(a+bcosx),a=0=>$dx/b/sin(π/2-x)=- 1/bln|cos(π/4-x/2)|+1/bln|sin(π/4-x/2)|+C =1/bln|tg(π/4-0,5x)|+C,[a-b;a+b]
    1
  1507. L{e^3tcosh2t}=$(0;∞)(e^2t+e^-2t)/2*e^ ((3-p)t)dt=0,5e^((5-p)t)/(5-p)+0,5e^((1-p) t)/(1-p)(0;∞)=0-0,5/(5-p)-0,5/(1-p)=0,5/(p-5)+0,5/(p-1)
    1
  1508. y'/y=x/(x²+9) lny=ln(x²+9)/2+c y=(x²+9)⁰,⁵c
    1
  1509. 1+х³+х⁶/2!+..(0;1)=1+1+1/2!+1/3!+1/4!- 1-0-0-0=1 17/24 n!n/(n+1)≥10,n≥4
    1
  1510. $ctg⁷xdx=$-cos⁷x/(1-cos²x)⁴dcosx=$-y⁷/(y²-1)⁴dy=$(A/(y-1)+A1/(y-1)²+A2/(y-1)³ +A3/(y-1)⁴+A4/(y+1)+A5/(y+1)²+A6/(y+ 1)³+A7/(y+1)⁴)dy A(y⁷+y⁶-3y⁵-3y⁴+3y³+3y²-y-1)+A1(y⁶+2y⁵-y⁴-4y³-y²+2y+1)+A2(y⁵+3y⁴+2y³-2y²-3y-1)+A3(y⁴+4y³+6y²+4y+1)+A4(y⁷-y⁶-3y⁵+3y⁴+3y³-3y²-y+1)+A5(y⁶-2y⁵-y⁴+4y³-y²-2y+1)+A6(y⁵-3y⁴+2y³+2y²-3y+1)+A7(y⁴-4y³+6y²-4y+1)=-y⁷,{A+A4=-1,-A1+2A4-A5=1,1/2A2+2A4- 2A5+1/2A6=-1/2,-1/6A3+1 1/3A4-1,5A6 -1/6A7=1/6,2/3A4+1/3A5-1,5A6-1/3A7=13/24, 1/3A5+2 7/36A6-1/4A7=34/72, 503/180A6-23/60A7=59/360, A7=-7697/5186;
    1
  1511. 1/2017(ln|x-2015|-ln|x+2|)+c
    1
  1512. √(11²+(4√3)²)=13
    1
  1513. √(13+4√3)=2√3+1
    1
  1514. S∆=3,5*35*3/5=73,5
    1
  1515. 719!*120 719+120=839
    1
  1516. b-W(a^blna)/lna=x,{a(0;1),b<loga(-1/e/lna);=> 2 корня,1 из которых функция Ламберта
    1
  1517. |х-1|-|х|+|2х+3|=2х+4,[{х≥1,х-1-х+2х+3=2х +4;{хє[0;1),-х+1-х+2х+3=2х+4;{хє[-1,5;0),- х+1+х+2х+3=2х+4;{х<-1,5,-х+1+х-2х-3=2х +4;[{х≥1,0=2;{хє[0;1),-2х=0;{хє[-1,5;0),0=0;{х<-1,5,-4х=6;[0/,х=0,хє[-1,5;0),0/;хє[-1,5;0]
    1
  1518. $(e^x-1)/xdx=En=1;∞x^n/n!/n+c
    1
  1519. -2/(n+1)/n/x=0
    1
  1520. (1-b-c)/(1-b)/(1-c)<1/a a,b,c(0;1)
    1
  1521. f(x)'+sinxlncosx=cosxlncosx f(x)=lncosx*0,5ln|cos²x-1|+0,25En =1;∞1/n²(cosx)^(2n)
    1
  1522. S∆=15(cm²)
    1
  1523. √2/2ln(√2/2)-(ln|tg0,5x|+cosx)(π/2;π/4)=√2/2ln(√2/2)-ln(√2-1)-√2/2
    1
  1524. cosx*sin^(-4 2/2025)x/(4 2/2025)+ $dxsin^(-3 2/2025)x/(4 2/2025)+c
    1
  1525. x³+17=x³-1=-1;0;1
    1
  1526. 6x-180°+2*2x=180° x=36°
    1
  1527. En=1;∞(-2e^(-2n)/n-e^(-2n)/n²+1/n²)=2ln(1-e-²)-Li2(e-²)+π²/6
    1
  1528. xln|sinx|-$ln|sinx|dx(0;π/2)=-$(0;π/2)ln|1-2sin²(π/4-0,5x)|dx=Ei=1;∞(ncosx+(1+ n(n-1)/4)x-n(n-1)/8sin2x+..)/n(0;π/2)=Ei =1;∞((n-1)/4π/2+..)=∞
    1
  1529. 2/(5cosa)=sina arcsin(4/5)/2=a S=8(1/2+5/4)/0,5=28
    1
  1530. 1+1,5+0,5²*3²+...=∞
    1
  1531. [x²-x-2=0,x²+x-1=0;[x=2,x=-1,x=(-1±√5)/2.
    1
  1532. S∆=1/30a²=1 a²=30
    1
  1533. *-2*2°3-*4+>х хє(3;4]
    1
  1534. (2+2)!+2-2+2=26
    1
  1535. у=1/(х-1) х=2;0 у=1;-1{(2;1)(0;-1)}
    1
  1536. y+x=z $dzcos²z/(1+cos²z)=x+c tgz=t,z=arctgt,dz=1/(1+t²)dt $(1/(1+t²)-1/(2+t²))dt=arctgt-arctg(t/√ 2)/√2=x+c y-arctg(tg(y+x)/√2)/√2-c =0✓
    1
  1537. aED/2-45=EDa/4 EDa=180 b/a= 900/a² ba=900
    1
  1538. (1+1/3)/(1-1/3)=2 (n+1/(n²+n+1))/(1-n/(n²+n+1))=n+1 π/2✓
    1
  1539. -cosx+x/2(0;7/6π)+cosx-1/2x(7/6π;11/6π)-cosx+1/2x(11/6π;2π)=1/3π+2√3
    1
  1540. 2*50*49/2,2*150*151/2 20200
    1
  1541. S1,S2,8-S2,16-S1 S1+8-S2=3,S2=S1+5 S1S2=S3S4 S1(S1+5)=(3-S1)(16-S1) 24S1=48 S1=2 S4=14cm².
    1
  1542. 10√(25+12√3) 83°-arcsin(1,5/√(25 +12√3)) 10√(50-40cos83°+12√3-30 sin143°)✓
    1
  1543. ВАГОН*2=СОСТАВ 7 цифр С=1,В≥5 Н≠0 В(0;5)ГОН*2=1О1Т(0;5)В,В:2,В=6;8 60¹Г2⁰¹(3;8)*2=121Т06× 65¹Г3Н*2=131Т56× 80Г6Н*2=161Т08× 85¹6¹7¹9*2=171358 2Г=9+Т,Г[5;9] Г,Т=(6;3)✓
    1
  1544. {x+y=±3,x-y=±1;{(2;1)(-2;-1)}
    1
  1545. √(9-a²)+2/3a=a 9-a²=1/9a² a=9/√10cm S=8,1-3=5,1(CM²)
    1
  1546. Т.Э.Уртрсрнрэ=Х.А.Цухуфуруа Сълндпсдх молы энъ поъпамнэца поърыруъзяъм.=Фэоржфжх...
    1
  1547. (х²+2х-24)/х=√(3х²+2х-24)≥0-*-6+°0-*4+>х хэ́[-6;0)U[4;≠) x⁴-x³+10x²+48x-288=0 х=-4;3{-4}
    1
  1548. (a/2)²+(4-a√3/2)²=4 12-4√3a+a²=0 a=2√3✓ S=3,5√3 √2204√2026<2025
    1
  1549. x=log2(1±k-¹)
    1
  1550. f(x)+2f(1/(1-x))=x,f(1/(1-x))+2f(-1/x+1)=1/(1-x),f(-x-¹+1)+2f(x)=-x-¹+1 f(x)+2f(1/(1-x))=x,f(1/(1-x))+2f(-1/x+1)=1/(1-x),f(-x-¹+1)=-4/9/(x-1)-2/ 9x-x-¹/9+1/9{f(x)=2/9(x-1)-¹-+1/9x- 4/9x-¹+4/9,f(1/(1-x))=-1/9/(x-1)+4/ 9x+2/9x-¹-2/9, f(-x-¹+1)=-4/9/(x-1)- 2/9x-x-¹/9+1/9;
    1
  1551. x=2^(5log6(3))
    1
  1552. a<4✓
    1
  1553. {x(-≠;-√2]U[√2;≠),(x-1)(x+1)(2x+3)=0; x=±1;-1,5{-1,5}
    1
  1554. $(0;π/4)2√(4+5tgx)cos-²xdx=2(4+ 5tgx)¹,⁵/7,5(0;π/4)=76/15
    1
  1555. tgA=(1-tg33°)/(1-ctg78°)=sin24°/cos24° A=24° ?=24°+33°=57°
    1
  1556. L=7(1/3π)+4/3π=11/3π
    1
  1557. {sin(-π/2+2x)=sin2x,y=π/2-x;[-1/4=n,x=3/8 π+0,5πn;y=1/8π-0,5πn.{3/8π+0,5πn;1/8π- 0,5πn}
    1
  1558. ​{a/d+b/e+c/f=2 7/96,a:b:c=15:25:9,d:e:f= 4:3:2; 199/45a/d=199/96 a/d=15/32 b/e=25/24 c/f=9/16
    1
  1559. x y z% x+zy/100,y+xz/100{x=0,5y(1-z/50)/(1-z/200),0=-12'500+125z+z²;z=(-125+25 √105)/2{-62,5+12,5√105%}
    1
  1560. x=(-2m+31)/(4m-9),x≠-3,m≠1
    1
  1561. [{a=b,x≠±b²,xR;{0≠b,[-b(1+b²)/(1-b)/(1-b+ b²)≠a,{a≠1,-b(1-b)/(1-b+b²)≠a;x=(a+b)/(a-b);
    1
  1562. X³+1=A(2x-√2)(x²+√2x+1)+B(x²+√2x+1)+C(2x+√2)(x²-√2x+1)+D(x²-√2x+1){A=1/2-√2/8,C=√2/8,B-D=0,D=1/4;(1/2-√2/8)ln(x²-√2x+1)+√2/4arctg((x-√2/2)√2)+√2/8ln(x²+√2x+1)+√2/4arctg((x+√2/2)√2)+c
    1
  1563. $(0;≠)(12,5lnt-1,25ln(t¹⁰+1))dt=12,5(t lnt-t)-1,25En=1;∞(-1)^(n-1)/n*t^(10n +1)/(10n+1)(0;=)~0, по-любому сходится
    1
  1564. 3-2*1*2/5=2 1/5 h=√21/5 AE=√190/5
    1
  1565. (|х|-|4-|у||-4)²≤4 {|х|-|4-|у||-4≤2,|х|-|4-|у||-4≥-2;{|х|-|4-|у||≤6,|х|-|4-|у||≥2; {[{х-|4-у|≤6,х≥0,у≥0;{х-|4+у|<6,х≥0,у<0;{-х-|4-у|≤6,х<0,у≥0;{-х-|4+у|≤6,х<0,у<0;[{х-|4-у|≥2,х≥0,у≥0;{х-|4+у|≥2,х≥0,у<0;{-х-|4-у|≥2,х<0,у≥0;{-х-|4+у|≥2,х<0,у<0;{[{4-у≤-6+х,4-у≥6-х,х≥0,у≥0;{4+у≥-6+х,4+у≤6-х,х≥0,у<0;{4-у≥-6-х,4-у≤6+х,х<0,у≥0;{4+у≥-х-6,4+у≤х+6,х<0,у<0;[{4-у≤-2+х,4-у≥2-х,х≥0,у≥0;{4+у≤-2+х,4+у≥2-х,х≥0,у<0;{4-у≤-2-х,4-у≥2+х,х<0,у≥0;{4+у≤-2-х,4+у≥2+х,х<0,у<0; {[{у≤10-х,у≥-2+х,х≥0,у≥0;{у≥-10+х,у≤2-х,х≥0,у<0;{у≤10+х,у≥-2-х,х<0,у≥0;{у≥-х-10,у≤х+2,х<0,у<0;[{у≥6-х,у≤2+х,х≥0,у≥0;{у≤-6+х,у≥-2-х,х≥0,у<0;{у≥6+х,у≤2-х,х<0,у≥0;{у≤-6-х,у≥-2+х,х<0,у<0;
    1
  1566. u'(x)-u/c=-c1/c u=c2e^(x/c)-c1e^(-x/c)
    1
  1567. a+b√2+c√3 {ab=1/2,ac=1/2,bc=1/2; {a=1/√2,b=1/√2,c=1/√2; 1/2(1+2+3)=3 √2/2+1+√6/2✓
    1
  1568. y=3x²+6x+1,x=(-6±√(36-4*3))/6=-1±√6/3
    1
  1569. (x-1-y)(x+1)✓
    1
  1570. lnx=0;±5¹/⁴ x=1;e^(±5¹/⁴) x=e^(±100¹/⁴/2)(cos(100⁰,²⁵/2)±isin(100 ⁰,²⁵/2))
    1
  1571. (π1/2)^2/2-(-1/4+π*0,5^2/4*2)-0,5*0,5^2*arccos0,3/0,5-(0,5*0,5^2*sin(180°-arccos0,6)-(1/2*arcsin 0,8-0,5*0,8))=π/8+1/4-π/8-1/8*arccos0,6-0,125√(1-0,6^2)+0,5arcsin0,8-0,40=-0,25+0,375arcsin0,8 (1-√(1-x^2))^2+(x-1/2)^2=1/4, 1-2√(1-x^2)+1-x^2+x^2-x+1/4-1/4=0, -2√(1-x^2)=x-2,4-4x^2=x^2-4x+4, -5x^2+4x=0, x=0, x=-4/-5=0,8,
    1
  1572. d=-a-b-c 3(c²+c(a+b)+ab)/(ab+ca+cb+c²)= 3
    1
  1573. 40-25i I=44/89√89sin(100πt-arctg(5/8))
    1
  1574. √5-√4=√5-2✓
    1
  1575. И ещё дурное правительство.
    1
  1576. 6√2,(6√2)²/12=36*2/12=6,6+14+2=22,
    1
  1577. {1/r=a/b,a=b+√(1+r²);{a=b/r,b/r=b+√(1+r ²);b=r√(1+r²)/(1-r) r²(1+r²)/(1-r)²+(1+r²)/(r-1)²=(2r)²,(1+r²)(r²+1)=4r²(r-1)²,{r²+1=2r² -2r,r²+1=-2r²+2r;{-r²+2r+1=0,3r²-2r+1=0;{r= (-2±√(4-4*-1))/-2,r=(2±√(4-4*3))/6;{r=1± √2,r=1/3±√-2/3;1-r>0,r<1,r=1-√2
    1
  1578. 4,3 4²+3²=25=r²,r=5 10*9=90
    1
  1579. tg/_B=3/4,tg0,5/_B=r/BA1,tg/_B=2tg0,5/_B/(1-tg²0,5/_B),3/4-3/4tg²/_0,5B=2tg0, 5/_B -3/4tg20,5/_B-2tg0,5/_B+3/4=0,tg0 ,5/_B=(2±√(4-4*-3/4*3/4))/(-3/2)[tg0,5/_B =-3,tg0,5/_B=1/3;tg0,5B>0 tg0,5B=1/3, 1/3=r/BA1,BA1=3r r+2r+3r=12,r=2
    1
  1580. R-1,2√(R*1) (R-1)²+4R=(R+1)²,2√2 2√2*2 =4√2
    1
  1581. 4+x,(4+x)/(4-x)=tg/_A,tg(90°-/_A)=ctg/_A, ctg/_A=.../3,1/((4+x)/(4-x))=.../3,...=3(4- x)/(4+x),/_=45°-arctg(3(4-x)/(4+x)) 3((4+ x)/√(160-64x+10x²)+(12-3x)/√(160-64x +10x²))*√(32+2x²),xє[0;8] Sє[0;28,004]
    1
  1582. y,50/y,y<13,y>0 (13-y)(50/y-2)=650/y-26- 50+2y=650/y-76+2y x=50
    1
  1583. √(x²+b²)=3,x+1=b x²+(x+1)²=9,2x²+2x-8 =0,x=(-2±√(4-4*2*-8))/4[x=-1/2+√17/2,x= -0,5-√17/2;x>0 x=-0,5+√17/2 b=0,5+√17/ 2 (-0,5+√17/2)(0,5+√17/2)=-0,25+17/4=4
    1
  1584. y=-tg15°x,(x-1)²+(y+1)²=1,x²-2x+1+(-tg15° x+1)²=1,(1+tg²15°)x²+(-2-2tg15°)x+1=0,x= (1+tg15°±√(2tg15°))/(1+tg²15°) ((1+tg1 5°-√(2tg15°))/(1+tg²15°);(-tg15°-tg²15°+ tg15°√(2tg15°))/(1+tg²15°))((1+tg15°+√(2tg15°))/(1+tg²15°);(-tg15°-tg²15°- tg15°√(2tg15°))/(1+tg²15°)) 2√(2tg15°)* cos15° A=90° S=π*1²/4-0,5sin90°)=π/4 -0,5
    1
  1585. Дорогой Павел! Можете ли Вы пройти тест на мировоззрение,а то я не знаю,какое мировоззрение у других людей?
    1
  1586. 5-²/-2-4-²/-2=9/800
    1
  1587. е^(1/(1+n^-x))=1✓
    1
  1588. √(9+a²+3a) arcsin(a/√(9+a²+3a)√ 3/2),60°-arcsin(a/√(9+a²+3a)√3/2) a²=9 a=3 y=3√3,R=3✓
    1
  1589. 4√6 10/0,5=4√6/sinx x=✓arcsin(√6/5);×π-arcsin(√6/5)(0;150°)B)
    1
  1590. (2-y)⁵+y⁵=32-80y+80y²-40y³+10y⁴ {√x=16-40y+40y²-20y³+5y⁴,√(x+32)=16-40y+40y²-20y³+5y⁴-y⁵; 0=y¹⁰-10y⁹+40y⁸-80y⁷+80y⁶-32y⁵-32 0,2+2(y-1)²+(y-1)⁴≥0 (y-1)((y-1)⁴+10(y-1)²+5)≤0 y≤1 y=1-√3,x=76²=5776{(5776;1-√3)}
    1
  1591. limx->0 1/(e^x/n+e^(2x)/n+...+e^(nx)/n)*(e^x/n+e^(2x)*2/n+...+e^(nx)/n*n)=1/n+2/n+...+1=(1/n+1)/2*n=(n+1)/2=9, n=17.
    1
  1592. cossinx*sincosx=-sinsinx*cosx*sincosx-cossinx*coscosx*sinx -cossinxsincosx+si nsinx*sinxsincosx+(2sinsinxsinx-cossimx)coscosxcosx
    1
  1593. 2(x+1/x)²+(a-2)(x+1/x)-2=0 x+1/x =(-a+2±√((a-2)²+16))/4 x=(-a+2±√((a-2)²+16))/8±√(2(a-2)²- 48±2(-a+2)√((a-2)²+16)))/8 -a+2<√((a-2)²+16),[a[2-√8;2],a>2; a[2-√8;∞)
    1
  1594. AE=AB-CE=AB-16+BD AG=√2/3AB DG=√(BD²-4/3BDAB+5/9AB²) EG=√(256-32BD+BD²-64/3AB+4/3BDAB+5/9AB²) DG²+EG²=(AB-BD)²+(AB-16+BD)² -8/9AB+32/3=0 AB=12 S=12²*0,5=72(cm²)
    1
  1595. √(32+6²)=√68=2√17 C)
    1
  1596. Самоубийство.
    1
  1597. 1+log√2√(x+4)+log0,5(13-x)/(|x²+2x-3|-|2x²-10x+8|)≥0 {x+4≥0, x+4>0,13-x>0,|x²+2x-3|-|2x²-10x +8|≠0;{x>-4,x<13,|x²+2x-3|≠|2x²-10x+8|;{xє(-4;13),х²+2х-3≠2х²-10х+8,х²+2х-3≠-2х²+10х-8;{xє(-4;13),-х²+12х-11≠0,3х²-8х+ 5≠0;{хє(-4;13),х≠(-12±√(144-4*1*-11))/-2, х≠(8±√(64-4*3*5))/6;{хє(-4;13),х≠1,х≠11, х≠5/3,х≠1;хє(-4;1)U(1;1 2/3)U(1 2/3;11)U (11;13) (1+log2(x+4)-log2(13-x))/(|x²+2x-3|-|2x²-10x+8|)≥0,log(2)(2(x+4)/(13-x))/|(x-1)(x+3)|-2|(x-1)(x-4)|)≥0, -4**1+*1 2/3+*11->x 2*5 2/3/(11 1/3)=10 4/3/(11 1/3)=1 xє(1;1 2/3)U(1 2/3;11)
    1
  1598. (2√х-х¹,⁵+х²)/(2-х)=0{[х=0,х¹,⁵-х+2=0; х≥0,х≠2;[х=0,{x⁰,⁵=1/3+(-26/27+√(26²/27²+(-1/3)³/27))^(1/3)-(26+15√3)) ^(1/3)/3~-1 259/1440;Хэ[0;2)U(2;∞);{0}
    1
  1599. 2√(rR) arctg√(R/r), arctg((r+R+2√(rR))/2/R) arctg(-√(r/R)-2)+π,?=90°+arctg(2+√(r/R))
    1
  1600. {y≥0,5,y²+0,25=x.
    1
  1601. S=π/4*12²-π/4*8²-(12+8)/2*4+π/4*8 ²-π/4*4²-(4+8)/2*4=32π-64
    1
  1602. 2-5a>0,a(0;2/5),lim=∞,a=2/5,lim=1,a(2/5;1),lim=0
    1
  1603. x=2±√2,y=2-+√2,x>y,(2+√2;2-√2) √2-1
    1
  1604. 6+х²=(12-4√х)/(2+х⁴)≥6,х≥1/9 -√х≥1,5х⁴≥0 х0,⁵≤0,х=0 6=12/2✓{0}
    1
  1605. S=9*15-3*6/2+9*6/2=135-9+27=153
    1
  1606. (a-1)²+(b-2)²=25 окружность с центром в точке (1;2) и радиусом 5
    1
  1607. y"-5y'+6y=x²+x,k²-5k+6=0,k=(5±√(25-4*6))/2[k=3,k=2;y0=c1e^2x+c2e^3x,yp=a0x²+a 1x+a2,2a0-5(2a0x+a1)+6(a0x²+a1x+a2)=x²+x,{6a0=1,-10a0+6a1=1,2a0-5a1+6a2 =0;{a0=1/6,a1=4/9,a2=17/54;yp=1/6x²+ 4/9x+17/54,y=c1e^2x+c2e^3x+1/6x²+4 /9x+17/54
    1
  1608. N>4,8 n=8,8*3=24 B)
    1
  1609. {√x=-+√y/2±√(-3/4y+a), 2a*-+*±√y*√(-3/4y+a)=b²-a²-ay,z=±√(xy);0=(b²-a²)²+(-2b²-2a²)ay+4a²y² y=(b²+a²±√((-b²+3a²)(3b²-a²)))/4/a {(0;0;0;0;0)(a;b;(√((b²+a²±√((-b²+3a ²)(3b²-a²)))/4/a)/2*-+*±√((-3/16b²+ 13/16a²-+3/16√((-b²+3a²)(3b²-a ²)))/a))²;(b²+a²±√((-b²+3a²)(3b²-a ²)))/4/a;(-√((b²+a²±√((-b²+3a²)(3b² -a²)))/4/a)/2±*±√(-3/4(b²+a²±√((-b² +3a²)(3b²-a²)))/4/a+a))√((b²+a²±√ ((-b²+3a²)(3b²-a²)))/4/a))}
    1
  1610. y=(14x-71)/(3x-17)=4+(2x-3)/(3x-17)\>4 2/3 x0=5 2/3 (6;13)(11;5 3/16)× x=14 (14;5) (4;3)4=4+(2x-3)/(3x-17),x=1,5×{(6; 13)(14;5/(4;3)}
    1
  1611. (x²+y²)(x+y-3)=2xy≤x²+y² x+y-3≤1 y≤4-x (0;3)(0;0)(3;0) {x+y=a,xy=b; (a-1)³+(-2b-3)(a-1)+2b-2=0 a-1=(-b+1+√((b-1)²+(-2b-3)³/27))¹/³+(-b+1-2√2√(-b(b²+1,125b+13,5))/3/√3)¹/³ D>0,b<0 D=0,b=0 уже рассматривал, D<0,b>0.0 a,b=(1+(2+√(10 7/27))¹/³+(2-√(107/27))¹/³;-1) 2 71/81 a-1=-2b+2,(a-1)²+(-2b+2)(a-1)+4b² -10b+1=0×(1;1)(4;4) [{y=1-x,-1+x-x²=0;{y=4-x,-4+4x-x²=0;x=2 y=2 {(0!0)(0;3)(3;0)(2;2)}
    1
  1612. ±5√5±13√5=±18√5 B)
    1
  1613. 2tg^3x+2tg²x-tgx-1=0 (tg²x-0,5)(tgx+1)=0 [tgx=±√0,5,tgx=-1;[x=±arctg√0,5+πn,x=-π/4+πn.
    1
  1614. sin²x=(-a+6±(a+2))/2=4;-a+2≥0,<1 a≤2,≥1; cs2x=-3+2a x=±0,5arccos(-3+2a)+πn
    1
  1615. {y=e^(2|x|),{x≠0,y≠0,a≠0, (|x|⁴+2a|x|²)e^(4|x|)=2-2a²; (4x⁴+4x³+8ax²+4ax)e^(4x)=0 x(x³+x²+2ax+a)=0[x=0,(x+1/3)³+(2a-1/3) (x+1/3)+1 2/3a-4/27=0;x=-1/3+(-5/6a+ 2/27+√(216a3+398,25a²-72a+3)/27)¹/³+(-5 /6a+2/27-√(216a³+398,25a²-72a+3)/27)¹/³ +0**+>x 0=2-2a²=>a=±1 ((-1/3+(-5/6a+2/27+√(216a3+398,25a²-72a+3)/27)¹/³+(-5/6a+2/27-√(216a³+398,25a²-7 2a+3)/27)¹/³)⁴+2a(-1/3+(-5/6a+2/27+√(2 16a3+398,25a²-72a+3)/27)¹/³+(-5/6a+2/ 27-√(216a³+398,25a²-72a+3)/27)¹/³)²)e^ (-4/3+4(-5/6a+2/27+√(216a3+398,25a² 72a+3)/27)¹/³+4(-5/6a+2/27-√(216a³+39 8,25a²-72a+3)/27)¹/³)=2-2a² -1/3+(-5/6a+ 2/27+√(216a3+398,25a²-72a+3)/27)¹/³+(-5/6a+2/27-√(216a³+398,25a²-72a+3)/27)¹/³<0 (-22,5a+2+√(216a3+398,25a²-7 2a+3))¹/³+(-22,5a+2-√(216a³+398,25a²-7 2a+3))¹/³<1 а<0,095
    1
  1616. {(x²/³+y²/³)²-2x²/³y²/³=17,(x²/³+y²/³)((x²/³+y²/³)²-3x²/³y²/³)=65;{x²/³+y²/³=a,x²/³y²/³=y;{b=0,5a²-17/2,a³-51a+130=0;a=(-65+√(65²-17³))¹/³+(..-..)..=2√17cos (1/3arccos(-65/17/√17)+2/3πn), b=34cos²(1/3arccos(-65/17/√17)+ 2/3πn)-8,5{y=±(√17cos(1/3arcco s(-65/17/√17)+2/3πn)-+√(-8,5cos (2/3arccos(-65/17/√17)+4/3πn))) ¹,⁵, x=±(√17cos(1/3arccos(-65/17/√17)+2/3πn)±√(-8,5cos(2/3arcco s(-65/17/√17)+4/3πn)))¹,⁵,n=0;2.
    1
  1617. cos2x=0,5 x=±π/6+πn
    1
  1618. (√5-√3)⁶=1792-494√15 3584✓
    1
  1619. (y+x²/4)'²-(y+x²/4)=1 (y+x²/4)'/√(y+x²/4) =±1, (y+x²/4)⁰,⁵/0,5=±x+c y=±0,5xc+0,25c ² y+x²/4=c1 -c1=1,c1=-1 y=-1-x²/4[y=±0,5x c+0,25c²,y=-x²/4-1
    1
  1620. (х-9+8/х)(х-6+8/х)=7 (х+8/х)²-15(х+8/х)+47=0 х+8/х=(15±√37)/2 х²-(7,5±√37/2)х +8=0 х=3,75±√37/4±√(33,5+15√37/2)/2
    1
  1621. 11/18R,11/18r r=7/11R R/√(R²+32 4)=1/18R R=0× R=3√(18±√203)≥5,5 7*2 5/9+23²/36²>7✓ S=99
    1
  1622. (8-R+(64-16r)^0.5)^2+r^2=(R+r)^2,(R-8)^2(32r+r^2)+32r(r+8)(R-8)+256r^2=0,R[0;8] R=8+(-16r+-16r(8^2-16r)^0,5)/(32+r^2) S=0,5r(8-R)=8r^2(1-+(64-16r)^0,5)/(32+r^2)
    1
  1623. ((x/3)³-1)³-(x/3+1/2)*16=0 3(((x/3) ³-1)²(x/3)²-16/9)=0 (x/3)³-x/3-+4/3 =0 min=-2/3/√3-4/3<0;-2/3/√3+4/ 3>0 x=3((2/3+√(11/3)/3)¹/³+(..-..)..) -*+>x min=(((2/3+√(11/3)/3)¹/³+(..-..)..)³-1)³-16((2/3+√(11/3)/3)¹/³+(..-..)..)-8~-25<0 x=(1+√5)/2;-1
    1
  1624. (√7+1)(√3-√2)=√21-√14+√3-√2
    1
  1625. (M-1/3)³-1/3(m-1/3)-47/64/27=0 m-1/3=(47/128+√((47/128)²-1))¹/³/3+(..-..)..=2/3cos(1/3arccos(47/12 8)+2/3πn) m=1/3+2/3cos(1/3arccos(47/12 8)+2/3πn)
    1
  1626. S=50/8-25√2+25√2-25=-24,75
    1
  1627. Т°6;8 и+2о=0,к=3;8≥6 к=8 и=о=0× и+2о=21,к=2≤4 о[6;9],(3;9)×(5:8)× (9;6)✓{9}
    1
  1628. x¹/⁶=(-5±13)/4=2;-9/2>=0 x=64
    1
  1629. {a<3log(3)x,ax≥9,|x-9|+|x-27|≤18; ОДЗ:x>0,{{a<3log(3)x,a≥9,[{x-9+x-27≤18,х≥27,{х-9-х+27≤18,хє[9;27){-х+9-х+27≤18;х<9;{9<3log(3)x,a≥9,[{2x≤54,х≥27,{18≤18,хє[9;27){-2х≤-18;х<9;{3³<x,a≥9,[x=27,[9;27)0/;{а≥9,х>27,хє[9;2 7] 0/
    1
  1630. log(1/7)log3((|-x+1|+|x+1|)/(2x+1))≥0, 0<log3((|-x+1|+|x+1|)/(2x+1))≤1,{(|-x+1|+|x+1|)/(2x+1)≤3,(|-x+1|+|x+1|)/(2x+1)>1; +;-1+;+*1-;+>x [{(x-1+x+1)/(2x+1)≤3,(x-1|x+1)/(2x+1)>1,x≥1,{(-x+1+x+1)/(2x+1)≤3,(-x+1+x+1)/(2x+1)>1,xє[-1;1){(-x+1-x-1)/(2x+1)≤3,(-x+1-x-1)/(2x+1)>1,х<-1;[{2х/2/(x+0,5)-3≤0,2x/2/(x+0,5)-1>0,x≥1,{2/2/(x+1/2)≤3,2/2/(x+0,5)-1>0,xє[-1;1){-2х/(2x+1)-3≤0,-2х/(2x+1)-1>0,х<-1;[{(х-3х-1,5)/(x+0,5)≤0,(x-х-0,5)/(x+0,5)>0,x≥1,{(1-3х-1,5)/(x+1/2)≤0,(1-х-0,5)/(x+0,5)>0,xє[-1;1){(-х-3х-3/2)/(x+0,5)≤0,(-х-х-0,5)/(x+1/2)>0,х<-1;[{(х+0,75)/(x+0,5)≥0,+-°+>х x+0,5<0,x≥1,{(х+1/6)/(x+1/2)≥0,+°*+>х(х-0,5)/(x+0,5)<0,+°-*+>хxє[-1;1){(х+3/8)/(x+0,5)≥0,+°-*+>х,(х+0,25)/(x+1/2)<0,+°-*+>хх<-1;[{хє(-∞;-0,75]U(-0,5;+∞),x<-0,5,x≥1,{xє(-∞;-0,5)U[-1/6;+∞)xє(-0,5;0,5)xє[-1;1){хє(-∞;-0,5)U[-3/8;+∞),xє(-0,5;-0,25),х<-1;[0/,хє[-1/6;0,5),0/, хє[-1/6;+0,5)
    1
  1631. 54^х√3^((5х-10)/(х+2))/√(2х+9)≤81*2^х*(2х+9)^-0,5/3^((х-2)/(х+2)),2^х3^(3х)*3^((2,5х-5)/(х+2))/√(2х+9)-81*2^х/√(2х+9)3^(-(х-2)/(х+2))≤0,2^х*3^(-(х-2)/(х+2))(3^(3х+3,5 (х-2)/(х+2))-81)/√(2х+9)≤0, {3^((3х²+6х+3,5х-7)/(х+2))-81≤0,2х+9>0;{(3х²+9,5х-7)/(х+2)≤4, х>-4,5;{(3х²+9,5х-7-4х-8)/(х+2)≤0(1),х>-4,5;(1) (3х²+5,5х-15)/(х+2)≤0,(х-(-5,5+√(5,5²-4*3 15))/6)(х-(-11/12-√(30,25+120 30)/6)/(х+2)≤0,-11/12-√180,25+*2-*-11/12+√180,25/6+>х хє(-∞;-11/12-√180,25/6]U(-2;-11/12+√180,25/6],x>-4,5 xє(-4,5;-11/12-√180,25/6]U (-2;-11/12+√180,25/6] 180,25=13,..2 1/6\2+11/12=2 13/12, 2 1/6\2-11/12=1 3/12
    1
  1632. 3(x+1)²=(x+1)(x-11)[x=-1,x=-7.
    1
  1633. y=π/2-arctg((a-2x)/2/√(ax-x²)) y'=1/(ax-x²)⁰,⁵
    1
  1634. $(0;π/3)tg⁷odo=1/6tg⁶o-1/4tg⁴o+1 /2tg²o+ln|coso|(0;π/3)=3,75+ln0,5
    1
  1635. {-x²-2x+3≤0,-2x²-3x+27>0;{(x-1)(x+3)≥0 +*-*+>x (x+4,5)(x-3)<0+°-°+>x;{x(-∞;-3]U [1;∞),x(-4,5;3);x(-4,5;3]U[1;3)
    1
  1636. {1/3x'-2/3x=y,x''-3x'-10x=0;k²-3k-10=0 k=(3±√49)/2=5;-2 x=c1e^(5t)+c2e ^(-2t) y=c1e^(5t)-4/3c2e^(-2t)✓
    1
  1637. x=y✓,x≠y (x¹/³-y¹/³)²≥0✓
    1
  1638.  @alexanderburov3253  не в 40, а в 16.
    1
  1639. N(n-1)*2^(N-2)+2n*2^(n-1)=n*2^(n-2)(n+3)
    1
  1640. √(1-x)=y x=1-y² dx=-2ydy $(0;1)2dy/(1+y²)=2arctgy(0;1)=π/2
    1
  1641. En=0;∞(-1)^n/(2n+1)!*(1/2)^(2n+ 1)/80/π=sin0,5/80/π
    1
  1642. (-1)*2=-2
    1
  1643. 0,5 3,1,3,1,3,1
    1
  1644. 2+2/3√3 S=2+2/3√3(m²)
    1
  1645. ln(4^log(48)(30√5)n^log(48)(5/8√5)/5)/ln(5n)/ln(4n)≥0-°1/5+°1/4-*(5/4^log48 (30√5))^log (5/8√5)48+>n,nє(1/5;1/4)U [(5/4^log48(30√5))^log(5/8√5)48;∞)
    1
  1646. 100'060'004
    1
  1647. √y=5,√x=5{(25;25)}
    1
  1648. R/sin35°sin15°=OE R/sin35°sin15 °/sin15°=R/sin(180°-a) 35°(-1)^n+ 180°n=a,a(15;160°) a=35°;145° B)
    1
  1649. 2√3/sin100°sin60°*2cos10°=6
    1
  1650. √((8+√24)²+5²)=√(113+32√6)
    1
  1651. X+y+1=xy,-xy+x+y+1=0, -x(y-1)+y-1=-2, (y-1)(-x+1)=-2,{y-1=1,-x+1=-2;{y-1=2,-x+1 =1;{y-1=-1,-x+1=2;{y-1=-2,-x+1=1; {y=2,x=3;{y=3,x=0;{y=0,x=-1;{y=-1,x=0;(2;3)(3;2)
    1
  1652. (10-x/2)²+(10-x)²=10² 100-30x+5x²/4=0 x=(30±20)/2,5=20;4<10 x=4 {16m²}
    1
  1653. c=6, 7a+b=40, ae[31/7;40/7]a=5 b=5, 556
    1
  1654. r/(15-r)=8/17, 17r=120-8r, r=120/25=4,8
    1
  1655. (a-c)x+(b-c)y≥(b-c)(x+y)=-(b-c)z≥0
    1
  1656. Никакая эта пропаганда.
    1
  1657. x=(7-3√5)/2 S=1/(1-x)=(5+3√5)/10
    1
  1658. 5n=15*ab*3367 b:/2
    1
  1659. 50+2*50*2/3+2*50*(2/3)²+..=50+200=250(m)
    1
  1660. a∞=3;-1 a(n+1)=(4an+3)/(an+2)=4-5/(an +2)\> a1{-1}U(3;∞),a∞=-1, a1(-1;3],a∞= 3,a1<-1,0/
    1
  1661. z⁴+3z³-2z²-6z+4=0,z=1, z³+4z²+2z-4=0, z=-2, z²+2z-2=0, z=(-2±√(4-4*(-2)))/2=-1±√3,
    1
  1662. -2x²+(3-a)x+9|x|+a²-6a=0 [{x=a/2, a≥0;{x=-a+6,a≤6;{a>0,x=-a;{a<6,x=-3+a/2.
    1
  1663. }x≤1,-63,5=x;{-63,5}
    1
  1664. {(x+y)/45=0,52,x/25+y/20=0,53;{x+y=23,4,-0,25y=10,15;{x=64,y=-40,6;
    1
  1665. (y1-8)²+(y2-6)²=9 y1[5;11],x1[-2;2] z=(x1+y1)/2+0,5(±√(4-x1²)±(6+√(9- (y1-8)²)))i
    1
  1666. f(0)/f'(0)t+f(0)=f(x) f(0)=f'²(0) f'(0)t+(f'(0))²=f(x)✓
    1
  1667. (x-1,5)⁴-11,5(x-1,5)²+75(x-1,5)+10 11/16=0 z³-23/4z²+179/32z-5625/64=0 z=-0.534797451064311+3.5499219185585*i;6.81959490211297 x=1,5-√6.81959490211297±2√(0,5√(0.534797451064311²+3.5499219185585²)-0.267398725532156)
    1
  1668. {6x²-5xy+y²+x-y-2=0,y=ax-5; (6-5a+a²)x²+(26-11a)x+28=0 a²-5a+6=0,a=2;3[x=-7,x=5,6; a≠2,a≠3 x=(-26+11a±(3a-2))/2/(a²-5a+6)=7/(a-3);4/(a-2) y=(2a+15)/(a-3);(-a+1 0)/(a-2)✓{(2;-7;-19)(3;5,6;11,8)(aR \{2}\{3};7/(a-3);(2a+15)/(a-3))(aR\ {2}\{3};4/(a-2);(-a+10)/(a-2)}
    1
  1669. a+c+d-e-h a,b,c,d e,a-d+e+f-g h,f,g,a+b+c+d-f-g-h b+c+d-e-f a+c-g=h a+b+c+d=22 4 1,2,7,12 e=11 11,5 f=8 5,8,3,6 g=3 2 Можно, только не получилось.
    1
  1670. 5sin37° S∆=10sin37°*10cos37°*0,5=25sin74°
    1
  1671. n=±√(m²+6m),m=0;-6 n=0 m[-8;2] m=-8,n=±4 m=2,n=±4{(2;4)}
    1
  1672. π(4²-3²)*30/360=7π/12cm²
    1
  1673. А зачем Олег Ермолов закрепляет откровенно вредные комментарии?
    1
  1674. X[π/6+2πm;5/6π+2πm]U(7/6π+2π m;11/6π+2πm),mєZ ряд расходится условно и абсолютно x(5/6π+2πm;7/6π+2πm]U[11/6π+2πm;13/6π+2πm),mєZ ряд сходится абсолютно и условно
    1
  1675. х=1,х²+3х+3=0×{1}
    1
  1676. ab=-1/2 42 3/16+1/32=42 7/32
    1
  1677. DC=16cos/_C BO2=2√(25cos²15°+16+40 cos15°cos/_C) BO2=√((10cos15°)²+8²+16 0cos15°cos/_C)✓ 0=0 S∆BCO2=40cos15 °cos15°+64cos²15°=26√3+52
    1
  1678. у=4х/(х-2)/3=4/3(1+2/(х-2)) х=3n n=1;2;0;-1;-2 x=3;6;0;-6 y=4;2;0;1{(3;4)(6;2)(-6;1)}
    1
  1679. X>0 \>=/> (7+5√2)^x-¹=x³ x(1,5;2)(3+2√2?27/8) x=1,69..✓
    1
  1680. I(1-i)=1+i z=3(ln²√2+π²(1/4+2/3n)(1/4+2m)+i*πln2(1/3n-m))/(ln²√2+(π/4+2πm)²)
    1
  1681. {z=1-x-y,x=(1-y±√(-3y²+2y+9))/2, [y=0,y=2,y=-1;{(2;0;-1)(-1;0;2)(0;2;-1)(-1;0;2)(2;-1;0)(0;-1;2)}
    1
  1682. z=-i
    1
  1683. Мне кажется или телеведущий похож на Азаренко?
    1
  1684. (1-b)/a=(1-c)/b=c/(1-a) a=(1-b)b/(1 -c),1-c-b(1+c)+b²=0, a=(-2+3c+c²±c√(-3+6c+c²))/2/(c-1) b=(1+c±√(-3+6c+c²))/2 -√(2-4c-6c²+6c³+4c⁴±2(-1+c+2c³)√(-3+6c+c²))/2/(c-1)-1/(c-1)/2√(2+6c² ±2(1+c)√(-3+6c+c²))≥1,5√2,c[0;1] (9c³+20c⁴)/(1+3c²)-6c²-2c+1×
    1
  1685. B²+3b-40=0 b=(-3±13)/2=5 125✓
    1
  1686. x,y,w>0,x,y≠1,z>0,z≠1/(xy) logw(x)=1/24,logw(y)=1/40,logw(xyz)=1/12 logw(z)=1/60 logz(w)=60
    1
  1687. 15 шт. i-1+i+..+i=8i-7✓
    1
  1688. S=1/3πR²+R²√3/4 p=1/3+√3/4/π
    1
  1689. X¹⁰-2525x⁵+1=0 x=((2525±551√21)/2)¹/⁵ 2525¹/⁵=4,.. √733/2-25/4=a× ((2525+551√21)/2)⁴/⁵/((2525+551 √21)/2)⁸/⁵+1)
    1
  1690. y'/y=2x+1/x y=e^x²*xc y(1)=1 y=e^x²*x/e
    1
  1691. {XO²+ON²/4=361,XO²/4+ON²=484; XO²+ON²=169*4 XY=26
    1
  1692. (x-2/27)³-4/243(x-2/27)-259/3⁹=0 x=2/27+(259/2+45√33/2)¹/³/27+(..-..)..=1/3✓
    1
  1693. 8/13a+15=a a=39 S∆=45
    1
  1694. amF/M/I=t,I=1 A t=0,6552(с)
    1
  1695. У Вас всё-таки есть ирония в видео.
    1
  1696. 2(2cos²ф-1)²-1=8cos⁴ф-8cosф+1 sin4ф=4sinфcosф(2cosф²-1)
    1
  1697. X1+x2=5/3,x1x2=1/3 ((a+b)²-2ab)/(ab)²=19/25B)
    1
  1698. √-lnx=u x=e^-u² dx=e^-u²*-2udu $(0;1)√-lnxdx=$(0;∞)e^-u2*2u²du=-ue^-u²+√πФ(√2*u)(0;∞)=0,5√π
    1
  1699. S=12√3-4π m²
    1
  1700. 1251'000*23663=29'602'413'000 руб.
    1
  1701. a1a(n-1)/a0/an≥n² 1≥1,(-0,25a1²/a0+a2)/a2≤0 a2(0;0,25a1²/a0], (-1/9a1a2/a0+a3)/a3≤0 a3(0;1/36a1³/a0²], an(0;1/n!²a1^n/a0 ^(n-1)]
    1
  1702. (a-R)²+(b-R)²=R² a=R+√(2bR-b²) cos(45°-arctg(√(2bR-b²)/b))=5/√ (2bR) b[0;5√2],R=(25-5√2b+b²)/b ab=(25/b)b=25
    1
  1703. 4х-2^х=0 4-2^xln2=0 x=log2(4/ln2) +*->x max=4log2(4/ln2/e)>0 x=4;0,31
    1
  1704. √x+√y=5√2, (0;50),(50;0),(2;32),(32;2),(8;18),(18;8)
    1
  1705. [х+1/2]=1/2х⁶-[х] 1/2х⁶єZ x:2,x=2n [2n+1/2]=1/2(2n)⁶-[2n] 2n-32n⁶+2n=0, 32n(n⁵-1/8)=0, n=0, n=1/8^(0,2) {x}є[0;0,5) 2[х]-0,5х⁶=0,≤2х-0,5х⁶,>2(х-1)-0, 5х⁶ {-0,5х(х⁵-4)≥0,*+*4⁰,²->х-0,5х⁶-2х-2<0;{хє(-∞;0]U[4⁰,²;+∞),x⁶+4x+4>0;{хє(-∞;0]U[4⁰,²;+∞),xєR, xє[m;m+0,5)U[4⁰,²;1,5)U[m;m+0,5),х=4^(1/6) 6х⁵+4=0,х=(-4/6)^(1/5)=-(2/3)⁰,² 2/3(2/3) ⁰,²-4*(2/3)⁰,²+4=-3 1/3(2/3)⁰,²+4>0
    1
  1706. 3²⁶:5=3²:5=ост.4 26:4=6(ост.2)
    1
  1707. an=-5,75*2^n+8n+2
    1
  1708. √(38+2*6)=5√2,x=5
    1
  1709. h=ab/√(a²+b²) ..=a²/√(a²+b²) (a²/√ (a²+b²)-1)²+a²b²/(a²+b²)=16,(b²/√ (a²+b²)+1)²+a²b²/(a²+b²)=16 A²/√(a²+b²)-1=±(b²/√(a²+b²)+1) [(A²-b²)/√{a²+b²)=2,√(a²+b²)=0; a⁴-a²(2b²+4)+b⁴-4b²=0 a²=b²+2±2√(2b²+1)≥0 -=>b{0}U[2;∞) 2(√(2b²+1)-+1)b²+ b⁶+22b⁴+11b²+16±(5b⁴+25b²+16)√(2b²+1)=0 [b⁶+22b⁴+9b²+16+(5b⁴+27b²+16)√(2b²+1)=0×,b¹⁰-6b⁸+25b⁶-1004b⁴-1288b²-832=0;b=3,44≥0 a=1,97 S∆=0,5*3,44*1,97=3,39
    1
  1710. (2x+y/(1+x²y²))dx+(x/(1+x²y²)-2y)dy=0, y'(x/(1+x²y²)-2y)+2x+y/(1+x²y²)=0,
    1
  1711. (y+x)dy-(y-x)dx=0,y+x=u,y'+1=u',u(u'-1)dx-(u-2x)dx=0,uu'-2u+2x=0,u0u0'-2u0=0,u0'-2=0,u0=2x+c,up=kx+b,(kx+b)k-2(kx+b)+2x =0,x(k²-2k+2)+bk-2b=0,{k²-2k+2=0,bk-2b =0;{k=1±√-1,[b=0,k=2;{k=1±√-1,b=0;u=2x+ c+(1±√-1)x y=(2±√-1)x+c
    1
  1712. 2x-5y-8=0 2x-5y+c=0 2*3-5*-1+c=0,c=-11 2x-5y-11=0
    1
  1713. $-dx/(x-1)/(1+x²) -1=A(x²+1)+B(x-1)*2x+C(x-1) {A+2B=0,-2B+C=0,2B+C=1;
    1
  1714. 2π(2sin2+cos2-1)
    1
  1715. y³-3x²y+2x3-16=0 y=(-x³+8+4√(-x³+4))¹/³+(..-..)..{(-1;3)(5;6)(2;0)}
    1
  1716. ydy/(2+y²)=dx*x/(4+x²) (2+y²)e^2c=4+x²✓
    1
  1717. √(81-r²) (√(81-r²)-r)²=4*9 √(81-r²)-r=6 0=2r²+12r-45 r=-3+√116/2 S=(-6+√116)√((43+√805)/2)+√ ((43-√805)/2))
    1
  1718. х²=а(а+10) а=-5+√(х²+25) х/(2,5 +0,5√(х²+25))=х/√(х²+25) 0=х
    1
  1719. 2^(x+1)+2^(1/x²)=6 2^(1+x-²)(x³* 2^(x-x-²)-1)x-³ln2=0,x>0 x³*2^(x-x²)=1 x=1 x²*2^(x-x²)(3+ln2* x-2x²ln2)=0 x=0;1/4±√(ln2+24)/(4√ ln2)-*-..+*0+*+..->x max=(1/4+√(ln2+24)/(4√ln2))³*2^ (1/4+√(ln2+24)/(4√ln2)-(1/4+√(ln2 +24)/(4√ln2))³)~75/94/1,19/1,37 -*1+*1,45->x min=2²+2=6 max=4*1,41⁰,⁹+2^(400/841)>6 x=-0,6{1;-0,6}
    1
  1720. √(3,5²+2²)=√16,25
    1
  1721. {b=√5-a,a(√5-a)=1;-a²+√5a-1=0 a=(√5±1)/2,b=(√5-+1)/2
    1
  1722. {(-2,4;5,25;-15/7)(1;1;10)(-2;7;-2)}
    1
  1723. 0,5(x-14)/(x-14,5)✓
    1
  1724. c=6270/(ab(6a²+2ab+3b²)),a,b,c≥2 a=10,c=627/(b(600+20b+3b²))× a=11,c=570/(b(726+22b+3b²)×
    1
  1725. 64*4/5=256/5
    1
  1726. [{x≥3-5=5;{x[-2;3),x=-2;{x<-2,5=5; x(-∞;-2]
    1
  1727. {b≤30-a,b=17-a,[a=12,a=5;c=13
    1
  1728. 1-4log2(x)+3log²2(x)=0 log2(x)=1;1/3 x=2;2¹/³
    1
  1729. 5tg(45°-Arctg(3/5))=5/4(cm)
    1
  1730. 4,5x(1-x)(-1;1) x(1/2-√17/6;1/3)U(2/3;1/2+√17/6) сходится и абсолютно, и условно х(-=;1/2-√17/6)U(1/3;2/3)U(1/2+√17/6;=) расходится абсолютно n≥1;n(-1)^n расходится и абсолютно,и условно n≥1;n*4,5^n аналогично, аналогично, аналогично абсолютно сходится при х(1/2-√17/6;1/3)U(2/3;1/2+√17/6), абсолютно расходится хє(-=;1/2-√17/6]U[1/3;2/3]U[1/2+√17/6;≠), условно сходится х(1/2-√17/6;1/3)U(2/3;1/2+√17/6), условно расходится х(-∞;1/2-√17/6]U[1/3;2/3]U[1/2+√17/6;=)
    1
  1731. x=21,36;18,64 E=40
    1
  1732. -1+2x²/(x²-c)=y
    1
  1733. 2+cos(4a)-cos(2a)=sin(4a)+sin(2a) tga=t,[t=1,t=1/6+(73+6√89)¹/³/6+(..-..)..,t=-0,5+(3+2√183/9)¹/³/2+(..-..)..;a(0;60°),t(0;√3)(t+1/6)³-1/12(t+1/6)-53/108=0 t=-1/6+(53+6√78)¹/³/6+(..-..)..✓ a=45°;arctg(1/6+(73+6√89)¹/³/6+(..-..)..);arctg(-0,5+(3+2√183/9)¹/³/2+(..-..)..)
    1
  1734. f=2x⁵-30x⁴+170x³-449x²+548x-241 f(6)=84*6-241=263
    1
  1735. 37/x=11/x(3-121/x²)/(1-363/x²) x=55
    1
  1736. Нарушение технологии. Вот и всё.
    1
  1737. √3*5 √3*6 r/sin30°=10/sina=x/sin(180°-30°-a) r/sin30°=12/sinb=x/sin(180°-30-b) a=arcsin(5/r)(-1)^n+πn 2r=x/sin(150°-a)=x/(0,5cosa+√3/2*sina) =x/(±0,5√(1-25/r²)+√3/2*5/r),x=±√(r²-25)+5√3 b=arcsin(6/r)(-1)^n+πn 2r=x/sin(150°-b)=(±√(r²-25) +5√3)/(0,5cosb+√3/2*sinb)=(±√(r²-25) +5√3)/(±0,5√(1-36/r²)+√3/2*6/r) ±√(r²-36)+6√3=±√(r²-25)+5√3, ±√(r²-36)-+√(r²-25)=-√3, r>0,r≥6 r²-36±2√(r²-36)(r2-25)+r2-25=3, ±2√(r²-36)(r²-25)=-2r²+64≤-8 4(r⁴-25r²-36r²+900)=4r⁴-256r²+64², r²=a, 4a²-244a+3600-4a²+256a-64²=0, 12a=-3600+3600+480+16, a=496/12=41 1/3 r=√41 1/3
    1
  1738. -cosx-x-tg(x/2-π/4)+c
    1
  1739. (x-3)²+(y+4)²=25-k k≤25,r(4;6) ..(16;36),k(-11;9)✓
    1
  1740. 5=r*2+2r+3r=7r r=5/7
    1
  1741. гл(а)(а).. Нет б,е,и,й,к,п,р,с,т,у,ф,ы. Гладь!
    1
  1742. 9996-200x+x²=0 x=100±2=102;98✓
    1
  1743. 2*4^x=2^x 2^x=0,5,x=-1
    1
  1744. 2pq/(p+q),(p+q)/2 pq/(2pq/(p+q)+(p+q)/2) r+t=>r(r+t)/(2r+t) pq/(2pq/(p+q)+(p+q)/2)*r(r+t)/(2r+t)/(pq/(2 pq/(p+q)+(p+q)/2)+r(r+t)/(2r+t))✓
    1
  1745. b=√(400/√3-a²) ab√3/4+√3/4((b-a)² *3/4+(a+b)²/4)=√3/4(a²+b²)=100
    1
  1746. 8^2016²⁰²¹:100=4(2^(3*2016²⁰²¹-2):25) 25(1-1/5)=20 12*4⁴⁰⁴¹-2:20,4⁴⁰⁴¹:5,4¹:5, 12*56-2=670=10 4*24=96
    1
  1747. (-h²/x²)/h²=-1/x²
    1
  1748. х²/4-3х+8=0 х=(3±1)/0,5=8;4
    1
  1749. (х-0,5-√(15,25+10√2)(х-0,5+√(15,25+ 10√2))<0+°-°+>х хє(0,5-√(15,25+10√2);0,5 +√(15,25+10√2))
    1
  1750. A=b+5,3(b+5)x²+2(b-1)x+1>0{b>-5,(b-7)(b+2)≤0;b[-2;7] (3+7)/2*5=25
    1
  1751. Сделать общенациональной собственностью.
    1
  1752. {√a=12,√b=5;{(144;25)}
    1
  1753. $(-1;1)x²dx/(1+e^x)=$(1;-1)x²d-x/(1+e^-x) =$(-1;1)x²e^xdx/(e^x+1) 2$(-1;1)x²dx/(1+e^x)=$(-1;1)x²dx=x³/3(-1;1)=1/3-(-1/3) =2/3 $(-1;1)x²dx/(1+e^x)=1/3
    1
  1754. B=7a/(a-7)=7+49/(a-7) (8;56)(14;14)(56;8)(6;-42)(-42;6){64;28;-36}
    1
  1755. $(0;π/4)(2cos²0,5x-1)ln(1-2sin²0,5x) dx=2√(1+√2/2)ln(2√2-1+2√(2-√2))- $((2cos²0,5x-1+√2sin0,5x)ln(1-√2 sin0,5x)+(-√2sin0,5x+2-cosx)ln(1+√ 2sin0,5x))dx(0;π/4)-π/4-√2/2+√2ln (√2/2)
    1
  1756. X≥0 0=x2-2x-15 x=1±4=5;-3{5} S∆1=0,5*2*(√2)=√2(m²){2√2m²}
    1
  1757. 2/(x-1)=3/(4-x) 8-2x=3x-3,2,2=x S∆=(2+3)/2*3-0,5*1,2*2-0,5*1,8*3= 7,5-1,2-2,7=3,6 S(1,8;6) 1,8*6²=64,8(4)
    1
  1758. x=lnk-*+>x min=k-klnk=0 k=0×;e
    1
  1759. 8⁸/2=2²³=2^(3x) x=23/3
    1
  1760. 8^x*-1/8=-8 x=2
    1
  1761. (1-c)²-3ab=1+c ab=-c+c²/3 {b=1-c-a,a(1- c-a)=-c+c²/3; -a²+a(1-c)+c-c²/3=0 a=(1-c ±√(1+2c-c²/3))/2 b=(1-c-+√(1+2c-c²/3))/2 (c-3-√12)(c-3+√12)≤0 c[3-√12;3+√12]
    1
  1762. c=3c1 4=3(c1-1)²+n² c1-1[-1;1] c1=0;1;2 n=1;2;1 c=0;3;6 a=1;0 a=0;-2 a=-2;-3 b=0;1 b=-2;0 b=-3;-2 {(0;1)(1;0)(0;-2)(-2;-3)(-3;-2)}
    1
  1763. Тонкий намек на Понасенкова.
    1
  1764. (x²+4x-45)/(x²-25)=0 x=-2±7=5;-9{-9}
    1
  1765. (5x-8)(3x+5)=(x-1)(14x+12) x²+3x-28=0 x=(-3±11)/2=4;-7{4;-7}
    1
  1766. 81=(x+1)² x+1=±9{8;-10}
    1
  1767. (3;9)(4;5) Максимум=9/20{(4;5)}
    1
  1768. arcsin(3/5)=/_C
    1
  1769. {PQ²+PS²-PQPS=100,1,3(PQ²-PS²+100)/(26PQ-10PS)=cos/_1; S=π(2,06PQ²+100±PQ√(100-3/4P Q²)-1,6PQ²(PQ/2±√(100-3/4PQ²))* 1,3(1,5PQ-+√(100-3/4PQ²)))/(10,5PQ-+5√(100-3/4PQ²)))/4/(1-1,3²PQ²(1,5PQ-+√(100-3/4PQ²)) ²/4/(10,5PQ-+5√(100-3/4PQ²))²)
    1
  1770. 8√2/√3/(√2/2)*1/2=8/√3
    1
  1771. 75°,h=2,5√6-2,5√2,a=2,5√2+2,5√6 60°,(x; x√3) 2,5√6-2,5√2+√3x=2,5√6+2,5√2-x x= 2,5(√6-√2) S=25/2+37,5=50
    1
  1772. (35-x³)¹/³=b{x(5-x)=6,b=5-x; x²-5x+6=0 x=2;3✓
    1
  1773. 0:45 это про мою мать!(А иногда и про отца)
    1
  1774. πR²/4/(π/√3²R²/2)=1,5
    1
  1775. {x=2±√(1/3y²-4/3y+1/3),10/3y²-13 1/3y+ 3 1/3=0;y=2±√3 x=2 (2;2±√3)
    1
  1776. {z=9-x-y,x=(-y+9±√(-3y²+18y-15))/2; y[1;5] y=1;5;2;4 x=4;2;5;2;4;1 z=4;2;2;5;1;4{(4;1;4)(2;5;2)(5;2;2)(2;2;5)(4;4;1)(1;4;4)}
    1
  1777. √(x²-16²)+4=x x≥16,30=x✓
    1
  1778. 1+2^х+2^(2х+1)=у², х,уєZ [у>1, у<-1; (1+2^х*0,5)²+2^(2х)*1,75=у², х<0, ((2^(-х)+0,5)²+1,75)/2^(-2х)\>1, при х=0, 4=у², у=±2, ((2^(-х)+0,5)²+1,75)/2^(-2х) будет равняться (1;4), а на этом промежутке квадратов целых чисел нет. х=1, 1+2+ 2³=11, у=+√11, х=2, 1+2²+2⁵=5+32=37, у= ±√37, х=3, 1+2³+2⁷=9+128=137, у=±√137, 1+2^х+2^(2х+1)-1-2^х1-2^(2х1+1)=у²-у1²>0, 2^х1(2^(х-х1)+2^(2х+1-х1)-1-2^(х1+1)) =(у-у1)(у+у1),:/2,:4, х1≥2, потому что скобка не кратна 2, а значит взаимно проста со степенью, НОД(у1,(у-у1)/2)=1, иначе решений нет. 1+2+8=11 равноостаточно с простым числом, а квадрат целого числа не может давать остаток как у 11 при делении на простое число:11:3=3(ост.2)х=3, 0^2=0,1²=1,2²==1, короче говоря, при х>0 решений нет.
    1
  1779. 72+3(52+х)¹/³(20-х)¹/³*6=6³ 1040-32х-х²=8³ -х²-32х+528=0 х=-16±28=12;-44
    1
  1780. y"+4y=5e^-x k²+4=0 k=±2i y0=c1sin2x+c2 cos2x y=c3e^-x c3e^-x+4c3e^-x=5e^-x,c3= 1 yp=e^-x y=c1sin2x+c2cos2x+e^-x
    1
  1781. 1+limk->∞2/kln(1+e^(-k))=1
    1
  1782. x=±1/x+2πn x²-2πnx-+1=0 x=πn±√(π²n²±1) nZ,nZ\{0}
    1
  1783. Это аннунаки с планеты Нибиру.
    1
  1784. (a-1 1/62b)³-375/62²b²(a-1 1/62b)-787 5/62²/31b³=0 a-1 1/62b=5((126+√(126 ²-125))¹/³+(126-√(126²-125))¹/³)/62b D>0 a=(63+5(126+√(126²-125))¹/³+(126-√(1 26²-125))¹/³)/62b
    1
  1785. S=R²π/12 R=6√(3,14/π)~6(cm)
    1
  1786. v,км/ч|t,ч|s,км в.|s/t|t|s м.|s/(t-4)|t-4|s в.+м.|s/t+s/(t-4)|1,5|s 0=t²-7t+6,t=1;6≥4 t=6(ч)
    1
  1787. {y=2-+√20i,x=2±√20i;{(2±√20i;2-+√20i)}
    1
  1788. log(1/3)(x²-3x-1)+log(1/3)(2x²-3x-2)≤log (1/3)(x²-2x-1)²+log3(4)-2,{-log(3)(x²-3x-1) log(3)(2x²-3x-2)+log(3)(x²-2x-1)²-log3(4) +2≤0,(x-(3+√13)/2)(x-(3-√13)/2)>0,+(3 √13)/2°-(3+√13)/2°+>x(x-2)(x+0,5)>0, -0,5+°-°+2>x x≠1±√2;{log3((x²-2x-1)²/(x²-3x-1)/(2x²-3x-2)/4*3²)≤0,хє(-∞;(3-√ 13)/2)U((3+√13)/2;∞),хє(-∞;-0,5)U(2;∞), x≠1±√2;{9(x²-2x-1)²/(x²-3x-1)/(2x²-3x-2)/4≤1,хє(-∞;-0,5)U((3+√13)/2;∞);{(x⁴-2x² +1)/(x-(3+√13)/2)/(x-(3-√13)/2)/(x-2)/(x+0,5)≤0, хє(-∞;-0,5)U((3+√13)/2;∞);{(x-1)²(X+1)²/(x-(3+√13)/2)/(x-(3-√13)/2)/(x-2)/(x+0,5)≤0,+*-1+°-0,5-°(3-√13)/2+*1+°2-°(3+√13)/2+>x хє(-∞;-0,5)U((3+ √13)/2;∞);{хє{-1}U(-0,5;(3-√13)/2)U{1}U (2;(3+√13)/2),хє(-∞;-0,5)U((3-√13)/2;∞);хє{-1}U{1}U(2;(3+√13)/2)
    1
  1789. 50+5=55
    1
  1790. {(х+у)(х²+у²)=65,(х-у)(х²-у²)=5;{х³+ху²+х² у+у³=65,х³-ху²-х²у+у³=5;{х³+у³=35,ху²+х²у =30;{(х+у)(х²-ху+у²)=35,Ху(х+у)=30;{(х+у) ³=125,Ху(х+у)=30;{х+у=5,Ху=6;{у=5-х,5х -х²=6;-х²+5х-6=0,х=(-6±√(25-4*-1*-6))/-2,[х=2,х=3;[у=3,у=2;
    1
  1791. L^-1{1/s⁴/(s-1)}=-1-1/6t³+e^t A/s+B/s²+C/s³+D/s⁴+E/(s-1)=1/s⁴/(s-1),A s3(s-1)+Bs²(s-1)+Cs(s-1)+D(s-1)+Es⁴=1,As⁴-As+Bs³-Bs²+Cs²-Cs+Ds-D+Es⁴=1,{A+E =0,B=0,-B+C=0,-A-C+D=0,-D=1;{A+E=0,B= 0,C=0,-C+D+E=0,D=-1;{A=-1,B=0,C=0,E=1, D=-1;
    1
  1792. Уважаемый автор аудио статей! Это дело белых шляп и СВПО.
    1
  1793. Log2(n)=8 n=256
    1
  1794. (2n+k)(k+1)=2^2025,kZ,k≥0 k=0,n=2^2024,k=2^2025-1,n=1-2^2024
    1
  1795. -3x¹/³/(1+x¹/⁶+x¹/³)/(1-x¹/⁶)=∞
    1
  1796. limx->3(2(x-3)/(3-x))=-2
    1
  1797. $(0;2π)sin(sinx-x)dx=sin(1-π/2)*π/2-sin(1 -π/2)*π/2=0 sinx-x=πn,sinx=x+πn,(0;0)(π;-1)(2π;-2) sinx-x=π/2+πn,(2,354;-1)
    1
  1798. 2/4=.../1,..=0,5 (2h-2)*2=h,h=4/3 5/3*5 /6/2*2*4+(10/3)²=50/9+100/9=50/3
    1
  1799. 5'000/12,36=404 164/309 лет
    1
  1800. 1 1/4+1/24=1 7/24 1/8*3=3/8 2,4✓
    1
  1801. 11-a,-2+a A a,13-a 22-2a-2+a=20-a=13 a=7 13-a-(-2+a)=15-2a=1{1}
    1
  1802. o=arctg(12/x)-arctg(3/x) o'(x)=-12/(x²+144)+3/(x²+9)=0 x=±6-+->x E)
    1
  1803. {7,5ar+(a-r)a√(r²-20,25)=√(28²-a²)(7,5(a-r)-r√(r²-4,5²)),0=(-52r/615√ (r²-20,25)+(a-r)(4r²+534)/615)(7,5ar +(a-r)a√(r²-20,25))/(7,5(a-r)-r√(r²-20, 25))+(154/615r²-112/615ar)√(r²-20, 25)-534/615ar+8/615r⁴-4ar³/615-16 2/615r²,b=√(28²-a²);
    1
  1804. $(0;1)x^a/(1+x²)dx+$(1;∞)x^a/(1+x ²)dx=En=1;∞(-1)^(n-1)(1/(2n+a-1)+ 1/(2n-a-1))
    1
  1805. Мечты сбываются,то не у вас и не у всех.😂😂😂
    1
  1806. n(n-1)=1 n²-n-1=0 n=(1±√5(/2 y=c1x^((1+√5(/2*x)+c2x^((1-√5)/2*x)
    1
  1807. 15,24,33,42,51,60 6/90=1/15
    1
  1808. {[х=а²,х=а;(х-2)(х+1)<0+°-1-°2+>х;[{х=а²,ає(-√2;√2);{х=а,ає(-1;2).
    1
  1809. 5х+|2х-|х-а||=10|х+1|,х≥0 [{а≥4,х=-1/6а-5/ 3;{а≥2,х=а/8-5/4;{а<-4,х=а/14-5/7;{а>2, х=-1/12а-5/6.ає(-∞;-4)U[2;∞)
    1
  1810. $(0,25cos3√x+0,75cos(√x))dx⁰,⁵=0,25sin(3√x)+0,75sin(√x)+c
    1
  1811. (x+x-¹)²-10/3(x+x-¹)+1=0 x+x-¹=3;1/3 x²-3x+1=0 x=(3±√5)/2✓
    1
  1812. X=5+1/(2+1/x) 2x-10x-5=0 x=(5±√35)/2>5 x=(5+√35)/2 ..=(1+√35)/2
    1
  1813. 49(5²+4²)=35²+28² ±63;±7
    1
  1814. z²/2+ln|z-1|(-1;1)=1/2-∞-1/2-ln2=-∞ 1/8+ln0,5-1/8-ln1,5=ln(1/3)
    1
  1815. 2=0,5*4cosa*4sina 1/2=sin(2a) a=15°;75°✓
    1
  1816. -1/3ln|sinx|-ln|cosx|-ln|x| f'(x)=-1/3ctgx+tgx-1/x
    1
  1817. ∆p≥0,5*10^-25кг*м/с
    1
  1818. y'=cosx=√2/2(-1)^n y'=-sinx=-√2/2(-1)^n /_=arctg(2/3√2)
    1
  1819. (х²+3х-k/2-4,5)²+(3,5k+13,5)x-0,25k²-4,5k -84,25=0 -0,5k-4,5>9/4,k<-13,5 min=-0,25 k²-8,75k-104,5=-0,25(k+17,5)²-31,4375<0 решений 2,k=-13,5:(x+1,5)⁴-2,5*13,5x-3 5,4375=0 50,625-35,4375>0,0/ k>-13,5: \*/-1,5*\-1,5+√(0,5k+6,75)*/min:0?(k²-10 k+706)²+k40*1379+3⁴*1873-4*353²≥241'125+81*1873>0 1400,5+1,1875²-13,5√ 6,75>0,38,8125²-104,5+13,5√6,75>0 0/ k<3 6/7,
    1
  1820. x>0 ln((x+2)/x²)/lnx<0 x²-x-2=0 x=2;-1 °-1°0-°1+°2->x x(0;1)U(2;∞)
    1
  1821. 4(log2(x)-1)/log⁴(2)x(0,5+logx(2)x)(1+log2(x))(log2(x)-0,5)≤10
    1
  1822. Xn=arctg(ctgx1*..ctgx(n-1)) cosx1*..cosx(n-1)/√(1+ctg²x1..ct g²x(n-1)) cosx1*..cosx(n-2)(-1+ctg²x1..ctg²x(n-2)ctg⁴x(n-1))sinx(n-1)/(1+ctg²x1..ctg²x(n-1))¹,⁵=0 x(n-1)=±arcctg(ctgx1..ctgx(n-2))¹/²*-°0+*-*+°π-°2π>x(n-1) max=cosx1*..cosx(n-2)√(ctgx1*..ctgx(n-1))/√(1+ctgx1*..ctgx(n-2))/√(1+ctg³x1..ctg³x(n-2))=cos^(n-1)x1/√(1+ctg^(2n-2)x1) (n-1)cos^(n-2)x1(-1+ctg^(2n)x1)sinx1=0[x1=π/2+πn,x1=±π/4+πn;°0+*π/4-*π/2(+;-)°π(+;-)*1,25π(-;+) *1,5π-°2π>x1 max=1/√2^n
    1
  1823. y'+f(x)y=z y''=-f'(x)y-f(x)y'+z' y'''=-f''y-2f'y-fy''+z'' y'''-lnx/3/x²y''+1/3/x²y=0 z''-z'(f+lnx/3/x²)+(lnx/3/x²f-2f' +f²)z+(-lnx/3/x²f²+3ff'-f³+f'lnx/3/x²- f''+1/3/x²)y=0 -lnx/3/x²f²+3ff'-f³+f' lnx/3/x²-f''+1/3/x²=0 u=f'-f²,u=cx^(-x-¹/3)e^(-1/3x-¹)e^$ fdx+1/3$dxx^(1/x/3-2)e^(1/3x-¹) e^-$fdx y=x^nlnx x^)n-2)(n²-n+1/3) lnx+(2n-1)x^(n-2)-1/3x^(n-3)(nln²x +lnx)
    1
  1824. A≥0,7-(A²-7)²=A (A²+A-7)(A²-A-6)=0 A=(-1+√29)/2✓;(-1-√29)/2×;×3;-2×
    1
  1825. (арс)(акр)(арс)(ак)(кс) Нет а,в,д,е,и,л,м,н,о,п,т,у.Арракс?
    1
  1826. 6⁰,⁷⁵х*6⁰,²⁵=6х
    1
  1827. x²sinx✓
    1
  1828. h+h1,5=2 h=0,8 LM=0,8√2
    1
  1829. [{x≤1/9,>0;{log(1/3)x<-1,×;x(0;1/9]
    1
  1830. А почему такое название?(Моя пустота,щель,пробел и т.д.)
    1
  1831. (log(3)x-1)(log3(x)-1/3)/(2+log3(x))/(log3(x)+0,5)≤0+°-2-°-0,5+*1/3-*1+>log3 (x) log3(x)(-2;-0,5)U[1/3;1] x(1/9;√3/3)U[3 ¹/³;3]
    1
  1832. a=-b±√(4b²+37) 37=(n-2b)(n+2b) [{n=19,b=9;{n=19,b=-9;{n=-19,b=9;{n=-19, b=-9; a=-9±19=10;-28 a=9±19=28;-10
    1
  1833. 4²*4/8=8
    1
  1834. y=a(x-3)²+1,5=a(4-3)²+1,a=4 y=4(x-3)²+1
    1
  1835. Опять народ надувают?!
    1
  1836. 3/2=(S1+35)/(96+S2) 109+1,5S2=S1 (144+2,5S2)/180=S2/40 72=S2✓,S1=217✓
    1
  1837. У=ах²+bx+c y=k(x-/_a)+B ax²+(b-k) x+k/_a+c-B=0{a/_a²+b/_a+c=B,a(/_ b+/_a)+b=k;|(/_a;/_b)ax³/3-a(/_a+/_b)x²/2+(-a/_a-b/_a)x=a(-1/6/_b²-2/_b/_a/3-1/6/_a²-/_a(1+b/a))(/_b-/_a)=a/6(/_b-/_a)³ b=a(-1/3/_b²//_a-5/6/_b-1/3/_a-1) ✓
    1
  1838. πR²-πr²=π(h²+2²-h²-1²)=3π
    1
  1839. {x=280/27,y=64/27.
    1
  1840. (√a+√b)²/4≤(a+b)/2,≥√(ab)✓
    1
  1841. (x-y+z)²=x²-y²+z²,x²+y²+z²-2xy+2zx-2yz=x²-y²+z²,-2y(-y+x)+2z(x-y)=0,(x-y)(-2y+2z)=0, [x-y=0,-2y+2z=0;[x=y,y=z.
    1
  1842. {(x+1-√(1-a))(x+1+√(1-a))≤0,+*+>x (x-2-√(4+6a))(x-2+√(4+6a))≤0+*+>x;{x[-1-√(1-a);-1+√(1-a)],x[2-√(4+6a);2+√(4 +6a)];a≤1,a≥-2/3,a[-2/3;1] -1-√(1-a)≤2+√(4+6a) [{x[-1-√(1-a);-1+√+1-a)],a[-1;0),x[2-√(4+6a);-1+√(1-a)],a[0;1].
    1
  1843. m=2^m1,n=2^n1 (m1*2^m1+n1*2^n1)/2^(n1+m1)= 7/2^2,5{m1=2-n1,n1=0,5;1,5.(2^1+1)/(2¹-1)=3 (2-¹+1)/(2-¹-1)=-3 C)
    1
  1844. (1-tg(45°-a))/(1-tga)=tg50° a=25°+π n/2(0;90°) a=25° ?=70°
    1
  1845. y'(0)=0 y'(1)=2 y'(0)=±√x=0 y'(1)=±√2 /_=0°;/_=arctg((-4+5√2)/7);π-arctg((4+5√2)/7)
    1
  1846. 0,185*1,200/0,200=1,11 переплата
    1
  1847. R²/2/√2=2√2 R=√8(cm) S=π-2 cm²
    1
  1848. А это и есть научпоп, а не подделка.
    1
  1849. En=1;∞($(1/(n+1);1/n)dx/xln(x-1/(n-1))+ln(1-n)*ln(n/(n+1))-(ln²(n+1)-l n²n)/2+n/(n-1)²ln(1+n)+(2-n)/(n-1)/(n+1)-n(1/(n-1)²+1/(n+1))ln2-n/(n-1)²lnn))~0,25
    1
  1850. {Fc=1185,91 Н,Fb=790,54 Н, Fd=1694,1 Н.
    1
  1851. S=64*arccos(1/2/√2)-8√7 128arccos(√2/4)-16√7(cm²)
    1
  1852. anx^{n-1)=a^(n+1)x^n²[a=0,{(0,5±√3/2*i)^(0,5-+√3/2i)=a^n,n=(1±√3*i)/2;
    1
  1853. Какая Соня Софи!
    1
  1854. Хуже.
    1
  1855. х²=-240+20²=160 х=±√160
    1
  1856. x=6/5,x+4=3 x=-1 |x|=0;1 x=0;±1 °-4-•°-1-°0-°1+*1,2->x x(1;1,2]
    1
  1857. ((9^x²-1)²+3)((2^x²-0,5)²+0,75)*5^((0,5*9^ x²-2^x²)/(2^x²-0,5)/(9^x²-1))≥6(9^x²-1)(2^x ²-0,5)*5^((0,5*9^x²-2^x²)/(2^x²-0,5)/(9^x²- 1)),>4,x≠0;
    1
  1858. (x²+3x+1-y)(x²+3x+1+y)=1×
    1
  1859. 1+19+199+1999=2218
    1
  1860. {y=(4a+1)/(a²+5a+15),[a=0, x=(a-55)/2/(a²+5a+15). a²-7a+12=0 a=3;4✓
    1
  1861. По аналогии с теорией относительности?
    1
  1862. x=1 100/169
    1
  1863. f(x)=(1+x)/(1-x) -1/x, Подставив 4 раза функцию в функцию, получим x.
    1
  1864. (х+0,5-√(9-(у-1,5)²))(х+0,5+√(-(у-3/2)²+ 9))>0,+°-°+>х,хє(-∞;-0,5-√(9-(у-1,5)²))U (-0,5+√(9-(у-1,5)²);∞),ує[-1,5;4,5],хєR,ує(-∞;-1,5)U(4,5;∞)
    1
  1865. {y=(26-x^(2x))^(0,5/x),x^(2(26-x^(2 x))^(0,5/x))+(26-x^(2x))^((26-x^(2x)) ^(0,5/x)/x)=5,x^(x+(26-x^(2x))^(0,5/x))+(26-x^(2x))^((x+(26-x^(2x))^(0, 5/x))/2/x)=7;{x=2,1322,y=0,9349; 2,9601~✓
    1
  1866. x²+y²=1,(2x+y+1)/(3x+y+5) (2x+√(1-x²)+1)/(3x+√(1-x²)+5)'=((2+0,5(1-x²)-⁰,⁵*2x)(3x+√(1-x²)+5)-(2x+√(1-x²)+1)(3-x(1-x²) ⁰,⁵)/(3x+√(1-x²)+5)²=0 7(1-x²)⁰,⁵=2x+3,49 {(1-x²)=4x²+12x+9,x≥-1,5;-5x²-12x-8=0, x= 1,2±√-216/10 0/,+>x ...[-1/2;3/8],(2x-√(1 -x²)+1)/(3x-√(1-x²)+5)'=((2-0,5(1-x²)-⁰,⁵*-2 x)(3x-√(1-x²)+5)-(2x-√(1-x²)+1)(3+x(1-x²) ⁰,⁵)/(3x+√(1-x²)+5)²=0 (1-x²)⁰,⁵=-1/7-4x/7 {1-x²=1/49+8/49x+16/49x²,x≤-1/4;-1 16/4 9x²-8/49x+48/49=0 x=(-4±56)/65[x=4/5, x=-12/13;-*-12/13+*4/5+>x min=-8/11 [-8/11;3/8]
    1
  1867. (1+a²)x²+(-2-4a)x+4=0 x=(1+2a±√(-3+4 a))/(1+a²),a≥3/4 [0≤(a-1)(a-3),\(3)*0/1* (0)\*2(-5)/a[3;∞);[{a[0;2],0≥(a-1)(a-3)+*-* +>a; a[2;∞);[a[3;∞),a[1;∞);a[1;∞)
    1
  1868. (R-3)²=3²+(R-4)² R=8 S=23π
    1
  1869. 48*98=4704Дж
    1
  1870. 28+5√9,25-5√9,25=28
    1
  1871. 2f(x+y)+6y³=f(x+2y)+x³ y=0,2f(x)=f(x)+x³ f(x)=x³
    1
  1872. limx->∞(8sin(1/3/x)/(1/3/x))=8
    1
  1873. tg/_1=3/x tg2/_1=24/(x+12) tg2/_1= 2tg/_1/(1-tg²/_1) x²-4x-12=0 x=2±4=6;-2>0 x=6✓
    1
  1874. 1/sinx=1/sinxsin(20°+x)/sin(60°-x) x=20°✓
    1
  1875. y=-ax+a³,x+ay=1,x-a²x+a⁴=1,x=(-a⁴+1)/(-a²+1)=a²+1,a≠±1,y=-a
    1
  1876. {x=±5,x<0;{-5}
    1
  1877. En=1;∞(E(-∞)-E(-ln(n+1)²))-0,5+π²/12 1,24-ln(2ln(n+1))+Ei=1;∞(-1)^(i- 1)*((2ln(n+1))^i+(2ln2)^i)/i!/i -∞✓
    1
  1878. ln(2/(πn)²(2n+1)²)=ln(8/π²)? -1+π²/6 (2n-1)(2n+1)³/(2n)³/(2n+2)
    1
  1879. -2-2√3i-4(1-√3i)+8=2+2√3i a^(n-1) *0=0 a-2=-1+√3i (1+√3i)²/2=-1+√3i 2³*1=8
    1
  1880. $(0;π)xsinmxdx=-xcosmx/m+sinm x/m²(0;π)=-2π(-1)^m/m
    1
  1881. Окружность с центром (0;0) и радиусом 1, бисектрисы 1 и 2 квадранта, площадь за окруностью, включающая ось Ох и между биссектрисами.
    1
  1882. x=rcost,y=rsint x=a^tcost,y=a^tsint
    1
  1883. (x-y)(x+y+1)(x+y+2)✓
    1
  1884. 0,1125/1,1125=9/89=10 10/89%
    1
  1885. х-12=0,85х х=80у.е.
    1
  1886. 3(a+c)(a+b)/(a+b)/(a+c)=3
    1
  1887. {x=a±√(-(y+2a)²+(1+a)²),x²+y²+4(x-y)a=4+4a-7a²;-0,24/a-0,16±√(-0,81-1,08a+22,14a²+ 27a³+99/4a⁴)/5/a=y;a>0,x=+,y>1,125a-1/4- 3/8/a x=a±√(-(2a-0,24/a-0,16±√(-0,81-1,0 8a+22,14a²+27a³+99/4a⁴)/5/a)²+(1+a)²) 9*123876/121²/25²-12288/1331/25a+(a²+6/11a+903/121/25)²≥0 +*-0,18*0,19 +>а ає(-∞;-0,18]U[0,19!∞){-0,18;0,19}
    1
  1888. 50*21+20*(50-16-14)=1450
    1
  1889. {x+y+z=6,x2+y²+z²=38,x³+y³+z³=144;
    1
  1890. 5^(k+1)/(k+1)-5^k/k 5²/2-5/1+..+5^(n+1)/(n+1)-5^n/n=-5+5^(n+1)/(n+1)
    1
  1891. 4*2^log2(81)=324
    1
  1892. (xc;-3/4xc-9)(xc+12;-3/4xc+7)y=kx+b {-3 /4xc-9=kxc+b,-3/4xc+7=k(xc+12)+b;-16=-12k,k=4/3, b=-25/12xc-9 y=4/3x-25/12xc-9 x=6,75+25/16xc
    1
  1893. 20'000*72*(1+x)^72/((1+x)^72-1)= 16'200*48(1+x)^48/((1+x)^48-1) 0=-23(1+x)⁴⁸-23(1+x)²⁴+27 x=-1+((-23+√3013)/46)¹/²⁴=-0,015 Нету тут правильного ответа.
    1
  1894. 4[x]²-36[x]+45<0 ([x]-(36+√(36²-4*4*45))/8)([x]-(9-6)/2)<0,([x]-7,5)([x]-1,5)<0+1,5 °-°7,5+>[x] [x](1,5;7,5),[x][2;7],x[2;8)
    1
  1895. n=1,m=21,n=3,m=20,
    1
  1896. Z=-x-y,x²+y²+xy=2,2x⁴+4x³y+6x²y²+4xy³+2y⁴=2(x2+xy+y²)²=8
    1
  1897. 130=26*5,78,104 10√(13²-5²)=120 x,x-62 2/5 (x-62,4)/(78²/130)=50/120 x=81,9 S= 81,9*130=9647
    1
  1898. (xy+y²)'=x y=-x/2±√(3x²/4+c)
    1
  1899. c=3b/a-a-b=a(a²-2a+6)/(-a²-a+3) 3a²/(-a²-a+3)=b A=1 b=3,c=5 abc=15
    1
  1900. y^(1/(y+2))=x^(1/x²) e^(lny/(y+2))(1/y/(y+ 2)-lny(y+2)-²)=0 1+2/y-lny=0 y=4,3+*->y max=4,3^(1/6,3) e^(lnx/x²)(1-2lnx)x-³=0 x=e^0,5(•->x max=e^(0,5/e) 4,3^(1/6,3) >e^(0,5/e) y=1,x=1; y=2,x=2;(-2;-2){(1;1)(2;2)(&2;-2)}
    1
  1901. z=(√2±√2i)/2 z⁷=cos(45°•7/±isin(45°•7)= √2/2-+i√2/2 z⁷+1/z⁷=√2/2
    1
  1902. $√2/2(-cos(π/4-x)+1,5/cos(π/4-x))/cos³x dx=-0,5tgx-3$1/(cos2x+1)/cos2xdx+1,5 ln|u-√0,5|+1,5ln|u+√0,5|-3ln|u|+0,75u-²+u ²/2=-0,5tgx-3ctg(x-π/4)/2/cos2x-3/8sin ²(x-π/4)+3/4ln|cos(x-π/4)|-3/4ln|sin(x-π/4)|+1,5ln|cosx-√0,5|+1,5ln|cosx+√0,5|-3ln|cosx|+1,25/cos²x+c cosx=u x=±arccosu dx=-+1/√(1-u²)du 0,75=A(u⁴+√0,5u³)+B(u⁴-√0,5u³)+C(u⁴-0,5 u²)+D(u³-0,5u)+E(u²-0,5){B=1,5,A=1,5, C=- 3,D=0,E=-1,5;
    1
  1903. {-1/3x'(t)+2/3x=y,x''(t)-2x'(t)-3x=-3e^t. k2-2k-3=0 k=1_2=3;-1 x0=c1e^3t+c2e^-t x(t)=ce^t ce^t-2ce^t-3ce^t=-3e^t c=3/4 x(t)=c1e^3t+c2e^-t+3/4e^t y(t)=-1/3c1e^3t+c2e^-t+1/4e^t
    1
  1904. {a≥-x²,x=±y,[y=1+√3,y=-√2; y=√2,y=-1-√3;{(a≥-4-2√3;1+√3;1+√3)(a≥-2;-√2;-√2)(a≥-2;-√2;√2)(a≥-4-2√3;1+√3;-1-√3)}
    1
  1905. X[1;√2),x=1 x[√2;√3),0=x²-x-1 x=(1+√5)/2 x[√3;2),0=x²-x-2 x=(1±3)/2=2×;-1× {x³}=√5-2
    1
  1906. x=(-i±3i)/2=i;-2i
    1
  1907. (2x+6)²+(9x+6)²=169x² -7x²+11x+6=0 x=(-11±17)/-14=-3/7;2>0 S=0,5*10*24-0,5*4*18=84(cm²)
    1
  1908. x=i±3i=4i;-2i
    1
  1909. 116,(6)*10⁶/12/(60-18)=9,361(6)*10⁶/42=2,23*10⁵₽/мес.
    1
  1910. y=1,x=4 S∆=2*4*0,5=4
    1
  1911. S=a²√3/2 a²√3/2/(a²*1,5√3)=1/3
    1
  1912. z=iarcsh(π/2+2πn)+2πm
    1
  1913. {x²+y²=80,y=0,4√5(x+16)-4√5; 1,8x²+9,6x-51,2=0 x=(-8±8√5)/3 /_1=2arctg(5/4/√5)+arcsin(-2/15√ 5+2/3)+arcsin(2/15√5+2/3) x=2*4√5sin(arctg(√5/4)+arcsin(-2/15√5+2/3)/2+0,5arcsin(2/15√5+2/ 3))=400√21/63✓
    1
  1914. X²+x+1 arctg((x+0,5)/√3*2)/√3*2+c
    1
  1915. sin2a=0,5 2a=30°,a=15°
    1
  1916. π^(1-х)=е^х,(1/π/е)^х=1/π,х=log(1/π/e)(1/π)
    1
  1917. ±3/2√(b-d)=a b-d=0×;4✓ d=0;1;3..5 b=4;5;7..9 a=6 c=0;1;..;5;7;8;9 10+2d=20
    1
  1918. arcsin²√x(0;1)=(π/4)²-0=π²/16
    1
  1919. V=π(√3/6*4)²√3=4/3π√3 A)
    1
  1920. 328=256+64+8 (8;3;1)(6;4;1)(3;8;4)
    1
  1921. x=3(3+1)+1...=3^n+3^(n-1)+...+1=(3^(n+1)-1)/(3-1)=0,5*3^(n+1)-0,5, 2^nf(1/(0,5*3^(n+1)-0,5))=1-0,5(1-f(1/(0,5*3^(n+1)-0,5)), f(1/(0,5*3^(n+1)-0,5))=0,5/(2^n-0,5),f(x)=0,5/(2^(log(3)((1/x+0,5)/,05)-1)-0,5)=1/(2^(log(3)(2/x+1))-1)
    1
  1922. (x-k)(x²+x(k-4)+k²-4k+4)=0 x=k,x=(-k+4±√(-3k²+24k))/2,k[0;8]
    1
  1923. X(0;1/2)U(1/2;1)U(1;3)U(3;4),ln(x+5)/ln(4-x)*ln(log2(10-x))/ln(x+1)/sinx/ln(2x)*lnx≤0°0+°1/2-°1+°3-°π+°4>x,x(1/2;1)U(3;π)
    1
  1924. 5х⁴-209=0 х=±41,8¹/⁴+*-*+>х max=167,2*41,8¹/⁴+56>0 min=-167,2*41,8¹/⁴+56<0 3 решения х=3,74;0,27;-3,87 E~0,14
    1
  1925. y=(x²+2x-4/5)²+2x+44/25 \*1 3/5/-1* \*-2/5/ y=kx+b,(x²+2x-4/5)²+(2-k)x+44/25 -b=0 k<0,9+5/8b,k>13/25+b, k<-2,4+2,5b b<1 1/75, b>1 71/75,k<23/15 $(x⁴+4x³+ 12/5x²+(-6/5-k)x+12/5-b)dx=x⁵/5+x⁴+4/5 x³+(-3/5-0,5k)x²+(12/5-b)x+c,x=±√(12/5 -2(6/5b-6/5k+(2-k)²/8-396/125)^(1/3))/2 ±√(2(6/5b-6/5k+(2-k)²/8-396/125)^(1/3) +24/5±(4-2k)/√(12/5-2(6/5b-6/5k+(2-k)²/8-396/125)^(1/3)))/2-1+i(±√(12/5 -2(6/5b-6/5k+(2-k)²/8-396/125)^(1/3))/2 ±√(2(6/5b-6/5k+(2-k)²/8-396/125)^(1/3) +24/5±(4-2k)/√(12/5-2(6/5b-6/5k+(2-k)²/8-396/125)^(1/3)))/2-1),где -b+k+102/2 5=0,x=±√(-2(b-k-102/25)/3/(-3/5b+3/5k+ (2-k)²/16+√((b-k-102)³/27+(6/5b-6/5k -(2-k)²/8-396/125)²/4)+198/125)^(1/3)+ 2(-3/5b+3/5k+(2-k)²/16+√((b-k-102)³/27+(6/5b-6/5k-(2-k)²/8-396/125)²/4)+19 8/125))^(1/3)+12/5)/2.... S=(x2⁵-x1⁵)/5+(x2⁴-x1⁴)+4/5(x2³-x1³)+(-3/5-0,5k)(x2² x1²)+(12/5-b)(x2-x1) S=(x3⁵-x2⁵)/10+(x3⁴- x2⁴)/2+2/5(x3³-x2³)+(-3/10-0,25k)(x3²-x2 ²)+(6/5-0,5b)(x3-x2) S=(x4⁵-x3⁵)/5+(x4⁴-x 3⁴)+4/5(x4³-x3³)+(-3/5-0,5k)(x4²-x3²)+(1 2/5-b)(x4-x3) k=23/13,b=3
    1
  1926. x²=lg2+2x x²-2x-lg2=0 x=1±√(1+lg2)
    1
  1927. x¹⁸-x¹³+x¹⁰-x⁷+x²-x+1>0 (x²-x+1)(x¹⁶+x¹⁵-x¹³ x¹²-x¹¹+x⁹+2x⁸+x⁷-x⁶-3x⁵-2x⁴+x³+3x²+2x+( 3x+1)/(x²-x+1))>0 x(x-1)(x¹⁶+x¹⁵+x¹⁴+x¹³+ x¹²+x⁸+x⁷+x⁶+1)+1>0,x(-∞;∞)
    1
  1928. Анал,говно,нет?!
    1
  1929. (x0-x1)²+(√(16-x0²)-y+√(9-(x-x1)²))² =25 -2x0x1+y²-x²+2xx1-2y√(16-x0²)=(-2√(16-x0²)+2y)√(9-(x-x1)²), (y²-2y√(16-x0²)-2x0x+x²+16)x1²+2x1((-0,5x0-0,5x)y²-16x+xx0²+0,5x0x²-0,5x³+y(x0+x)√(16-x0²))+0,25y⁴+0,25x ⁴+y²(7-x0²+0,5x²)+(18y-x²y-y³)√(16-x 0²)-144+16x²+9x0²-x0²x²=0 min=√(x²+y²)-7=5 x²+y²=144 x=√72 V=72*12=864 D)
    1
  1930. (x⁵+x+1)/(x²+x+1)=x³-x²+1
    1
  1931. a=11/61b-40/61 61a-11b+50=10
    1
  1932. 25¹³<27¹³ ²/³
    1
  1933. {3х²-7х+4=0,3х-4=у;{х=(7±√(7²-4*3*4))/6,у=3х-4;{[х=4/3,х=1;[у=0,у=-1;{4/3;0}{1;-1}
    1
  1934. {12х²=12,у=8х²-3;{х=±1,у=8х²-3;{[х=1,х=-1;[у=5,у=5.
    1
  1935. {х2+3у²=31,2*31=31х;{х=2,у=±3.
    1
  1936. {у⁴+х⁴=17,[у=±1,х=±1;{[у=±1,х=±2;[х=±1,у= ±2;(±2;±1)(±1;±2)
    1
  1937. {4х-2у=-4,х+6у=25;{4х-2у=-4,-26у=-104;{х=1,у=4.(1;4)
    1
  1938. {-х+5у=2,6х+10у=28;{-х+5у=2, 28/3у=20/ 3;{х=11/7,у=5/7.
    1
  1939. X1=x2+x3,х-1+х-2+х3=-b, x1x2+x1x3+x2x3=c, x1x2x3=-d,x1=-b/2, b²/4+x2x3=c, x2x3=-d/-b*2, c-b²/4=2d/b, -x2²-b/2*x2+b2/4-c=0, x2=(0,5b+√(0,25b²-4(-1)(b²/4-c)))/(-2), x3=-025+0,5√(1,25b²-4c),
    1
  1940. limn->∞(e)=e (-e;e) En=0;∞(-e)^n/(2*e^n+3) 0 сходится, En=0;∞e^n/(2*e^ n+3) расходится Хэ(-е;е]
    1
  1941. S1=8/√3 a=√(64/3-32/√3) S2=16√3/3-8 S=8√3-8
    1
  1942. {y=x³+2x²+2x,z=y³+2y²+2y,[x=0,x=-1,0=x²(x+1)²((x²(x+1)+(x+1))((x+1)⁴+2(x+1)²)-(x+1)³)³+3(x+1)((x²(x+1)+(x+1))((x+ 1)⁴+2(x+1)²+1)-(x+1)³)²+3(((x²(x+1)+(x+1))((x+1)⁴+2(x+1)²+1)-(x+1)³)+2x(x+1)(((x²(x+1)+(x+1))((x+1)⁴+2(x+1)²+1)-(x+1)³)²+2(x²+1)(x+1)((x+ 1)⁴+2(x+1)²+1)-(x+1)⁴)+2x²((x+1)⁵+3(x+1)³+3(x+1))+4x((x+1)³+2(x+1))+4(x+1)+3(x+1){(0;0;0)(-1;-1;-1)}
    1
  1943. а=-3/8,-68=b✓
    1
  1944. 1/(51*95)²=4845-²
    1
  1945. 2x²+7xy-4y²=0 x=(-7±9)/4y=0,5y;-4y x²-5xy+y=-11[-2,25y²+y+11=0,36y²+y+11=0;[y=22/9,y=-2;0/;(11/9;22/9)(-1;-2(
    1
  1946. (а*5+2)(5b+3)=276,(0;27)(2;4)(18;0)(-1;-19)(-5;-3)(-28;-1) a+b=27;6;18;-20;-8;-29
    1
  1947. {x+y=9/4,x-y=-1/6.-1/3✓
    1
  1948. (x+1)e^-x+x^2/2-1=0 x=0(-e^-x+1)x=0 x=0+*0+>x htitybt vj;tn ,snm njkmrj1/ Gj'njve lheub[ htitybq ytn/
    1
  1949. (a-2√2)(3+2√2)=b a=3,b=1 (a-3)*2√2+3a-8=b
    1
  1950. {(cosx-1/6)³-7/12(cosx-1/6)+7/216=0,2cos2x=AB;cosx-1/6=(-7/432+7√-27/432)¹/³+(-7/432-7√(-27)/432)¹/³=√7/3cos(1/3 arccos(-1/2/√7)+2/3πn) cosx=1/6+√7/3 cos(1/3arccos(-1/2/√7)+2/3πn),n=0;1;2 x=±arccos(1/6+√7/3 cos(1/3arccos(-1/2/√7)+2/3πn))+2πm x(0°;45°) x=arccos(1/6+√7/3cos(1/3arccos(-1/2/√7))),[-arccos(0,605);-arccos(50/53)]U [arccos(50/53);arccos0,605]
    1
  1951. -0,5x-¹ln(1+x²)+arctgx(1;√3)=-1/√3 *ln2+π/12+0,5ln2
    1
  1952. √((-10+√170)/14)
    1
  1953. (-7-2√10)/3
    1
  1954. tg2x=-√3 x=-π/6+πn/2
    1
  1955. √65>8
    1
  1956. r=2e^(-0,5o) $(0;π)2e^(-o)do=-2e^-o(0;π)=-2e^-π+2 (-2;-π;-2)
    1
  1957. {47,5I2=I,I1=33,5I2;R=(2I1+2,4(I1-I2))/I=58/19(Om),U=20(V) I=190/29(A)
    1
  1958. f(x+1)=f(x)-f(x-1)=-f(x-2)=(-1)^([(x+1)/3])f(3{(x+1)/3}) f(2012)=f(2)=1
    1
  1959. q=BCtg(/_B/2) p=AB/2/cos(/_B-90°) pq=AB*BC/4/cos²(0,5/_B) R=BC/2/sin/_A sin/_C=sin/_Acos²/_C+2cos/_Asin/_Ccos/_C+cos²/_Asin²/_C/sin/_A ч.т.д.
    1
  1960. 4/sinx=10/sin(3x) x=0,5arccos0,75 √(116-80cos(2x))=√56 √191 S∆=55√7/4
    1
  1961. 17:17 всё по "Мадагаскару".😂😢
    1
  1962. 462/n(м/с)=v
    1
  1963. 2√2+2 S=π*8√2(m²)
    1
  1964. n=6m:[(n+4)/6]-[(n+3)/6]+[(n+2)/6]=[n/2]-[n/3],m-m+m=3m-2m,m=m; n=6m+1: m-m+m=3m-2m✓:n=6m+2:m+1-m+m=3m+1-2m,m+1=m+1✓;n=6m+3:m+1-(m+1)+m=3m+1-(m+1)✓;n=6m+4:m+1-(m+1)+m+1=3m+2-(2m+1)✓;n=6m+5:m+1-(m+1)+m+1=3m+2-)2m+1)✓
    1
  1965. 6cos2o 6/sin(3o)*sino+3=6cos2o ±π/12+0,5πn=o,o(0;π/6) o=π/12✓
    1
  1966. ..ур(п)(п) Нет а,б,в,д,з,е,и,к,л,м,н,о, с,т,ь,я.ЫЭЮ шуруп?
    1
  1967. y'=a(2x-x1-x2) x=x1;x2 y'=a(x1-x2);-a(x1-x2) /_a=b✓
    1
  1968. 10√2=(2√5+2√10)√r r=10(3-2√2)(m)✓
    1
  1969. |2x-1|+|2x+1|+4/√3*|y|=4, -1/2 0 1/2 2x-1+2x+1+4y/√3=4,{y=-√3x+√3, x>=1/2,y≥0, {x>=1/2,y≥0, 2x-1+2x+1-4y/√3=4, y=√3x-√3, x>=1/2,y≤0, {x>=1/2,y<0, -2x+1+2x+1+4y/√3=4,{y=0,5√3, 1/2>x>=-1/2,y≥0, {0,5>x>-1/2,y≥0, -2x+1+2x+1-4y/√3=4,{y=-0,5√3, 1/2>x>=-1/2,y≤0, { 0,5>x>-0,5,y≥0, -2x+1-2x-1+4y/√3=4,{y=√3x+√3, x<-1/2,y≥0, {x<-0,5,y≥0, -2x+1-2x-1-4y/√3=4,{ y=-√3x-√3, x<-1/2,y<0, { x<-1/2,y<0, /-|^y\_>x \___/ √3*1+√3*(1-0,5)*0,5*2=√3+0,5√3=1,5√3
    1
  1970. На 22.52 рубля я ошибся с переводом, пришлось возвращать их за 15.
    1
  1971. $(0;π/2)lncosx*cosx/(1-cos²x)dcos x=lncosx*-0,5ln|cos²x-1|-0,25En=1; ∞1/n²(cosx)^(2n)(0;π/2)=π²/24
    1
  1972. -cos²2a+(cos2a)²=0
    1
  1973. limn->∞(n³/(n+1)³)=1 0,5n+0,25n²sin(2/n)-0,25n³cos(2/n)+...c(1;∞)=-∞
    1
  1974. x=1,x³-9x²+26x-24=0 ((x-3)²-1)(x-3) =0[x=3,x=2,X=4;{1;2;3;4}
    1
  1975. 2√(4+r²),√(20-4r²) 2²=(√(20-4r²)+2r)(√(20-4r²)-2r) 4=20-8r² r=2⁰,⁵ S=1/4π(2√2)²=2π
    1
  1976. 100N+5A=U*44,A:4 A=0;4;8 U:5,U=5 N=(44-A)/20 A=4 N=2 2+4+5=11
    1
  1977. En=0;-∞(2/3)^-n=1/(1-2/3)=3
    1
  1978. a(a+2R)=5² a=-R+√(25+R²) (R-5/3)³+50/3(R-5/3)-30 5/54=0, R≥0 R-5/3=5/6((26+6√33)¹/³+(..- √..)..) R=5/3+5/6(26+6√33)¹/³+5/6 (26-6√33)¹/³✓ x=2R*R/√(25+R²)= 5/3(2+(26+6√33)¹/³+(26-6√33)¹/³) ²/√(16+(2+(26+6√33)¹/³+(26-6√33) ¹/³)²)
    1
  1979. |√(х-1)-2|+|√(х-1)-3|=1 √(х-1)[2;3] х-1[4;9],х[5;10]
    1
  1980. y=x±√(4x+c)
    1
  1981. 9(x²-2/3x+1)(x²+2/3x+1)
    1
  1982. $(-1;3)dy$(0,5y²-0,5;y-1)dx=-y³/6+y²/2-0,5y (-1;3)=-2 2/3
    1
  1983. 03.1117г. типа начало славянского календаря
    1
  1984. 2log2(x)=3log3(x) (2-3/log(2)3)log2(x)=0, x=1
    1
  1985. 12sin75° 72sin75°cos75°=18D)
    1
  1986. AC=1,h=1/(ctg15°+ctg30°) BC=2/(ctg15°+√3) sin60°=h/EB EB=√3/(2√3+2)=(3-√ 3)/4 DE=(3√3-5)/4 hDE=(9-5√3)/8,..(DE)= (3√3-5)/8,A...=-√3/24+5/8 tg/_1=(20+11√ 3)/3,/_1=arctg((20+11√3)/3) /_2=30° x=a rctg((20+11√3)/3)+30° √3/2=2cos²15°-1
    1
  1987. DC²+(DC-4)²=2a² a=√(DC²-4DC+8) √(a²+DC√(2a²-DC²))=√8 FO=√(FD²+2(DC-2)²-2FD(DC-2)) -0,5DC²+3DC-4=FD≥0 DC[2;4] DC=4 FD=0 DB=4√2
    1
  1988. Ek=0;n (k+1)²Cn;k=Cn;0+Cn;2+..+Cn;n+ 3Cn;1+..+3Cn;n+...+(2n+1)Cn;n=2^n+3 (2^ n-1)+..+(2n+1)(2^n-2^n+1)=((n+1)n-3/4n ²+1/4n+1)2^n
    1
  1989. 4cos(10°+60°)/sin20°=4
    1
  1990. R=20⁰,⁵ R1=40⁰,⁵ S=5π-20√2cm²
    1
  1991. $(0;∞)dx/(x^p+x^q)=$(0;∞)dx*x^(p +q-2)/(x^p+x^q)=0,5En=1;∞(-1)^(n- 1)(∞-1/(p(-n+1)+qn-1)-1/(-pn+q(n- 1)+1))=∞,p≥1,q≤1
    1
  1992. b=±√(50-a²) a+√(50-a²) 1+(50-a²)-⁰,⁵*-a=0 a=5+*->a max=5+5=10
    1
  1993. X=(6-6^(y+1))/(1+6^y) xy=6(1-6^y)(1+6^y)y 6(-36^y-2*6^yln6*y+1)/(1+6^y)²=0 y=0+*->y max=0 (6^y-1)/(1+6^y)y=6 y~±6 ab=-36✓
    1
  1994. tg³x/3-3tgx+3ln|cosx|-x-0,5ln|tg(x π/4)|(0;π/6)=-28√3/27+3ln(√3/2)- π/6-0,5ln(2-√3)
    1
  1995. Y'=y''(y'-1) √2=y'/(√2/2±√(y+c+1/2)) √(y+c+1/2)=z,y=z²-c-1/2 y'=2zz' ±√2/2=z'(1-+√2/2/(z±√2/2)) ±√2/2*x+c1=z-+√2/2ln|z±√2/2| ±√2/2*x+c1=√(y+c+1/2)-+√2/2*ln|√(y+c+1/2)±√2/2|
    1
  1996. х^х!=6^720/>{6}
    1
  1997. А вот Юрий Абарин говорит ,что иезуиты возникли сразу после катастрофы 16 века, чтобы подчистить историю и убедить всех, что Ватикан со своей религией очень древний.
    1
  1998. x:/2,2;x:3,3;(x²-3):p,p>3, через малую теорему ферма доказывается, что таких чисел нет.
    1
  1999. $e^(xi(π+2πn))dx=(-icos(x(π+2πn))+sin(x(π+2πn)))//(π+2πn)+c
    1
  2000. BQ=5BP/√(BP²-25) BC/DQ=√(BP²- BC²)/√((BQ-BP)²-DQ²)=BP/(BQ-BP) {BP=5,BC=0;AB=∞D)?
    1
  2001. limx->0(x²/((1+5x)¹/⁵-1-x))=0/0=limx->0(2 x/((5x+1)-⁴/⁵-1))=0/0=limx->0(2/(-4(5x+1) -¹ ⁴/⁵))=-0,5
    1
  2002. x¹/³=u x=u³ dz=3u²du $(0;∞)3u³/(1+u²)/(u²-√3u+1)/(u²+√3u+1)du=-0,5ln|1+u²|+0,25ln|u²-√3u+1|+0,25√3arctg((u-√3/2)/0,5)/0,5+0,25ln|u²+√3u+1|-0,25√3arctg ((u+√3/2)/0,5)/0,5(0;∞)=-∞+∞+∞+√3* π/3=-∞ 3u³=A(2u⁵-2u³+2u)+B(u⁴-u²+1)+C(2u⁵+√3 u⁴+u³-u-√3)+D(u⁴+√3u³+2u²+√3u+1)+E (2u⁵-√3u⁴+u³-u+√3)+F(u⁴-√3u³+2u²-√3u+1) {A=-0,5, B=0, C=0,25,D=0,25√3, E=0,25, F=-0,25√3;
    1
  2003. a/4+a/3=7/12a=7 a=12(m) S=144(m²)
    1
  2004. M,n≥7,mn=206=2•103× mn=117=9*13 9-7+13=15B)
    1
  2005. xsinu+cosu(-∞;0)=1+∞sin-∞+cos∞ неопределенность
    1
  2006. $r²dp4/3πR³=4/3πp$r²*3R²dR==4/3*3r⁵/5*π=4/5*πpR⁵=3/5mR², (0,6mR²-0,6mR²)2π/24/60²sin23,5°*2π/24/60²cos23,5°=M1, 0,6mR²*2π/24/60²cos23,5°+(0,6mR²-0,6mR²)2π/24/60²sin23,5°*0=M2, 0,6mR²2π/24/60²sin23,5°+(0,6mR²-0,6mR²)*0*2π/24/60²cos23,5°=M3, M1=0,M2=0,000014πcos23,5°mR²,M3=1,4*10^(-5)πsin23,5°mR²,
    1
  2007. x=log0,2(20/11)
    1
  2008. c=√(d²+16-8√(d²-h²)),h=d√(1/2±d/32√(32-d²)),d[√(-8+√(32h²+64));√(8-√(64-16h²))]U[√(8+4√(4-h²));√(16+h²)],d≥√(-8+√(32h²+64)) h²<16 4√2/3?h d≥4,-✓ +✓,4√((1+2√21/9) ¹/³+(..-..)..)≥d √(c²+36-12c*√(1-h²/c²)) (2+d(√(1/4+|d²/64-1/4|)-+√(1/ 4-|d²/64-1/4|))/√(d²+4+2d(√(1+|d²/16-1|)±√(1-|d²/16-1|)))=d√((1/2±1/ 2√(1-(d²/16-1)²))/(36+d²-6d(√(1+|d²/16-1|)-+√(1-|d²/16-1|))) h+=>d=5,65,h-=>d=× S=4h=11,3*1,48=16,724
    1
  2009. 0=2cos²2x+9cos2x-5 cos2x=(-9±11)/4=0, 5;-5 2x=±π/3+2πn,x=+π/6+πn
    1
  2010. A=1,b=9,11c+2d=81 c=7,d=2 {1972}
    1
  2011. y'=3-3t²,x'=2-2t,y'(x)=-3(t-1)(t+1)/-2/(t-1) =1,5(t+1) y"x=1,5/(-2t+2)=-0,75/(t-1),y'''x=- 0,75/(t-1)/(-2t+2)=0,375/(t-1)²
    1
  2012. (√x+x^-0,25)⁹=x⁴,⁵+9√x⁸x^-0,25+9!/2!/7!√x⁷x^-0,5+9!/3!/6!√x⁶x^-0,75+9!/4!/5!√x⁵x^-1+9!/5!/4!√x⁴x^-1,25+9!/6!/3!√x³x^- 1,5+9!/7!/2!√x²x^-1,75+9√xx^-2+x^-2,25 =x⁴,⁵+9x^3,75+36x^3+84x^2,25+126x¹,⁵+126x^0,75+84+36x^-0,75+9x^-1,5+x^-2,25
    1
  2013. $dx/2/(x²-2x+4,5)=0,5arctg((x-1)/√3, 5)/√3,5+c
    1
  2014. 13xy45z:728=2³*7*13, 45z:8,2+z:8,z=6, 13*10^5+xy*10³+456:7,3+xy*6+4=6xy:7, xy:7,13*10⁵+xy*10³+456:13,(12xy+1):13, xy≥0,≤973:13=74(ост.9),Ху=0,1:/13,х=7, 84у+1:13,6у+1:13,у=2, 1372458,1327458, х≤9,1 х, а значит и у.
    1
  2015. {2a+b=3,1,4b=-9,8;{a=5,b=-7.f(x)=5x-7 f(1, 6)=1
    1
  2016. (x/2-150)*2/3-70=50 x=660(руб.)
    1
  2017. {c=2022-ab,a=(2023-2022b)/(1-b²); min=(2023+√4045)/2~1043 max=(2023- √4045)/2~980 (a;b)=(2023;0)(10109/35; 6)× c=2022(2023;0;2022)
    1
  2018. [x=πn,x=π/2+2πn,x=2arctg(-7,67);2arctg1,86;2arctg0,43;2arctg(-0,82)+2πn.
    1
  2019. Дорогой создатель канала! А ты знаешь, что Трушин однажды решал задачу про партию Ведро.
    1
  2020. 2,4-2=0,4 cos(arctg(4/3)-45°)=7/10√2=2,4/(√2a) a=12/7 S=144/49
    1
  2021. a/(a+b)*1/3l3 2a/(a+b)-1=a/(a+b) *1/3 a=3/4b S∆=29,4
    1
  2022. (2n-3)/2/(2n-2)*X/(1+x²)^(n-1) +(2n-3)(2n-5)/2²/(2n-2)/(2n-4)*x/(1+x²)^(n-2)+..+(2n-3)!!/2^(n-1)/(2 n-2)!!*x/(1+x²)+(2n-3)!!/2^(n-1)/(2 n-2)!!arctgx(1;=)=-(2n-3)/2²/(2n-2)- (2n-3)(2n-5)/2³/(2n-2)/(2n-4)-..+(2n 3)!!/2^(n-1)/(2n-2)!!*π/2 n*(-1/(2n 5)!2^(n-3)*(n-2)!²-1/(2n-7)!2^(n-4)* (n-3)!²-..+π/2)*(2n-3)!/(n-1)!/(n-2)!/2^(2n-4)
    1
  2023. 21√(8*2)=84(cm²) R=84/(24-17)= 12(cm)
    1
  2024. у'=8х³е^(-2у),у(1)=0 0,5е^(2у)*2у'=8х³,0,5е^(2у)=2х⁴+с у=0,5ln(4х⁴+2с) 0=0,5ln (4+2c),c=-1,5 y=0,5ln(4x⁴-3)
    1
  2025. -6cos²x-15cosx-6=0 cosx=(5±3)/-4= -2;-0,5≥-1 x=±2/3π+2πn
    1
  2026. 800/50=16 S=(16+41)/2*12=342
    1
  2027. 3x²-9,6x+7,68=0 x=1,6✓
    1
  2028. {z=40-xy,[y=27/5,y=3;x=(y+21)/(y-1);{(6;27/5;38/5)(12;3;4)}
    1
  2029. 4cos50°/√3sin20°,1,10° √(16cos²50°/3sin²20°+1-8cos50°/√3sin20°cos10°) o=arccos((-3√3-8 cos10°)/√(32cos40°+23-8√3cos10 °))
    1
  2030. (x+(7k-6)/(k-2))/(x+3)>0,k≠2+°-3-°(7k-6)/(k-2)+>x x(-≠;-3)U((7k-6)/(k-2);∞)
    1
  2031. x=(m-1±√(-4m+1))/m m≤1/4 m(x-(m-1+√(- 4m+1))/m)(x-(m-1-√(-4m+1))/m)<0+°-°+>x [{x((m-1-√(-4m+1))/m;(m-1+√(-4m+1))/m),m>0,{x(<=>),m<0;{x<-1,m=0.
    1
  2032. 9=0,5a*6sin75° a=3(√6-√2) 3(√6-√2)/sina=6/sin(105°-a) √3/3=tga a=30°
    1
  2033. (y-¹)'+y-¹(e^x*e^e^x -(-e^x)*e^-e^x)=-e^(-e ^e^x+e^-e^x) y-¹=e^(-e^e^x+e^-e^x)c-x y=1/(ce^(-e^e^x+e^-e^x)-x)
    1
  2034. y=1+2sin((x-1)/(x+1)) y=(-arcsin(0, 5x-0,5)(-1)^n-πn-1)/(arcsin(0,5x-0,5)(-1)^n+πn-1)
    1
  2035. (-3/2±3√3/2i)³=27(-1±0)=-27
    1
  2036. 1/cos24,37°=1/0,916=1,09
    1
  2037. Не двойной плагиат, а бродячий сюжет.
    1
  2038. 224/2,54=88,19$ 168,19$.×
    1
  2039. 25=1+2r r=12 S=172π
    1
  2040. -2x/(x-2),f(x)+f(x/(x-1))+f(2x/(x-2)) =x,f(0)=0{f(3)+f(1,5)+f(6)=3,f(6)-f(-6)=1,5,f(6)+f(6/5)+f(3)=6,f(3)-f(-3)=9/5;1,5/1,8=5/6
    1
  2041. ((х+11)²+(у-13)²)/у/х=0 {х=-11,у=13.
    1
  2042. (320-(2^-x)²/4)/(128-2^-x)≥2,5 ((2^-x)²/4-2,5*2^-x)/(2^-x-128)≥0,2^-x(2^-x-10)/(2^-x-128)≥0,+°-7-*log(2)10+>x xє(-∞; 7)U[-log(2)10;+∞)
    1
  2043. 2/3√3 2/3√3/(4/3√3)=1/2 arctg(1/3) 4/3√1,5 S∆=8/3√0,5
    1
  2044. 3^(100*1/2*4/5)=3^40 3²²⁰¹¹⁰¹⁹=3¹⁹=65 61²*27=61²*27=3721*27=567=67
    1
  2045. {х=1,5,z=5/3,y=2/5.xyz=1
    1
  2046. 1/(a³+b³+3abc)+1/(a³+c³+3abc)+1/(b³+c³+3abc)≤3/(a³+b³+3abc)≤3/(5c³), a≥b≥c>0
    1
  2047. 2/50/(53/40)=8/265
    1
  2048. х>0, 2х/(х+1)=1,5 х=3✓
    1
  2049. 4,5*9-2*1/3*4,5*3=31,5(cm³)
    1
  2050. (5x+2)(x2-4)=0[x=-2/5,x=±2.
    1
  2051. 16,5-14,3*9/13=6,6
    1
  2052. 10²⁰⁰-3*10¹⁹⁰+..+3²⁰-3²¹/(10¹⁰+3) 1+460'353'200/10'000'000'003 1+1=2✓
    1
  2053. 2xsinx+x²cosx✓
    1
  2054. BD=8ctg20°sin80°-8√3sin80°=8
    1
  2055. -2b-2a+2w=/,180°-b-6a+w=4a,-b+4a=180°-w-4a {w=b+20°,20°=a.C)
    1
  2056. f)x+1)=f(1)^(x+1)-1*f(1)^(x-1)-..-(x-1)f(1)-x=f(1)^(x+1)-f(1)(f(1)^x-1)/(f(1)- 1)²+x/(f(1)-1) f(x)=f(1)^x-f(1)(f(1)^(x- 1)-1)/(f(1)-1)²+(x-1)/(f(1)-1) f(2025)=-1013
    1
  2057. -xe^-2x/2-e^-2x/4(0;ln2)=-ln2/8+3/ 16
    1
  2058. X³-2x-1=0[x=-1,x²-x-1=0;x=(1±√5)/2 {-1;(1±√5)/2}
    1
  2059. U=-2y²+xy³/3+c U(y,y)=y⁴/3-2y²+c=y⁴/3-y² c=y²? U=xy³/3-y²
    1
  2060. U'(x)=sin(x+2y)+2xy U(x,2x)=2x³ U(x)=- cosxcos(2y)+sinxsin(2y)+x²y+c U(x,2x)= -cos(5x)+2x³+c=2x³ c=cos(5x) U(x,y)=x²y
    1
  2061. U'(x)'(y)=sin(x+y) U(0,y)=y³ U(x,0)=-sinx =-sin(x+y)+cy+c1 U(0,y)=-siny+cy+c1 U(x,0)=-sinx+c1 c1=0 -y³+cy=siny y=0 c=1 U(x,y)=-sin(x+y)+y
    1
  2062. a=180°-3o,b=180°-3ф о+ф>122/3° а-180°+b=180°-3o-3ф х=о+ф>40 2/3°В)
    1
  2063. E^(x/2)-+x=0 e^(x/2)*0,5-+1=0 x=2ln2;×-*+>x min=2-2ln2>0 -2W(-0,5)×;..×=x x=-2W(0,5)
    1
  2064. 1/37=0,(027) C=1;2;3 ab=27;54;81 ba=72✓;45;18
    1
  2065. {a=1-1/b,c=1/(1-b); c+1/@=-1/(b-1)+ b/(b-1)=1
    1
  2066. ln(20-x)=ln³x x(0;20)\>=/> x=4,07..: log(4,07)15,93..=ln²4,07..
    1
  2067. (2√10-√(R²-a²/4))²+(2√10-a/2)²=R² R=a/√2,a≤0 (-√10+a/2)²+(-√10+√ (R²-a²/4))²=20-6√5R+R²=R² R=2/3√5
    1
  2068. $(1;≠)dn/ln3/(n+3^(n-m))+1/ln3*ln (1+3^(1-m))-1+0,5/(1+3^(1-m))[3/ln² 3/(1+3^(1-m))+log3(1+3^(1-m))-1+0, 5/(1+3^(1-m));1/ln²3*3^(-1+m)+log3 (1+3^(1-m))-1+0,5/(1+3^(1-m))] [15/ln²3/256+5/512;45/512+1/ln² 3/2]
    1
  2069. {y=x²-3x,[x=0,x=4,1±√3=x;{(0;0)(4;4)(1±√3;1-+√3)}
    1
  2070. Эй, Делягин, зачем вы в видео повторяетесь?
    1
  2071. х=-2√2+(√2+1)²=3
    1
  2072. limx->0(1+x+x²)/(3-x²)=1/3 limx->02(0,5x)²/x²=0,5 limx->0 2sin²(0,5x)/x²=0,5
    1
  2073. limx->0(sin1,5x/sin(0,5x))=3 limx->3(1/(x²-5x+7)*(2x-5))=1
    1
  2074. limn->∞1/(1-1/3)/(1/(1-1/4))=1,5/(4/3)=1,125 limn->∞(1+n)/2*n/((1+2n-1)/2*n)=1/2
    1
  2075. (R-r)²+288/π=(R+r)² 72/π=Rr, R-r=√(72/π){-√(18/π)+√(90/π)=r, R=√(18/π)+√(90/π);S=π/2(R²+r²)=π/2(216/π)=108
    1
  2076. 70°+2a=180°,a=55°✓
    1
  2077. $(-R;R)dx$(-√(R²-x²);√(R²-x²))2√(R²-x²)dy= 4(R²x-x³/3)(-R;R)=4(R³-R3/3)-4(-R³+R³/3)= 16/3R³ V=(2π+16/3)R³
    1
  2078. 1-(x+a+1)²=y,y≤1 2^|x-a|=z≥1[y=z, {y=0,z=1;[{x=-0,5,a=-0,5;{[a=0,a=-1; x=a;{(-0,5;-0,5)(0;0)(-1;-1)}
    1
  2079. A(n+1)x²+B(n+1)x+C(n+1)=(An/2+Bn/2)x²+nx-(An+Bn)2-2n{A(n+1)=n-2+1/2^n, B(n+1)=n,C(n+1)=-6n+8-2^(-n+2);A1=-1,B1=0,C1=4✓ A1=-1,B1=0,C1=-4
    1
  2080. 4πx/3=±π/6+2πn x=±1/8+1,5n
    1
  2081. ~~`~ ~`~ ~~~`~ ~~`~ ~`~ ~~~`, ~` ~`~ ~ ~`~ ~`~, ~ ~`~ ~~` ~~`? 4 8 18 4 9 50, 4 2 600 4? 500 1 600 700?
    1
  2082. y''y'=siny/cos³yy',y≠c y'cosy/√(1+2c- 2csin²y)=±1 y=arcsin(√(1+2c)sin(±x+c1))(-1)^n +πn,c≠-1/2
    1
  2083. Ei=1;∞(-1)^(i-1)ln(1+x^i)~x/(1-x)=∞
    1
  2084. k=5,7*10-²/(380*10-⁹)=150*10³!
    1
  2085. 2$(0;π)sin²⁵xsin(17x)dx=0
    1
  2086. X+y=288° x=y x=144°
    1
  2087. 1500/230=6,52
    1
  2088. 35²+50²-31²=691*4 2√691✓
    1
  2089. Х=√3/2±1/2i x¹⁰⁰⁰=-1/2±√3/2i -1✓
    1
  2090. {a0+..+a(n-1)=1/2,a0(2^(n-1)-1)+..+a(n-2)=-1/6,..,a0(n^(n-1)-1)+..+(n-1) a(n-2)=1/(n+1)-1/2;f(x)=xa0(x-1)(x- 2)..(x-n)+x(a(n-1)-a0n!(-1)^n) f(n+1)=a0(n+1)!(1-(-1)^n)+(N+1)A(n -1) n=1,f(2)=1 n=2,f(3)=1/2 n=3,f(4)=1{1}
    1
  2091. a=2/3¹/⁴ 4/√3=AP²*7 AP=2/3¹/⁴/√7 arccos(2√7/7),60°-arccos(2√7/7) S∆=1/7
    1
  2092. πЕn=1;≠(2n-1)!/n!²*0,5^(2n-1)~√πS(1,5)
    1
  2093. Это Вы тут повторяет слова Левашова. Есть ролик на канале Знания Н.В.Левашова.
    1
  2094. √2а³+3/(ab-b²),a>b>0 √2а³+3/(ab-b²)'= 3√2a²+3/b*(a-b)^-2=0,3√2a⁴-6√2a³b+3 √2a²b²-3/b=0,a²-ab=±√(1/√2/b),a²-ab-+ √(√2/2/b)=0,a=(b±√(b²±4√(√2/2/b)))/2 **+*(b+...-..)-*(b+...+..)+>a,..+..+ ±4√(√2/2/b)>0,min=0,5√2b³+3*2^0,25 √b+(0,5√2b²+2^-0,75/√b+1,5*2⁰,²⁵)√(b² +4√(√2/2/b))≥10
    1
  2095. 1¹2³820²5*4=512820(✓?)
    1
  2096. xln-¹x+c
    1
  2097. 2(10^n-1)/3
    1
  2098. ЯНКА+119=ЯКУБ А=0,5670+119=5789 987 Макс. Б=0,А=1 423¹1+119=4350 мин=053.
    1
  2099. Ассимптоты:у=0,2х(х=±∞).
    1
  2100. 3х+3=Ах+2А+Вх-В{А+В=3,2А-В=3;{А=2,В=1;
    1
  2101. X=y^log12(9) y^log12(5/3)-y^log12(4/3)=1 y=12,x=9 x/y=3/4
    1
  2102. R(1+√2)=√2 R=√2(√2-1)/1=2-√2
    1
  2103. ((x+0,5)³-0,75(x+0,5)-2,25)(x+0,5)=0 x=-0,5,x=-0,5+3/2=1{-0,5;1}
    1
  2104. [х=1,х=(5±4)/3.{1;3;1/3}
    1
  2105. X=(362±38√91)¹/⁵ 38√91=362,52 2,85/2~1,425 a=±√((362±38√91)³/⁵+(362-+38√ 91)³/⁵-3)
    1
  2106. Lnx=u,x=e^u,dx=e^udu -0,25ln5+arctg2(🎉😢😮😅)
    1
  2107. $(0;1)(2+42lnx+70ln²x+14ln³x)dx= 2x+42(xlnx-x)+70(xln²x-2xlnx+2x)+14(xln³x-3xln²x+6xlnx-6x)(0;1)=2+ 42(-1)+70(2)+14(-6)=16
    1
  2108. b,c<a,c-2,a-2<b a=c(b+1)/(b-1)>8 c=-0,5b+12,5-12/b≥0 (b-24)(b-1)≤0 b[1;24] b=3,c=7,a=14× b=8,c=7,a=9✓ b=24,c=0,a=0×{504}
    1
  2109. x=11(log9(11)-1)/9
    1
  2110. F(2x)-F(0)+1/2/π(x²(F(2π)-F(0))+2x(2πF(2π)-$(0;2π)dtF(t))+4π²F(2 π)-4π$F(t)dt|2π+$(0;2π)2dt$F(t)dt)= sin(2x)+a,F(2x)=a+sin(2x)+F(0)-1/2/π(a1x²+bx+c),f(x)=cosx-1/4/π(a1x+ b),{0=b,a1=0; f(x)=cosx
    1
  2111. X=2(cos(π/4+πn/2)+isin(π/4+πn/2))
    1
  2112. a=50°-+arccos(1/3)+2πn -cos(2arccos(1/3))=7/9 D)
    1
  2113. $(0;1)((1+x²,⁵)⁵/²-2(1+x²,⁵)³/²+(1+ x²,⁵)¹/²)x¹,⁵dx=(1+x²,⁵)³,⁵/3,5/2,5-(1 +x²,⁵)²,⁵/2,5²+(1+x²,⁵)¹,⁵/1,5/2,5(0;1) =212*2¹,⁵/525-116/525
    1
  2114. (k-log(10/7)10)/k>0+log(10/7)10°-°0+>k k(-∞;0)U(log(10/7)10;∞) (k+log0,7(10))/(k+1)>0+°log0,7(10)-°-1+>k,k(-∞;log0,7 +10))U(-1;∞) k(-∞;log0,7(10))U(-1;0)U(lo g(10/7)10;∞)
    1
  2115. {(2;3)(3;2)(1;5)(5;1)}
    1
  2116. -1+а²/(a²-b²)=b²/(a²-b²)
    1
  2117. 1+a²+2=7² a=±√46≥0 S=46
    1
  2118. (4sinxsin2x-sin²2x-4+4cos²x)/√(16-2^(x -5)²)≥0,{16-2^(x-5)²>0,2^(x-5)²<16,(x-5)²<4,{x-5<2,x-5>-2;{x<7,x>3;хє(3;7) 4sinx*2sinxcosx-4sin²xcos²x-4+4cos²x≥0,8(1-cos²x)cosx-4(1-cos²x)cos²x+4cos²x-4≥0,8cosx-8cos³x-4cos²x+4cos⁴x+4cos²x-4≥0,4cos⁴x-8cos³x+8cosx-4≥0,(cosx-1)(4cos³x-4cos²x-4cosx+4)≥0,(cosx-1)² (cos²x-1)≥0,(cosx-1)³(cosx+1)≥0, -1+*-*1+>cosx cosxє(-∞;-1]U[1;+∞) [x=π+2πn,x=2πn;x=πn.>3,n>3/π=0,..,πn<7, n<7/3,14=2,.. n=1;2,x=π;2π{π;2π}
    1
  2119. h=-12+√319 h1=√319 a=9*2=18 S=-216+18√319✓
    1
  2120. {ab=22,a²+b²=100;{a+b=12, a-b=±√56;{(6±√14;6-+√14)}r=1
    1
  2121. (x²+2x-7)²-64=(x-3)(x+5)(x+1)²
    1
  2122. (111^2-777)/2=(12321-777)/2=11544/2=5772
    1
  2123. x³/√(288-x²)+x²-288=0 {-x²+288≥0,-x²+288≠0;{(x-√288)(x+√288)≤ 0+*-*+>x,x≠√288; xє(-√288;√288) х³+(х²-288)√(288-х²)=0, -√(288-х²)³=-х³, -√(288-х²)=-х, 288-х²=х²,х≥0, 288=0 неверно 0/
    1
  2124. (2+i)(1+2i)/5=i n=4m,mZ
    1
  2125. |A|=2*5-(-6)*-1=4 A-¹=1/4(2 -1;-6 5)=(0,5 -0,25;-1,5 1,25)
    1
  2126. (x+8)*1=(R-h)(R+h)=8*3 x=16
    1
  2127. 15/16
    1
  2128. 2x²+x(-2y+9)+y-2=0 x=(2y-9±√(4y² -44y+97))/4 (2y-11-n)(2y-11+n)=24 [{y=9,n=5;{y=8,n=1;{y=3,n=1;{y=2,n= 5; x=(9±5)/4=3,5;1 x=(7±1)/4=2;3/4 x=(-3±1)/4=-0,5;-1 x=(-5±5)/4=0;-2,5 {(1;9)(2;8)(-1;3)(0;2)}
    1
  2129. y=x+5+4/(x-3) x-3=±1;±2;±4 x=4;2;5;1;7;-1 y=9+4/1=13;7+4/-1=3; 10+4/2=12;6+4/-2=4;12+4/4=13;4+4/-4=3 {(4;13)(2;3)(5;12)(1;4)(7;13)(-1;3)}
    1
  2130. Arccos(15/8/√13),AC*7/12, arccos(13/14) AC=(13√607+45√3)/2/√39, x=AC*7/12-4=14,7E)
    1
  2131. √(11+√57)=√(19/2)+√(3/2)
    1
  2132. КОКА+КОЛА=ВОДА,6 букв А=0 К≥1,≤4 2О+1=..О,О=9 К0¹К+К9Л=В0Д{К+Л=10+ Д,2К+1=В;К≥2,Д≤5,Д≥1 К=2:Л=8+Д,Л=1, Д=9 0/,К=3:Л=7+Д,Л=1,Д=8 В=7✓ К=4: Л=6+Д,Л=1,Д=7,Л=2,Д=8 В=9
    1
  2133. ✓✓×××;×✓✓××;××✓✓×;×××✓✓ 1/4 шанс умереть ответ: лучше стрелять.
    1
  2134. (3¹/²-1)/16✓
    1
  2135. 2lnsec(2^x¹/³)*cos-¹2^x ¹/³sin2^x¹/³*2^x¹/³ln2/3x-²/³
    1
  2136. 0,6*3,5+7,3/2*0,4+1,9*0,6=4,7
    1
  2137. 2,5^(x+2)>1 x+2>0,x>-2
    1
  2138. {x-y²=5,√x/y+y/√x=13/6;√x/y=z z=-13/12±5/12=-2/3;-3/2[{[×,×;[y=-1,5√x,y=-2/3√x;×
    1
  2139. S∆=1/30a² a²=30
    1
  2140. S=8π-16
    1
  2141. $(0;π/2)tgxdx/√2/(tgx+1)=$(0;=)dt* t/(1+t²)/(t+1)/√2=√2/8ln(1+t²)+√2/ 4arctgt-√2/4ln|t+1|(0;=)=√2*π/8 tgx=t,x=arctgt,dx=1/(1+t²)dt t√2/2=A*2t(1+t)+B(1+t)+C(1+t²) {A=√2/8,C=-√2/4,B=√2/4;
    1
  2142. √3/5=h/(2+h√3/9) 3√3/7=h X=3
    1
  2143. [{x=3,y=3+a;{[x=5+√(7+a),{a[-7;-3], x=5-√(7+a);{a(-3;1],x=1+√(1-a); x=1-√{1-a);y=x+a.
    1
  2144. 10+Ek=7;16tg(15°(k+1))tg(15°k)=14 +6√3 Tg(15°k)tg(15°(1+k))
    1
  2145. 108√5=13,5h h=8√5 r=4√5 8√5/21=2tg0,5a/(1-tg²0,5a) 4√5/21-tg0,5a-4√5/21tg²0,5a=0 tg0,5a=(-21+√761)/(8√5) (21+√761)/2 (21+√761)²/4=l(l-x), (9,5-√761/2)²=(√720-l)(√720-l+x) {2√(-42-2√761)/3=x✓, l=(37√5+√5√761+2√(-42-2√761))/6.√(-42-2√761)≥2/9
    1
  2146. 128>125,..>..
    1
  2147. F(p)=5/p+24/p⁵+6p/(p²+9)²
    1
  2148. arccos((a²+4)/4/√10/a)=arcsin ((a²+20)/4/a/√10) a⁴-56a²+208=0 a²=28±24=52;4 a=2√13;2[-2√5+2√10;2√5+2√10] a²-4>0,✓;× a=2√13 S=52
    1
  2149. Мин=√13+2√13=3√13
    1
  2150. a²+(x-2021)²=|x-a-2021|-|x+a-2021|,[{x≥a+ 2021,a²+(x-2021)²=-2a;{хє[-а+2021;а+2021);a²+(x-2021)²=-2x+ 4042;{х<-а+2021,a²+(x-2021)²=2a;[{x≥a+ 2021,x=2021±√(-а(а+2))+*-2-*+0>а;{хє[-а+2021;а+2021);x²-4040х+2021²-4042+а²=0;{х<-а+2021,x=2021±√(-а²+2a);[а=0,х=2021,{хє[-а+2021;а+2021), х=2020±√(1-а²);{х<-а+2021,ає(0;1), a(a-1)<0 +0°-°1+>a;[a=0,x=2021,aє[0;1],х= 2020±√(1-а²);ає(0;1),х=2021-√(-а(а-2));
    1
  2151. Ax²/2+bx=a/2+b=1 a/3+b/2=1 {a=-6,b=4;-2✓
    1
  2152. log²(2)(x+1)/(2x-1)-log(2)(x+1)/(2x-1)≤0 y=log(2)(x+1)/(2x-1) y(y-1)≤0+*0-*1+>y ує(-∞;0]U[1;+∞) [{(x+1)/(2x-1)>0,(x+1)/(2x-1)≤1,(x+1)/(2x-1)≥2;[{(x+1)/(x-1/2)>0, +°-1-°+0,5>x (x-2)/(x-1/2)≥0+°0,5-*+2>x;(x-1)/(x-1/2)≤0+°0,5-*1+>x;[{хє(-∞;-1)U(0,5;+∞),хє(-∞;0,5)U[2;+∞); хє(0,5;1];[хє(-∞;-1)U[2;+∞),хє(0,5;1];хє(- ∞;-1)U(0,5;1]U[2;+∞)
    1
  2153. 2,5*2⁰,⁵-2 11/12+π/8
    1
  2154. a+3=R,5²+(a+2)²=(a+3)² 25=2a+5,a=10,R=13 10-4,8=5,2 5,2/12*5=13/6 S∆=0,5*5,2*13/6=169/30
    1
  2155. 3^(x-1)(ln3*x-1)x-²=0 x=log3(e)-*+>x min=e/3*ln3=2,992/3<1 x=1;0,8..✓
    1
  2156. 4+3loga(b)=4+3*4=16
    1
  2157. c=b²/a, (a+b+b²/a)/3=b+2, 1/3/a*b²-2/3*b+a/3-2=0, b=(2/3±√(4/9-4/3/a*(a/3-2)))/(2/3/a)=a±√(a²-3a²(a/3-2))=a±√(a²-a³+6a²)єN, -a²(a-7)≥0, +0+7->x aє(-∞;7] 1±√(7-1)1±√6є/N, 2±√(4*7-8)=2±√20є/N, 3±√(7*9-27)=3±√36=9єN,c=9²/3єN 4±√(7*16-64)=4±√48є/N, 5±√(7*25-125)=5±√50є/N,6±√(7*36-216)=6±√36=12єN,c=12²/6єN 7±√(7*49-343)=7єN, c=7²/7єN(3²+3-14)/(3+1)=-0,5 (6²+6-14)/7=4, (7²+7-14)/8=5,25
    1
  2158. x^(k-1)cos(πx/2)*2/π+(k-1)x^(k-2) sin(πx/2)*4/π²+..-(k-1)!cos(πx/2+π/2(k-1))(2/π)^k(0;1)=(k-1)*4/π²+..-(k 1)!(cos(π/2k)-cos(π/2(k-1)))(2/π)^k a(k+2)=-4/π²(k+1)(-1+ak-(k-1)(k-1)!(cos(π/2k)-cos(π/2(k-1)))(2/π)^k) kak=((π/2)^(k-2)/(k-2)!+..-(cos(π/2k) -cos(π/2(k-1))))k!(2/π)^k=∞ 2)∞3)∞
    1
  2159. a*a/√(a²+4) 4/√(a²+4)*√(a²+4)=4
    1
  2160. у"+2у'+2у=0 у=е^(ах) а²+2а+2=0 а=(-2±√ (4-4*2))/2=-1±√-1 у=е^(-х+ix) y=e^(-x-ix) y=c1e^-xcosx+c2e^-xsinx
    1
  2161. {y≤√(2-x),y≥-√(2-x),y≥-x,y≥-2+x;x≤2,2-x=X²,x²+x-2=0, x=(-1±√9)/2[x=1,x=-2;-x=2+x,x= -1 2-x=(2-x)²,[2-x=0,2-x=1;{2;1} S=$(-2;1)(√(2-x)-x+2)dx+$(1;2)(√(2-x)+x)dx=-(-x+2) ¹,⁵/1,5-x²/2+2x(-2:1)+(-x+2)¹,⁵/-1,5+x²/2(1: 2)=12 1/6+0/-1,5+2 1/6=14 1/3
    1
  2162. (63√2+55)¹/³=3√2+1 5,2-3,2=2 54/3=18 21√18=63√2✓
    1
  2163. (x+2/3)/(x+1)/(x+0,5)/(x+2)<0+-2°-1-°+-2/3°-°-0,5+>x x(-2;-1)U(-2/3;-0,5)
    1
  2164. [y=2πn,x=2πn,y=-x+2πn.
    1
  2165. e^x-x=0, e^x-1=0, x=0, -*+ минимум 1 т.е. решений не существует
    1
  2166. $dx*(4/(cos2x-1)²+1/sin²x+1/cos² x)=-1/3cosx*(sinx)-³+2/3/sin2x+ 1/6En=0;∞C(-0,5;n)(-1)^n(cosx)^ (2n-1)/(n-0,5)-2ctgx+tgx+c cos²x=u,x=±arccos√u,dx=-+0,5/√(u-u²)du
    1
  2167. M~R⁴/³ а для чего это мне? М+5lgr=М0+5, r=k-⁵/¹⁶tg(a/2)-¹³/⁸*(I0*10 ^(-0,4M))⁵/¹⁶ M0=3/8M-5+45/16lg(k-⁵tg (a/2)-²⁶I0⁵) вроде так.
    1
  2168. {12x+15y=321,400'000x+600'000y? y=2 1,4-0,8x 400'000x+600'000(21,4-0,8x)= -80000x+12'840'000\>,≤12'840'000,≥-1'740'000+12'840'000=11'100'000
    1
  2169. a(2n)=a2an+1, a(2n+1)=a2an-2, a7=2, a1e(0;1) a25=? a25=a2a12-2=a2(a2a6+1)-2=a2(a2(a2a3+1)+1)-2=a2³(a2a1-2)+a2²+a2-2=a2⁴a1-2a2³+a2²+a2-2 a2=a2a1+1, a2=1/(1-a1)є(1;+∞),а7=а2а3-2=1/(-а1+1)*(1/(1-а1)*а1-2)-2=(а1-2+2а1-2(а1-1)²)/(-а1+1)²=(-2а1²+6а1-4)/(а1-1)², 2а1²-4а1+2=-2а1²+6а1-4, -4а1²-10а1+6=0, А1=(10±√(100-4*(-4)*6))/(-8)=-1,25±14/8, А1=0,5 ,а25=1/(1-0,5)⁴*0,5-2³+2²+2-2=16*0,5-4=4
    1
  2170. x^2^√2=2^√2^x {x>0,x=2^2^(0,5*2^(2^.. -√2)-√2);
    1
  2171. 0/ (0;±1)
    1
  2172. X=y^(log(2)12/4),y^(log2(5/3)/4)-y ^(log2(4/3)/4)=1 y=2^(4n) (5/3)^n-(4/3)^n=1,n=2✓ y=2⁸,x=12² y-x=256-144=112 C)
    1
  2173. $(1/cos²x+1/cosx)dx=tgx+ln|tg(π/4-x/2)|+c
    1
  2174. bn=±2am |bn|/|am|=2
    1
  2175. X²=1,x=±1 16=15^x⁴+x²\>*0/>
    1
  2176. X=1,0=√x/2-1 x=4{1;4}
    1
  2177. 8^(5/3)*2=a a=2⁵*2=64
    1
  2178. (x³/18-3/2)³=9(2x+3) 0,5((x³/18-3/2) ²*x²-36)=0 x⁴-27x-+108=0 z³±27/2z-729/64=0 z=(1/2+√2049/2)¹/³*9/4+(...-..)..;- (1/2+√2049/2)¹/³*9/8-(...-..)..±√(3/4 ((1/2+√2049/2)¹/³*9/4+(...-..)..)²+2 7/2)i z=9*2¹/²cos(1/3arccos(1/32/√2)+2/3πn) x=√((1/2+√2049/2)¹/³* 9/4+(...-..)..)±2√(0,5√(((1/2+√2049/ 2)¹/³*9/4+(...-..)..)²+27/2)-(1/2+√204 9/2)¹/³*9/16-(...-..)..) ×+*+>x max=((√((1/2+√2049/2)¹/³*9/4+(...-..)..)-2√(0,5√(((1/2+√2049/2)¹/³*9/4+(...-..)..)²+27/2)-(1/2+√204 9/2)¹/³*9/16-(...-..)..))³/18-1,5)³-18 (√((1/2+√2049/2)¹/³*9/4+(...-..)..) 2√(0,5√(((1/2+√2049/2)¹/³*9/4+(...-..)..)²+27/2)-(1/2+√2049/2)¹/³ 9/16-(...-..)..))-27?0 min=((√((1/2+√2049/2)¹/³*9/4+(...-..)..)+2√(0,5√(((1/2+√2049/2)¹/³*9/4+(...-..)..)²+27/2)-(1/2+√204 9/2)¹/³*9/16-(...-..)..))³/18-1,5)³-18 (√((1/2+√2049/2)¹/³*9/4+(...-..)..)+ 2√(0,5√(((1/2+√2049/2)¹/³*9/4+(...-..)..)²+27/2)-(1/2+√2049/2)¹/³* 9/16-(...-..)..))-27<0 3 решения х=4,85;-1,85;-3✓
    1
  2179. Полен классная оговорка.
    1
  2180. х²+(1/у-3у)х-3=0 х=(-1/у+3у±√((-1/у+3у)²+ 12))/2 (х²+у²+Ху)/(х²-у²-ху)=(±(-0,5/у+2у) (1/у+3у)+у-²/2+2,5+7у²)/(±(-0,5/у+у)(1/у+3у)+у-²/2+0,5+2у²)=[(3+13у²)/5/у²,-1+(2+7у²)/(-у⁴+1+у²).
    1
  2181. (x-3)(x-5/3)=0 x=3;5/3✓
    1
  2182. (1;-6),y=ax²-4x+c -2-a=c 2=a,c=-4 f(-3)=2*9-4*-3-4=26
    1
  2183. 9,47/28*9,19/28*9,17/28*9,-99/28 35/9,28/9,56/9 S=-99/4(cm²)
    1
  2184. X=0,985 100x⁹⁹-30x⁹-2=0 9900(x⁹⁰-3/110)x⁸=0 x=0;±(3/110)¹/⁹⁰+*-0-*+>x max=27 3/11(3/110)⁰,¹ 2>0 min<0 x=-0,74+*+>x max>0,min<0 x=1,02;-0,5;-0,87
    1
  2185. X=8n+..,y=-37n+..,8(y+5x)=1+3x,{y+5x=-1,x=-3;(-3;14){8n-3;-37n+14}
    1
  2186. z=3n1+0;1 z=6n+1;3
    1
  2187. √(4-2r²)=r r=2/√3 S=πr²/2=π*2/3
    1
  2188. sin((x2+x+1)/2/x)+cos((x²-x+1)/2/x)=(x²-4x+1)/xcos(π-2)
    1
  2189. {z=1-x-y, x²+y²+(1-x-y)²=2, x^3+y³+(1- x-y)³=3; {z=1-x-y, x²+y²+1+x²+y²-2x-2y +2xy=2, (x+y)(x²-xy+y²)+1-3(x+y)+3(x+y)²-(x+y)³=3; 2y²+(-2+2x)y+2x²-2x -1=0, (x+y)(x²-xy+y²-3+3x+3y-(x+y)²)-2=0; y=(2-2x±√((2-2x)²-4*2(2x²-2x-1)))/4, (x+ 0,5-0,5x±√(0,25-0,5x+0,25x²-x²+x+0,5))(x²-x(0,5-0,5x±√(-0,75x²+0,5x+0,75))+(0,5-0,5x±√(-0,75x²+0,5x+0,75))²-3+3x+3(0,5-0,5x±√(-0,75x²+0,5x+0,75))-x²-2x(0,5-0,5x±√(-0,75x²+0,5x+0,75))-(0,5-0,5x±√(-0,75x²+0,5x+0,75))²)-2=0; (0,5x+0,5±√(-0,7 5x²+0,5x+0,75))(1,5x²-0,5x-+√(-0,75x²+0, 5x+0,75)+(0,5-0,5x)²±(1-x)√(-0,75x²+0,5x+0,75)-0,75x²+0,5x+0,75-x²-x+x²-+√(-0,75x²+0,5x+0,75)-(0,5-0,5x)²-+(1-x)√(-0,75x2+0,5x+0,75)+0,75x2-0,5x-0,75)-2=0;(0,5x+0,5±√(-0,7 5x²+0,5x+0,75))(1,5x²-1,5x-+2√(-0,75x²+0,5x+0,75))-2=0, (0,5x+0,5)(1,5x²-1,5x)-+(x+1-1,5x²+1,5x) √(-0,75x²+0,5x+0,75)-2(-0,75x²+0,5x+0,75)-2=0, -+(-1,5x²+2,5x+1)√(-0,75x²+0,5x+0, 75)=-0,75x³+0,75x²-0,75x²+0,75x-1,5x²+x+1,5+2, (-1,5x²+2,5x+1)(-0,75x²+0,5x+0,7 5)=(-0,75x³-1,5x²+1,75x+3,5)² x=(-2,5±√ (6,25-4(-1,5)))/-3, x=-1/3, x=2, x=(-0,5±√ (0,25-4(-0,75)*0,75))/-1,5 x=1/3±2√2,5/3, (x+2/3)³+(-7/3-4/3)(x+2/3)-14/3-8/27+ 22/9=0, x+2/3=(-68/27/2+√((34/27)²+(-11/3)³/27))^(1/3)+(-34/27-√(34²/27²-1331/27²))^(1/3), x=-2/3+(-34+√(115 6-1331))^(1/3)/3+(-34-√-175)^(1/3)/3=-2/ 3+√1331^(1/3)*cos(1/3*arccos(-34/√1331))+2πn/3)*2/3=-2/3+2√11/3*c os(1/3*arccos(-34/√1331)+2πn/3) (-2/3+2√11/3cos(1/3*arccos(-34/√1331)))⁵+(-2/3+2√11/3*cos(1/3*ar ccos(-34/√1331)+2π/3))⁵+(-2/3+2√ 11/3*cos(1/3*arccos(-34/√1331)+4π/3))⁵=8,83..
    1
  2190. X=chu,dx=shudu $dx/x⁴/√(x²-1)=$ 8du(2e^(2u)/(e^2u+1)³-2e^(2u)/(e^(2 u)+1)⁴)=-x-²(x-+√(x²-1))²+x-³(x-+√(x ²-1))³/3+c 0=e^2u-2xe^u+1,e^u=x±√(x²-1)
    1
  2191. (a*3^d-b*2^c)*5⁴=2^c*3^d+337[375;8113],a*3^d-b*2^c=1;..;12 c,d[2;5],b[1;9],a≤33 625-337=288=2⁵*3² a*9=b*32+1 (25;7) 1875-337=1538=2*769× 3125-337=2788=4*697× 4375-337=4038=2*3*673× 5625-337=5188=4*1297× 6875-337=6538=2*3269×{(25;7;5;2)}
    1
  2192. z=-x-y, (x⁴+y⁴+(x+y)⁴)/(x²+y²+(x+y)²)²=(x⁴+y⁴+(x²+2xy+y²)²)/4/(x²+y²+xy)²=(2x⁴+2y⁴+6x²y²+4x3y+4xy³)/4/(x⁴+y⁴+3x²y²+2x³y+2xy³)=0,5
    1
  2193. (5^х-3)²/(5^х-1)/(5^х-1/5)≤0+°-1-°0+*log5 (3)+>х x(-1;0)U{lpg5(3)}
    1
  2194. ?|?|?|?|*|?|?|?|? ?|?|*|?|?|?|*|?|? ?|?|*|?|?|?|*|?|? ?|?|?|?|?|?|?|?|? ?|?|?|*|*|*|?|?|? |*|?|?|?|?|?|*| ?|?|?|?|?|?|?|1|1 ?|?|*|?|?|?|*|2|6 ?|?|*|?|?|?|*|4|8
    1
  2195. Насчёт цветов скажу 1: почти все люди видят цвета одинаково.
    1
  2196. Но если кто говорит о личных качествах, то это не значит, что в принципе никогда не будет вести по-другому.
    1
  2197. X=sinu,dx=cosudu $dx/x/√(1-x²)= $du/sinu=ln|tg(u/2)|+c=ln|(1-√(1-x ²))/x|+c
    1
  2198. (2tg²x+5tgx)/(sin2x+2,5cis2x+5/2)=0{2tgx (tgx+2,5)=0,√7,25sin(2x+arccos(1/√7,25))+5/2≠0;{[tgx=0,tgx=-2,5;x≠-0,5arccos(1/√7, 25)+0,5arcsin(-5/√29)(-1)^n+πn/2;{[x=πm, x=arctg-2,5+πm;[x≠-π/4+πn, x≠-arctg(5/2) +0,75π+πn; 7/3,-1 {πm;arctg-2,5+πm}
    1
  2199. A зачем пишете с ошибками?
    1
  2200. |6RA->+2AB->+AC->|=6
    1
  2201. 1080=(6*5¹/³)¹/³ -1/3✓ {x=11/42,y=6/7;5 1/3✓
    1
  2202. 2:3*b√(0,5sin²_b:sin²(_a+_b)+0,5-0,2 5sin²_a:sin²(_a+_b)),2:3b√(0,5+0,5sin²_a:sin²(_a+_b)-0,25sin²_b:sin²(_a+_b)) h=S∆*2/b=b√((1/3√(0,5sin²_b:sin²(_a+_b)+0,5-0,25sin²_a:sin²(_a+_b))+1/3√(0,5+0,5sin²_a:sin²(_a+_ b)-0,25sin²_b:sin²(_a+_b))+1/2)(-1/3√(0,5sin²_b: sin²(_a+_b)+0,5-0,25sin²_a:sin²(_a+ b))+1/3√(0,5+0,5sin²_a:sin²(_a+ b)-0,25sin²_b:sin²(_a+_b))+1/2)(1/3√(0,5sin²_b: sin²(_a+_b)+0,5-0,25sin²_a:sin²(_a+ b))-1/3√(0,5+0,5sin²_a:sin²(_a+ b)-0,25sin²_b:sin²(_a+_b))+1/2)(1/3√(0,5sin²_b: sin²(_a+_b)+0,5-0,25sin²_a:sin²(_a+ b))+1/3√(0,5+0,5sin²_a:sin²(_a+ b)-0,25sin²_b:sin²(_a+_b))-1/2))*2
    1
  2203. En=1;∞(-1)^(n-1)e(n-1)!=-∞
    1
  2204. ​x=y+(1±√(25(2y-1)²+359)/2)/5 359=(10n+3-10y)(10n+10y-7)[{n=18,2,10y=18,4;{n=18,2,y=-17,4;{n=-17,8,y=-17,4;{n=-17,8,y=18,4;×
    1
  2205. (x/3)^(x/3)=27^3³ x/3=27{81}
    1
  2206. (a+b)/(a(a-b))*2a=2(a+b)/(a-b)
    1
  2207. 380'000/150/10⁶=2,5*10-³Вот поэтому и орбита выглядит как округленный 12-угольник.
    1
  2208. 1,5√2+1,5/√2=2,25√2(см) 1,5√3(см) а,√(1,125-а²) (0,75√6-√(1,125-а²))²+(1,5√3-а)²=3² √(1,125-а²)=-√2а+√1,5/2 0=3а²-√3а+1/2 а=(√3±√3i)/6 V=(4√(√545+4)+12√(√733+27)-12√(√733-27)-√(2√745-54)+9√6-10√(2√745+54)±i(4√(√545-4)+12√(√733+27)-12√(√733-27)+11√6-√(2√745+54)+√(2√745-54))i)/384 V1=(4√(√545+4)+12√(√733+27)-12√(√733-27)-√(2√745-54)+9√6-10√(2√745+54)±i(4√(√545-4)+12√(√733+27)-12√(√733-27)+11√6-√(2√745+54)+√(2√745-54))i)/64
    1
  2209. (2^(n-m)-1)/2^n=3/k n=m+2 k=2^(m+2) n=m-2 k=-2^m
    1
  2210. 1/9/4/5=1/180
    1
  2211. 4*(3+6)/2=18✓
    1
  2212. 6/13=0,(461538)
    1
  2213. {x=1000-2018y-¹,1000y²-3009y+2018=0;y=(3009±991)/2000=2;1,009 x=991;-1000{(991;2)(-1000;1,009)}
    1
  2214. a=a1³,2a1⁵+2a1⁴+2a1³+2a1²+2a1+2+2/(a1-1)=b,a1-1=±1;±2 a1=2:0;3;- 1 b=127;-2;729;-1 a=8;0;27;-1{(8;12 7)(0;-2)(27;729)(-1;-1)}
    1
  2215. (5+x)^2+x^2=(x+10)^2,x>0, 25+10x+2x^2-x^2-20x-100=0, x^2-10x-75=0, x=(10±√(100+4*75))/2=5±10=15;-5 x=15
    1
  2216. V=162π(cm³)
    1
  2217. X≥0 0<1,≠>0 E! ±x-(√3-√2)^x=0 ±1-(√3-√2)^xln(√3-√2)=0 +×,x=log(√3-√2)(log(√3+√2)e),-✓ +>x+*->x max=log(√3+√2)(log(√3+√ 2)e/e)<0 x=0,53✓
    1
  2218. x=-arccos(siny/√(sin²y+1))±arccos(cosy/√(sin²y+1))+2πn t=(cosy+√2)/(sin²y+1)* sin²y (cosysin²y+√2sin²y)/(sin²y+1)'=siny (-sin⁴y-sin²y+2cos²y+2√2cosysin²y+2√2cosy-2√2sin²ycosy)/(sin²y+1)²=0 [siny=0, (cos²y+2√2cosy-6,5)²+24√2cosy-40,25=0;[y=πn,cosy=\(-88,25-24√17)*/*-√2(-16)\* -√2+√8,5(-88,25+24√17)/ -545/192*√2- 2√8,5,cosy=3572/4303√8,5-1 2064/4303 √2;*0+arccos0,32*-*π+*2π-arccos0,32-•2π>y max=98053/118600 min=0,max=980 53/118600,min=0
    1
  2219. limx,y->0,0(x²sin²y/(x²+2y²))=0/0=limx, y->0,0(sin²y/1)=0
    1
  2220. limx,y->0(x²y/(x+y))
    1
  2221. (х-1)(х+х-¹-3)(х+х-¹-4)=0 [х=1,х=(3±√5)/2,х=2±√3.
    1
  2222. 6->94=36*2+3*6+4,7->46=7*6+6,8->18=2*8+2,5->182;-48;-28
    1
  2223. f(x)=±(x-3)+2=x-1;-x+5✓
    1
  2224. $(0;1)xarcsinxdx=x²/2arcsinx+0,25 (-arcsinx+x√(1-x²))(0;1)=π/4+0,25(- π/2)=π/8
    1
  2225. X≥1 x(x+1)=56 x=-0,5±7,5 x=7;-8{7}
    1
  2226. х³+2х²+17х+6|х-3 х³-3х² х²+5х+32 5х²+17х 5х²-15х 32х+6 32х-96 102
    1
  2227. -(-1+2cos17°)(1+2cis17°)/2/cos²17° /_1=77°
    1
  2228. x=logi(2)=-iln2/(π/2+2πn)
    1
  2229. sin65°-cos85°,(sin65°-cos85°)/sin55° (sin65°-cos85°)ctg55° sin85°+(sin65°-cos 85°)ctg55° sin65°/(sin85°+2cos40°sin25° tg35°)=tg? x=55°-arctg(cos25°cos35°/(sin 50°+0,5cos50°+0,5sin10°))
    1
  2230. В ев щвуцчуц - ыри ывс екьротгръ щвгм\прывеефъ икучи, евлкбчт, ири, Уир кнр пвщнвлвки, аряцычиыцки чкь] Гкпорурс Зросчрс!
    1
  2231. z-z'(x0)x=-z'(x0)x0+z0,z-z0=z'(y0)(y-y0) -z'(x0)x-z'(y0)y+z+z'(x0)x0+z'(y0)y0-z0=0 z'(x)=ln(xy-5)+x/)xy-5)*y z'(y)=x/(xy-5)*x -6x-4y+z+23=0
    1
  2232. z=2+2i±i=2+3i;2+i
    1
  2233. $(1;a)lnxdx=xlnx-x(1;a)=alna-a+1=2 a=e^W(1/e)
    1
  2234. S=11*14*0,5-7*4=49
    1
  2235. c²+b²-cb=3/4a² c=b/2±√3/2√(a²-b²) √((b/2+√3/2√(a²-b²))²+3/4a²+(b+√3 √(a²-b²))²√3√(a²-b²)/(b-√3√(a²-b²))) x=30°
    1
  2236. 36+(a-2)²=a²+2² a=9 S=0,5*6*7+0,5*9*2=30
    1
  2237. X≥0 x⁴-9x²+3²*2=0 x²=(9±3)/2=6;3 x=√6;√3
    1
  2238. $(0;1)dx/(2+x)/√(2-x²)=$(0;π/4)du/(√2+sinu)/√2=$(0;√2-1)dz/(z²+√2z+ 1)=arctg((z+√2/2)/(√2/2))√2(0;√2-1) =arctg(3-√2)√2-π/4*√2 x=√2*sinu,dx=√2*cosudu tg(u/2)=z u=2arctgz,du=2/(1+z²)dz
    1
  2239. (4-R)²+2²=R² 20-8R=0 R=2,5
    1
  2240. 0,33*1,16=0,3828 -61,72%
    1
  2241. {[x=πn,x=-arctg2,5+πn;[x≠-π/4+πm, x≠0,5π+πm;{πn;-arctg2,5+πn}
    1
  2242. 321/52=6 9/52 ~14.12.2016
    1
  2243. R=√(g²-h²) V=1/3πR²h=π/3(g²h-h³) π/3(g²-3h²)=0 h=g/√3+*->h max=2πg³√3/27A)
    1
  2244. a²+9+6a*√(1-9/a²)=25 a=10⁰,⁵ x=√2
    1
  2245. (х⁵-992)¹/⁵=х-2 0=(х-1)⁴+2(х-1)²-99 (х-1)²=-1±10=9;-11≥0 х-1=±3 х=4;-2
    1
  2246. 4/5*(5/4)^2х-1/5*1,25^х-1=0 1,25^х=(1±9)/8=5/4;× х=1
    1
  2247. √(2Ro(1-R))o'(t)=v(t) E=mv²/2=p(l0 -Ro)Ro(1-R)o'(t)²
    1
  2248. X¹/²+y¹/²=1 y=(1-√x)² $(0;1)(1-2√x+ x)dx=x-2x¹,⁵/1,5+x²/2(0;1)=1/6 L=$(0;1)2√2√(0,25+(x⁰,⁵-0,5)²)dx⁰,⁵= 2√2(0,5(x⁰,⁵-0,5)√(0,25+(x⁰,⁵-0,5)²)+ 0,125ln|x⁰,⁵-0,5+√((x⁰,⁵-0,5)²+0,25)|)(0;1)=1+0,5√2ln(√2+1)
    1
  2249. {x=3,y=1.
    1
  2250. 3(a-b)(b-c)(c-a)
    1
  2251. 7:30 перчатка Таноса.
    1
  2252. /_A=arctg2+arctg3 tg/_A=(2+3)/(1-2*3)= 5/-5=-1,/_A=135°
    1
  2253. lg³x-1=7 lgx=2 x=100
    1
  2254. 4047(2023²+2024):5°1
    1
  2255. S∆=27/2+20-49/2=9
    1
  2256. b=a/2 3a²/(0,5a²)=6
    1
  2257. у=(Ах+В)е^х у'=(Ах+А+В)е^х у''=(Ах+2А+В)е^х (-Ах+А-В)е^х=4х е^х{А=-4,-4=В;Ур=(-4х-4)е^х у=с1е^-х+с2е^(2х)+(-4х-4)е^х
    1
  2258. x¹⁰-123x⁵+1=0 x⁵=34+55(1±√5)/2 5;8,13,21,34,55 x=(3±√5)/2 (x⁹+1/x⁹)/(x⁸+1/x⁸)=5778/2207
    1
  2259. (3x-arccos-0,5)()/()
    1
  2260. х=(-1/2+√(1/4+2021³/27))^(1/3)+(-1/2+√(1/4+2021³/27))^(1/3)=(-0,5+√33'018'621'021'071/6/√3)^(1/3)+(-0,5-√33'018'621'021'071/6/√3)^(1/3) 2021 2021 2021 4042 4042 4084441 *2021 4084441 8168882 8168882 8'254'655'261*4=33'018'621'044+27=33'018'621'021'071
    1
  2261. 5500/269500=0,02 от всех оценок. Неплохо.
    1
  2262. √7=2,65..>13/8*1,5..=39/16..=2,43..
    1
  2263. Дорогой Павел! Это может быть либо СВПО, либо белые шляпы.
    1
  2264. 68 2/3
    1
  2265. Х≤0 -36=х✓
    1
  2266. х²+0,5=±4,5 х²=4;-5≥0 х=±2
    1
  2267. 2023/(2021+2025)=1/2
    1
  2268. Tgx=t,x=arctgt,dx=dt/(1+t²) $(0;π/4) dt/(1+2sin²x)=$(0;1)dt/(1/3+t²)/3= arctg(t√3)√3/3(0;1)=π√3/9
    1
  2269. E^(-n-¹)c=F(n) f(n)=e^(-n-¹)n-²c✓
    1
  2270. 199К=89Т-О К≤3,Т≥3 К≠0,Т≠0 К=3 89Т-О=597 Т[6 45/89;6 52/89]× К=2,398=89Т-О Т[4 42/89;4 51/89] К=1,199=89Т-О Т[3;2]××
    1
  2271. 9..9 m=2+17m1× 15=9+6 9799,9800
    1
  2272. 2021/7=288 4/7 577? ходов
    1
  2273. X=-∞;∞ |(0;0)±π(a²-y²)¹,⁵/3=0 2π/3a³(?×)
    1
  2274. 2016=2⁵*63=2⁵(2⁶-1) [a=11,b=5.
    1
  2275. R²+(R-2)²=2R²-4R+4=2a² a=√(R²-2R+2) 90°-2arcsin(√(R²-2R+2)/2/R) (R-2)²+R²-2(R-2)R*2√(R²-2R+2)/2/R*√(3R²+2R-2)/2/R=R²-2R+2,R≥2 0=(R-1)⁴-6(R-1)²+1 (R-1)²=3±√8 R=1±(√2±1)=2+√2✓;-√2×;√2×;2-√2× S=0,5(2+√2)√2=√2+1
    1
  2276. (5 2|1) (0 1|-1/3) ..=1/3{x=√2+3,y=-3√2-1.
    1
  2277. X=8/17
    1
  2278. {x=z³-y²,[y=0,y=-1;z=0,z=1,z=(1±√5)/2;z=0,2z⁵-z³+z±√(z³-z)(z²-1)=0;[{z=0,yR;{z≠0,[y=z,y=±√(z³-z); 4z⁹-4z⁷-z⁶+5z⁵+3z⁴-2z³-3z²+z+1=0 36z⁸-28z⁶-6z⁵+25z⁴+12z³-6z²-6z+1=0 z[-1;0]U[1;≠)+ z=-0,43{(0;0;0)(-1;-1;0)(0;1;1)(1/2±√5/2;1/2±√5/2; 1/2±√5/2)(-0,43;-0,59;-0,43)}
    1
  2279. х≥16,5 -0,25х²+25,5х-1208,25=0 х=51±2√(-558)×
    1
  2280. {x>2,x[-0,5;3];x(2;3]m=3 {x≥0,x(|x-1|-2)≤0*-1*0-*3+>x;x[0;3] Сумма крайних значений 3.
    1
  2281. k=a(xC-3) -1/a/(xC-3)=k1 y=-1/a/(xC-3)(x-3)+9a 3/a/(xC-3)+9a=axC² √3/(xC-3)/√(xC+3)=a (-1,5+0,5xC;4,5a+xC²a/2)=(1,5;4,5a +xC²a/2) -1,5+0,5xC=1,5,xC=6 a=√3/9,y=√3/9x⅔
    1
  2282. 4:00 Вестник бкри разоблачил миф о ''самоварах''.
    1
  2283. |x|x/2-|x-1|(x-1)/2(-1:2)=2²/2-1²/2+1²/2+2*-2/2=0
    1
  2284. 2cos(x-30°)C)
    1
  2285. 41-40cosa=45+36cosa cosa=-1/19 S=0,5*5*4sina+0,5*3*6sina=6√10
    1
  2286. (2ab+(a²-b²)i)/(a²+b²)=(8-15i)/17 {a=1/4b,b≠0.
    1
  2287. z=2+i(π+2πn)/ln2
    1
  2288. AD=2√3/tg(60°-arctg(2√3/7))-2= 16/5(cm)
    1
  2289. 40^2a=40⁴ 2a=4{2}
    1
  2290. 200/80=2,5 раза,16/200=8%—обычно наоборот.
    1
  2291. (10^3^n-1)/9:3^n=0(mod..)
    1
  2292. S∆=√((8+r)(-4+r)(4+r)(8-r))/4 h=√((8+r)(-4+r)(4+r)(8-r))/2/(8+r)=√ ((6+a)(-2+a)(2+a)(6-a))/2/(6+a)=√ ((10+a+r)(-2+a+r)(2+a+r)(10-a-r))/2/(10+a+r) {r³-8r²+(-a³+6a²-12a-12 0)/(6+a)r+8(-a³+6a²+20a+72)/(6+a) =0,(-4+a²)(6-a)=(6+a)(-4+(a+r)²)(10- a-r)/(10+a+r);(r;a)=×(4;6)(5,25;4,19)✓ S=48π✓
    1
  2293. x^(logx(e-¹))=e-¹
    1
  2294. а,7/3а 24/а,6/а,18/а 12/а 1,5а S=18/a*5/6a=15
    1
  2295. 3/4х+7=1/3х+20 х=156/5л 30 2/5л✓
    1
  2296. nln3+ln2-ln((n+1)(n+2))=°
    1
  2297. (1,5^x)²+1,5^x-2=0 1,5^x=-0,5±1,5=1;-2>0 x=0
    1
  2298. (q-1)!*n^(-q-p), сходится при q+p>1, расходится при q+p≤1
    1
  2299. УЖ≥10*10¹/³,≤99999¹/³ УЖ[22;47]✓
    1
  2300. А почему Вас, Сигизмунд, так назвали?
    1
  2301. {mn-pq=16,mn+pq=90;{mn=53,pq=37;5+3+3+7=18
    1
  2302. √ctgx(sin²x-1/4)=0,ctgx≥0,хє(πn;π/2+πn],[x=π/2+πn,sinx=±1/2;[x=π/2+πn,x=±π/6+2πn,x=±5/6π+2πn;[x=π/2+πn,x=π/6+2πn,x=1 1/6π+2πn.
    1
  2303. xtg(x/2)+ln|cos(x/2)|(0;π/2)=π/2+ln (√2/2)
    1
  2304. А почему у Делягина раскос глаз 45°?
    1
  2305. F(x)=a(x-x0)²+y0,f'(x)=2a(x-x0) {8/9a=y1,4/9=x1,y0=16/9a;y1=x1=>a=1/2 f(x)'=x-x0
    1
  2306. {х=-z(5,y=z-1;(x+y)/(x+z)=4/5
    1
  2307. 65±60=125;5 [sin²x*4=3,sin²x*4=1; [cos(2x)=-1/2,cos(2x)=1/2;x=±1/3π+πn;±π/6+πn
    1
  2308. -sinx+√3/2x=0,x=0,sinx/x=√3/2× +*0->x max=1,min=√3/16π²
    1
  2309. {[b=156,b=65;[a=65,a=156.
    1
  2310. $sin201x*sin¹⁹⁹xdx
    1
  2311. (n+1)^-n((n+1)^(n-1)+(n-1)^(n-2)n+..+n^(n- 1))^-n*n^(n²+n) limn->∞(1/(e-1)/(n-1) e²*e^2n)=∞
    1
  2312. 0,5(9)-⁰,⁵(12)+1=9
    1
  2313. 3xf-4x=2f-20 f=(4x-20)/(3x-2) f(5)=0
    1
  2314. log(72)√18=log(72)n n=√18
    1
  2315. y=7x/3-x'/3 y'=10x-4y, 7/3x'-1/3x''=10x-2 8/3x+4/3x',-1/3x''+x'-2/3x(t)=0, 1/3k²+k 2/3=0,k=(-1±1/3)/(-2/3)[k=1,k=2;x(t)0=c1e ^t+c2e^2t,y=2c1e^t+5/3c2e^2t
    1
  2316. x²-4xy+4y²+2x+y+1 2x-4y+2=0,x=2y-1-*+ >x 4x+8y+1=0,y=1/2x-1/8*+>y min={x= 2y-1,0=-5/8;5y[-2,5;7,5]
    1
  2317. n+(n-1)*2+..+n*1=n(n+1)(n+2)/6=n² (n-1)/4 -n²+9n+4=0 n=(9+√97)/2 У меня не получилось.
    1
  2318. (5/12)/(5/4)=1/3✓
    1
  2319. {c=4-a-b,a=-0,5b+2±√(-3/4b²+2b+1),40/27-7/3(b-4/3)+(b-4/3)³=0; b=4/3+(-20+√57)¹/³/3+(..-..).. a=1 1/3-(-20+√57)¹/³/6-(..-..)..±√(-3/4((- 20+√57)¹/³/3+(..-..)..)²+7/3),c=1 1/3 -(-20+√57)¹/³/6-(..-..)..-+√(-3/4((-20 +√57)¹/³/3+(..-..)..)²+7/3) a⁴+b⁴+c⁴=(1 1/3-(-20+√57)¹/³/6-(.. -..)..+√(-3/4((-20+√57)¹/³/3+(.. -..)..)²+7/3))⁴+(1 1/3-(-20+√57)¹/³/6-(..-..)..-√(-3/4((-20+√57)¹/³/3+(..-..)..)²+7/3))⁴+(4/3+(-20+√57)¹/³/3+(-20-√57)¹/³/3)⁴
    1
  2320. (x+1)(x²-x+1)(x²+x+1)=(√2+2)(3+ √2)(5+3√2)=65+39√2
    1
  2321. n³+an²+bn+c≠m²,a,b,cZ✓
    1
  2322. $e^axcosbxdx=e^ax(b1sinbx+b2cosbx)+c =e^ax(1/(b+a²/b)sinbx+a/b/(b+a²/b)cosb x)+c ae^ax(b1sinbx+b2cosbx)+e^ax(b1bcosbx -bb2sinbx)=e^axcosbx,{ab1-bb2=0,ab2 +bb1=1;{ab1-bb2=0,b2=a/b/(b+a²/b);{b1=1/(b+a²/b),b2=a/b/(b+a²/b).
    1
  2323. 4√5 h=8/√5 4/5√5 a=12/5√5*4√5*0,5=24
    1
  2324. y=-1-2/(x-²*c-1)
    1
  2325. 4^2024:10=2(2^2:5)=8
    1
  2326. 2x-2y+1+(x-y+1)y'=0 x-y+1=z y=-z+1+x y'=-z'+1 3z-zz'=1 [z=0,3x+c=z;zp=1/3 [y=1+x,y=-2x-c+1,y=2/3+c.
    1
  2327. 4+d²-2d√3=b²+4-2b√3 [b+d=2√3✓,b=d×.
    1
  2328. у=х+4coso+1,y=-x+4coso-3 х=-2
    1
  2329. AC=√(6√(34+5KC)+18-5KC-KC²) AK=√(AC²+KC²)=√(6√(34+5KC)+18 -5KC) AC/AB=KC/BK -KC³-8,6KC²-2 5KC+90=(1,2KC²-30)√(34+5KC),((KC+43/15)³+26/75(KC+43/15)-90+22 1903/15³)/(KC-5)≤0;
    1
  2330. (e^(sin(sin(3/4x))lnchx)-e^(sh(shx)lnchx))/(arcsintgx-x/√(x²+1))= (1/8-135/256x²+243/2048x⁴-chx/2)/3=-1/8
    1
  2331. $(-2;2)(x⁴-4x²)dx=x⁵/5-4x³/3|(-2;2)=32/5- 4/3*8-(-32/5-4/3*-8)=-4 4/15+32/5-32/3 =0
    1
  2332. 10⁵*7,74=S r=496,5м
    1
  2333. x,y>0 x=-y²/(y-1)
    1
  2334. -(sin80°-sin40°)/sin20°=-2cos60°sin20°/sin20°=-2*0,5=-1
    1
  2335. 1/120-1/12cos2x+5cos²2x/24=0 cos2x=(1±√3/2)/5 x=±1/2arccos(1/5±√3/10)+πn
    1
  2336. x²-|3x-2|≥0 [x≥2/3,(x-1)(x-2)≥0+*+>x;{x<2/3,(x+1,5-√4,25)(x+1,5+√4,25)≥0+* +>x;[{x≥2/3,x(-∞;1]U[2;∞);{x<2/3,x(-∞;-1, 5-√4,25]U[-1,5+√4,25;∞);[x[2/3;1]U[2;∞),x (-∞;-1,5-√4,25]U[-1,5+√4,25;2/3);x(-∞;-1,5-√4,25]U[-1,5+√4,25;1]U[2;∞)
    1
  2337. 0+3+..+3n-3=(3n-3)/2*n
    1
  2338. (1 logx(y) logx(z))²=(3 4logx(y) 5logx(z)) (logy(x) 2 logy(z)). (4logy(x) 6 6logy(z)) (logz(x) logz(y) 3). (5logz(x) 6logz(y) 11) adjA²=(30 -14logx(y) -6logx(z)) (-14logy(x) 8 2logy(z)) (-6logz(x) 2logz(y) 2) adjagjA²=(12 16logx(y) 20logx(z)) (16logy(x) 24 24logy(z)) (20logz(x) 24logz(y) 44) |adjagjA²|=12*24*44+16*24*20+20*16*2 4-20*24*20-16²*44-12*24*24=24*480-11264=256
    1
  2339. (x+6)³+20(x+6)-225=0 x=-6+(225/2+5/2√167'865/9)¹/³+(..-..)..
    1
  2340. {x-y=2,x+y=1,5;(1,75;-0,25)
    1
  2341. $dx((x+1)¹,⁵-(x+1)0,⁵-(x-1)1,⁵-(x-1)⁰,⁵)/2=(x+1)²,⁵/5-(x+1)¹,⁵/3-(x-1)²,⁵/5-(x- 1)¹,⁵/3+c
    1
  2342. AG/GB=GB/(4/9AG) 2/3AG=GB k=1,5 BF=18/1,5=12
    1
  2343. X-√(64-x²),x-√(100-x²) x[√50;8] 64-x√(64-x²)=x√(100-x²) 1024-82x²+1105/1024x⁴=0 x²=512(82±48)/1105=1024/17; 1024/65 x=32/√17✓;32/√65×
    1
  2344. 0;1;2;3=2;1 1 или 2 числа нечетны, остальные четны. d≤n/4,a≥b≥c≥d,a+b+c+d≤n a²+b²+c²+d²=n²-6,n≥3 n=3,(1;1;1;0)(1;1;0;-1)(1;0;-1;-1)(0;-1;-1;-1) n=4,(2;2;1;±1)(2;2;-1;-1)(2;1;±1;-2)(1;±1;-2;-2)(-1;-1;-2;-2) Почти для всех n.
    1
  2345. Ну не знаю, может быть.
    1
  2346. En=1;∞(x^n(1+(-1)^n)+C(n;i)(-x)^i)/n²
    1
  2347. 1/4(-e^(-3t)+5e^t)✓
    1
  2348. 6^36/6³⁵=6
    1
  2349. (-1+√3)/2+(-√3+√5)/2=(-1+√5)/2 (-129+13√5)/2✓
    1
  2350. (R-7)²+9²=R² -14R+130=0,R=65/7
    1
  2351. |x-4|=3-2x x≤1,5 x=-1✓
    1
  2352. 16+x²-2x(-1;3)=16+3-3=16
    1
  2353. у=а/2(е^(х/а)+е^(-х/а)) y=-a/2(e^(x 1/a)+e^(-x1/a))+AB y=-a1/2(e^(x1/1a)+e^(-x1/a1))+AB 1/(e^(x1/a)-2+e^(-x1/a))(e^(x1/a1)- 2+e^(-x1/a1))(e^(X/a)+e^(-X/a)-e^(x 1/a)-e^(-x1/a))=e^(X/a1)+e^(-X/a1)- e^(x1/a1)-e^(-x1/a1),a=a1/(e^(0, x1/a)-e^(-0,5x1/a))²(e^(0,5x1/a1)- e^(-0,5x1/a1))² a/2(e^(x/a)+e^(-x/a))-a/2(e^(x1/a)+e^(-x1/a))+AB?
    1
  2354. (2x+y/(1+x²y²))/dy=(-x/(1+x²y²)+2y)/dx (1-x²y²)/(1+x²y²)²=(-1+x²y ²)/(1+x²y²)² ±x-¹=y✓
    1
  2355. xe^(2x)x'(t)=te^-t xe^(2x)/2-e^(2x)/4 +c=-te^-t-e^-t e^(2x)(x/2-1/4)+(t+1)e^-t+c=0
    1
  2356. (y+y-¹)y'(o)=sino*o y²/2+ln|y|=-ocos o+sino+c y²/2+ln|y|+ocoso-sino-c= 0
    1
  2357. y'(t)/cos²y=2t tgy=t²+c y=arctg(t²+c)+πn π/4=atctgc+πn {c=1,n=0;y=arctg(t²+1)
    1
  2358. y'e^2y=8x³ e^2y/2=2x⁴+c y=0,5ln(4x⁴+2c) 0=0,5ln(4+2c) c=e/2-2 y=0,5ln(4x⁴+e-4)
    1
  2359. M(x,y)/dy=(-cos-²y+xy-¹)/dx M(x,y)'(y)=y-¹ M(x,y)=ln|y|+c c не зависит от у (-tgy+xln|y|)'-2x-¹(-tgy +xlny)-2x-¹tgy=c
    1
  2360. (x-1/2)/(x-3)lnx<0°0-°1/2+°1-°3+>x x(0;1/2)U(1;3)
    1
  2361. 3*16^(x²-16x-15 3/4)=48+24+.. 2^(4x²-64x-63)=2⁵ 4x²-64x-63=5 4x²-64x- 68=0 x=8±9=17;-1
    1
  2362. 3^(1/2/x)≥9 0,5/x≥2 (x-0,25)/x≤0 x(0;0,25]
    1
  2363. tg2x+sin2x=16/15ctgx,x≠π/4+πn/2,x≠πm cosx(-cos²2x-16/15cos2x+1)/cos2x/sinx =0[x=π/2+πn,cos2x=3/5,cos2x=-5/3;[x=π/2+πn,x=±1/2arccos(3/5)+πn;{π/2+πn;±1/2arccos(3/5)+πn}
    1
  2364. {х>-1,(х-(1+√5)/2)(х-(1-√5)/2)≤0. хє((1-√5)/2;(1+√5)/2)
    1
  2365. a=2/3¹/⁴(cm) a1√7=2/3¹/⁴ a1=2/√7/3¹/⁴(cm) arcsin(√3/√7),60°-arc sin(√3/√7) S∆=1/√7√(1/7)=1/7 (cm²)
    1
  2366. Ф(х√2)>хФ(√2),х(0;1)
    1
  2367. [x=-1,(x+5/6)³-21 7/12(x+5/6)+26 11/27=0;x+5/6=(-13 11/54+√((13 11/54)²+(-21 7/12)³/27))¹/³+(..-..)..= 1/3*259¹/²cos(1/3arccos(-2852/ 259/√259)+2/3πn) x=-5/6+1/3*259¹/²cos(1/3arccos (-2852/259/√259)+2/3πn){-1;-5/6+1/3*259¹/²cos(1/3arccos (-2852/259/√259)+2/3πn)}
    1
  2368. c=42ab/(ab-42a-42b) a+b+42+42²(a+b)/(ab-42a-42b) 1-42²b²/(ab-42a-42b)²=0 a=84b/(b-42)-+>a min=84²/(b-42)+b+168 84²(b-42)-²+1=0,b=126;-42*+>b min=84+126+168=378
    1
  2369. √4,5+√1,5 acsin(√6/8) 60°-arcsin(√6/8)✓
    1
  2370. [x²+0,5x-3=0,x²+0,5x+4=0;x≠-1/2 x=(-0,5±3,5)/2=1,5;-2✓
    1
  2371. log(2)²(ax)+log²(2)((1-a)/x) x наименьшее, а максимально {ax>0,(1-a)/x>0;[{a≥1,x>0,x<0;{aє[0;1) х>0,х>0;{а<0,х<0,х>0;[0/,ає[0;1)х>0,0/;[ає[0;1)х>0 2log(2)(ax)*1/(ax)*a+2log(2)((1-a)/x)*1/((1-a)/x)*(1-a)*-x^(-2)=2log(2)(ax)/x-2l og(2)((1-a)/x)x^-1=0, log(2)(ax/((1-a)/x)) =0,ax/(1-a)*x=1, x²=(1-a)/a, x=±√((1-a)/a) -+>x min log(2)²(a√((1-a)/a))+log²(2)((1-a)/√((1-a)/a))=0,25log(2)²((1-a)a) +0,25log(2)²((1-a)a)=0,5log(2)²((1-a)a) 0,5*2log(2)(a-a²)*1/(a-a²)*(1-2a)=0, [log(2)(a-a²)=0,1-2a=0; [a-a²=1,a=1/2; -a²+a-1=0,a=(-1±√(1-4-1*-1))/-2[a=0,5±√-3/2 0/, +*->a {0,5}
    1
  2372. (n⁷-n):2,:3,:7 :42✓ (7⁷+11):101 ..:4242✓
    1
  2373. Sin(x+arccos(8/17))=1 x=-arccos(8/17)+π/2+2πn cygx=15/8 B)
    1
  2374. Z=2ln2(ln2-i(π/2+2πn))/(ln²2+(π/2+2πn)²)
    1
  2375. (a 2 3|2) (0 a²-4 a-6|a²-4) (0 0 a+1|0) [{A≠-1,a≠0,a≠±2, z=0,y=1,x=0;{a=0,z=0,y=1,xR;{a=-1,zR,y=1-7z/3,x=-5/3z;{a=±2, z=0,yR,x=±(1-y).
    1
  2376. {a<8,a≠7,x=(a±√(a²-20))/10; a(-≠;-√20]U[√20;7)U(7;8)
    1
  2377. a=2*3⁰,²⁵ y=3⁰,⁷⁵/2,x=3¹,²⁵; tg/_A=3⁰,⁵/6 (3⁰,⁵/6+1/6)x=2*3⁰,²⁵ x=2*3¹,²⁵(3⁰,⁵-1) 3⁰,⁵/6*x-2*3⁰,²⁵=1/6*x,x=2*3¹,²⁵(3⁰,⁵+1) S=447- 36√3
    1
  2378. (lnx+ln3)(lnx+3ln3)≥0 °0+*1/27-*1/3+>x,x(0;1/27]U[1/3;1)U(1;∞)
    1
  2379. y=xt,y'=t+xt' 1/x=t'/t/(t+1) ln|x|+c= ln|t|-ln|t+1| -1/c/(cx-1)-x-1/c=y
    1
  2380. ab-a+b-1=ab b=a+1
    1
  2381. a=m,b=6 42+12m=n x=-m=6 m=-6 n=-30
    1
  2382. {x=±√(1/2±√(r²-3/4)),y=-1/2±√(r²-3/4);(±√(1/2+√(r²-3/4));-1/2+√(r²-3/4))(±√(1/2-√(r²-3/4));-1/2-√(r²-3/4)) r=±1
    1
  2383. x/21=(3/7)^logx(9),{x>0,x≠1;хє(0;1)U(1; +∞),log(3/7)(x/21)=logx(9),log(3/7)x-log (3/7)21-log(3/7)9/log(3/7)x=0,log²(3/7)x- log(3/7)21log(3/7)x-log(3/7)9=0,log(3/7)x=(log(3/7)21±√(log²(3/7)21-4*-log(3/7)9))/2,[x=2+2log(3/7)7<0,x=-1;0/
    1
  2384. (3^x-81)/(3^x-27)≥0+°3-*4+>x x(-∞;3)U[4;∞)
    1
  2385. Председатель! Тебе нужен прибор-сканер через землю, тогда ты сможешь видеть очертания предметов под землёй.
    1
  2386. 4;4;4²;4⁴;4¹⁶;.. 4²^2^7
    1
  2387. (3 2|7) (0 1|1/2) X-¹=2{(1/2;2)}
    1
  2388. x=e^W(ln100)
    1
  2389. Алзим:х+у.Ера:2020-х+у.х=1010?✓
    1
  2390. 5/6=?/5 ?=25/6(cm)
    1
  2391. x²e^x-2xe^x+2e^x(0;1)=e-2e+2e-2=e-2
    1
  2392. x=(2n-1±1)/2=n;n-1
    1
  2393. f(2x)=2f(x)-4x² f(2^n)=2^nf(1)-4*2^(n-1)-..- -4*2^(2n-3)-4*2^(2n-2)=2^nf(1)-4*2^(n-1)(2^n-1) f(x)=xf(1)-2x(x-1) f'(x)=f(1)-4x+2 1=f(1)+2 f(1)=-1 f(x)=-2x²+x
    1
  2394. [{a(1/4;5,75),[x=a,x=-a+6;{a[0,5;5,5],x=0,5;
    1
  2395. 2a²/b⁴
    1
  2396. 4/sino=5/sin(3o),o=0,5arccos(1/8) x=√(4²+5²-2*4*5*1/8)=6
    1
  2397. У Вас внешность просто прелесть, а ещё и ум.
    1
  2398. y''-2x/(x-1)²y+n(n+1)y/(x-1)²=0 (u'-x/(x-1)²)' +(u'-x/(x-1)²)²=-(n²+n-2)/(x-1)²-1/(x-1)⁴ z-¹/ 1+x=c,z=1/(x-c) zp=a(-1)x-¹+a(-2)x-² {a(-1) =0,5±√(-n²-n+2,25),[a(-2)=0,a(-1)=1; a(-2)= ±i;z=x-¹±ix-² [u'=1/(x-1)+1/(x-1)²+1/(x-c), u'=1/(x-1)+1/(x-1)²+x-¹±ix-²;[u=ln|x&1|+(x 1)-¹/-1+ln|x-c|+c1,u=ln|x-1|+(x-1)-¹/-1+ln|x|±ix-¹/-1+c1;[y=(x-1)e^(-1/(x-1))(x-c)c1,y=(x- 1)e^(-1/(x-1))x(c1sin(1/x)+c2cos(1/x).)
    1
  2399. X-1/x=u x=(u+√(u²+4))/2 $(-∞;∞) e^-u²*(u²+4)-⁰,⁵u/2du+0,5√π=√π/2
    1
  2400. (k+5)(K²-6k+30)=0{-5}
    1
  2401. E^(-xlnx)(-lnx-1)-4^(x+1/16)ln4=0 e^(-xln(4x))ln(ex)=-2¹/⁸ln4 +*->x max<0 0/
    1
  2402. (3а+5b+c):7,11a+9b+13c=-(3a+5b+c):7
    1
  2403. X=-648i
    1
  2404. √2√(x⁰,⁵+√(x-1))√(√x-√(x-1))=√2
    1
  2405. √(2πn)<e(e/2)^n✓
    1
  2406. {x=±2,y=2^±1;{(2;2;)(-2;1/2)}
    1
  2407. f(x)'=f²(x)+c (-1)^(n+1)n!(x+c1)^(-1 n)=n(-1)^n(x+c1)^-n*-(n-1)!(x+c1)-¹ × √c*tg(x√c+c1)^(n)=c²cos-⁴(x√c+c 1)(-2cos(2x√c+2c1)+4)=3√c³tg²(x√ c+c1)*√ccos-²(x√c+c1)√c× f(x)=-2√(-c)/(e^(2√(-c)x)c1-1)-√(-c) f(x)^(n)=-2^n?*n!(-c)^(1/2+n/2)(e^(2 √(-c)x)c1-1)^(-1-n)e^(2√(-c)x)c1=n(-√(-c)^(n-1)(2(e^(2√(-c)x)c1-1)-¹+1)^ (n-1)*2√(-c)(e^(2√-c*x)c1-1)-²e^(2√ c*x)c1,c=0,f(x)=0
    1
  2408. (5х+3/х)²+5х+3/х-72=0 5х+3/х=(-1±17)) 2=8;-9[5х²-8х+3=0,5х²+9х+3=0;[х=1,х=-0,6,х=(-9±√21)/10;
    1
  2409. √(8^2-4²)=4√3 6√3,10√3cm
    1
  2410. x=1/1500+lg(2)/3000
    1
  2411. {2+log2(1+log3(2)/4)}
    1
  2412. e^(1/C/Rt)c=q t=25с
    1
  2413. 5a=(b/12)² a:5,a=5a1² b=±60a1
    1
  2414. (f(1)+f(2)+..+f(n-1))/(n²-1)=f(n) f(n)=(f(1)+f(2)+..+f(n-2))(n-1)/(n-2)/n/(n+1)=f(1)(n-2)!/(n+1)/n f(n)=1996(n-2)!/(n+1)/n
    1
  2415. x≥3,7/6=x×
    1
  2416. -4=4(b-1)-2b-6 3=b a=2 f(-6)=2*36+3*-6-6=48
    1
  2417. tg(x/2)=t $4t/(-2+(t-1)²)/(1+t²)dt= 0,5ln|t-1-√2|+0,5ln|t-1+√2|-0,5ln|t²+1|-arctgt+c=0,5ln|tg(x/2)-1-√2|+ 0,5ln|tg(x/2)-1+√2|-0,5ln|tg²(x/2)+1| -x/2+c 4t=A(t-1+√2)(t²+1)+B(t-1-√2)(t²+1) +C(t-1+√2)(t-1-√2)*2t+D(t-1+√2)(t- 1-√2){A=0,5,B=1/2,C=-0,5,D=-1;
    1
  2418. Ek=1;nak=(b+1)^(n-1)a
    1
  2419. (x+4)¹/³(5-x)¹/³=(a³-9)/3/a a³-15a+18=0 a=(-9+√(81-5³))¹/³+(..-..)..=2√5cos(1/3arccos(-9/√12 5)+2/3πn) x=0,5±√(-185,75+(4500cos²(1/3 arccos(-9/√125)+2/3πn)-243)/(-6+ 10√5cos(1/3arccos(-9/√125)+2/3π n)),n=0;2{4;-3}
    1
  2420. limn->∞sin(2πn(n+1/6..))=sin(1/3π)=√3/2
    1
  2421. Kln²k-k*2lnk+k*2-0,5ln²k(1;n)=nln²n&2nlnn+2n-0,5ln²n-2 n^(1-a)ln²n-2n^(1-a)lnn+2n^(1-a)-0,5ln²nn^-a-2n^-a≠0,a≤1 n^(2-a)/(2-a)(ln²n-1/(2-a)*4lnn+1/(2-a)²*4+2)=∞ расходится при а(1;2] Сходится при а>2.
    1
  2422. (y')'/cosy'+1=0,$(y')'/sin(π/2-y')dx+x=C,ln|tg(π/4-y'/2)|+x=C,tg(π/4-y'/2)=±e^(-x+C), π/4-y'/2=arctg(Ce^-x)+πn,y=-2$arctg(C e^-x)dx+(π/2-2πn)x+c1
    1
  2423. 998+1000'001=1'000'999
    1
  2424. $(-@;=)2^n/√(2π)/0,5/√n*e^(-(x-0,5n) ²/0,5/n)dx=2^(n+1)/√(2πn)
    1
  2425. x=cos(2πn/11)+isin(2πn/11) Ek=0;10|a^k-0,5i|²=Ek=0;10(-sin(2πnk/11)+1,25)= 1,25*11-sin(2πn*0/11)-sin(2πn/11)-..-si n(2πn*10/11)=[13,75;13,75-0,5√2;13,75
    1
  2426. En=1;≠(1/(a-πn)+1/(a+πn))(-1)^n, a(-π;π) сходится
    1
  2427. ln(x+4)/ln(3-x)≥0°-4-*-3+°2-°3>x x[-3;2)
    1
  2428. (5^x-125)/(5^x+31)/(5^x-0,2)≤0+°-1-*3+>x x(-1;3]
    1
  2429. {x≥-2,(3^x-14-√193)(3^x-14+√193)≥0+*-*+ >x;{x≥-2,x(-∞;-log3((14+√193)/3)]U[log3 (13+√193);∞);x[log3(14+√193);∞)
    1
  2430. log5(25-x²)(-∞;1]U[2;∞)[{x(-∞;-√20]U[√20; ∞),x(-5;5);x=0;x(-5;-√20]U{0}U[√20;5)
    1
  2431. (ln|y|)'+1/x*y'$dxy-¹=-4/x $dxy-¹=z y=1/z' y'=-z'-²z'' xz''-4z'-z=0 z=En=0;∞anx^n En=0;∞(a(n+1)*(n+1)(n-4)-an)x^n =0 a4=0,a0=0,anR z=En=5;∞a5*5!/n!/(n-5)!x^n y=1/En=5;∞a5*5!/(n- 1)!/(n-5)!x^(n-1) a5=1/En=5;∞5!/(n-1)!/(n-5)!,a5=-(En=5;∞1/(n-1)!/(n-5)!)-²En=5;∞1/5!/(n-2)!/(n-5)!/2 y=1/En=5;∞1/(En=5;∞1/(n-1)!/(n-5)!)/(n-1)!/(n-5)!x^(n-1)
    1
  2432. х=(-3±√5)/2 8-+3√5✓
    1
  2433. 10tg22,5° l=10(√2-1) r=5(2-√2)(cm) ✓
    1
  2434. ±6/√7=n 36/7/(8/7)=4,5
    1
  2435. a(n+2)=4(a(n+1)-an) q²-4q+4=0 q=2 an=2^n(an+b)✓ bn=a(n+1)-2an=2^(n+1)a
    1
  2436. х²-6х+25=0 х=3±4i{2}
    1
  2437. a2m=a(2m-1)+1,a(2m+1)=2a2m a2=a1 +1=2 a3=2a2=2²,a5=2^(n-1)-2^(n-3)...
    1
  2438. $(0;3)(-1/(x-4)²-4/(x-4)³)dx=-(x-4)-¹/-1-4 (x-3)-²/-2(0;3)=1/(3-4)+2/(3-4)²-1/-4-2/(- 4)²=1 1/8
    1
  2439. 1/2*2024/2023/(1/2023)=1012
    1
  2440. f(x+1)=4f(x)f(1)-f(x-1)=-f(x-2) f(2010)=f(0)
    1
  2441. (2-tg15°)²+1²=4 x=2
    1
  2442. $(0;2)f(x)dx=c,f(x)=2xc-6 4c-12=c,c=4,f(x)=8x-6 f(2)=10 $)-3;3)(8x-6)dx=4x²-6x(-3;3)=-36B
    1
  2443. А когда такое было,что в гостях у него были шизофреники.
    1
  2444. Н. Н -. - Н-С-С-ОН -. - Н. Н Н3ССН2ОН+5Н2О=(ОН)3СС(ОН) 3+5Н2|/\ 2*12+6*1+16=46 5*(2*1+16)= 80 46/126*100%=37%, 46/110*100=42% 46/94*100=49% 46/78*100=58% 46/62* 100=74(%)
    1
  2445. x²+x-y²-y-10=0 x=(-1±√(4y²+4y+41))/2 40=n²-(2y+1)²[{n=11,y=4;{..=7,..=1;{..=7,..=-2;{..=11,..=-5; x=5;3{(5;4)(3;1)}
    1
  2446. 31/32=0,96875<0,97312<0,992
    1
  2447. √x^√x^√5=20 e^(x^(√5/2)*0,5lnx)* 0,5(lnx+1)x^(√5/2-1)=0,x=0;1/e-*+>x min=e^(-0,5e^(-√5/2))<1 x=20^n √5/2n=⁰,⁵,n=√5/5{20^(√5/5}}
    1
  2448. {z=2-x-y,2±√(8-(x-2)²)=y;✓
    1
  2449. x=±100'000,5-1,5{99'999;-100'002}
    1
  2450. N=4 P(x)=a0x⁴+..+a3x+a4 a0(a0x⁴+..+a3x+a4-1)⁴+..+a3(a0x⁴+..+a3x+a4- 1)+a4=x¹⁶+1{a0=1,a1=0,a2=0,a3=0,[a4=1,a4=0;P(x)=x⁴+1;x⁴ P(2)=17;16
    1
  2451. (4^x-1)(16^x+4^x+2)=0 x=0
    1
  2452. a²+2b(2b-3c)/(3c+1)a+(3c-1)(2b+ 1)+2b(2b+1)/(3c+1)=0 a=-b(2b-3c)/(3c+1)±√((2b²-3cb)²-(2b+1)(2b+9c² 1)(3c+1))/(3c+1) (3c+1)(2b+1)=( 2b²+3cb+3c+1±√((2b²-3cb)²-(2b+1)(2b+9c²-1)(3c+1)))(-1+(2b+1)(-1/(3 c+1)+2)) max=12
    1
  2453. $-sin(cosx)dcosx=coscosx+c
    1
  2454. a=arccos(1-1/R) x=0,5arccos(1-1/R)R²-0,5√(2R-1)(R-1) x=(2R-1)²π/4-0, 5(π-arccos(1-1/R))R²-0,5√(2R-1)(R-1) 0=2R²-4R+1 R=1+√2/2 S=1*(2R-1)=1+√2
    1
  2455. (5-x)²+(5-2/x)²=25 21-10(x+2/x)+(x+2/x)²=0 x+2/x=5±2=7;3 [x²-7x+2=0,x²-3x+2=0;x=1;2
    1
  2456. X⁰,⁵=-1±√10i x=-9-+2√10i
    1
  2457. S=ab,P=(a+b)*2 S1=ab-c²=2(a+b) P1=ab=2(a+b) c=0 a=2+4/(b-2){(3;6)(6;3)(4;4)}0✓
    1
  2458. x=0,5+i(π+2πn)/ln2/2
    1
  2459. y'=x²y²-xy+x²-2y²+2y+xy²-x²y+x-2=x²(y²-y+1)+x(y²-y+1)-2(y²-y+1)=(y²-y+1)(x²+x-2),y'/((y-1/2)²+3/4)=x²+x-2,arctg((y-1/2)/(√3/ 2))/√3*2=x³/3+x²/2-2x+c,y=√3/2tg(√3/6x ³+√3/4x²-√3x+√3/2c)+0,5
    1
  2460. $(0;1)dye^y=e^y(0!1)=e-1
    1
  2461. Sin72°/sin18°/((1+√5)/2)=√((5+√5)/2)
    1
  2462. (3 -4|8) (0 1|1) ..=4{x=0,19,y=2/25.
    1
  2463. $(0!4)sin(π/2[x])dx=1*1+1*-1=0 $(2012;2015)sin(π/2[x])dx=1
    1
  2464. (2^(0,5x)-2/3)³-4/3(2^0,5x-2/3)-32 16/27=0 x=2log2(2/3+(55+12√21)¹/³*2/3+(..-..)..)=4
    1
  2465. e^x(0;3)-e^-x(-1;0)=e³-2+e
    1
  2466. y'(x)+xy(x)=x y(x)=ce^$-xdx+$xdxe^ $xdx=ce^(-x²/2)+e^(x²/2)✓ ce^(-x²/2)+e^(x²/2)=x²/2+ce^(-x²/2) -e^(x²/2)-ce-²+e² x²=2ce-²-2e²×
    1
  2467. S=4²/2-0,5*4²(π/2-1)=16-4π
    1
  2468. ​z=-16/17n+4ni/17
    1
  2469. Царь и великий князь росссийский Иван Васильевич премудрый и храбрый. Где царь царства 3 Казарское,Астраханское,Сибирское:победив державу,собой покорив,и много шведов победив,много России владев. Первый венец восприятия.
    1
  2470. (x-2√3)²+(x+2)²=12 x²+(2-2√3)x+2=0 x=-1+√3+√(2-2√3)× P∆=-6+6√3+6√(2-2√3)
    1
  2471. (X²-4)(x-1)=0[x=±2,x=1.
    1
  2472. А почему у Делягина косоглазие?
    1
  2473. (-1+√5)/4✓
    1
  2474. АБ:37,АБ=37;74 ВГ=21✓ ВГ=6× ВГ=37;74 А*5=Б≤9 А=5,Б=1✓ 1Б*2=Б*3≤27 АБ[10;13],Б[2;3]×
    1
  2475. ∆y=3x²∆x+3x∆²x+∆³x-7(2x∆x+∆²x)=3*5²*0,01+3*5*0,01²+0,01³-7(2*5*0,01+0,01²)=0,050801
    1
  2476. π/3-2+1/√3✓
    1
  2477. n:2,a=b=1,1+2c=2n1²×
    1
  2478. 9a+b+1:13 a=1,b=3 a=2,b=7 a=4,b=2 a=5,b=6 (7;1)(8;5)(9;9)
    1
  2479. {2x≥x-1,2x-1≤x;{x≥-1,x≤1;x[-1;1] -2..2,-1..1 [x[-1/2;0),x[0;1/2). x[-1/2;1/2)
    1
  2480. x³-x-1=0 2(u+v-2)/(1+u+v-uv)-3 u²+u(v-1)+v²-v-1=0,(v-1/3)³-4/3(v-1/3)-38/27=0 v=1/3+(19+3√33)¹/³/3+(..-..).. u=1/3-(19+3√33)¹/³/6-(..-..)..±√(- 1/3((19+3√33)¹/³+(..-..)..)²+5 1/3)/2 2(-4/3+(19+3√33)¹/³/6+(..-..)..±√(-1/ 3((19+3√33)¹/³+(..-..)..)²+5 1/3)/2)/(5/3+(19+3√33)¹/³/6+(..-..)..±√(- 1/3((19+3√33)¹/³+(..-..)..)²+5 1/3)/2-(1/3-(19+3√33)¹/³/6-(..-..)..±√(- 1/3((19+3√33)¹/³+(..-..)..)²+5 1/3)/2)(1/3+(19+3√33)¹/³/3+(..-..)..))-3
    1
  2481. (a+1)³/b+(b+1)³/c+(c+1)³/a 3(a+1)²/b-(c+1)³a-²=0 a=-0,5+√(0,25+√((c+1)³b/3))-*+>a min=(b+1)³/c+(4b-¹+b-⁰,⁵√((c+1)³/3))√(0,25+b⁰,⁵√((c+1)³/3))+2b-¹+ 1,5b-⁰,⁵√((c+1)³/3)≥3(c+1)³/c≥3/4 3(b+1)²/c+(-b-²-3,125b-¹,⁵√((c+1)³/3)-5b-¹(c+1)³/12)*(0,25+b⁰,⁵√((c+ 1)³/3))-⁰,⁵-2b-²-0,75b-¹,⁵√((c+1)³/3) =0 (-1-3,125b⁰,⁵√((c+1)³/3)-5b(c+1) ³/12)²=b¹,⁵√3/16(c+1)⁴,⁵+1+19/4b⁰, ⁵√((c+1)³/3)-3(b²+b)²/c-29/64b(c+1) ³+(9c-²-13,125/c)b⁰,⁵√((c+1)³/3)(b²+ b)²+9/4(b²+b)²/c² 6(c+1)²(c-1/2)/c²= 0 c=1/2-*+>c
    1
  2482. [х=3±1,х=-3±1.{4;2;-2;-4}
    1
  2483. -185,368±18,432
    1
  2484. 4/n=0 y=±√(r²-x²) ±b√(r²-x²)=r²-ax 0=r⁴-b²r²-2r²ax+(a²+b²)x² x=(r²a±br√(-r²+a²+b²))/(a²+b²) y=±r√(a⁴+a²b²-r²(a²-b²)-+2rab√(-r²+a²+b²))/(a²+b²)
    1
  2485. y=x/(1-1/4x) (-0,5x-3x)/(-1/4x+2x)=2
    1
  2486. ysinxe^cosxdx+y^-1dy=0,-e^cosxdcosx+y^-2dy=0,-e^cosx+y^-1/-1=c,y=1/(-e^cosx-c)
    1
  2487. 1/(x-1)+5/(6-3√(-x²+x+6))>1/(|x-1|+1),[{xє[1;3],(√(-(x+2)(x-3))-2-5/3x²+5/3x)/x/(x-1)/(√(-(x+2)(x-3))-2)>0;{xє[-2;1),((2x-3)√(-(х+2)(х-3))-5/3х²+х+8/3)/(√(-x²+x+6)-2)>0;°-1°2>х (X+2)(x-3)≤0,-2+*3*+>x хє[-2;3],-х²+х+ 6=4,-х²+х+2=0,х=(-1±√(1-4*-1*2))/-2[х=-1,х=2;-5/3*1,5²+1,5+8/3=-3 3/4+1 1/2+2 2/3=5/12≠0,(2x-3)√(-(х+2)(х-3))-5/3х²+ х+8/3=0,(2x-3)√(-(х+2)(х-3))=5/3х²-х-8/3,(4х²-12х+9)*-(х+2)(х-3)=25/9х⁴+х²+64/9 10/3х³-80/9х²+16/3х,(5/3х²-х-8/3)/(2х- 3)≥0,-(4х²-12х+9)(х²-х-6)-25/9х⁴+10/3х³+ 71/9х²-16/3х-64/9=0,(х-(1+√(1-4*5/3 8/3))/(10/3))(х-(1-√(169/9))/10*3)/(х-1,5)≥0;-1+°1,5-1,6+>х 4х⁴+4х³+24х²+12х³-12х²-72х-9х²+9х+54-25/9х⁴+10/3х³+71/9х²-16/3х-64/9=0хє [-1;1,5)U[1,6;+∞),-61/9x⁴+19 1/3x³+10 8/9x²+3 2/3x+46 8/9=0,хє[-1;1,5)U[1,6;+ ∞),x⁴-174/61x³-89/61x²-33/61x-422/61=0, учитывая 1-ое неравенство хє [-1;1), -450/61<-207/61 (х²-87/61х-6499/61²)² 3(40931+58*6499)/61³х-422/61-6499²/61⁴=0,\ (2653,5-√(6499²+7569/4*3721))/3721<-1*/87/122*\*87/122+√(6499²+8 7²/2²*61²)/61²>1/ -1'553'619/3721²/61 (2653,5-√(6499²+7569/4*3721))-422/61-6499²/61⁴<0,(-9'670'326,5-422*3721*61- 6499²)/3721²<0,(-1'553'619/61*(2653,5 +√(6499²+7569/4*3721))-422*3721*61-6499²)/3721²<0, 7'768'095 4'660'857 6'214'476 67582426,5
    1
  2488. v=-6t²+26t v(4)=-96+104=8(m/s)
    1
  2489. А думал,что Вы рассказываете о Начальном.
    1
  2490. f(x)=-x²+4x-1/2+cos(πx)/2 x[0;1] 2$(0;1)(-x²+4x-1/2+cos(πx)/2)dx=2(-x³/3+2x²-0,5 x-sin(πx)/π/2)|(0;1)=2(-1/3+2-0,5-0)-2(0+ 0-0-0)=2 1/3
    1
  2491. x[-7;5] 0=18-11x+x² x=(11±7)/2=9;2 {2}
    1
  2492. y=(x²-4x)⁴(x+3)¹,⁵/(2x³+6)⁵ y'=2(x²-4x)³(x+ 3)⁰,⁵(-5,5x⁵+17x⁴+132x³+28,5x²+6x-144)/(2x³+6)⁶
    1
  2493. (0,75^х+1-1,25^х)(1-1,5^х)=0 [х=0,х=2.
    1
  2494. π³/8+$1/2arctg²xdx(0;∞)=-π³/8-π/2+π/2(π/4x-¹|0+ln(1+x²)|∞)-0,5En= 1;∞(-1)^(n-1)/n(x^(2n-1)/(2n-1)-x^ (2n-3)/(2n-3)+..+(-1)^(n-1)x+(-1)^n arctgx)|∞+lnx|∞+En=2;∞(-1)^(n 1)/(2n-1)²x^(2n-1)|∞=∞
    1
  2495. S1=(√2-1+√2)/2*1=√2-1/2 √2-1/2-π/4{2√2-1-π/2}
    1
  2496. {x=2,y=5.
    1
  2497. x²f(x)+f(1-x)=2x-x⁴ f(1-x)+(1-x)-²f(x)=2(1- x)-¹-(1-x)² f(x)=(-x⁶+2x⁵-1-2x³+2x²)/(x⁴-2x ³+x²-1)=-x²+1
    1
  2498. (x-1/3)³-1/3(x-1/3)-47/64/27=0 x-1/3=(47/2+√(47²-128²)/2)¹/³/12+(..-..)..=2/3cos(1/3arccos(47/128)+2/3πn) x=1/3+2/3cos(1/3arccos(47/128)+2/3πn)
    1
  2499. А он озвучивал какой-либо мультфильм?
    1
  2500. limx->0(x²/2-..)/x⁴=∞
    1
  2501. 8/π³(π²/32arcsin((t-π/4)/(π/4))+(t- π/4)√(π²/16-(t-π/4)²)/2)(0;π/2)=1/4 π³/64-π³/32=-π³/64
    1
  2502. 3*7²+2*7+5=166 166/7=23ost.5 23/7=3ost.2 3/7=ost.3 325,{10}
    1
  2503. BC=AB√3 DH=AB√3/(ctg15°+ctg 30°)=AB(3-√3)/4 HF=(AB/2-DH)√3 *2=AB(-√3+3)/2 HF=2DH SDEFH=AB²(3-√3)2/8=24-12√3
    1
  2504. (-1/64)^m,√3/4(-1/64)^m,(-1/64)^m/8,-1/32(-1/64)^m,-√3/64(-1/64)^m S=(134+15√3)/65
    1
  2505. (cos(π/n)-1/6)³-7/12(cos(π/n)-1/6) +7/216=0 cos(π/n)-1/6=(-7/2+7√ (1/2²-7))¹/³/6+(..-..)..=1/3√7cos(1/3 arccos(-1/2/√7)+2/3πm) n=π/(±arc cos(1/6+1/3√7cos(1/3arccos(-1/2/√7)+2/3πm))+2πk) m=0✓;1✓;2✓{7}
    1
  2506. o(0;45°) √(36+l²-12lcoso),√(9+l²-6lc os(3o)) √2*sin(3o)√(5+sin(6o)-2sin(4o)-2s in(2o)-2cos(4o)-2cos(2o))=-0,5+sin(2o)+cos(2o)+sin(4o)-cos(4o)+0,5 cos(6o)-0,5sin(6o),3cos(3o)+3sin3 o=l,l≥3cos(3o) 2*sin²(3o)(5+sin(6o)-2sin(4o)-2sin (2o)-2cos(4o)-2cos(2o))=(-0,5+sin(2o)+cos(2o)+sin(4o)-cos(4o)+0,5 cos(6o)-0,5sin(6o))² o=15,3°;28,7°✓
    1
  2507. arctg0,6 45°,h(0,6+1)=3,h=1 7/8 EF=1 7/8/√1,36 AF=√(225/64+25²/8²)=5√34/8 5√34/8/(15/8/√1,36)=5/3
    1
  2508. C=2-a-b,-a²+a(2-b)-b²+2b-1=0 a=(2-b±√(-3b²-12b+8))/2 a-b=(2-3b±√(-3b²-12b+8))/2 3(-1±(-3b²-12b+8)-⁰,⁵(-b-2))/2=0 b2-4b+1=0 b=-2-+√5+*->b*+>b max=4+2√5 min=4-2√5
    1
  2509. e^x^(1/(x-1))=y
    1
  2510. 4:3,7:6 28:24:21
    1
  2511. z=2√(1-x²) $(-1;1)dx$(-√(1-x²);√(1-x ²))dy$(0;2√(1-x²))dz=16/3
    1
  2512. (2+2*16)/(16²-1)=34/15/17=2/15
    1
  2513. (Sin(π/2-x))²=sin(x-π/4)√2 (cosx+1)((cosx+1/3)³+2/3(cosx+1/3)-34/27)=0[x=π+2πn,x=±arccos(-1/3+(17+3√33)¹/³/3+(..-..)..)+2πn.cos²x-2ctgx=∞;(-1/3+(17+3√ 33)¹/³/3+(..-..)..)²-2(-1/3+(17+3√33) ¹/³/3+(17-3√33)¹/³/3)/√(1-(-1/3+(1 7+3√33)¹/³/3+(17-3√33)¹/³/3)²)=-1 B)
    1
  2514. √2/2+√2/2i+√2/2-√2/2i=√2
    1
  2515. 3|a-1|+2|a-3|≤6,3|-4+a|+2|2+a|≤41+ 7¹/⁵ a[0,6;3],a[-6,6-0,2*7¹/⁵;9,6+7¹/⁵/5] a[0,6;3]
    1
  2516. Tg(2a)=(5+3√5sina)/(3√5cosa) 0=√5/6-sina/2-sin²a√5/3 sina=(3±7)/(-4√5)=-√5/2×;√5/5 a=arcsin(√5/5) S∆=0,5*3√5cosa(5+3√5sina)=24
    1
  2517. √(x²+4)√(x²+9)=5x≥0 x⁴-12x²+36=0 x²=6 x=±√6{√6}
    1
  2518. (11⁵+12)/(
    1
  2519. tg36°/sino=√5/sin(126°-o) arctg(√(2-2√5/5)/(1+√5))=o{18°} 48+22√5≠-2√5/5 0,32..=18,24° √(2-0,4√5)/(1+√5)
    1
  2520. А почему Вы полысели?
    1
  2521. X=π/2-2x+2πn,x=π)2+2x+2πn[x=π/6+2πn/3,x=-π/2-2πn.
    1
  2522. у=х²,у=5/4-х, у=0, х²(5/4-х2-х) - Макс.хє[0;1,25] Х⁴-х³+1,25х², -4х³-3х²+1,25х=0, х=0, 4х²+3х-1,25=0, х=(3±√(9-4*4*-1,25))/8,х=3/8±√29/8,х=3/8+√29/8, +**+*3/8+√29/8- макс.площ. (3/8+√29/8)²(1,25-(3/8+√29/8)²-3/8-√29/8)=(9/64+6√29/64+29/64)(1,25-19/32-3√29/32-3/8-√29/8)=38/64*(40-19-12)/32-19/32*√29*7/32+3√29/32*9/32-3√29/32*19√29/32²=(342*2⁴-57*29)/2¹⁵-106√29/1024=51819/32768-53√29/1024 3342. 57 *16. *29 20052. 513 3342 114 53472 1653 -1653 51819 1024 * 32 2048 3072 32768
    1
  2523. $(1;e)lnu*udu=u²/2lnu-u²/4(1;e)=e²/4+1/4
    1
  2524. (2+3cos2x-4sinx+13cosx)/(cosx-3 sinx+5)²=0 (cosx+13/12)⁴-161/72(cosx+13/12)²-26/27(cosx+13/12)+38'849/144²=0 x=arccos0,904+2πn;arccos0,334+2πn+*+*->x max=1,285 min=0,597 [0,597;1,285]
    1
  2525. a-1/a=b,b-1/b=c,c-1/c=a (a²)³-1/3(a²)²+ 2/3a²-1/3=0, a≠0;±1 (a²-1/9)³+17/27(a ²-1/9)-191/729=0 a²-1/9=(191/1458+√(1 91²/1458²+(17/27)³/27))^(1/3)+(191/2 -13,5√77)^(1/3)/9,a=±√(1+(95,5+13,5 √77)^(1/3)+(95,5-13,5√77)^(1/3))/3 b=± √(1+(95,5+13,5√77)^(1/3)+(95,5-13,5√ 77)^(1/3))/3-+3/√(1+(95,5+13,5√77)^ (1/3)+(95,5-13,5√77)^(1/3)),c=±√(1+(95, 5+13,5√77)^(1/3)+(95,5-13,5√77)^(1/ 3))/3-+3/√(1+(95,5+13,5√77)^(1/3)+(95, 5-13,5√77)^(1/3))-1/(±√(1+(95,5+13,5√7 7)^(1/3)+(95,5-13,5√ 77)^(1/3))/3-+3/√(1 +(95,5+13,5√77)^(1/3)+(95,5-13,5√77)^ (1/3))) 1/a/b+1/a/c+1/b/c=-1,37..
    1
  2526. 2-1/x=x -x²+2x-1=0 x=1.
    1
  2527. $(0;1)(x+2x³)√2√(0,5+x²)dx=√2/2(x²+ 0,5)¹,⁵/1,5+$2√2x³√(x²+0,5)dx(0;1)=√2/3 *1,5¹,⁵-√2/3*0,5¹,⁵+$(√0,5;√1,5)(2√2u⁴-√2 u²)du=0,5√3-1/6+2√2u⁵/5-√2u³/3(√0,5; √1,5)=0,9√3-0,1 (x²+0,5)⁰,⁵=u,x=√(u²-0,5) dx=(u²-0,5)-⁰,⁵ udu
    1
  2528. 6*8/2=24
    1
  2529. √3/3=2x/(x²+3) √3/3x²-2x+√3=0 x=√3 1/sina=√3/sin(150°-a) √3/3=tga,a=30°
    1
  2530. Гон..о Нет б,ж,к,п,р,ч. Гонуо?
    1
  2531. (копт)(копт)(оп)(кп)(пт)(копт) Нет а,в,е,р.
    1
  2532. 2->4->16->49->169->256->169
    1
  2533. limx->0(cosx+sinx)/(cospx*p+sinpx*p)=1/p
    1
  2534. $(a;∞)(bcost+csint)e^(-2t)e^-ptdt= e^(-(p+2)a)((bp+2b+c)cosa+sina(cp +2c-b))/((p+2)²+1) {c=-e^6(2cos3-sin3),b=e⁶(cos3+2sin3),a=3. Y=e⁶(cos3+2sin3)cost-e⁶(2cos3-sin3)sint
    1
  2535. (x+(1-k²/2)/kb+(1-k²)y/2)²-(0,5k⁴-0,5 k²+k+2)b/ky-(0,25k⁴+k+1)/k²b²-((1-k ²)²/4+1)y²≥0,f(x)=0
    1
  2536. mV-¹=1000Mn=4165(g/ml)B)
    1
  2537. {5|x|+12|y-2|=60,y²-a²=4(y-1)-x²;[{y=7-5/12x,x≥0,y≥2;{y=-3+5/12x,x≥0,y≤2;{y=7+5/12x,x≤0,y≥2;{y=-3-5/12x,x≤0,y≤2;y ²-4y-a²+4+x²=0;y=2±√(a²-x²);ує[-3;7] √(а²- х²)≤5,а²≤25+х²,≥х² а²≥0,≤169,ає[-13;13] 2-√(а²-х²)≥-3,√(а²-х²)≤5 ає[-13;13]
    1
  2538. 0,5/sin24°,sin54°/sin24° sin54°/sin74°,sin54°/sin24°/sin74°*sin84° Cos36°/cos16°/sinx=cos36°/cos 16°*cos6°/sin42°/sin(162°-x) 1/√3=tgx x=30°✓
    1
  2539. x,..,43x/29 29/x 9-x+43/29x=11, x=29/7,S=(9-29/7)* 29/(29/7)=34/7*7=34
    1
  2540. 4,5 R=12,5/2=6,25 (6,25-r)²=r²+(r-1,75)² 0=r²+9r-36 r=(-9±√225)/2=3;-12>0 r=3{9π}
    1
  2541. Arccos(24/25)E)
    1
  2542. Это не было бы проблемой, если бы судили справедливо.
    1
  2543. √(3²+2²-3*2)=√7 l=6/5√3 S1=14/25(π/6-0,5) S2=21/50√3-14/25(π/6-0,5) S=21/50√3
    1
  2544. 4x/(x²-4)=8/(6-x) 0=3x²-6x-8 x=(3+√33)/3
    1
  2545. 2sin55°/sin70°=1/siny siny=sin35° y=35°;145°<110° y=35° D)
    1
  2546. [tgx=0,tgx=±1;[x=πn,x=±π/4+πn.
    1
  2547. 2⁵⁶ 5²⁴,2⁷=128>5³=125
    1
  2548. (1-x)f(x²)-f(3x+40)=40 x=1, f(43)=-40,x=4;5 -3f(16)-40=f(52),-4f(25)-40=f(55) -3f(16)-112=224 x²-3x-40=0 x=(3±13)/2=8;-5 f(25)=8,f(64)=-8 f(16)=-112
    1
  2549. xln|sinx|-$ln|sinx|dx(0;π/2)=-0*-∞- tgxln²|sinx|/2+..(0;π/2)=0
    1
  2550. у''+5у=-180х²е^(5х) а²+5=0 а=±√-5 у=c1cos√5x+c2sin√5x y=(ax2+bx+ c)e^(5x)y'=(2ax+b)e^(5x)+(ax²+bx+c)e^(5x)*5,y"=(2a+10ax+5b)e^(5x)+(5ax²+5bx+5c+2ax+b)e^(5x)*5 (2a+10ax+5b+25ax²+25bx+25c+10ax+5b)e^(5x)+5(ax²+bx+c)e^(5x)=-180x^2e^(5x) 25ax²+(20a+25b)x+2a+10b+25c+5ax² +5bx+5c=-180x², {30a=-180, 20a+30b=0, 2a+10b+30c=0, a=-6,b=4,c=-28/30; y=(-6x²+4x-14/15)e^(5x) y=c1cos√5x+c2sin√5x+(-6x²+4x-1 4/15)e^(5x)
    1
  2551. -х+(у+10)^(1/3)=1, {х²(-х)-у=10;
    1
  2552. $(0;1)dx$(0;x²)xcosydy=$(0;1)dx|(0;x²)xsin y=$(0;1)dx(xsinx²)=-cosx²/2(0;1)=-cos1/2 +1/2
    1
  2553. Y'√(1-y²)=±y'' x/2+c1=$dy/(arcsiny+ y√(1-y²)+2c)
    1
  2554. [{2≤a,y=√(8a+34)/2-√2/2, x=(1+2a-√(4a+17))/2; {a>2,y=√(-a+4,5+|a-4|)+√(-a+4,5-|a-4|),x=(-2a+1+√(-4a+17))/2;{a[4;17/4],y=√2/2-√(-8a+34)/2, x=(-2a+1-√(-4a+17))/2.|2a-8|
    1
  2555. arcsincosx=cosarcsin(x-a)≤π/2,-π/2 arcsinsin(π/2-x)=sin(π/2-arcsin(x-a)) [{π/2-x=√(1-(x-a)²),π/2-x≤π/2,≥-π/2,arcsin(x a)є[-π/2+2πn;π/2+2πn];{π/2-x=-√(1-(x-a)²),π/2-x≤π/2,≥-π/2,arcsin(x -a)є[π/2+2πn;3π/2+2πn];{π-(π/2-x)=√(1-(x-a)²),π/2-x≥π/2,≤π,arcsin(x -a)є[-π/2+2πn;π/2+2πn];{π/2+x=-√(1-(x-a)²),π/2-x≥π/2,≤π,arcsin(x -a)є[π/2+2πn;3π/2+2πn];[{π²/4-πx+x²=1-(x-a)²,x≥0,≤π,arcsin(x-a)є[-π/2;π/2];{π²/4-πx+x²=1-(x-a)²,x≥0,≤π,arcsin(x-a)=π/2;{(π/2+x)²=1-(x-a)²,x≤0,≤-π/2,arcsin(x -a)є[-π/2;π/2];{(π/2+x)²=1-(x-a)²,x≤0,≥-π/2,arcsin(x-a)=π/2;[{x=(π+2a±√(π²+4aπ+4a²-2π²+8-8a²))/4π²/4,x≥0,≤π,x-aє[-1;1];{x=(π+2a±√((π+2a)²-4*2(π²/4-1+a²)))/4,x≥0,≤π,x-a=1;{x=(-π+2a±√((π-2a)²-4*2(π²/4-1-a²)))/4,x≤-π/2,x -aє[-1;1];{(π/2+x)²=0,x≤0,≥-π/2,x-a=1;[{x=0,25π+0,5a±√(-(π-2a)²+8)/4,x≥0,≤π,xє[a-1;a+1];{a+1=π/4+0,5a±√(-π²+4πa-4a²+8)/4,x≥0,≤π,x=a+1;{x=-π/4+0,5a±√(-π²-4πa+8+12a²)/4,x≤-π/2,xє[a-1;a+1];{x=-π/2,x≤0,≥-π/2,x=a+1;[{x=0,25π+0,5a±√(-(π-2a)²+8)/4,π-2a≤√8,π-2a≥-√8;aє[-1;1+π],xє[0;π]xє[a-1;a+1];{(0,5a+1-π/4)²=(-π²+4πa-4a²+8)/16,x≥0,≤π,x=a+1;{x=-π/4+0,5a±√(-π²-4πa+8+12a²)/4,(a-(4π+√(16π²-4*12(-π²+8)))/24)(a-(π/6-√(16π²+48π²-364)/4)≥0,+**+>а a≤1-π/2,x≤-π/2,xє[a-1;a+1];{x=-π/2,a=-π/2-1; {x=0,25π+0,5a±√(-(π-2a)²+8)/4,a≥0,5π-√2,a≤0,5π+√2,aє[-1;1+π],xє[0;π]xє[a-1;a+1];ає[0,5π-√2;0,5π+√2]ає[0,339;0,512] хє[1,339] [ає[0,339;0,512] хє[1,339],ає[π/6-√(4π²-22,75);1-π/2]x=-π/4+0,5a±√(-π²-4πa+8+12a²)/4,x≤-π/2,xє[a-1;a+1],а⁴-2πа³-(-1,5π²+4,25)а²+-(2+0,5π³-4,5π)а-17/16π²+π/2+π⁴/16+3=0, ає[-1;π-1]x≥0,≤π,x=a+1;х=-π/2,а=-π/2-1;[ає[π/6-√(4π²-22,75);1-π/2]U{-π/2-1}U[0,339;0,512],{a=2,26..,a=0,06,a=0,33,a =3,62>2,14.. aє[-1;π-1] ає[π/6-√(4π²-22,75);1-π/2]U{0,06}U{0,33}U[0,339;0,512],
    1
  2556. cos(π/4+2x)=(2sin²(π/4+2x)+√2sin(2x+π/4)-1)/6/sin(π/4+2x) 0=(sin²(π/4+2x)+0,05 √2sin(π/4+2x)-0,4775)²-0,00225√2sin(π/4 +2x)+1/40-0,4775²
    1
  2557. y'=z,z'-4z=0,k-4=0,k=4,z=c1e^(4x) y'=c1 e^4x,y=c1e^4x/4+c2
    1
  2558. RG=5√(4²+7²)=5√65 RQ=33/7√65 QD=8/7,AQ=13/7 AQ:QD=13:8
    1
  2559. ГОЛ*У=УГУ У≠1 989/102=9,.. У=2 10¹6*2=212✓ У=3,1О²7*3=313× Г=1,У≠3;4;6;7;8;9,У=5,ОЛ=03✓
    1
  2560. 1+1/x=y,x=1/(y-1) f(y)=1/(y-1)² f(x)=1/(x-1)²
    1
  2561. 7/√193=x/√(x²+9) 7/4=x
    1
  2562. 30;15 ×41 30;15 122;60 125;90;15
    1
  2563. y"-3y'+2y=e^tsint a²-3a+2=0, a=(3±√(9-4 2))/2 a=1,a=2 y=e^x y=e^(2x) y0=c1e^x+ c2e^(2x) y=(c3x+c5)e^tcost+(c4x+c6)e^t sint e^t((c3x+c5+c3+c4x+c6)cost+(c4x-c 3x+c6-c5+c4)sint)+e^t((c3+c4)cost-(c3x +c4x+c3+c5+c6)sint+(c4-c3)sint+(c4x-c3 x+c4+c6-c5)cost)-3(e^t ((c3x+c5)cost+(c 4x+c6)sint)+e^t(c3cost-(c3x+c5)sint+c4 sint+(c4x+c6)cost))+2 ((c3x+c5)e^tcost+(c4x+c6)e^tsint)=e^t sint,(-c3-c4x+2c4-c3x+3c6-c5)cost+(c3x-c4-2c3-c4x-2c5)sint=sint, -c4x-c3x-c3+2c4+3c6-c5=0,c3x-c4-c4x-2c3-2c5=1; {-c4-c3=0,-c3+2c4-c5+3c6=0,-1 c3-c4=0,-c4-2c3-2c5=1*1/2; {-c4-c3=0,-3c4-c5+3c6=0,-2c4=0,-0,5c4+c5=-0,5;{c3=0,-c5+3c6=0,c4=0,c5=-0,5; c3=0,c4=0,c5=-0,5,c6=-1/6, y=-0,5e^tcost -1/6e^tsint y=c1e^x+ c2e^(2x)-0,5e^tcost -1/6e^tsint
    1
  2564. nm+1=3n m=3-1/n>0 n=1 m=2 P(x)=kx+b $(0;x)(kx+b)²dx=kx³ (kx+b)³/3/k(0;x)=x((kx+b)²+(kx+b)b +b²)/3 (k²-3k)x²+3kxb+2b²=0{k=0;3,[k=0,b=0;b=0;P(x)=0;3x
    1
  2565. $(-∞;∞)sinu/2025u-¹du=π/2025
    1
  2566. e^(√3π/6±√3*πm+i(±π/6+πm))=a f(x)=0;e^(√3π/6±√3*πm+i(±π/6+ πm))x^(0,5±√3/2*i)
    1
  2567. {x<-1/2,x≥0,0≥2;0/
    1
  2568. 4/1✓ {x=32n+,y=-45n+;(20;-28){x=32n+ 20,y=-45n-28.
    1
  2569. -(5-x²)⁰,⁵(1;2)=-1+2=1
    1
  2570. En=0;∞C(1/3;2n)*2Ei=0;nC(n;i)((-1) ^i+(1/3)^(3i+1))/(3i+1)✓
    1
  2571. √(208+16√(144-x²)) √(104+8√(144-x²)) 104+8√(144-x²)+8²-2√(104+8√(144-x²))*8cos(45°+ arccos((8+√(144-x²))/√(208+16√(1 44-x²)))=12² x=5
    1
  2572. (a-1)/1=(3-a)/a a=±√3≥0 S=3✓
    1
  2573. a,a+1,a+2 a(a+1)(a+2)=8(3a+3) [a=-1×,a=4,a=-6×;4²+5²+6²=77
    1
  2574. log(1/4*2^√x-1)=log(√2^(√x-2)+2)-2log2 {2^(√x-2)-1=(√2^(√x-2)+2)/4,2^(√x-2)-1≥0;{√2^2(√x-2)-1/4*√2^(√x-2)-0,5=0,√x≥2;{√2 ^(√x-2)=(1/4±√(1/16-4*-0,5))/2,x≥4;{[√2 ^(√x-2)=1/8+√33/8,√2^(√x-2)=1/8-√33/8;x≥4;{√x-2=log√2(1/8+√33/8),x≥4;{x=(2+l og√2(1/8+√33/8))²,x≥4;0/
    1
  2575. 1,2,8,89 и другие магические числа в химии 13,21,34,55,89
    1
  2576. x+c=y²ln|tg(y/2-π/4)|-$2yln|tg(y/2- π/4)|dy+xln|siny|-$ln|siny|dx
    1
  2577. xdx(x²+1)-¹=y-¹dy ln|x²+1|/2=ln|y|+c √(x²+1)=yc y=c1√(x²+1)
    1
  2578. (π*400/12-1/2*20^2*sin30°+(√3/2*20-1/2*20)^2/2)*4=(33,(3)π-100+200(3/4-√3/2+1/4))*4=133,(3)π+400-400√3
    1
  2579. 25,33₽, 10₽
    1
  2580. 12sin135°=6√2 S=6²=36
    1
  2581. 1/2(ln(y²+1)-0,5ln(y²-√3y+1)-0,5ln(y²+√3y+1))+√3π/3=√3π/3
    1
  2582. 176-30x+x²=√(64-x),x(-∞;8]U[22;64] (X-15)⁴-98(x-15)²+(x-15)+2352=0 (z-1/4)(z²-48,75z+1/16)=0 z=1/4,z=24,375±√(191*199)/8 x-15=-0,5±√199/2;0,5±√191/2 x=14,5-√199/2;15,5+√191/2 22+13/28>22,8 15/28×
    1
  2583. lgx=y,(z-1)(z²+z+4)=0 z=1;-1/2±√3,75i y=1±√3 x=10^(1±√3)
    1
  2584. X⁰,⁵=y,x=y²,dx=2ydy $dy(2-2/(1+y²))=2y-2arctgy+c=2√x-2arctg√x+c
    1
  2585. x=-2y±√(3y²+19) y[-5;5]×
    1
  2586. 19!*21²
    1
  2587. 2^(-32,5х+20,5)=2⁸ х=5/13 у=1,5*5/13 -8,5=-7 12/13
    1
  2588. sin²x+sin²y=1 siny=±cosx cot(x+y)=0/(±sin²x±cos²x)=0
    1
  2589. π•7²/4-0,5*7*2=49/4π-7
    1
  2590. z=(7+i±(1+7i))/2=4+4i;3-3i
    1
  2591. z=(5+5i±(3+1i))/2=4+3i;1+2i
    1
  2592. y'y''=-e^yy' y'≠0 y'²/2=-e^y+c 0=-e^c¹+c y'/√(-2e^y+2c)=±1 2e^-y-2c=z y=-ln(z/2+c) y'=-0,5z'/(z/2+c) -z'/√(z+2c)/√(2c)/√(z+2c -2/c)=±1 [{c=0,z=-x²-+c1ix+0,25c1²;{c≠0, z=-2c+e^(-+√(2c)x)c1;[{c=0,y=-ln(-0,5x²-+ 0,5c1ix+0,125c12+c);{c≠0,y=±√(2c)x-ln(c 1/2).
    1
  2593. x³-4x²+4x=0, x=0, x²-4x+4=0, x=2, x⁴/4-4*x³/3+4x²/2|(0;2)=4-32/3+8-0=1 1/3
    1
  2594. -x²+x+7-(x²+3x+3)=-2x²-2x+4=0, x=(2±√(4-4*(-2)*4))/(-4), x=-2, x=1, S=-2x³/3-2x²/2+4x|(-2;1)=-2/3-1+4-5 1/3+4-4*(-2)=9
    1
  2595. y=2x²+x+2,y=2-3x,
    1
  2596. S=6,25arcsin(√5/5)-2,5
    1
  2597. R=√2-1 S=π(3-2√2)(m²)
    1
  2598. x³/2Co(2flnx)-En=1;∞(-1)^(n-1)3^(2 n+1)f^(2n)(x³/3(lnx)^(2n)-x³/3²*2n (lnx)^(2n-1)+..-x³/3^(2n+1)(2n)!)/4/n/(2n)!(0;1)=ln(1+f²)/4
    1
  2599. $(3x³+5x²-25x-1)/(x³-3x+2)dx=$(3+(5x²- 16x-7)/(x-1)/(x²+x-2))dx=$(3+A/(x-1)+B/(x-1)²+C/(x+2))dx=3x-6(x-1)^-1/-1+5ln|x+2|+C 5x²-16x-7=A(x-1)(x+2)+B(x+2)+C(x-1)² =A(x²+x-2)+Bx+2B+Cx²-2Cx+C=Ax²+Ax-2A+Bx+2B+Cx²-2Cx+C,{A+C=5,A+B-2C=- 16,-2A+2B+C=-7|•-0,5;{A+C=5,-B+3C=21,B +1,5C=1,5;{A+C=5,-B+3C=21,4,5C=22,5;{A=0,B=-6,C=5;
    1
  2600. (х⁴-3х+2)/(х⁵-4х+3)=(х³+х²+х-2)/(х⁴+х³+х²+х-3)=1/1=1
    1
  2601. cosyy'-sinx=0,y'=sinx/cosy
    1
  2602. -x³/3-x²/2+2x(-2;1)=4,5
    1
  2603. x=cos(π/4+πn/2)+isin(π/4+πn/2)
    1
  2604. (2x/(1+x²))²⁰²¹+((1-x²)/(1+x²))²⁰²²=1,≤1,≥-1 (-1+2/(1+x²))²⁰²²≥0,≤2,-1+2/(1+x²)≤2^(1/2 022),≥-2^(1/2022);{1+x²≥2/(2^(1/2022) +1),1+x²≤2/(-2^(1/2022)+1);{[x≥√(2/(2^ (1/2022)+1)-1),x≤-√(2/(2^(1/2022)+1)-1); x²≤2/(-2^(1/2022)+1)-1<0;x=0:0+1=1,x=1: 1+0=1,\>x=-1:-1+0≠1.\>{0;1}
    1
  2605. y'=(-ae^(narctg(y/x))*ny-x(x²+y²)⁰,⁵)/((x²+y²)⁰,⁵y-ae^(narctg(y/x))nx)
    1
  2606. Sin(7x/2)sin(x/2)+cos(7x/2)cos(x/2)= cos²3x,sin4x-cos²3x=0,2sin2xcos2x-(cos6x+1)/2=0,2sin2xcos2x-2cos³2x+1,5cos2 x-1/2=0,±2√(1-cos²2x)cos2x=2cos³2x-1,5cos2x+1/2,4(1-cos²2x)cos²2x=4cos⁶2x+2,25cos²2x+0,25-6cos⁴2x+2cos³2x-3/2cos2x,-4cos⁶2x+2cos⁴2x-2cos³2x+1,75cos²2x+1,5cos2x-0,25=0,-0,5=-0,5 cos2x=-1,-4 cos⁵2x+4cos⁴2x-2cos³2x+1,75cos2x-0,25=0,2x=π+2πn,x=π/2+πn,x=±0,194+πn,x= ±0,712+πn,x=±1,111+πn.
    1
  2607. r/(√12-r)=2/4 r=2/3√3 V=4/3π(2/3√3)³=32π/27√3
    1
  2608. {y=2,x=±0,5;x²+y²=4,25
    1
  2609. 16*38,5/π=196 28/157cm²
    1
  2610. Ek=0;∞(1/(k-3)!+6/(k-2)!+7/(k-1)!+1/k!)=e+6e+7e+e=15e
    1
  2611. X=1+(3-e)/(e+2),x=-2+e^-2/(-e^-2+4)
    1
  2612. K=|x'y''-x''y'|/(x'²+y'²)¹,⁵(?✓)
    1
  2613. ((3x+2)/(2x+3))³=u u+1/u=18 u=9±4√5 (3x+2)/(2x+3)=(3±√5)/2 x=(-+√5-3)/2✓
    1
  2614. $(x-1)³(x+1)0dx=c
    1
  2615. Cosx*e^((-2n+1)x)/(-2n+1)/2+sinx e^((-2n+1)x)/(-2n+1)²/2(0;=(=1/2/(2n-1) 0,5arctg1=π/8{π/4}
    1
  2616. 54800*0,036=1972,8 бел. руб.
    1
  2617. Это окно Овертона в действии.
    1
  2618. {b=2a/(3a-2),[a=0,a=1;c=3a/(4a-3);{(0;0;0)(1;2;3)}
    1
  2619. {a=a1²,b=±a1³,c=c1²,d=±c1³;c1²-a1²=9 [{a1=-4,c1=5;{a1=0,c1=3;{a1= 4,c1=5;{a1=4,c1=-5;{a1= 0,c1=-3;{a1=-4,c1=-5;(16;-+64;25;±125)(0;0;9;±27)(16;±64;25;± 125)
    1
  2620. (1+cos2°)/sin2°✓
    1
  2621. y''+c=y'²/2 y''/(y'²-2c)=1/2[{c>0, [y=-3√(2c)x+c2,y=-√(2c)x+2En=1;∞c1^(n-1)e^(√(2c)x(n-1))/(n-1)+c2;{c=0,y=-2ln|x+2c1|+c2;{c<0,y=-2ln|cos(√(-2c)/2x+c1√(-2c)|+c2.
    1
  2622. C=1/8/(ab) 1,5a²((1-1/(a³+1))-⁰,⁵(a³+1)-²-(1/8³/b³/(1/8³/b³+a³))-⁰,⁵/512/b³(1/512/b³+a³)-²) =0[a=0,a⁴-8ba³+a-1/64/b²=0; 0*-*+>a {[a=1/2,a=1/2/7¹/³;±(b³+1)b √(b⁴+4b)=b⁶+3b³+7/32;[a=b, a=(-b²±√(b⁴+4b))/2/b; 0=-7b⁶+43b³+191/64 b=((43±√31921/4)/14)¹/³(+=>+)(-=>-) a=(-(43±√31921/4)²/³±√((43 ±√31921/4)¹/³(99±√31921/4))/14 ¹/³/2/(43±√31921/4)¹/³ +*1/2/7¹/³- 1/2+*1,84..->a+*0,26*1/2/7¹/³-- 1/2*+>b min=1/3*3=1
    1
  2623. 1'/(20'/6)=0,3см 5288,6км минимальный размер для наблюдения.
    1
  2624. (10а+в)/(10в+с)=а/с, 10ас+вс=10ва+са, 10а(с-в)=с(а-в),с=а*10в/(9а+в)а=1,в=1,с=1;в=6,с=4;в=9,с=5, а=2,в=2,с=2, в=6,с=120/24=5, а=3,в=3,с=3, а=4,в=4,в=9,с=360/45=8, а=5,в=5, с=в+в(а-в)/(9а+в) ,а=в
    1
  2625. 0/0=-sinx/1=0
    1
  2626. 22=1(ост.7)
    1
  2627. x=πn,x=πm✓
    1
  2628. a²(3*7⁴-5*7³a+5*7²a²-21a³+a⁴):7⁵ a:7=ost.0✓ b:7 (a/7)⁷+(b/7)⁷=(ac) ¹⁹⁹⁵ 1995:7=285×0/
    1
  2629. F(2x)=f(x)^lnf(2) f(2^n)=f(1)^ln^nf(2) f(x)=f(1)^x^logf(2)lnf(2),f(2)(1;∞)
    1
  2630. (1+1/54)^84=4,67..
    1
  2631. lnxln(1+lnx)-lnx+ln|1+lnx|+c
    1
  2632. Х≤а/3,х²+3х+8-а=0 х=(-3±√(-23+4а))/2 ±√(-23+4а)≤2а/3+3,а≥23/4✓
    1
  2633. √(c²-h²), (a+b)/2*h=S S1=0,5S=(2a1 +√(c²-h²))/2*h (a+b)/4-√(c²-h²)/2= a1 Сложу основания трапеции,поделю на 4 равные части, проведу высоту из левого верхнего угла и возьму горизонтальный катет. Потом поделю его на 2 и от 1/4 суммы оснований отниму половину горизонтального катета. Получившийся отрезок отложу по верхнему основанию из левого угла и проведу вертикаль.
    1
  2634. 52²=2704✓
    1
  2635. -1/2-+√3/2i-1/2±√3/2i-1=-2
    1
  2636. 6tgo/3=1/sino 2-coso-2cos²o=0 o=arccos(((-1+√17)/4) 13°=arctg(√(-26+10√17)(9+√17)/128(-2+√(2+2√17)))×
    1
  2637. F(x)=(x-f(0))²/2025 f(0)=f(0)²/2025 f(0)=0;2025 f(x/=x²/2025;(x-2025)²/2025
    1
  2638. En=0;≠√3/2/2^(2n)+En=0;∞-√3/4/ 2^(2n)=2√3/3-√3/3=√3/3
    1
  2639. 38000/16242=2,34 раза маловато!
    1
  2640. {x(-1;0)y=ax²+bx+c,a,b,c<0,5 x≤y≤0,5(x²+ 1);x²+1≥2x,(x-1)²≥0 x=1,y=1:1=a+b+c,c=1 -a-b>0,a(0;0,5),b(0;0,5) y(0)=c,y(-1)=a-b+ c=1-2b (a-0,5)x²+bx+c-0,5≤0,{b²-4(a-0,5)(c-0,5)<0,a-0,5<0;{(b+2a-1)²<0, a<0,5;b+2a -1=0,b=1-2a,x≤ax²+(1-2a)x+a,-ax²-2ax-a≤0,-a(x+1)²≤0,a≥0 2020(a²+b²-c²)=2020(a²+b²-(1-a-b)²)=2020(a²+b²-1-a²-b²+2a+2b-2ab)=2020(1-4a+4a²)>=0,≤2020
    1
  2641. x≠2;3;-4;-5 x²+7x+11=±(x²-7x+11)[x=0,2x²+22=0;{0}
    1
  2642. (x²+9x+20,5)²-1089x-32820,25=0 x=-4,5+(33/2)²/³-+>x 16,5*16,5¹/³-1089 16,5²/³-27919,75<0 2 реш. x0~2 1/48 x=9,96;15,7
    1
  2643. sin3x(cos3x-cosx)/cosx/cos2x/cos3x=0 [x=πn/3,x=πn,x=0,5πn,x≠π/2+πm,x≠π/4+0, 5πm,x≠π/6+1/3πm;n≠1+2m,n≠(1+2m)/3 {πn/3}
    1
  2644. (3+3√3/2)/0,5=6+3√3 1/(1+√3)= (√3-1)/2 /_1=π-arctg(-√3+4) arctg(2+√3)=75° -75°+arctg(-√3+4)✓
    1
  2645. (a²-8)²/4/a²+(a²-6)²/4/a²=1 a⁴-16a²+50=0 a²=8±√14 a=√(8±√14)≥√7-1,≤√7+1 ±√2[-2;2] arccos(-+√2/2)=135°
    1
  2646. X,y:5 x1y1=52 (1:52)(4:13)(13;4)(52;1){(5;260)(20;65)(65;20)(260;5)}
    1
  2647. 10+2a,100+31a+2a²,..,a⁴⁰+..+10⁴⁰= 210 a=5 15,20,..,15+5*39=210{25}
    1
  2648. f(xf(x)+f(y))=f²(x)+y, f(f(0))=f2(0), f(f(x)x+f(-f²(x)))=0,f(f(-f²(0)))=0, f(f(-f(f(0))))=0, a0an^n+a1an^(n-1)+...+an=an², an=0, a0an^(n-1)+a1an^(n-2)+..+(a(n-2)-1)an+a(n-1)+1=0, a(n-1)=-a0an^(n-1)-a1an^(n-2)-..-(a(n-2)-1)an-1, a0(a0(-a0an^n-a1an^(n-1)-...-an)^n+a1(-//-)^(n-1)+..+an)^n+a1(a0(-//-)^n+a1(-//-)^(n-1)...+an)^(n-1)+...+an=0,
    1
  2649. (log2(x)-3)(log2(x)+3)/(log2(x)-5) ²≥0 °0+*1/8-*8+°32+>x x(0;1/8]U[8;32)U(32;∞)
    1
  2650. U''(x)u'(x)+(u⁵(x)-u²(x))u'(x)=0 u'(x)²/2+u⁶(x)/6-u³(x)/3=c u'(x)/√(-1/3(u³(x)-1)² +1/3+2c)=±1 u(x)F1(1/3;1/2;1/2;4/3; u(x) ³/(1+√(1+6c));u(x)³/(1-√(1+6c)))/√2=±x+ c1 $√3/√(-x³+1+√(1+6c))/√(x³-1+√(1+6c))dx =$-+√3/3(1±(-u²+1+6c)⁰,⁵)-²/³(-u²+1+6c)- ⁰,⁵du √(-(x³-1)²+1+6c)=u, x=(1±(-u²+1+6c)¹/²)¹/³,dx=-+1/3(1±(-u²+1+6c)⁰,⁵)-²/³(-u²+1+6c) -⁰,⁵*udu
    1
  2651. 3^n=x,3n*3^3n=2*3² n=2/3{3²/³}
    1
  2652. Y(x)=x²/2+$(2;x)-ty(t)dt y'=x-xy y'+xy=x y=ce^(-x²/2)+e^(x²/2) 2e^(x²/2)-x²/2=-ce^-2+e²,c=e⁴ y=e⁴e^(-x²/2)+e^(x²/2)
    1
  2653. -a²+8a-13[3;√23] {a=4,a²-8a+13+√23≥0; a=4 cos(8x+9)=-1 x=1/8π+1/4πn-9/8
    1
  2654. h=80√5/7 S=0,5*80√5/7•20√5-0,5(8√5)²=4000/7-160=2880/7m²
    1
  2655. 0,156,y=csint+.. yp=sint*c(t) 2ctgtc'(t)+c''(t)=1/2/cos²0,5t c(t)=$dt$dt/(cost+1)²/(1-cost) y=csint+sint*((ln(1-sin(t/2)^2)-1/(sin(t/2)^2-1))/12-ln|sin(t/2)|/2-ln|cos(t/2)|)
    1
  2656. $√(sin²x+1)dx=3/2-cos2x/2?...
    1
  2657. 258-216=42,42-36=6 (1;2;3)✓
    1
  2658. {а(х+2)+у=3а,а+2х³=у³+(а+2)х³;{у=-ах+а,а +2х³-(-ах+а)³-ах³-2х³=0;а+а³х³-3а²х²*а+3аха²-а³-ах³=0,(а³-а)х³-3а³х²+3а³х+а-а³=0, а=0,хєR,(х-а³/(а³-а))³-3а²/(а²-1)²(х-а²/(а²-1))+(-3а²+1)/(а²-1)³=0,х-а²/(а²-1)= ((1,5а²-0,5)/(а²-1)³+√((1,5а²-0,5)²/(а²-1)⁶+(-3а²/(а²-1)²)³/27))^(1/3)+(1,5а²-0,5-√((1, 5а²-0,5)²-а⁶))^(1/3)/(а²-1) {х=а²/(а²-1)+ (1,5а²-0,5+√((1, 5а²-0,5)²-а⁶))^(1/3)/(а²-1) +(1,5а²-0,5-√((1,5а²-0,5)²-а⁶))^(1/3)/(а²- 1),у=-а³/(а²-1)-а(1,5а²-0,5+√((1, 5а²-0,5)²-а⁶))^(1/3)/(а²-1) а(1,5а²-0,5-√((1,5а²-0,5)²-а⁶))^(1/3)/(а² 1)+а.
    1
  2659. Y'=-1/(cosx-²+sinx-²)*cos-⁰,⁵x-²sin -⁰,⁵x-²x-³
    1
  2660. x²-290x=289√x x⁰,⁵(x¹,⁵-290x⁰,⁵-289)=0[x= 0,x⁰,⁵=(289/2+√(144,5²+(-290)³/27))^(1/3) +(289/2-√(-71'493'289,75)/9)^(1/3)=2√(2 90/3)cos(1/3arccos(867/168200√870)+ 2πn/3);✓,-..,-.. [x=0,x=1160/3cos²(1/3arcc os(867/168200√870)).[√(x-x⁰,⁵)=0,√(x-x⁰,⁵) =√(1160/3cos²(1/3arccos(867/168200√ 870))-2√(290/3)cos(1/3arccos(867/1682 00√870)))=18 2/3...16,.. .
    1
  2661. 6√(14n),n=14n1²
    1
  2662. (1 2 b|1) (0 4/5 b-3/5|-b/5) Z=(-b-4y)/(5b-3) x=(b²+5b-3+y(-6b+6))/(5b-3) (b²-y(b-3))/(5b-3)Z,b≠3/5,y=3n b=0,z=4n,x=-6n+1✓
    1
  2663. A=1/x/(1-x)≥4 B=1+1/x²+1/(x-1)²+1/(x²-x)² 2(x²-x)-³(x²-x+2)(2x-1)=0 x=1/2*+>x min=1+4+4+4²=25
    1
  2664. 1/sin(/_B+/_C)=AB/sin/_C=AC/(2sin/_C) AC=2AB,2/AC-2cos/_C= ±√(1-4sin²/_C) 4/AC²-8/ACcos/_C+ 3=0 AC=4/3(cos/_C-+√(cos²/_C-3/ 4)) -+(±(-24cos/_C+32cos³/_C))-12cos/_C+16cos³/_C=(±(-16 cos²/_C+3)±(16cos²/_C-6))√(cos²/_C-3/4) [[/_C=30°,/_C(+)= 0,5arccos(-1/4+3√5/8);/_C=30°, 3=±(3√5/2+1×);/_C=30°,/_B=90°,/_A=60° S∆=1/6√3
    1
  2665. 55(-3²/³*176+154*3¹/³+335)/1879
    1
  2666. 21²+(√(R²-9²)-16)²=R² 85/4=R
    1
  2667. $lnx(e^(x(lnx-1))+e^(x(1-lnx)))dx=e ^(x(lnx-1))-e^(x(1-lnx))+c Lnx-1+x*1/x=lnx 1-lnx+x*-1/x=-lnx
    1
  2668. k(x^(1+2/n)-2^(1/n)x^(1/n))=2(x³+x) 1+1/n=2,n=1 k(x³-2x)=2(x³+x) x(f(x²)-2x²-2)=f(2x) (e^(x²/4)+e^(-x ²/4)-2)/x-x=f(x) En=1;∞(2^(4n+1) 1)/4^2n/(2n)!/(4n+1)-1,5 A)
    1
  2669. 1+log(4)x=6/log(4)x, z²+z-6=0, z=(-1±√(1-4*(-6)))/2, z=2, z=-3, x=16, x=1/64.
    1
  2670. 1/1!-1/2!+1/2!-1/3!..+1/k!-1/(k+1)!=1-1/(k +1)! 2019(1-(1-1/(2019)!))=1/2018!
    1
  2671. R,2a-R,(2a-R)²+a²=R²,4a²-4aR+R²+a²-R²= 0,R=5/4a 5/4a=5,a=4 S=32
    1
  2672. [x=0,x=0,1.{0;0,1}
    1
  2673. 5 и 6;1 и 1,..,6 и 6 n=24 m=36 p=2/3
    1
  2674. a2a3+..+a(n-3)a(n-2)-(a1+0,5(a3+..+a(n-2)+2a(n-1)))²+(a3+..+a(n-2))²/4+a(n-1)(-a2+a(n-2))≤0
    1
  2675. En=1;∞(-1)^(n-1)(x^(4n-3)/(4n-3)lnx- x^(4n-3)/(4n-3)²)/(2n-1)!|∞=?
    1
  2676. 3-4(1/4+1/5+1/6)=8/15
    1
  2677. x/(x-6)✓
    1
  2678. Cos²a/(cosa-sina)-sin²a/(-sina+cosa)= cosa+sina
    1
  2679. 116,71/237=0,492..
    1
  2680. (1-12i)(5+i)/26=(17-59i)/26
    1
  2681. 2((x-5/6)³-25 1/12(x-5/6)-8 35/108)=2(x -5/6-√301/3cos(1/3arccos(899/301²√301)))(x-5/6-√301/3cos(1/3arccos(899/301² √301)+2/3π))(x-5/6-√301/3cos(1/3arcco s(899/301²√301)+4/3π)) (899+√(899²-301³))¹/³/6+(..-..)..=√301/3 cos(1/3arccos(899/301²√301)+2/3πn)
    1
  2682. $(0;π)πsin²xdx=π*0,5(π)=0,5π²
    1
  2683. {x≥3,[x=(7+√13)/2,x=1;{(7+√13)/2}
    1
  2684. 2/x,4/x/(1-4/x²)=-6/(4-x) 0,5x²+4x-6=0 x=-4+√28 S=12+6√7-4π
    1
  2685. X⁰,⁵=y,x=y²,dx=2ydy $(0;=)ye^-y²*2ydy=-ye^-y²+√πФ(√2*y)(0;=)=0,5√π
    1
  2686. R=4(2-√2) S=64√2-80-16(3-2√2)π
    1
  2687. 4⁴+4³(x1²+..+x4²)+4²(x1²x2²+..+x3²x 4²)+4(x1²x2²x3²+..+x2²x3²x4²)+(x1x 2..x4)²=1654 9/16=125/16m m=26473/125✓
    1
  2688. AB=(6+x)sina±√(4²-(6+x)²cos²a) ((6+x)sina-√(16-(6+x)²cos²a))/sin?=4/sina ?=arcsin(((6+x)sina-√(16-(6+x)²cos² a))sina/4) /_1=180°-2a-arcsin(((6+x)sina- √(16-(6+x)²cos²a))sina/4) x=-6+8√((1-sin2a)/(6,5-6sin2a-0,5cos4a+ 2cos2a-sin4a)), a[π/4; 1,25π] (-72sin2a+ 72)(1+9cos2a+3(cos2a +1)x+x²(cos2a+ 1))+(2-cos²2a)x⁴+(27-12sin2a-3cos²2a+ 12(1-cos2a-sin2a)(1+cos2a))x³+(-4,5cos 4a+180sin2a+8cos2a+316,5-18sin4a)x²+((24-12sin2a)(-36sin2a+88)+12(1-cos2a- sin2a)(1+9cos2a))x+(-36sin2a+88)²=36x²
    1
  2689. y=m(x-4)-9 x=0,y=-4m-9 y=0,x=9/m+4 S=4m+9/m+13≥25(2)
    1
  2690. 1/3*0,5*0,5*3/4*2√2/2=1/16√2
    1
  2691. En=0;∞e^-l*l^x/x!(x-l)=l-l=0 мода~l 0,5=Ex=0;xe^-l*l^x/x! 0,5e^l~e^l x>l?
    1
  2692. F(x+1)=f(x)²f(1)=f(0)^2^(x+1)f(1)^(2^(x+1)-1) f(x)=(f(0)f(1))^2^x/f(1) f(0)=f(0),[f(1)=0,±1=f(0); f(x)=0;f(1)^(2^x-1)
    1
  2693. y=-3/4x+9;4/3x+9;3/4x-5 (0;9) x=28/3,(9;16),x=-180/7,y=3/7 (-180/7;3/7) AB(9;7),AC(-180/7;-60/7),BC(-243/7;-109/7) AA1(-117/14;-11/14) AM(-39/7;-11/21) (-39/7;8 10/21)
    1
  2694. En=0;∞(0 a;-a 0)^n/n! (0 a;-a 0)²=-a²(1 0;0 1) (cosa sina;-sina cosa)✓
    1
  2695. ((a+b)²-2ab)²-(2ab)²+12=5
    1
  2696. Cos(y-x)(0;π/2)=sinx-cosx -cosx-sinx(0;π/2)=-1+1=0
    1
  2697. F=-600N Mx=-2800N*m y=14/3(m) My=-900N*m x=1,5m✓
    1
  2698. f(x+1)=f(x)f(1)-f(1)-x+2=f(1)f(1)^x-f(1)(f(1)^x-1)/(f(1)-1)-((f(1)^x-1)/(f(1)- 1)-x)/(f(1)-1) f(x)=f(1)^x(1-(f(1)²-f(1)+1)/f(1)/(f(1)-1)²)+(f(1)²-f(1)+1)/(f(1)-1)²+(x-1)/(f(1)-1)=-x²+3x-1 f(1)=1
    1
  2699. x²-5x+6=0 x=(5±√1)/2{3;2}
    1
  2700. АЕ=(у/х+1)ОС КО=ОС(у²+х²)/2/у/х у=х✓ 34/64=(y-x)/x 32/49=x/y
    1
  2701. {x[-1;1],y[-1;1],(x-a)²+(y-a)²≤|a|;a[-2;2]
    1
  2702. (x+2y)²-y²+z²=9-98²+102²=809
    1
  2703. 1'700/12=141,(6)
    1
  2704. (x⁴-0,5x)²+0,75(x-2/3)²+2/3>0✓
    1
  2705. (x²+y²)/(x²-y²)=(k+-√(k²-4))/2 x²+y²=(0,5k ±0,5√(k²-4))x²-(0,5k±0,5√(k²-4))y² x^2=(-0,5k-+0,5√(k²-4)-1)y²/(1-0,5k-+0,5√(k²-4)) (x⁸+y⁸)/(x⁸-y⁸)+(x⁸- y⁸)/(x⁸+y⁸)=((-1-0,5k-+0,5√(k²-4))⁴/(1-0,5k -+0,5√(k²-4))⁴y⁸+y⁸)/((-1-0,5k-+0,5√(k²-4))⁴/(1-0,5k -+0,5√(k²-4))⁴y⁸-y⁸)+((-1-0,5k-+0,5√(k²-4))⁴/(1-0,5k -+0,5√(k²-4))⁴y⁸-y⁸)/((-1-0,5k-+0,5√(k²-4))⁴/(1-0,5k -+0,5√(k²-4))⁴y⁸+y⁸)=((-1-0,5k)⁴-+4(-1-0,5k)³*0,5√(k²-4)+4!/2!/2!*(-1-0,5k)²*0,25√(k²-4)²-+4(-1-0,5k)*0,125√(k²-4)³+√(k²-4)⁴*0,0625+1)/(((-1-0,5k)⁴-+2(-1-0,5k)³√(k²-4)+1,5(-1-0,5k)²(k²-4)-+0,5(-1-0,5k)√(k²-4)³+0,0625(k²-4))²)/(1-4*0,5k+6*0,25k²-0,5k³+0,0625k⁴+ 1,5(1-k+0,25k²)(k²-4)+0,0625k⁴-0,5k²+1-+√(k²-4)(2(1-3*0,5k+3*0,25k²-0,125k³)+0,5(1-0,5k)(k²-4))-1)+(0,5k⁴-2k³+k²+4k-5-+√(k²-4)(2,0k²-0,75k³-k))/((-4+4k+k²+2k³+0,5k⁴-+(-2k-2k²-0,5k³)√(k²-4))/(0,5k⁴-2k³+k²+4k-4-+√(k²-4)(2,0k²-0,75k³-k))+1)=1/(0,5k⁴-2k³+k²+4k-5-+√(k²-4)(2,0k²-0,75k³-k))/((-4+4k+k²+2k³+0,5k⁴-+(-2k-2k²-0,5k³)√(k²-4))*(0,5k⁴-2k³+k²+4k-4-+√(k²-4)(-0,75k³+2,0k²-k))+1)+(0,5k⁴-2k³+k²+4k-5-+√(k²-4)(-0,75k³-2,0k²-k))/((0,5k⁴+2k³+k²+4k-4-+(-0,5k³-2k²-2k)√(k²-4))(0,5k⁴+k²+4k-4±√(k²-4)(-0,75k³+2k²-k)+2k³)/((0,5k⁴+k²+4k-4-+√(k²-4)(-0,75k³+2,0k²-k))²-4k⁴)+1)
    1
  2706. f(x)≤2-xf(1) f(1)≤1 y(2-xf(1))+x(2-y f(1))=2(x+y)-2xyf(1)≤2
    1
  2707. {c=-a-b,a²/b/c+b²/a/c+c²/a/b=3;A)
    1
  2708. 22000/6,06/2,44/2,56=36,3/4,2464=8,7кг/м^3 1818 3820 3636 184 1464 1220 288 42464
    1
  2709. X²=2(y+2) R=40y/√(80²-(116-y²)²) arccos((y-4)/2/√(2(y+2))=arctg(40 y/√(80²-(116-y²)²)/√(2(y+2)))+arctg (|116-y²|y/√(80²-(116-y²)²)/(y+4)) √(-y+16)=(y-4)√y(40(y+4)+√(2(y+ 2))|116-y²|)/(√((80²-(116-y²)²)*2(y+ 2))(y+4)-40y²*|116-y²|)*√(80²-(116- y²)²),y[6;14] (-y+16)(√((80²-(116-y²)²)*2(y+2))(y+ 4)-40y²*|116-y²|)²=(y-4)²y(40(y+4)+ √(2(y+2))|116-y²|)²*(80²-(116-y²)²) y=6,89;13,91 x=7,83;14,88 x+y=15,72;28,79
    1
  2710. AT=2a√(5-4cos/_C) AO1=2a/√(5-4 cos/_C) TB=a√(5-4cos/_C) O2B=a/√(5-4cos/_C) AT/TB=2
    1
  2711. 2(1/n-1/(n+1)) 2(1-1/(n+1))=2024/ 1013 n=1012
    1
  2712. y=x²/4 y=8/(x²+1) x=±√(-0,5+√32,25) y'=x/2=±√(-0,5+ √32,25)/2 y'=-(x²+1)-²*16x=-+√(-0,5+√32,25)(65-√129)/128 tga=-√(-2+2√129)(645+61√129)/248 arctg(√(-2+2√129)(645+61√129)/248)
    1
  2713. 1,5((1+x)-⁰,⁵+(1-x)-⁰,⁵)/((1+x)-²/³+ (1-x)-²/³)=1,5*2/2=1,5
    1
  2714. {y=(7-√x)²,x-7√x+12=0;√x=3,5±0,5=4;3 x=16;9 y=9;16{(16;9)(9;16)}
    1
  2715. 3tg(Arccos(3/5)-arccos(4/5))=7/8 a=3tg(arccos(3/5)-arctg(1/3))-7/8=125/104 S∆1=375/208 -27/14+√(x²+20281/9/196)=.. x²+160/9-9/14√10x=-x√10/3√(x²+20281/9/196)+4√(-2741/9/98+27/7√(x²+20281/9/196)) x=1,008 S∆2=2,750 S=3,952
    1
  2716. Х+7/х=у 0=у²-25у+144 у=(25±7)/2=16;9 [х²-16х+7=0,х²-9х+7=0;[х=8±√57,х=4,5±√53/2.
    1
  2717. √(5-2√2sin85°),arccos((1,5-√2/2sin85°-0,5cos40°)/√(5-2√2sin85°)/sin20°),200°-arccos((1,5-√2/2sin85°-0,5cos40°)/√(5-2√2sin85°)/sin20°) Arctg((-1,5+√2/2sin85°+0,5cos40°+cos20°√(5-2√2sin85°-(1,5-√2/2sin85°-0,5cos40°)²/sin²20°))/(cos20°(1,5-√2/2sin85°-0,5cos40°)/sin20°+√((2,5-√2sin85°)(1-cos40°)-(1,5-√2/2sin85°-0,5cos40°)²)+1))=x{6°}
    1
  2718. (а-8-3|а|)²-4(6-а)(3|а|+2)=(а-4+3|а|)²[х=log2(2+3|а|),х=log2(-а+6). 6≤a✓
    1
  2719. $x√(1-(x²)²)dx=$0,5√(1-u²)du=0,5(arcsinu-√(1-u²)u/2)+C=0,5arcsinx²-0,25√(1-x⁴)x² +C x²=u,
    1
  2720. x=±√3
    1
  2721. МУХА*2=СЛОН,8 букв,Мє[1;4],Сє[2;9] Н:2,М=1,1345*2=2690
    1
  2722. 14:40 содрали кожу с рук,обморозил, наверное.
    1
  2723. x⁶-9x⁵+14x⁴+51x³-91x²-78x+70=0 (x³-4,5x²-3,125x+11,4375)²+2 31/ 64x²-6,5990625x-50 209/256=0{-1,87;-1,29;0,70;2,29;4,29;4,87}
    1
  2724. СИНИЦА*2=ПТИЧКИ,9 букв И:2,Сє[1;4] Пє[2;9]14¹74Ц¹7*2=2948К4,1¹636*¹8×2=326**6,1¹898*4•2=378**8,С=3:342457•2=684914
    1
  2725. 3*9=(√2-1)r*√2r r=3√(3(2+√2)/2) S=0,5r²*π/4=π*27(2+√2)/16
    1
  2726. (x+1/5y+3/5)²+4/25(y-2,5)²≥0,36,(-1,1;2,5)
    1
  2727. x=(11±9)/10=2;0,2 5(x-2)(x-0,2) 4x²-5x-21=4(x-3)(x+7/4) D=361 x=(5±19)/8=3;-7/4 6x²+17x+5=6(x+0,5)(x+15/4) x=(-17±13)/8=-0,5;-15/4
    1
  2728. (65-х²)¹/⁶=-1-х¹/³≥0 х≤-1 0=-32+3х¹/³+7,5х²/³+10х+7,5х⁴/³+3х⁵/³+х² -16?16[х=1,х⁵/³+4х⁴/³+11,5х+21,5х ²/³+29х¹/³+32=0;x¹/³=-2 x=-8✓
    1
  2729. Мой комментарий 666!
    1
  2730. √(5A)-A/5,√(5A) 5A-√5/5A¹,⁵=A 4√5=A⁰,⁵ A=80
    1
  2731. $$Dxdxdy=$(0;√3)dx$(2+√(4-x²);4+√(4²-x ²))xdy+$(√3;2√3)dx$(x/√3;4+√(16-x²))xdy +$(2√3;4)dx$(4-√(16-x²);4+√(16-x²))xdy= x²-(16-x²)¹,⁵/3+(4-x²)¹,⁵/3(0;√3)+(2x²-(16-x ²)¹,⁵/3-x³√3/18)(√3;2√3)-2(16-x²)¹,⁵/3(2√3; 4)=38 1/6
    1
  2732. √8√i=±(2+2i(
    1
  2733. 2^(x+1)=64 x+1=6,x=5
    1
  2734. tg³A=-1,tgA≠1 tgA=-1,A=-π/4+πn
    1
  2735. 2/sin2A+1=2/sin(-π/2+2πn)+1=-1
    1
  2736. 0,5DC/sino/sin(-3o+150°)=DC/sin(2o) 3o-60°=±o+2πn[o=30°+πn, o=15°+π/2n;o(0;50°) o=30°;15°A)
    1
  2737. k/2=1,5+x2,2=1,5x2 x2=4/3 k=5 2/3
    1
  2738. AC=√2BC 50²+AK²=AB², AK=√(BC²-2500) KD²+(50-CD)²=BC², KD=√(BC²-(50-CD)²) AD=√(BC²-2500)+√(BC²-(50-CD)²) (√(BC²-2500)+√(BC²-(50-CD)²))²+CD²=2BC², BC²-2500+2√(BC²-2500)√(BC²-(50-C D)²)+BC²-(50-CD)²+CD²=2BC², √(BC²-2500)√(BC²-(50-CD)²)=(2500+2500+100CD+CD²-CD²)/2=2500+50CD, (BC²-2 500)(BC²-2500+100CD-CD²)=6'250'000+ 250'000CD+2'500CD², BC⁴-2500BC²+100 BC²CD-BC²CD²-2500BC²+6250'000-250'000CD+2500CD²-6'250'000-250'000CD-2'500CD²=0,BC⁴-5000BC²+100BC²CD-BC²CD²-500'000CD=0,BC²=(5000-100CD+CD²±√((5000-100CD+CD²)²-4(-500'000CD)))/2= 2500-50CD+0,5CD²+√(5000²-10*10⁵CD+100²CD²+CD⁴+10'000CD²-200CD³+2'000'000CD)/2=2500-50CD+0,5CD²±√((5000+ 100CD)²+CD⁴+10'000CD²-200CD³)/2>C D²,>50², BC²/2+CD*AD/2=1250-25CD+0, 5CD²+√((5000+100CD)²+CD⁴+10'000CD ²-200CD³)/4+0,5CD*(√(-50CD+0,5CD²± √((2500+500CD)²+0,25CD⁴+2'500CD²-50CD³))+√(50CD-0,5CD²±√((2500+50CD)² +0,25CD⁴+2500CD²-50CD³)))=1250-25CD+0,5CD²+√((2500+50CD)²+0,25CD⁴+250 0CD²-50CD³)/2+0,5CD*(√((-25CD+0,25CD ²+0,5(-1*(2500+500CD))+√(-25CD+0,25C D²-0,5√-1*(2500+500CD))+√((-25CD+0,25 CD²+√-1*(2500+500CD))+√(-25CD+0,25C D²-0,5√-1*(2500+500CD))
    1
  2739. абвгдеёжз ийклмнопр стуфхцчшщ ъыьэюя 17516 3761216211 3. |666|- 22. |5|- 11111|-|77 Максимально развитое лидерство, оптимальная энергия,тяга к знаниям, здоровья нет, воображение, умение работать руками,если во благо - золотой мастер, особое везение и миссия с неба, богатство не дано, памяти нет.
    1
  2740. $(1;∞)dx/(x⁴+x)=$(1;∞)dx(A/x+B/(x+1) +C(2x-1)/(x²-x+1)+D/(x²-x+1))=ln|x|-1/3ln|x+1|-1/3ln|x²-x+1|(1;∞)=∞-∞-∞-0+1/3ln 2=ln|x/(x+1)^(1/3)/(x²-x+1)^(1/3)|∞+1/3 ln2=0+1/3ln2=1/3ln2 A(x+1)(x²-x+1)+Bx(x²-x+1)+C(2x-1)x(x+1) +Dx(x+1)=1,Ax³+A+Bx³-Bx²+Bx+2Cx³+Cx²-Cx+Dx²+Dx=1,{A+B+2C=0,-B+C+D=0,B-C +D=0,A=1;{A=1,B+2C=-1,-B+C+D=0,2D=0;{A=1,B+2C=-1,3C=-1,D=0;{A=1,B=-1/3,C=- 1/3,D=0; 0,5-0,3865=0,1135 0,325;0,475 0,15*0,41=0,0615
    1
  2741. y'y=3x²/2+c y=±√(x³+2cx+2c1)
    1
  2742. 4√(29-2²)=20
    1
  2743. х=log2(6)
    1
  2744. Vf=c√2^t(cos(π/4*t)+isin(π/4*t))
    1
  2745. y''+8y'+16y=(6x-8)e^-4x+90e^5x(2cos3x+sin3x) k²+8k+16=0,k=-4 y0=c1e^-4x+c2x e^-4x yp=(a0x²+a1x)e^-4x+e^5x(c3cos3x+ c4sin3x) ((-16a0+6a1)x+2a0+(16a0-24a 1)x²+16a1x³)e^-4x+e^5x((-30c3+16c4)sin3x+(16c3+30c4)cos3x)+8(((-4a0+3a1)x² +2a0x-4a1x³)e^-4x+e^5x((-3c3+5c4)sin3 x+(5c3+3c4)cos3x))+16((a0x²+a1x³)e^-4 x+e^5x(c3co s3x+c4sin3x))=(6x-8)e^-4x+ e^5x(90sin3x+180cos3x){a0=-4,a1=1, c3=1,c4=2;yp=(-4x²+x³)e^-4x+cos3x+2sin3x y=c1e^-4x+c2xe^-4x+(-4x²+x³)e^-4x+c os3x+2sin3x
    1
  2746. X²-1,6xy+y²-1=0 x=(2y±√(-21y²+25))/5 -21y²+25=n²,y=0;±1 (5;0)(2;±1) x=±1;0{(±1;0)(0;±1)}
    1
  2747. Mz=30 Н*м Му= Мх=30√2 Н*м Му=-25 Н*м М=57,5Н*м
    1
  2748. (n+1)/(n+2)✓ arctg(n/(n+1))=π/4✓
    1
  2749. (x-6)²+(y+1)²=64 O(6;-1),R=8 C=16π
    1
  2750. (2+2х)/2*х=-2*-28,х²+х-56=0,х=(-1±√(1-4 *-56))/2[х=7,х=-8;{7;-8}
    1
  2751. (x/4)^(x/4)=2² {8}
    1
  2752. 3n²+18n+35
    1
  2753. X³+42x+336/x+512/x³ 3(x⁴+22x²+64)(1-8x-²)x-²=0 x=±√8 +*-°0-*+>x min=200√2 E)
    1
  2754. {x+y=a,xy=b;{b=16,a(-=;-√84]Y[√84;14],10=a; {y=10-x,x(10-x)=16;-x²+10x-16=0 x=5±3=8;2{(8;2)(2;8)}
    1
  2755. 30°,a,150°-a 150°-a+20°=60° a=110°{110°}B)
    1
  2756. Нет а,б,в,г,е,з,ы. (р)(но)(но)(нр)(о) Я не знаю такого слова.
    1
  2757. M=-900-250√2(N*m)
    1
  2758. 666/12=55 ост.6 11⁶:13=4³:13=3*4=12 666⁶⁶⁶==3⁶==9³==81*9=3*9=27=1
    1
  2759. (6*1,5^2x-5*1,5^x+1)/1,5^x/(1,5^x-1)≤0,(1,5^x-1/2)(1,5^x-1/3)/(1,5x-1)≤0 -1/3*+1/ 2*-1°+>1,5^x 1,5^x(-∞;1/3]U[1/2;1), x(-∞; log1,5(1/3)]U[log1,5(1/2);0)
    1
  2760. 4*1,5¹/⁴=4,40..✓
    1
  2761. y=6, 3/7=(x+2)/)4x-1) x=17/5✓
    1
  2762. y=4+3x-x², y=x+1, -x²+3x+4-x-1=-x²+2x+3=0, x=(-2±√(4-4*(-1)*3))/(-2), x=-1, x=3, -x³/3+2x²)2+3x|(-1;3)=-9+9+9-1/3-1+3=10 2/3
    1
  2763. v(x)(u(x)-1)=∞•0=v(x)lnu(x)=-∞ e^-∞=0 v'(x)=-v(x)/u(x)*u'(x)/lnu(x)
    1
  2764. limx->π/2(sin(π/2-x)/2/(π/2-x))=1/2
    1
  2765. limx->0(-1,5/(x-1/2)²)=-6
    1
  2766. limx->0(1,5x*(-0,5x))/(3x*(-2x))=0,125
    1
  2767. x(√(x²-1)-x)=x(-0,5x-¹+..)=-0,5;x->-∞=∞-
    1
  2768. ln->∞(4^n*√π(1/4)^n)=√π
    1
  2769. {(ab+a+b+1)(a+b)=2022,(a+b)(a²-ab+b²)=1933;{a+b=x,ab=y;{y=86 8/19,x=19;{b=9,5-+√(291/19)/2, a=9,5±√(291/19)/2.
    1
  2770. $6x^-4/(1-6x^-4)dx=$6/(x⁴-6)dx=$(A/(x-6⁰,²⁵)+B/(x+6⁰,²⁵)+C2x/(x²+6⁰,⁵)+D/(x²+6⁰,⁵))dx=-6⁰,²⁵/(1-6⁰,⁵)ln|x-6⁰,²⁵|+6⁰,²⁵/(-1-6⁰,⁵)ln|x+6⁹,²⁵|+6⁰,⁵/(-1-6⁰,⁵)arctg(x/6 ⁰,²⁵)/6⁰,²⁵+c A(X+6⁰,²⁵)(x²+6⁰,⁵)+B(x-6⁰,²⁵)(x²+6⁰,⁵)+2 x(x²-6⁰,⁵)C+D(x²-6⁰,⁵)=6,{A+B+2C=0,6⁰,²⁵A 6⁰,²⁵B+D=0,|•6^-0,25 6⁰,⁵A+6⁰,⁵B-2*6⁰,⁵C= 0,|•6^-0,5 6⁰,⁷⁵A-6⁰,⁷⁵B-6⁰,⁵D=6;{A+B+2C=0,2B+2C-6^-0,25D=0,4C=0,2B+2C+6^0,25D=-6⁰,²⁵;{A+B+2C=0,2B+2C-6^ 0,25D=0,C=0,(-6^-0,25-6⁰,²⁵)D=6⁰,²⁵;{A=-6^0,25/(-1-6⁰,⁵),B=6^0,25/(-1-6⁰,⁵), C=0,D=6⁰,⁵/(-1-6⁰,⁵);
    1
  2771. Z=(π/2+2πn-iln3)/(π/2+2πm)
    1
  2772. -π/2arctgcosx(0;π)=π²/4
    1
  2773. a²/√(a²+400)=9 a²=225,a=15 S=15*20=300
    1
  2774. (-x-1)e^-xcoslnx-e^-xcoslnx(0;∞)=1cos-∞+cos-∞=2cos∞
    1
  2775. A=R²-R²√3/4=(1-√3/4)(2+√3)=1,25+ 0,5√3 1,25-2,5√3(cm²),9/4(cm²)
    1
  2776. $(0;3)√(3x+16)dx=(3x+16)^1,5/1,5/3(0;3)=125/1,5/3-16*4/1,5/3=250/9-128/9=122/9=13 5/9
    1
  2777. 3,6,9,11,12,14{6}
    1
  2778. f(x+f(y))=x+y+1,x=0,f(f(y))=y+1,f(y)=ky+b,f(f(y))=k(ky+b)+b=k²y+kb+b²=y+1,{k²=1,kb+b²=1;[{k=1,b²+b-1=0;{k=-1,b²-b-1 =0;[{k=1,b=(-1±√(1-4*-1))/2;{k=-1,b=(1±√ 5)/2;f(x)=x-0,5±√5/2,f(x)=-x+0,5±√5/2,
    1
  2779. 4/5=(4-b)/a=b/(5-a) a=5-5/4b ab=5-5/4(b-2)²≤5,≥0
    1
  2780. 1/n=0.-n-=n/9...9,n²=10^m-1,m знаков у n n=√(10^m-1)≥10^(m-1) 10^m-1≥10^(2 m-2),-0,01*10^2m+10^m-1≥0,(10^m-(-1 +√(1-4*0,01*-1))/-0,02)(10^m-(-1-√0,9 6)/-0,02)≤0+*50-20√6*50+20√6+>10^m 10^mє[50-20√6;50+20√6],mє[lg(50-20√6);lg(50+20√6)]mє[1;1] m=1,n≥10,≤99 n=3
    1
  2781. √(х²-27/х²)=13,5/х³ х⁸-27х⁴-13,5²=0 х⁴=27(1+√2)/2,х=(27(1+√2)/2)¹/⁴см
    1
  2782. X¹,⁵=√(55±12√21)=2√7±3√3 x⁴,⁵=218√7±333√3 (218√7±333√3)/(218√7±333√3)/436/√7=√7/3052
    1
  2783. 3+37/27/ln(3e).
    1
  2784. u'(x)/u=n/x u=x^n*c c не зависит от х,u=y^n*c1 c1 не зависит от y,u=z^n*c2 c2 не зависит от z u=cx^n+c1y^n+c2z^n
    1
  2785. En=1;∞Ei=0;∞(1/(2i)!(2πn)^(2i-1)(-z^(2i-2)+z^(2i-3))(-1)^(i-1)π/2+1/(2i+1)!(2πn)^(2i)((0,5z²+1)ln(x²+z²)|∞+1-z²lnz-lnz)(-z²)^(i-1))=∞
    1
  2786. 4π√5+$(√5;3)π(9-z²)dz=π(18-10/3√ 5)
    1
  2787. 14/5=2,8
    1
  2788. 3√3/4a²=6, a=√(8/√3) √(8/√3)/3 y=-4/3* √3x y=-1/3/√3(x-√(24/√3)/6)+√(8/√3)/6 x=-√(8/√3/3)*2/11 y=√(8/√3)*6 10/33 5√(24/√3)√61/11; 2√(24/√3)√1993/33 2√(8/√3)√7/3 √(8/√3)/33(22√7-15√183 -2√5979) S=2/1089(22√7-15√183-2√597 9)²
    1
  2789. |(0;π/2)cos(6x)/24-cos(2x)/8-cos(4 x)/16=-1/12+1/4=1/6
    1
  2790. (a/2-x)²+(a/2-x/2)²=a²/4 a²/4-1,5ax +1,25x²=0 x=(6-√11)/10a 4=(4√5+√55)/20a a=16(4√5-√55)/5 S=256(27-8√11)/5
    1
  2791. {x=-2z+10,y=-z+2;(x+1)/1=(y-1)/0= (z-5)/-2 (x-10)/-2=(y-2)/-1=z ->k(x1;y1;z1) {x1=2z1,y1=-3z1; k(2;-3;1) (x-x0)/2= (y-y0)/-3=(z-z0)/1 {x0=-4z+10+2z0,y0=2+2z-3z0; {Y1=3(z-z1)+1,-2,5z+2z1+1,5=x1; √((x0-x1)²+(y0-y1)²+(z0-z1)²)=√(3,25 (z-55/13)²+14/13+14(z0-z1+1)²) {z=55/13,z0+1=z1;x0=-90/13,y0=136/13 (x+90/13)/2=(y-136/13)/-3=z/1
    1
  2792. A1(1;2) AA1(5;0) (10/3;0) G(-2/3;2), (-4;4) y=-x-2 y=x-2xB2-2 -3=xB2 y=x+4 (2;8) y=4x-2 y=-1/4x+4,25xA2-2 12/17=xA2 y=-1/4x+1.x=-12/5,y=1 3/5 H(-12/5;1 3/5)
    1
  2793. 1/а+1/b+1/c=1/2,a,b,cєN a=3,1/b+1/c= 1/6,b=7,c=42,b=8,c=24,b=9,c=18,b=10,c=15, b=12,c=12 a≤b≤c,a≤6 a=4,1/b+1/c= 1/4,b=5,c=1/20, b=6,c=12, b=8,c=8 a=5,1/b+1/c=3/10,b=5,c=10, a=6,1/b+1/c=1/3 b=6,c=6
    1
  2794. $(-2;0)(-x²-2x)dx+$(0;((1/2+√177/1 8)¹/³+(..-..)..)²)(√x-x²-2x)dx=5/3- ((1/2+√177/18)¹/³+(..-..)..))+2/3 ((1/2+√177/18)¹/³+(..-..)..))² X¹,⁵+2x⁰,⁵-1=0 x=((1/2+√177/18)¹/³+(..-..)..)²
    1
  2795. R(√2+1)=2√2 R=2(2-√2) S=3,5-3π(6-4√2)
    1
  2796. (4-R)²=R²+2√2√R,8-√2√R-4R=0 √R=(-√2+√130)/8,R=(33-√65)/16
    1
  2797. Y=xlog15(3) 5^log5(75)=75 C)
    1
  2798. S=54π/2-54=27π-54
    1
  2799. S=100arcsin0,8-48
    1
  2800. ВС=2Rsina,BD=2Rsin(45°-a/2), CD=2Rsin(135°-a/2) AD=√(AB(AB+2Rsina)) AE=√(AB²+3ABRsina+2R²sin²a-R²sin²(135°-a/2)) (AB²+2,5ABRsina+R²(sin²a-sin²(45°+a/2)))²=R²(AB²(0,125cos2a+0,37 5+0,5sina)+ABR(-sin³a+1,5sina+1, 5sin²a)-0,25R²(-cos2a+sina)²)ctg²54° cos²2a/sin²54°-(16+10ctg²54°) sin3a+2cos2a(1-ctg²54°)+256sin²a +(6ctg²54°-16)sina+1-3ctg²54°=0 a=15°A)
    1
  2801. /_1=180°-25°-115°=40° 65°,1,2sin25° √(1+4sin²25°-4sin25°cos65°)=1{65°}
    1
  2802. [{x=0,y=0;{2/√(-y+4)=x,y[2;4).{(0;0)(3;2)}
    1
  2803. y'²/2=x+c,y'=±√(2x+2c),y=±(2x+2c)¹,⁵/1,5/2+c1=±(2x+2c)¹,⁵/3+c1
    1
  2804. (y-10)/(x-4)=(19-y)/(44-x) y=3/16x+91/12 √(1 9/256x²-9 13/16x+21 121/144) +√(1 9/256x²-92 13/32x+2066 49/144)'=0,5(1 9/256x²-9 13/16x+21 121/144)-⁰,⁵(2 9/12 8x-9 13/16)+0,5(1 9/256x²-92 13/32x+20 66 49/144)-⁰,⁵(2 9/128x-92 13/32)=0 -(265x-8*157)/(265x-4*2957)=(1 9/256x² -9 13/16x+21 121/144)⁰,⁵/(1 9/256x²-92 13/32x+2066 49/144)⁰,⁵ f'<0, \>
    1
  2805. √(20-х)=(10+х)х{х(-=;-10]U[0;=),0=(x+5)⁴-50(x+5)²+(x+5)+600; (z-25/3)³-2425/12(z-25/3)-1'910'027/27/64=0 z=25/3+(1910027/2+√(1910027²/2²- 2425³))¹/³/12+(..-..)..;25/3-(1910 027/2+√(1910027²/2²-2425³))¹/³/2 4-(..-..)..±√(3/4((1910027/2+√(1910 027²/2²-2425³))¹/³/12+(..-..)..)²-242 5/12)i x=-5-√(25/3(1910027/2+√(1910027²/2²-2425³))¹/³/12+(..-..)..)+2√(0,5 √(-25/3((1910027/2+√(1910027²/2 ²-2425³))¹/³/12+(..-..)..)+((191002 7/2+√(1910027²/2²-2425³))¹/³/12+(..-..)..)²-4775/36)+25/6-(1910027/ 2+√(1910027²/2²-2425³))¹/³/48- (..-..)..) 77 277,7/2425>√97
    1
  2806. 9*10+9=99 x=11
    1
  2807. 4(π-2)=0,25R2(π-2) R=4 S=8π
    1
  2808. √(R²-8)+R=4,R[√8;4] 3=R✓
    1
  2809. 5√19 3√19,2√19 l=6 x=3√3
    1
  2810. a⁴+b⁴≥2a²b²=2(1-(a-1)²)²=2✓
    1
  2811. x=-2y±√(-y²+17) y=±1;±4 x=-2±4=2;-6 x=6;-2 x=-8±1=-7;-9 x=9;7
    1
  2812. π-arcsin(sin15°/a)>90° arcsin(sin15°/a)-15°=/_.. 105°-arcsin(sin15°/a)=/_? a/0,5=1/sin(45°+arcsin(sin15°/a)) a=√1,5-√0,5 1/1=1
    1
  2813. {у=65/(х+z),xz²+z(x²+48)-17x=0; {x=0,z=0;× z=(-x-48/x±√(x²+164+48²x-²))/2 z'=(-1+48x-²±(x²+164+48²x-²)-⁰,⁵(x-48² x-³))/2=0 [x=±√48,+=>x>0,x=0;-*-√48+°0+•√48->x-•-√48-°0 -•48->x min=√65 max=-√48+√65 z(4)=-8+9=1 z(3)=(-19+ √429)/2=1-13/84× z(12)=-8+9=1 z(-4)=17 z(-1)=(49+√(68+49²))/2× (x²+82)²-n²=34 *130:4 [{x=±32,n=1104;{x=±12, n=216;{x=±4,n=72;{x=0,n=68; x=-32;-12 z=(33,5+ 34,5)/2=34 z=(16+18)/2=17 {(4;13;1)(12 ;5;1)(-4;5;17)(-32;32,5;34)(-12;13;17)}
    1
  2814. 14/a=56/4/a✓ 2a*a/2=7 a=7¹/² R=1,5√7 S=63/8π-35
    1
  2815. $(ctg(π/8);1)-((1-u-²)ln-⁰,⁵u+2ln⁰,⁵u (1+u-²))/4*du=ln⁰,⁵u(u-u-¹)/2(ctg(π/8);1)=-ln⁰,⁵ctg(π/8)✓ 2ln⁰,⁵u*(u-u-¹)'+ln-⁰,⁵u(1-u-²)✓
    1
  2816. {a+b=c,ab=d;{c=19,d=1642/19;{19}
    1
  2817. a²-19a+1642/19=0 a=(19±√(291/19))/2
    1
  2818. х-6√х-7=0,√х=(6±√(6²-4*-7))/2[√х=7,√ х=-1;[х=49,0/;х=49
    1
  2819. 3log120(120)=3
    1
  2820. 2^(2^(2^(0,5x-1)-1)=2 x=2
    1
  2821. (-x²+4x+12)/(x+4)=0 x=2±4=6;-2
    1
  2822. (2¹⁷⁶-1)2⁸⁸/2⁴⁴/(2⁸⁸-1)=(2⁸⁸+1)2⁴⁴
    1
  2823. A,14/a 7-a,5-a -a²-5a+14=0 a=(-5±9)/2=2;-7 (2;7) (-7;-2) (5;3) (14;12)
    1
  2824. x=6ctg22,5°-3√2=3√2+6
    1
  2825. 231<(2n+m-1)/2*m<245,{0,5m²+(n-1/2) m-231>0,0,5m²+(n-1/2)m-245<0; {(m-(-n+ 1/2+√((n-1/2)²-4*0,5*231))/1)(m-(-n-√(n² -n+1/4+462)))>0+**+>m,(m-(-n+1/2+√((n-1/2)²-4 *0,5(-245)))/1)(m-(-n-√(n²-n+1/4+490)))<0;+°-°+>m {mє(-∞;-n+1/2-√(n²-n+462,25))U(-n+1/2+√(n²-n+462,25);+∞),mє(-n+1/2-√(n²-n+49 0,25);-n+1/2+√(n²-n+490,25)) mє(-n+1/2-√(n²-n+490,25);-n+1/2-√(n²-n+460,25))U(-n+1/2+√(n²-n+460,25);-n+1/2+√(n²-n+490,25)) 1/2+√460,25=1/2+21,9 2=22,42 1/2+22 6,25/44=22 28,25/44=2 2,6.. поэтому промежуток с ростом n будет уменьшаться и не останется ни одного целого числа.
    1
  2826. 0,5x-0,25sin2x(0;π/2)=π/4
    1
  2827. {y=a-1±√(-2a+1+r²),x=±√(2a-2±2√(-2a+1+r²));a-1=-+√(-2a+1+r²) a=r✓
    1
  2828. log(x+8)(x²-3x-4)≤2log(x-4)²|x-4| {x+8>0,x +8≠1,x²-3x-4>0,(x-4)²>0,(x-4)²≠1;{x>-8,x≠ 7,(x-4)(x+1)>0-1+°-°4+>x,x≠4,x≠-3,x≠-5;{xє(-8;-7)U (-7;-5)U(-5;-3)U(-3;4)U(4;+∞), хє(-∞;-1)U(4;+∞);хє(-8;-7)U(-7;-5)U(-5;-3)U(-3;-1)U(4;+∞).log(x+8)(x²-3x-4)≤1,[{x+8>1,x²-3x-4≤x+8;{x+8є(0;1),х²-3х-4≥х +8;[{х>-7,х²-4х-12≤0;{хє(-8;-7),х²-4х-12≥0;[{х>-7,(х-(4+√(16-4*4*-12))/2)(х-(2-√(4 +48)))≤0;+*+>х{хє(-8;-7),(х-2-√52)(х-2+√52)≥0; +-*+>х[{х>-7,хє[2-√52;2 +√52];{хє(-8;-7),хє(-∞;2-√52]U[2+√52;+ ∞);[хє[2-√52;2+√52],хє(-8;-7);хє(-8;-7)U [2-√52;2+√52],хє(-8;-7)U[2-√52;-5)U(-5;-3)U(-3;4)U(4;2+√52]
    1
  2829. a1=2,a(n+1)=√(4an-3) an²=4an-3,an²-4a n+3=0,an=(4±√(4²-4*3))/2=2±1[an=3,an =1;an≥0,an=1;2 a2=√5>2,a∞=3
    1
  2830. (f(x)-0,375x²)'²-(f(x)-0,375x²)=0,9375x²+4,5x+4 (f(x)-0,375x²)'(f(x)-0,375x²)-⁰,⁵=±1 (f(x)-0,375x²)⁰,⁵/0,5=±x+c,(f(x)-0,375x²)= (±0,5x+0,5c)² 2n-2=2,n=2 f(x)-0,375x²= a2x²+a1x+a0 3a2²x²+(4a2a1-a1)x+a1²-a0 =0,9375x²+4,5x+4{3a2²=0,9375,4a2a1-a1=4,5,a1²-a0=4;{a2=±0,25√5, a1=±9/8√5 +9/8,a0=15/32±81/32√5;[f(x)=0,625x² ±0,5cx+0,25c²,f(x)=(0,375±0,25√5)x²+(±9/8√5+9/8)x+15/32±81/32√5. 5=0,25 c²,c=±√20 f(0)=0,625x²±0,5√20x+5, 0/.
    1
  2831. a(n+3)=(a(n+1)-a(n-1))a(n+2)/an+a(n+1) a1=a2=a3=1 a5=1,a100=(a98-a96)a99/a97+a98 a6=2a4-1,a7=4a4-5+2/a4 a8=4a 4²-7a4+6-2/a4
    1
  2832. logy(1-x²+y)≥2[y(1;1/2+√(1,2 5-x2)],x(-1; 1);[x(-∞;-√1,25)U[-1;1]U(√1,25;∞),y(0;1); y[-√(1,25-x²)+0,5;0,5+√(1,25-x²)],x[-√1,25;- 1)U(1;√1,25];
    1
  2833. z=0;1 p¹³=cos(-15f)-isin(15f) f=2πn/15 p=1 z=cos(2πn/15)+isin(2πn/15), n=1;..;14
    1
  2834. А[4;9] А=5;6 Д=2;3✓
    1
  2835. {a+b=arctg7+πn,a-b=arctg5+πm;{a=0,5arctg7+0,5arctg5+π(n+m)/2, b=0,5arctg7-0,5arctg5+π(n-m)/2.
    1
  2836. x=e^u,dx=e^udu Ek=1;∞-(-1)^(k-1)/(k-1)^n+Ek=2;∞(-1)^(k-1)/(k-1)^n=0
    1
  2837. 142000'000*0,998^(х-2022)=0,5 х=2022+500*19,505=11774,5г.
    1
  2838. (p+0,5)⁴+2,5(p+0,5)²-(p+0,5)-52 3/16 =0 (z+5/12)³+155/12(z+5/12)-2363/16/27=0 z=-5/12+(2363/4+√65'165'769/4)¹/³/6+(..-..)..;-5/12-(2363/4+√65'165 '769/ 4)¹/³/12-(..-..)..±√(3/4((2363/ 4+√65'165'769/4)¹/³/6+(..-..)..)²+ 155/12)i p=-0,5+√(-5/12+(2363/4+√65'165'769/4)¹/³/6+(..-..)..)±√(0,5√(13+13/ 144+5/12((2363/4+√65'165'769/4)¹/³/6+(..-..)..)+((2363/4+√65'165'76 9/4)¹/³/6+(..-..)..)²)-5/24-(2363/4+√ 65'165'769/4)¹/³/24-(..-..)..)
    1
  2839. d(x-x-¹)√((x-x-¹)²+1) (x-x-¹)√((x-x-¹)²+1)/2+0,5ln|x-x-¹+√((x-x-¹)²+1)|+c
    1
  2840. x¹/⁶=y x=y⁶,dx=6y⁵dy $dx/(√x+x¹/³)= $6(y²-y-1/(y+1))dy=2y³-3y2-6ln|y+1|+c=2x¹/²-3x¹/³-6ln|x¹/⁶+1|+c -1-6ln2✓
    1
  2841. z=i/2✓
    1
  2842. 2√3/sina,4√3/sin(2a) 12/sin²a+48/sin²(2a)-48/sina/sin(2a)cos(180°- 3a)=16 0,5+4,5cos2a+7cos²2a=0 cos2a=(-4,5±2,5)/14=-1/7;-1/2 a=±arccos(-1/7)/2+πn,a=±1/3π+πn, a(0;60°) a=arccos(-1/7)/2 x=8/sin (2a)*sin(120°-2a)=3
    1
  2843. у=75°-х, sin²x+sin²(75°-x)=3/4, (1-cos2x)/2+(1-cos(150°-2x))/2=3/4, cos2x+cos(150°-2x)=1/2,2cos75°cos(2x-75°)=1/2, cos(2x-75°)=1/4/√((√3-1)²/4),2x-75°=±arccos(0,25/(√3-1)*2)+2πn,nєZ, x=37,5±0,5arccos(0,25(√3+1))+πn,nєZ, y=37,5-+0,5arccos(0,25(√3-1))-πn, -√3/2=2²-1, =√((-√3/2+1)/2)
    1
  2844. А что это у Вас такое странное имя?
    1
  2845. 27¹⁰ ¹/³<27¹⁰,⁵<49¹⁰,⁵ ...<..
    1
  2846. 2⁵=32, а больше решений нет
    1
  2847. (a-5)√2 √((a-5)²+0,5x²-(a-5)x)=b b,(a-x),√(-10a+25-0,5x²+(a+5)x) b√2=5√2b/√(-10a+25-0,5x²+(a+5) x) 0=0,5x²-(a+5)x+10a x=a+5±(a-5) =2a×;10✓
    1
  2848. 11/9*9/7*7/5*5/3*3/1=11
    1
  2849. 16x/(4+4x⁰,⁵+x)=f(x) f(16x/(4+4x⁰,⁵ +x))=(8x⁰,⁵/(2+3x⁰,⁵))² un=(2^(n+1) x⁰,⁵/(2+(2n-1)x⁰,⁵))²
    1
  2850. -12+16а-4а²=-4(а-2)²+4≤4 х1-х2=2
    1
  2851. f(x)=2x😊
    1
  2852. arcsin(637/677)=68°, ∆=2,234°
    1
  2853. х^х=2^2048=256^256 х=256
    1
  2854. √(50*128)=5*16=80
    1
  2855. {у=5/3,х=1/2;(1/2;5/3)✓
    1
  2856. 1,5^х+3^х=1/>1 корень х=-1✓.
    1
  2857. 7!*6!=х! 10!=х!{10}
    1
  2858. 3 27/990=3 3/110=333/110
    1
  2859. a=log60(5),b=log60(6) 12^((2a+b)/(1-a))= 12^(log12(25*6)(=150
    1
  2860. 31:16 обещание выполнялось с точностью до наоборот.
    1
  2861. -2πeCos(2πen!)(0,5+nlnn)*n!*n=-∞×
    1
  2862. (y-3)(xy-3)√(x-3)=0[{x=3,y=3a;{y=3,a(0;1],3=ax;{y=ax,a(0;1/3],x=√(3/a).
    1
  2863. (1,5t;1,125t²) t=0,5t√(1+(1,25t)²) ±4/5√3=t≥0 t=4/5√3
    1
  2864. аcos(2á)=(a²-2b²)/a=15 asin(2á)=2b√(1-b²/a²) b/cosá=ab/√(a²-b²) 2b√(1-b²/a²)-ab/√(a²-b²) =10 {b=√(a²/2-7,5a),a=39; b=6√13 S∆=0,5*√(39²-6²*13)*12√13=54*13=702
    1
  2865. (√(x+4,2)-2)(√(x+4,2)-1/2)/√(x+4,2) ≤0 °-4,2+*-3,95-*-0,2+>x x[-3,95;-0,2]
    1
  2866. 0,5En=1;=(-1)^(n-1)(1/p²)^n/n=0,5ln (1+1/p²)
    1
  2867. (3+9)/2*4=24 S+8S=24,S=8/3 6=6k+b, b=6-6k 4=kx+6-6k,x=(2-6k)/k (2-6k)/k*2- (-6+6k)/k=4/k-12+6/k-6=10/k-18 (5/k-9) *4=8/3,k=15/29 b=2 2/23 y=15/29x+2 2/23
    1
  2868. 37tg3x=11tgx tg3x=tgx(3-tg²x)/(1-3tg²x) (37(3-tg²x)/(1-3tg²x)-11)tgx=0[x=arctg5+ πn;x=πn.
    1
  2869. AB/sin102°sin54°/sinx=AB/sin(162 °-x) arctg(2/(√3√(10-2√5)+1+√5-(1 +√5)/2√(10+2√5))=x
    1
  2870. R=21✓.
    1
  2871. (π/6-0,5)/0,5=π/3-1=0,047!!?
    1
  2872. 484/(1934*49+6)=0,005 !
    1
  2873. (x-2)!=x/3 x=3(1=1)✓{3}
    1
  2874. f(x/f(y))=x/y f(x/f(1))=x/f(1)*f(1) f(x)=xf(1)
    1
  2875. Ч+ЧУ+Ч¹УР=УЧУ Ч+Р=10 101Ч+Р=У*90≤810 Ч≤8 У=9,Ч=8 Р=2✓
    1
  2876. √3/2-1/2+√5/2-√3/2=√5/2-1/2 (47-21√5)/4(7-3√5)=161-72√5
    1
  2877. xaxb-xaybi+iyaxb+yayb+xaxb+xaybi-yaxbi+yayb=2xaxb+2yayb=0,yb=-xaxb/ya ya²-+ ya√(4-(xa-xb)²)+xaxb=0,ya=(±√(4-(xa-xb) ²)±√(4-(xa+xb)²))/2 2|a|+|b|=2√(0,5xa²+2 0,5xb²±0,5√((4-(xa-xb)²)(4-(xa+xb)²)))+2 xb√(1+0,5/xa²(4-xa²-xb²-+√((4-xa²-xb²)² 4xa²xb²)))
    1
  2878. f(2x)=2f(x) f(2^(n+1))=2^(n+1)f(1) f(x)= xf(1)
    1
  2879. {x²+20x+y²-20y+75=|x²+y²-25|,x-y=a;>1 реш.[{х(х+5)≥0+*-5-0+>х,y=х+5,-5=a;{х²+у²<25,(x+5)²+(y-5)²=25,x-y=a;[{хє (-∞;-5]U[0;∞),y=x+5,a=-5;{у=5±√(25-(х +5)²),хэ́(-5;0);х-5+√(25-(х+5)²)=а;1+0,5 (25-(х+5)²)^-0,5-2(х+5)=0,(х+5)²/(25-(х +5)²)=1,(х+5)²=25-(х+5)²,(х+5)²=12,5 х= -5±√12,5,х=-5+√12,5+*->х максимум=-5+ √12,5-5+√(25-(-5+√12,5+5)²)=-10+2√12,5,-5-5+√(25-(-5+5)²)=-5,0-5+√(25-(0+5)²)=-5,ає(-5;-10+2√12,5],{-5}
    1
  2880. (0;±1)x⁶+3x³+1=y⁴ y²=√(x⁶+3x³+1)(x³+0,5; x³+1,5),y(-√(x³+1,5);-√(x³+0,5))U(√(x³+0,5);√(x³+1,5)) 0/
    1
  2881. f¹orty+ten*2=sixty 10 цифр✓f[1;8],s[2;9] en*2=..00 en:50,n=0,e=0;5 e=5 f¹or+2t+1= six f=1,s=2 or+2t+1=1ix,o=8;9 o=9 r+2t=9+ ix,i=1×f=2,s=3 or+2t=99+ix≤113,ix≤14 i=1 or+2t=109+x≥113 o=9,r=7,t=8,x=4 y=6 29786+850*2=31486 f=3,s=4 or+2t=99+ix, i=1 or+2t=109+x x=2,o=9,r=7,t=7× f;s=(6;7) or+2t=99+ix≤113,i=1 or+2t=109+x,x=2;3;4 o;r;t=9,5,8×;×;9,5,8× f;s=(7;8) or+2t=99+ix≤ 113,i=1 r+2t=19+x,o=9 12+5=17×s=9
    1
  2882. √(5/7)~0,84>log(7)5~0,615
    1
  2883. (2^(n-1)-1)2^n+1≥5×
    1
  2884. (±28;±27)(±8;±3)
    1
  2885. √(x²+1)+(x²+1)-⁰,⁵x²
    1
  2886. a^a=2^(√2/2)>1,a=√2:2^(0,5√2)✓ ab=2
    1
  2887. 📅📆🗓️
    1
  2888. a12ф+а11=144(1+√5)/2+89=161+72√5
    1
  2889. Потому что он выдумывал, когда рисовал картины.
    1
  2890. 1+npx+n(n-1)/2p²x²+..{p=1,n=2.
    1
  2891. 2√(7-4√3)=2(2-√3) √3-1✓ w=-0,5x-0,5y±√(-0,75x²-0,75y²-0,5xy+1/2) 0,5x²+xy+0,5y²-1/2±(x-y)√(-0, 75x²-0,75y²-0,5xy+1/2)≤0,≥-1 X+y+(-0,75x²-0,75y²-0,5xy+1/2)-⁰,⁵ (-1,5x²-0,5y²+1/2)=0 0=x⁴+2/3x³y+x²(4y²/3+1/3)+x(-y/3+2y³/3)+y⁴/3+1/12
    1
  2892. x1²y1²+2x1x2y1y2+x2²y2²?x1²y1²+ x1²y2²+x2²y1²+x2²y2² 2x1x2y1y2≤x1²y2²+x2²y1²✓
    1
  2893. 7c:b=c(ост.d){7≥b,6<b;b=7 d=0
    1
  2894. {х=3±√(а²+2а-9),[х≠а,х≠-0,5а;(а+1)²-10≥0 +*-*+>а ає(-∞;-1-√10]U[-1+√10;∞)[a≠9/4, a≠(-1±√217)/3;a(-∞;-1-√10]U[-1+√10;9/4) U(9/4;∞)
    1
  2895. От слов иметь мох?
    1
  2896. y'=3x²-2,y'(1)=1 y=x-2,x³-2x=x-2,x³-3x+2=0,[x=1,x²+x-2=0;x=(-1±√(1-4*-2))/2{1;-2} Q(-2; -4)
    1
  2897. logx=log(1+3+...+4019)*log(2010)11,x=10^(log(2010*2010)*log(2010)11)=11^2=121, (a+1/b)/(b++1/a)=10, a+1/b=10b+10/a, a^2+(1/b-10b)a-10=0, a=(-1/b+10b±√(1/b^2-20+100b^2+40))/2=-0,5/b+5b±0,5|1/b+10b|,a=10b, a=-1/b
    1
  2898. e^tydt+(te^t+2)dy=0,e^tdt/(te^t+2)+dy/y=0,ln|te^t+2|-tln(te^t+2)+$ln(te^t+2)dt= -ln|y|+c,
    1
  2899. X¹/⁴+(337-x)¹/⁴=7, X=168,5±175/2 x=256;81✓
    1
  2900. 22'000-419b²+b⁴=162b√(250-b²) b[0;8],b=5 a=15 S=a²=225✓
    1
  2901. 2cos16,875°✓
    1
  2902. A(1;4),B(xB;5-xB),C(xC;7xC-3)(xB-1)²+(1-xB)2=(xC-1)²+(7xC-7)² xB=±5(xC-1)+1 10=1,6(xB-1)² xB=1±2,5=3,5;-1,5 xC=1,5;0,5;0,5;1,5 y=(7xC-8+xB)/(xC-xB)(x-xB)+yB=-3x +12;1/3x+2 5/6;-3x+2;1/3x+7
    1
  2903. √(R²-6²)+R=18 R[6;18] √(R²-36)=18-R 10=R S=50π
    1
  2904. 0,5√(2π)
    1
  2905. $(0;1)dx$(2x;2)(x-y)dy=x²-2x(0;1)=-1
    1
  2906. {x=-y/2±√(1-3/4y²),z=-y/2±√(4-3/4 y²),3/4y²±1,5y√(1-3/4y²)=±(-1,5y± √(1-3/4y²))√(4-3/4y²); 117y⁴-120y²+16=0 y=±2√((5±2√3)/39) x+,z+,+ ✓ y=-2√((5+2√3)/39), +✓ y=2√((5-2√3)/39) x+,z- 13√3=±(-5,35+√3)+ -✓, 10+9√3=±(14-√3-6√(7-2√3))- +✓ x-,z+ 5±2√3-+3√(5±2√3)√(8-+2√3)=-+3√((5±2√3)(47-+2√3))-(11√3-+5) + -✓,- ✓ x-,z 10-9√3=±3(15+6√3) + -✓,±45=13√3 - +✓ {(√((5+2√3)/13)+√ ((8-2√3)/13);2√((5-2√3)/13);√((5+ 2√3)/13)+√((47-2√3)/13))} x+y+z=√(15+4√13)
    1
  2907. 1,5²+(1,5+y/2)²=(3-y/2)² -4,5+3y/2=0 y=3 x=1,5√2{3+1,5√2}
    1
  2908. {r3=-5r1-5/3r2+40/3-5a/12, (r1+r2)(8-4r1-2r2)+(-5r1-5/3r2+40/3-5a/12)(-40/3+3,4r1+32,2/3r2+2a/3)= b/4,r1r2(-5r1-5/3r2+40/3-5a/12)+(-5r1²-17/3r1r2-5/3r2²+ (40/3-5/12a)r1+r2(40/3-5a/12))(-40/3+4r1+2/3r2+2a/3)=c/4, r1r2(r1+1/3r2-8/3+a/12)(r1-10/3+17/6r2+a/6)=-1/16, r4=8-4r1-2r2-8r3/5;
    1
  2909. 53/75*75=53 S∆1=22cm²
    1
  2910. f(x+1)=f(x)f(1)-x=f(1)^(x+1)-(x-1)-(f(1)(f(1)^x-1)/(f(1)-1)-x)/(f(1)-1) f(x)=f(1)^x-(f(1)(f(1)^(x-1)-1)/(f(1)-1)-x-1)/(f(1)-1)
    1
  2911. Мальчишки и девчонки, а также их родители! Весёлые истории увидеть не хотите ли? Весёлые истории экран покажет наш, весёлые истории в журнале Ералаш.
    1
  2912. ln|y'+√(y'²+1)|=x+c -(-e^-x/c+e^x*c)/2+c1=y
    1
  2913. S=0,5*10*15=75
    1
  2914. 4/3a/(3c-1)-(a+3b)/(3c-1)+(8/3a+2,5b)/(3c-1)=(3a-0,5b)/(3c-1)
    1
  2915. (x²+5x-3)/(x-2)/(x2+3x+1)=A/(x-2)+B(2x +3)/(x2+3x+1)+C/(x2+3x+1)=1/(x-2)+2/(x ²+3x+1) x2+5x-3=A(x²+3x+1)+B(2x+3)(x-2)+C(x-2){A+2B=1,2 1/3B-C/3=-2/3,C=2;{A=1,B=0,C =2.
    1
  2916. x"+x'-2x=ft,x=e^kt,k²+k-2=0,k=(-1±√(1-4*2))/2[k=1,k=-2;x=c1e^t+c2e^-2t xp=c(t)(c1 e^t+c2e^-2t) c"(t)+c'(t)(3c 1e^t-3c2^-2t)/(c1e^t+c2e^-2t)=f(t)/(c1e^t+c2e^-2t),c '(t)=c3e^(-$(3c1e^t-3c2^-2t)/(c1e^t+c2e^ 2t))+e^(-3t+2/e^3t-2/(e^3t+c2/c1))$ft/(c1 e^t+c2e^-2t)*e^((3c1e^t-3c2^-2t)/(c1e^t+ c2e^-2t))dt x=c3$e^(-3t+2/e^3t-2/(e^3t+c 2/c1))+$e^(-3t+2/e^3t-2/(e^3t+c2/c1))$ft/(c1e^t+c2e^-2t)*e^((3c1e^t-3c2^-2t)/(c1e^t+c2e^-2t))dt x=c1e^t+c2e^-2t+c3$ e^(-3t+2/e^3t-2/(e^3t+c 2/c1))+$e^(-3t+ 2/e^3t-2/(e^3t+c2/c1))$ft/(c1e^t+c2e^- 2t)*e^((3c1e^t-3c2^-2t)/(c1e^t+c2e^-2t)) dt,0=c1+c2,c2=-c1, A(e^3t+c2/c1)+Be^3t=1,{A+B=0,Ac2/c1=1;{A=c1/c2,B=-c1/c2; 3=c1-2c2+c3 e^(2-2/(1+c2/c1))=c1-2*c1+c3e^(2-2/(1-c1/c1))=3c1+c3∞,c3=0,c1=1,c2=-1 x=e^t-e^-2t+$e^(-3t+2/e^3t-2/(e^3t+c2/c1))$ft/(e^t-e^-2t)*e^((3e^t+3e^-2t)/(e^t e^-2t))dt
    1
  2917. (a b)*(e f)=(ae+bg af+bh) )c d) (g h). (ce+dg cf+dh) [{b=0,a=0,c=0,[d=0,g=0;;{b=0,f=0, e=g-dg/c;{g=0,h=f-af/b,c=0;{g=0,h=f-af/b,e=0,[c=0,f=0;;
    1
  2918. E^x,xe^x,x(x+1)e^x,x(x²+3x+1)e^x,.. x(x+1)^(n-1)e^x'=(1+x(n-1)/(x+1)²)(x+1)^ne^x fn(1)=((1/2+√5/2)^(2n-1)+(1/2+√5/2)^(-2n+1))/√5e ((1/2-√5/10)e^(3/2+√5/2)+(1/2+√5/10)e^(3/2-√5/2))e
    1
  2919. AP=Sin60°/sin110° PD=sin50°/sin 70° AP/sina=PD/sin(60°-a) arctg(3/4/(√3/4+sin50°))=a~arctg 300/481=31 113/157°A)
    1
  2920. a1²+b1²=3c1², аналогично изначальному и опускаясь до 0, доказываем, что решений натуральных нет. (0;0;0)
    1
  2921. tg³x+0,75tgx-1/8=0 tgx=(1/16+√5/16)^(1/ 3)+(1/16-√5/16)^(1/3) 1 корень,x=arctg ((1/16+√5/16)^(1/3)+(1/16-√5/16)^(1/3))+πn
    1
  2922. х=2(у-0,25)²+4,875,х≥4,875 F(5;0) x=4,75
    1
  2923. S=2(π4²/4-π2²/4)+2²π/4*2=8π
    1
  2924. lnz*-z-¹-z-¹(1;∞)=1 сходится✓ 1/3Ei=1;∞(-1)^(i-1)/i(1/i-0,5(1/2/i-i/(2i-1)+..+(-1)^i))-Ei=1;∞(-4/3)^(i-1)/(2i-1)(1/(2i-1)-(2i-1)/1!/(2i-2)*0,5+..+(2i-1)*0,5^(2i-2))*2/3 сходится,но яне знаю,какивсе это свернуть z=A(z²-z+1)+B(z+1)(2z-1)+C(z+1) {A=-1/3,B=1/6,C=0,5;
    1
  2925. 9*10*5=450
    1
  2926. 1/60min-¹ t/60+(30-t)/12=1 t=22,5(min)
    1
  2927. S2=3√3
    1
  2928. (3 4 1 2|3) (0 0 0-0,5|-0,5) {0 0 0. 0|0) {х3=1-3х1-4х2,Х4=1;
    1
  2929. y=2x³+3x²-36x,[x=0,2x²+3x-36=0;[x=0,x=(- 3±√(9-4*2*36))/4;[x=0,x=-3/4±√303/4; y'=6x²+6x-36=0,x=(-6±√(6²-4*6*-36))/12 [x=2,x=-3;+*-32+>x max=2(-3)³+3(-3)²-3 6-3=-54+27+108=81,min=2*2³-3*2²-36*2=16-12-72=-68
    1
  2930. 1,73V1,41*ln4/ln3=1,41*4*0,41/2/0,73=5,64*0,205/0,73=1,128/0,73=1,55.., 3^√3>4^√2
    1
  2931. |(x-3)/(x+2)|=4[(x-3)/(x+2)=4,(x-3)/(x+2) =-4;[x=-11/3,x=11/5;{-3 2/3;2,2}
    1
  2932. (-1+x)⁰,⁵=1-(2-x)^(1/3)≥0,{[(2-x)^(1/3)=0, (2-x)^(1/3)=-1;(2-x)^(1/3)=2,(2-x)^(1/3)≤1;[x=2,x=3,0/;{2;3}
    1
  2933. 4,4/(±13/5-12/5)=22;-0,88
    1
  2934. х=5+25/(у-5) у=6;10;30;4;0×;-20 х=30;10;6;-20;×;4{(30;6)(10;10)(6;30)(-20;4)(4;-20)}
    1
  2935. 16x⁶-24x⁴+x³+9x²-1=0 96x(x⁵-x²+1/32x+3/ 16(=0[x=0,x=-0,4,(x-0,1)⁴+0,1(x-0,1)²& 1,616(x-0,1)-0,649=0;(z+0,01(6))³+0,163 (z+0,01(6))-0,044=0 z+1/60=0,212 z+1/60=-0,106±0,44i[z=0,195,z=-0,123+0,44i;y=1,263;-0,383 x=1,363;-0,283 {0;-0,4; 1,363;-0,283}
    1
  2936. Arcsin(2/a) 4cos(90°-arcsin(2/a))= 8/a S=8/a*a=8
    1
  2937. y'(y-1)=e^(-$1/(y-1)dx)c $1/(y-1)dx=z y=1/z'+1 e^(-z'-¹)z'=c1e^(e^(-z)c)
    1
  2938. S1=0,5√((-1+a²/4)(81-a²/4)) r1=√((-1+a²/4)(81-a²/4))/(10+a/2+√(82-a²/16)) r2= √((-1+a²/4)(81-a²/4))/(8+a/2+√(82-a²/1 6)) -5+a/4+√(82-a²/16)/2,a/4+√(72-a²/16)/2-4 a/4+√(72-a²/16)/2-4-(a/4+√(72 -a²/16)/2-5)=1
    1
  2939. ln(x+2)/ln(2-x)*ln(3-x)/ln(x+3)≤0 x>-2,<2,<3,>-3 x)-2;2) x=-1;2,x≠1;-2 °-2-*-1+°1-*°2>x x(-2;-1]U(1;2)
    1
  2940. (|x|-1-√24)/x²≤0+-1-√24*-°0-*1+√2 4+>x x[-1-√24;0)U(0;1+√24]
    1
  2941. log2(x)√((log2(x)-2)/log2(x))≤√2 [{x≥1,x≤2^(1+√3);x(0;1);x(0;2^(1+√3)]
    1
  2942. x√(3-3x²)≥-x²+x+0,5,x[-1;1][x[-1;0,5-√0,75]; x[-1;0,5-√3/2](z-9/64)³-9/256(z-9/64)-9/2¹²=0 z-9/64=(9/2¹³+3√-3/2¹³)¹/³+...=√ 3/8cos(π/9+2/3πn) z=9/64+√3/8 cos(π/9+2/3πn) y=√(9+8√3cos(π/9))/8+√(9+8√3cos(7/9π))/8-√(9+8 √3cos(13/9π))/8;√(9+8√3cos(π/9))/8-√(9+8√3cos(7/9π))/8+√(9+8 √3cos(13/9π))/8;-√(9+8√3cos(π/9))/8+√(9+8√3cos(7/9π))/8+√(9+8 √3cos(13/9π))/8;-√(9+8√3cos(π/9))/8-√(9+8√3cos(7/9π))/8-√(9+8 √3cos(13/9π))/8 x=1/8+√(9+8√3cos(π/9))/8+√(9+8 √3cos(7/9π))/8-√(9+8√3cos(13/ 9π))/8;1/8+√(9+8√3cos(π/9))/8-√ (9+8√3cos(7/9π))/8+√(9+8√3cos (13/9π))/8;1/8-√(9+8√3cos(π/9))/8+√(9+8√3cos(7/9π))/8+√(9+8√3c os(13/9π))/8;1/8-√(9+8√3cos(π/9))/8-√(9+8√3cos(7/9π))/8-√(9+8 √3cos(13/9π))/8
    1
  2943. у=-0,3(х-3)+2,5 у=-1,25(х-3)+3,5 х=4 3/17 у=2 5/34 Iy=$r²dS=38010/289+180130/ 289/3=5760/17 Ix=2(y-2 5/34)³(0;6)+2(y-2 5/34)³/3(6;10)=6'024'349/51/289
    1
  2944. х¹²-х⁹+х⁴-х+1=0 х¹¹-3/4х⁸+1/3х³-1/12=0 />х≤0 ..≤-1/12<0 [х=0,7,х¹⁰+0,7х⁹+0,49х⁸- 0,41х⁷-0,28х⁶-0,20х⁵-0,14х⁴-0,098х³+0,28х²+0,20х+0,14=0;-*+>х мин=(-0,657*0,7⁵+1) 0,7⁴+0,3>0 0/
    1
  2945. х²+3ах-а²+1=0,2 корня хє[-3;0],х=(-3а±√ (9а²-4(-а²+1)))/2=(-3а±√(9а²+4а²-4))/2=-1,5а±√(13а²-4)/2,13а²-4>0,(а-√(4/13))(а+√(4/13))>0+°-°+>а,ає(-∞;-√(4/13)) U(√(4/13);∞),{-1,5a+√(13a²-4)/2≤0,-1,5a √(13a²-4)/2≥-3;{√(13a²-4)≤3a,√(13a²-4)≤ 6+3a;{13a²-4≤9a²,13a²-4≤9a²+36a+36;{-2 2a²-4≤0,4a²-36a-40≤0;{a²+2/11≥0,(a-10)(a+1)≤0+*-1*+10>a;{aєR,ає[-1;10];ає[-1; 10],ає[-1;-√(4/13))U(√(4/13);10].
    1
  2946. {41=c,b≤81,40=b;{40;41} S∆=180
    1
  2947. y=x⁴/16 y=x³ y=(x¹,⁵/3+c/2)²
    1
  2948. 16ln8+31=64 11/37г.
    1
  2949. 100°=2o+180°-2b b-40°=o b-o=40° D)
    1
  2950. y=-2/sin(2x+π/3)+cos(x+π/6) y'=4sin-²(2x+π/3)(1-2sin²(x+π/6)- sin³(x+π/6)+sin⁵(x+π/6))=0 (sin(x+π/6)-0,64)(sin(x+π/6)+0,77)(sin(x+π/6)-1,..)=0 x=-π/6+arcsin0,6 4*(-1)^n+πn;-π/6+arcsin-0,77*(-1)^n +πn;π/3+2πn-*-1/6π-arcsin0,77+>x min=170/√(23*177)
    1
  2951. (x/y)^(x-y)=2³ y=3,x=6✓
    1
  2952. X-2y+(y-2x)i=5+i{x=-7/3,y=-11/3. z=-7/3-11/3i
    1
  2953. b²(2-√3)=2 b=√2(√1,5-√0,5)=√3-1✓ a=3√3-5✓
    1
  2954. 1/x+1/y=2/3,x=2,y=6, x=3,y=3
    1
  2955. 8х(2х²-1)(8х⁴-8х²+1)=1,хє[0;1]128х⁷-12 8х⁵+16х³-64х⁵+64х³-8х-1=0 128х⁷-192х⁵+ 80х³-8х-1=0 (х²-5/14)³-45/28/14(х²-5/14) -3/686=0 х²-5/14=(3/1372+√(9/1372²+(-45/28/14)³/27))^(1/3)+(3/1372+1√(1 -25*15/8)/4/343)^(1/3),D<0 x²=5/14+√ 15/7cos(1/3arccos(2/5/√15)+2πn/3) x=±√(5/14+√15/7cos(1/3arccos(2/5/√1 5)+2πn/3)),x[0;1] x=√(5/14+√15/7cos(1/ 3arccos(2/5/√15)+2πn/3)).
    1
  2956. (8x³+1)¹/³=2x²/³ (x-1/3)³-1/3(x-1/3)+11/216=0 x=1/3+2/3cos(1/3arccos(-11/16)+2/3πn)
    1
  2957. На самом деле не было никаго Святого Грааля,это вымысел.
    1
  2958. 12^x=y y²-12y+12=0 y=6±√24 x=log12(6±√24)
    1
  2959. g(f(x+y))=f(x)+(2x+y)g(y), g(f(x))=f(x)+2xg(0),g(f(y))=f(0)+yg(f(y)),g(f(y))=f(0)/(1-y), g(f(0))=f(0)=f(-y)-yg(y)=f(x)+xg(-x),=>y=-x, g(y)=f(-y)/y-f(0)/y,g(f(y))=f(0)/(1-y)=f(-f(y))/f(y)-f(0)/f(y), f(-x-y)/(x+y)+f(0)/(x+y)=f(x)+(2x+y)(f(-y)/y-f(0)/y),
    1
  2960. limx->π/4(f'(x)tgx+f(x)/cos²x)/4= (f'(π/4)+2f(π/4))/4=(4+2*2)/4=2
    1
  2961. (10k+7±3√(k²+k+1))/(k+1) 10+(-3-3√(k²+k+1))/(k+1) -1,5((k²+k+1)-⁰,⁵(k-1)-2)/(k+1)²=0 -3k²-6k-3=0,k=-1°-1->k min=4 max=7(a) 1,5((k²+k+1)-⁰,⁵(k-1)+2)/(k+1)²=0°-1+>k min=10,max=13(d)
    1
  2962. 1-e^(1-e^x)*e^x=0 0=x+*+>x x=0
    1
  2963. 4/sina/sin(90°-2a)=5/sina cos2a=4/5,cosa=3/√10 4cosa/sina/cos(2a)=15
    1
  2964. x²y''+xy'-y=xlnx (xu')²+x(xu')'-1,25=0 (xu')'/(xu')²+1/x=0,(xu')-¹/-1+ln|x|=c xu'=1/(ln|x| -c) xu'=c1:c1²-1,25=0,c1=±√1,25 [xu'=1/(ln|x|-c),xu'=±√1,25;[u=ln|ln|x|-c|+c1,u=± √1,25ln|x|+c1;[y=(ln|x|-c)c1,y=|x|^±√1,25 c1;yp=1/4xln²x-1/4xlnx xlnx=xlnx, y=c1ln|x|-cc1+1/4xln²x-1/4xlnx;c1|x|^±√1,25+1/4 xln²x-1/4xlnx
    1
  2965. $(0;ln2)2(x-ln2)(1+e^x)-²e^xdx=-2 (x-ln2)*(1+e^x)-¹+2(lne^x-ln(1+e^x))(0;ln2)=-2ln3+5ln2
    1
  2966. Госдура, кака оговорилась 1 телеведущая.
    1
  2967. 2sin10°/sinx=1/sin(160°-x) 2sin10°(sin 160°cosx-cos160°sinx)=sinx,sinx(-2sin10°cos160°-1)+2sin10°sin160°cosx=0,sin(x+arccos((2sin10°cos20°-1)/√((2sin10°co s20°-1)²+4sin²10°sin²160°)))=0,x+arccos((2sin10°cos20°-1)/√(3-2cos20°-4sin10°c os20°))=πn,x=-arccos(2sin10°cos20°-1)/√(3-2cos20°-4sin10°cos20°))+π=10°
    1
  2968. 2^(2х+1)+2^(х+3)-10=0,2*(2^х)²+8*2^х-10=0,2^х=(-8±√(8²-4*2*-10))/4[2^х=1,2^х=-5;[х=0,0/
    1
  2969. x≤(4+√3)/5 (2+2√3-4x)²=(4+√3-5x)(4√3+1-5x) -√3+(1+√3)x-x²=0 x=1;√3{1}
    1
  2970. (1;1:0)(2;1;2) OA×OB=√2√9*sinarccos(1/√2)=3√2*√2/2=3 √17,a=√17/3
    1
  2971. F(x)+f((x-1)/x)=2x-1,F((x-1)/x)+f(-1/(x-1))=(x-2)/x,F(-1/(x-1))+f(x)=-2/(x- 1)-1 f(x)=2x-2-2/(x-1)
    1
  2972. (5√4-4√5)/20+(6√5-5√6)/30+...=√4/4-√5/5+√5/5-√6/6+...=2/4=0,5
    1
  2973. х*256^х=1 х=1/4(1/4*4=1✓){1/4}
    1
  2974. (x-1/2)⁴-1/2(x-1/2)²-7(x-1/2)²+9(x-1/2)-1 11/16=0 (z-1/12)³+5/12(z-1/12)-631/32/27=0 z=1/12+(631+√(637²+392))¹/³/12 +(..-..)..;1/12-(631+√(637²+392))¹/³/24-(..-..)..±√(3/4((631+√(637²+392)) ¹/³/12+(..-..)..)²+5/12)i x=1/2+√(1/12+(631+√(637²+392))¹/³/12+(..-..)..)±2√(0,5√(61/144-1/12 ((631+√(637²+392))¹/³/12+(..-..)..)+((631+√(637²+392))¹/³/12+(..-..)..)²)+1/24-(631+√(637²+392))¹/³/48-(.. -..)..)
    1
  2975. (g(x)-x)e^-x=c,$(0;1)g(t)dt=c g(x)=ce^x+x c(e-1)+1/2=c c=0,5/(2-e) g(x)=0,5/(2-e)e^x+x
    1
  2976. 1/у время мотоцикла (1-ty)/(x+y) время между выход из трамвая и встречей -t/5+1/5/y-1=y/x 30/5=6
    1
  2977. 792=15
    1
  2978. √(a²-9)+a=6 a[3;6] a²-9=a²-12a+36 a=15/4 {a1²+b²+14/25a1b=36,c1=a1*2/√5 ±√(225/16-a1²/5),c2=-a1+c1*4/√5, c3=1,2a1/√5±√(225/16-a1²/5)*8/5 ±(-4/5/√5a1±3/5√(225/16-a1²/5)), b=0,48a1±√(225/16-a1²/5)*16/5/√ 5±(-8/25a1±6/5/√5√(225/16-a1²/5))±√(225/16-(1,2a1/√5±√(225/16- a1²/5)*8/5±(-4/5/√5a1±3/5√(225/ 16-a1²/5)))²/5),a=0,5arccos(3/5); a1=15/4,b=15/4 c3 c -,c1 c + (15/4=6,15×;3,75✓) c1=3√5(+) R=15/4/2/√(1/5)=15/8√5
    1
  2979. x=0,5/ay²+3/4a y=x²,0=x⁴-2ax+1,5a² 4x³- 2a=0,x=(0,5a)^(1/3) -*+>x min=-1,5*0,5^ (1/3)a^(1 1/3)+1,5a² -1,5*0,5^(1/3)*4/3a ^(1/3)-3a=0,[a=0,a^2=-4/27;+*0->a max=0 2 решения.
    1
  2980. 0=(y-x-1)z²-z(-x²+y²)-x²-x²y+y²x-y² [{y=x+1,z=(-x²-x-1)/(2x+1);{y≠x+1,z=(y⅔-x⅔±√((y²-x²)²-4(y&x-1)(-x²-x²y+xy²-y²)))/2/(y&x-1).{(0;0;0)(0;1;-1)(1;0;-1)(0;-1;1)(1;-1;0)(-1;0;1)(-1;1;0)} (y²+2(1-x)y+4x-3)²+4(-x³+4x²-7x+3)y+x⁴-4x³-16x²+20x-9=n² 0≥y²+2(x³-4x²+6x-2)y-0,5x⁴-2x³+8x²+14x+2,0≥y²+2(-x³+4x²-8x+4)y-0,5x⁴-2x³-8x²+14x-8 Похоже, что других решений нет.
    1
  2981. (sino-0,5)(sino-1)≥0 sino[-1;0,5]U{1} o[0;30°]U{90°}U[150°;180°]
    1
  2982. S=645/32
    1
  2983. (x-√2-√3)²-5=0 x²-2(√2+√3)x+2√6=0 x⁴-20x²+24-4√6x²=0 x⁸-40x⁶+352x²-960x²+576=0
    1
  2984. (ax+3)(5x²-bx+4)=20x³-9x²-2x+12 {5a=20,- ab+15=-9,4a-3b=-2,12=12;{a=4,b=6,16-18 =-2,✓;
    1
  2985. ad-bc≠0
    1
  2986. En=1;∞(-1)^(n-1)/(2n-1)!((K+1)^(2n 0,5)-k^(2n-0,5))π^(2n-0,5)/(4n-1)≤ En=1;∞(-1)^(n-1)/(2n-1)!*0,5k^(2n 0,5)/(k-4)π^(2n-0,5)=1/√(kπ),≥1/√((k+1)π) q=k-¹*2/(2n-1, 5)
    1
  2987. X=1+1/(1+log(3)5) log3(5)=1+1/(x-1) y=1+1/(1+2log(3)5)=(4x-2)/(3x-1)
    1
  2988. Красавчик. 10*3,5*60*60=126000Дж=0,035кВт*ч
    1
  2989. {[y=2^-3,5,y=2^1,5;[x=2^1,5,2^(-7/2)=x;x+y=33/16*2^0,5
    1
  2990. y=1±2/(x+1)² x+1=±1 x=0;-2 y=3;-1;3;-1{(0;3)(0;-1)(-2;3)(-2;-1)}
    1
  2991. L=L0(M/M0)^(10/3)=L0(T/T0)^-1 qM'(t)=4πR²L=4πR²oT⁴ M=M0(T/T0)^-0,3 $dtT-⁵,³T'(t)R-²=-40/3π/q/M0T0-⁰,³t+c tобщ=10¹⁰(M/M0)-³(ле т) 1/√3qt-¹/⁹*10-³⁵/⁹/2√(M0/L0/π)= R T=10⁷⁰⁰/³⁸⁷(7/43/q)¹⁰/⁴³T0³/⁴³L0 ¹⁰/⁴³t-⁷⁰/³⁸⁷
    1
  2992. √(25/4+√n/2)+√(25/4-√n/2)+..-..= 2√(25/4+√n/2)
    1
  2993. $dx/x²/√(1+x²)=$±(u²-1)^-0,5duu/(u²-1)/u=$±(u²-1)^-1,5du=-+(u²-1)^-0,5/u-$±(u²- 1)^-0,5u^-2du=-1/√(1+x²)/x-0,5x/√(1+x²) ^3-...-x^(2n-3)/n!/(1+x²)^(n-0,5)-...+C √(1+x²)=u,x=±√(u²-1),dx=±0,5(u²-1)^-0,5*2udu
    1
  2994. ±x-2^x=0 1-2^xln2=0 x=log2(log2(e)) +*->x max=log2(log2(e)/e)<0× x=W(ln2)/ln0,5✓
    1
  2995. √((45+1)/2)-√((45-1(/2)=√23-√22
    1
  2996. (2-x)^(x²+5x+6)=1[x=1,x=-2,x=-3,x=3;{1;-2;±3}
    1
  2997. $(0;π/4)(3sin4t-sin12t)/32dt=(-3/4cos4t+ cos12t/12)/32(0;π/4)=5/384
    1
  2998. $√3((x+5/3)¹,⁵+1/3√(x+5/3))dx=√3((x+5/3)²,⁵/2,5+(x+5/3)¹,⁵/4,5)+c
    1
  2999. 2³(11/2*10)²=8*55²=24200
    1
  3000. tg⁴A+ctg⁴A=((tgA+ctgA)²-2)²-2=14²-2=194
    1
  3001. -2ln(x²+1)-4(1+x²)-¹+c
    1
  3002. [{y=0,x=0;{r≥1/2,y=2r-1,x=±√(2r-1); r>1/2✓
    1
  3003. 2^xln2-1/3x-²/³=0 x=2/3W(±0,5/√3/ln⁰,⁵2)/ln2=-50/69;-30/69;17/69 ---*+>x max=1,5..>1 min=0,5..<1 x=0;1
    1
  3004. cos(ln(x+1)/2+lnx/2)/x=0
    1
  3005. Давно хотел спросить: а усы хоть настоящие или приклеенные?
    1
  3006. (п)р..(п)ет Нет а,б,и,з,к,л,о,р,ь. Трепет?
    1
  3007. 2г.6мес.-11дн.=903дн. 40'000^(х/903)=10⁵ х=981 12/23(дн.) 20.10.2024 если ничего не изменится
    1
  3008. {0,95}
    1
  3009. z=-xy/(x+y) (-3xy)/x/y=-3
    1
  3010. lg8/(1+lg3)=3(1-a)/(1+b)
    1
  3011. log((3x-4)/(x+1))(2x²-3x)≥log((3x-4)/(x+1))(17x-20-3x²),{(3x-4)/(x+1)>0,(3x-4)/(x+1)≠1,2x(x-1,5)>0,-3x²+17x-20>0;{(x-4/3)/(x+1)>0,+°-1-°4/3+>x x≠5/2,x(x-1,5)>0,+°0-°1,5+>x (x-(-1 7+√(289-4*3*-20))/-6)(x-(17/6+√(2 89-240)/6)<0+°5/3-°4+>x;{хє(-∞;-1) U(4/3;+∞),х≠2,5,хє(-∞;0)U(1,5;+∞),хє (5/3;4)\/°-1\°0°4/3/°\1,5/°\1 2/3|/°\|2,5/\°4/>х;хє(1 2/3;2,5)U(2,5;4) log((3x-4)/(x+1))((2x²-3x)/(17x-20-3x²))≥0,[{(3x-4)/(x+1)<1,(2x²-3x)/(-3x²+17x-20)≤1;{(3x-4)/(x+1)>1,(2x²-3x)/(-3x²+17x-20)≥1;[{(2x-5)/(x+1)<0,(2x²-3x+3x²-17x+20)/-3/(x-5/3)/(x-4)≤0;{(x-2,5)/(x+1)>0,+°-1-°2,5+>х (5x²-20x+20)/-3/(x-5/3)/(x-4)≥0;[{(x-2,5)/(x+1)<0,+°-1-°2,5+>х(x-2)²/(x-5/3)/(x-4)≥0+°5/3*2-°4+>х;{хє(-∞;-1)U(2,5;+ ∞),(х-2)²/(х-5/3)/(х-4)≤0+°5/3-*2-°4+>х;[{хє(-1;2,5),хє(-∞;5/3)U{2}U(4;+∞)\-1°/\°5/3/*2/°2,5°4\>х,{xє(-∞;-1)U(2,5;+∞) хє(5/3;4);[хє(-1;5/3)U{2},хє(2,5;4);хє(-1;5/ 3)U{2}U(2,5;4)=>хє{2}U(2,5;4)
    1
  3012. f(x)²/2+c=x f(x)=±√(2x-2c) 4=±√(2-2c) c=-7 f(x)=√(2x+14)
    1
  3013. S∆=24=2h,h=12 9+5=14 S=(4+14)/2*12=9*12=108
    1
  3014. {[b=-2,b=-4;a=b+6;{(4;-2)(2;-4)}
    1
  3015. t²x'(t)+3tx(t)=t⁴lnt+1,x=x0(t)+xp(t) t2e^u (t)u'+3te^u(t)=0,u'=-3/t,u=-3ln|t|,x0=c1e^(- 3ln|t|)=c1|t|^-3,xp=lntEn=0∞ant^n+Em=0 ∞amt^m,1/tEn=0∞ant^n+lntEn=0 ∞ann t^(n-1)+Em=0,∞am*mt^(m-1)+3/t(lntEn =0∞ant^n+Em=0 ∞amt^m)=t²lnt+1/t²,E n=0∞(annt^(n-1)+3ant^(n-1))=t²,n=3, 3a0t^-1+a1+3a1+2a2t+3a2t+3a3t²+3a3t²=t²,{3a0=0,4a1=0,5a2=0,6a3=1;{a0=0,a1= 0,a2=0,a3=1/6.1/t1/6t³+Em=0∞ammt ^(m-1)+3/tEm=0∞amt^m=1/t²,Em=0∞ am(m+3)t^(m-1)=-1/6t²+1/t²,{a-1*2=1,a3* 6=-1/6;{a-1=0,5,a3=-1/36.xp=1/6t³lnt+0,5t ^-1-1/36t³,x=c1|t|^-3+1/6t³lnt+0,5t^-1-1/3 6t³
    1
  3016. {z=6-x-y,x=3-y/2±√(-3/4y²+3y), x[0;6],y[0;6],[y=4,y=1;{(1;4;1)(4;1;1)(1;1;4)}
    1
  3017. R²+3R-2=0 R=(-3+√17)/2 S=R²(1+cosa)(1+sina)=(13-3√17)/2(5+√17)(7+√17)/36=8/9
    1
  3018. х≥1, 2-х=1-3√(х-1)+3(х-1)-(х-1)√(х-1), √(х-1)=(2-х-1-3х+3)/(-3-х+1),х-1=(-4х+4)²/(-х-2)², х³+4х²+4х-х²-4х-4=16х²+32х+16, х³-13х²-32х-20=0, (х-13/3)³+(-32-3*13²/3²)(х-13/3)+13³/27-(32+169/3)*13/3-20=0, х-13/3=(-2197/54+265*13/18+10+√((-40 37/54+201 7/18)²+(-265/3)³/27))^(1/3)+(-160 38/54+√((160 38/54)²-265³/27²))^(1/3),х=4 1/3+(-160 19/27+√11'539'184/54)^(1/3)+(-160 19/27-√11'539'184/54)^(1/3)=-6,34.., 169 265 160 *13 *13 *54 507 795 64 169 265 80 2197 3445|18 8640+38=8678 18 191. *8678 164 69424 162 60746 25 52068 18 69424 265 75'307'684 *265 -63'768'500 1825 11'539'184=16* 1590*721'199=16*23*37'957 530 70725 * 265 353625 144350 141450 15942125*4=63'768'500
    1
  3019. limx->-∞2x/e^-x=0
    1
  3020. S=12,5arcsin(4/5)-6
    1
  3021. h=25√3✓
    1
  3022. u=x²y+y²z+z²x u'(x)=2xy+z² u'(y)=x²+2yz u'(z)=y²+2zx u'(x)+u'(y)+u'(z)=2xy+z²+x²+ 2yz+y²+2zx=(x+y+z)²
    1
  3023. y'=1-1/(x+1) y=x-ln|x+1|+c
    1
  3024. XE^(sinh²xlnx)+c
    1
  3025. k²x+2013k+b+bk=2kx+2b+2013,{k²=2k,2013k+bk+b=2b+2013;{[k=0,k=2;b=(2013 -2013k)/(k-1)=-2013,k≠1;[{k=0,b=-2013;{k=2,b=-2013.f(x)=2x-2013
    1
  3026. 1/lnx<0 x<1,>0.
    1
  3027. logx²(2+x)<1 [{x)-2;-1]U[1;∞),0<(x-0,5)²-2, 25+°-1-°2+>x;{x(-1;0)U(0;1),0>(x-2)(x+1);[{x(-2;-1)U(1;≠),x(-∞;-1)U(2;≠);{x(-1;0)U(0; 1),x(-1;2);[x(-2;-1)U(2;≠),x(-1;0)U(0;1); x(-2;-1)U(-1;0)U(0;1)U(2;≠)
    1
  3028. {x(x-10/3)≤0+*0-*10/3+>x,(x-3)(x-1/3)>0+°1/3-°3+>x;{x[0;10/3],x(-=;1/3)U(3;∞);x[0; 1/3)U(3;10/3]
    1
  3029. {x((a-A)x+b-B)≤0,x((a+A)x+b+B)≥0;|b²-4ac|≤|B²-4AC|
    1
  3030. (1+Ae^(-kt))-²Ae^(-kt)*k
    1
  3031. dy/y/(lny+1)+tdt=0,ln|lny+1|=-t²/2+c,y= e^(±e^(-t²/2+c)-1)
    1
  3032. S=(√5+a)/2*√5+(a+b)/2*(a+b)-0,5 (√5+b)(√5+a+b)=10+√5b-√5b=10
    1
  3033. 8-r,r π/2((8-r)²+r²)=π(32-8r+r²)=17π (r-4)²=1 r=5;3 S=12,5π(cm²)
    1
  3034. 4*10^8/9,5/10^6=42 купюры=33 333₽
    1
  3035. A+360°-2a+60°=360° a=60° 120°✓
    1
  3036. Arcsin(120/a²) 13=a S∆=7140/169cm²
    1
  3037. b1=√(225-a1²) b=√(100-1/3a1²) a=√(25+1/3a1²) a²+b²=125
    1
  3038. (x+1)³-17(x+1)+24=0 D=24²/4+(-17)³/27= -37 26/27<0 x+1=2√(17/3)cos(1/3arccos (-108/289*√(17/3))+2πn/3),{-1+2√(17/3) cos(1/3arccos(-108/289*√(17/3))+2πn/3)}
    1
  3039. x(0;2),x[-2/√3;2/√3]x(0;2/√3]
    1
  3040. (9^x-2*3^x+4)/(3^x-5)+(2*3^(x+1)-51)/(3^x-9)≤3^x+5
    1
  3041. А почему выговаривает так странно р?
    1
  3042. Sin(14x)=sin(π/2-68x)[x=π/164+ 1/41πn,x=-π/108-1/27πn;x[0;2π) n[0;82],n[-54;0]
    1
  3043. {x>2|y|,x=2√(y²+1);|x|-|y|=2√(y²+1)-|y| (y²+1)-⁰,⁵*2y-1=0 y=√3/3-*+>y min=√3
    1
  3044. sgn(x²-4x+1)=1-2x,[{x²-4x+1>0,1=1-2x;{x²-4x+1=0,0=1-2x;{x²-4x+1<0,-1=1-2x;[{1>0,x=0;{0,25-4*0,5+1=0,25-2+1=-0,75, x=0,5;{-2<0,x=1;
    1
  3045. √(x-y+1)²=|x-y+1|=|1111-(-909)+1|=2021
    1
  3046. y^(0,5)+y=0 k⁰,⁵+1=0,k=1, y0=ce^x yp=En= 0;∞anx^n n=2,A2x²+(8/3/√πa2+a1,5)x¹,⁵+(a1+0,75/√πa1,5)x+(a0,5+ 2/√πa1)x⁰,⁵+ a0=x²+8/3/√πx¹,⁵{a2=1,a1,5=0,a1=0, a0,5= 0,a0=0;yp=x² y=ce^c+x²
    1
  3047. cos²2x/sin²2x/cos²2x=1/sin²2x
    1
  3048. (a+b)(X²+X(a+b)+ab)/(ab)=0 [a=-b,x=-a,x=-b.
    1
  3049. sin0,5/_1=15/b=√(0,5-0,5(b-a)/(a+ b)) 12/sin(arctg(2√(ab)/b))=b/2/sin(180°-arctg(2√(ab)/b)-arccos(15/b)) a=225b/(b²-225),30=b a=10 S=20*10√3=200√3
    1
  3050. CQ/sin(x-o)sino √(sin²(x-o)+(sino)²- 2cos126°sin(x-o)sino)CQ/sin(x-o)/sinx=CQ/sin(x-o)sino/sino [x=54°,x=o.
    1
  3051. (√5+2)¹/³=(1+√5)/2
    1
  3052. {y=6,x=-1.
    1
  3053. {y⁰,⁵=10-√x,x-10√x+10=0;√x=5±√15 y⁰,⁵=5-+√15{(40±10√15;40-+10√15)}
    1
  3054. n=2 2*2²+1=9✓ 3*2³+1=25✓{2;3}
    1
  3055. ((3x+4)/(4x+3))³=u 1/216-6u+8u²=0 u=(3±11√6/9)/8 x=0,3±0,7√6
    1
  3056. f(x+y)=fx+fy-xy,f(y)=f0+fy,f0=0 f(2x)=2fx -x²,f(2^(n+1))=2^(n+1)f1-2^(2n+1)+2^n,f(x)=2xf1-x²/2+0,5x,f1=2f1,f1=0 fx=-x²/2+0,5 x
    1
  3057. C=3-a-b a/(1+b²)+b/(1+(3-a-b)²)+ (3-a-b)/(1+a²) 1/(1+b²)+b(1+(3-a-b) ²)-²*2(3-a-b)+(a²+(2b-6)a-1)/(1+a²)² =0 b(1+a²)²*2(a+b-3)+((1+a²)²/(1+ b²)+(a+b-3)²-(b-3)²-1)(1+2(a+b-3)²+(a+b-3)⁴)=0*+>a min=1,5
    1
  3058. n(n-1)-3n+4=n²-4n+4=0 n=2 y=c1x²+c2x²lnx yp=x²f f''+x-¹f'=lnx*x-² f'=ln²x/2 f=xln²x/2-2xlnx+2x yp=x²(xln²x/2-2xlnx+2x) y=c1x²+c2x²lnx+x²(xln²x/2-2xlnx+ 2x)
    1
  3059. y'(xy-2x+4y-8)=xy+3x-y-3 y'(y-2)(x+4)=(y+3)(x-1) y'(y-2)/(y+3)=(x-1)/(x+4) y-5ln|y+3|=X-5ln|x+4|+c e^y/|y+3|⁵=e^x/|x+4|⁵*e^c
    1
  3060. Хє[0;π/4]U[3/4π;5/4π]U[1,75π;2π) [x=π/4+πn,x=2πn,x=-π/2+2πn;{π/4; 5/4π;0}S∆=0,5*2sin22,5°*2cos22,5°=√2/2 A)
    1
  3061. EC=BE√5/2 90°-arctg(2/BE),tg(90°-arctg (2/BE))=E.../EC,E...=BE²√5/4 S∆1/S∆2= BE*2/(√5/2BE*BE²√5/4)=3,2BE^-2=0,64, BE=√5
    1
  3062. a-x/2,55°-a+x/2 /_APC=125° A)
    1
  3063. n=1+[lgN] 1✓
    1
  3064. √(120+49)=13 b²-24b+119=0 b=12±5=7;17 EB=5√2 EA=√(289-120)=13 B)
    1
  3065. |(π/2;π)(0,75o+sono+0,125sin2o)= 0,375π-1 S=1,5π-4✓
    1
  3066. {a=2,5±√1,75i,b=-2,5±√1,75i.{-8}
    1
  3067. |х+2|≥1 хє(-∞;-3]U[-1;∞)
    1
  3068. АD(-2cosDcosA/sin(A+D))=AD √2sin(A+D+π/4)=cos(A-D) 180°-/_A-arctg(ADsin(D-90°)/sin(-A-D)/h/tg(/_A-90°))?180°-/_D-arctg(ADsin (A-90°)/sin(-A-D)/h/tg(/_D-90°)) /_A-/_D?-arctg(sin(D-90°)/sin(-A-D) *(1+tg(D-90°)/tg(/_A-90°)))+arctg (sin(A-90°)/sin(-A-D)(1+tg(A-90°)/tg(/_D-90°)))=arctg(2tg(A-D)/((2-co s(A+D))/cos(A-D)+1)) в вырожденным случае да
    1
  3069. (X+7/24)³-49/8/24(x+7/24)+235/27/8²/4=0 x+7/24=(-235+√(235²-49³))¹/³/24+(..-..)..=7/12cos(1/3arccos(-235/343)+2/3π) x=-7/24+7/12cos(1/3arccos(-235/343)+2/3π)
    1
  3070. (√5-2)^(2/3)=(3-√5)/2 1/(1-a)=(1+√ 5)/2
    1
  3071. (20-r)²+5²=(r+5)² 8=r{64π}
    1
  3072. Пk=0;∞(5^(1/2^k)+3^(1/2^k))/2 limk->∞ (5^(1/2^k)+3^(1/2^k))/2=1, сумма-0 неизвестно.limk->∞ln(5^(1/2^(k+1))/2+ 3^(1/2^(k+1))/2)/ln((5^(1/2^k)/2+3^(1/2 ^k)/2)=0/0=limk->∞(0,5ln5+0,5ln3)/(ln5+ ln3)=0,5 ряд сходится
    1
  3073. 1000=1*2*4*5*25✓
    1
  3074. 1:53 В лето sфкг от сотворения мира обновился сей град, видаемый делами. Мы, Иван самодержец, чем болгарской помощью и молитвами перстами владеющий нашей бч яив.
    1
  3075. х=1+√3±√10/2
    1
  3076. [sinx=log4(a),sinx=2-2a;2 решения хє[π/2;5π/2] {(-1+log4(a))/log4(a)≥0+°1-*4+>a,(1+log4(a))/log4(a)≥0+*1/4-°1+>a;{a(0; 1)U[4;∞),a(0;1/4]U(1;∞);a(0;1/4]U[4;∞) 2-2a≥-1,≤1;a≤1,5,≥0,5;[x=arcsinlog4(a)(- 1)^n+πn,x=arcsin(2-2a)(-1)^n+πn;[ a[1; 4],a(1/4;1),a[0,5;1,5];ає(1/4;4]
    1
  3077. En(2n+1) n=5 141
    1
  3078. 2a+1=3a-5 a=6 6&2=4✓
    1
  3079. {[{x=m+k,y=m-k,(m,k):(/)2;{x=m+k+ 1,y=m-k;1/4+n=a,[{(0;±1)(±1;0),n=0; a=1/4✓ tga=2sin0,5a√(1-sin²0,5a)/(1-2sin² 0,5a)✓ tg²a-4(tg²a+1)sin²0,5a+4(tg²a+1)sin⁴0,5a=0,sin0,5a=±√((tg²a+1±√(tg²a+1))/2/(tg²a+1))=±√(((-2cos(πxy) -1,5cos(2πx)-2cos(2πy)+6,5)²+1±√ ((-2cos(πxy)-1,5cos(2πx)-2cos(2πy)+6,5)²+1))/2/((-2cos(πxy)-1,5cos(2 πx)-2cos(2πy)+6,5)²+1))
    1
  3080. [{a=0,x=1,y=-14;{[a(-=;0)U[1,75;4], a(0;4];x=(8±4√(4-a))/a,y=±4√(4-a)-6;{x=-2/(a-2),y=-2a/(a-2)-14. A=2,x=4±2√2,y=±4√2-6 a=4,(2;-6),(-1;-18) a=1,75,(8/7;-12)(8;0) a(-∞;0)U(0;1,75) a(-∞;0)U(0;1,75]U{2}U{4}
    1
  3081. $0,5sinx²dx²=-0,5cosx²+c
    1
  3082. X-¹(x²-x+1)=3 x²-4x+1=0 x=2±√3
    1
  3083. (4x⁴+2x²-1)/(x²+1)=4x²-2+1/(x²+1)
    1
  3084. F(p)=(5p-1)/p²/(p-1)=A/p+B/p²+C/(p-1) 5p-1=A(p²-p)+B(p-1)+Cp² {C=4,A=-4,B=1;f(t)=-4+t+4e^t
    1
  3085. F(p)=(3p²+7p+10)/(p³+2p²+5p)=A/p+B(2p +2)/(p²+2p+5)+C/(p²+2p+5) 3p2+7p+10=A(p²+2p+5)+B(2p²+2p)+Cp {B=0,5,C=2,A=2;f(t)=2+e^-t*cos2t+e^-tsin2t
    1
  3086. 6sin²x+5√2sinx-8=0 sinx=(-5√2±11√2)/12=√2/2;-4/3√2 x=π/4+2πn;3/4π+2πn
    1
  3087. S∆=√((4,5+√17/2)(0,5+√17/2)(-0,5+√1 7/2)(4,5-√17/2))=√(16*4)=8
    1
  3088. log⁴x(2)-5log²x(2)-36<0 (log(x)2-3)(logx(2)+3)<0+°-3-°3+>log(x)2 logx(2)(-3;3) {(log2(x)-1/3)/log2(x)>0°0+°1-°2¹/³+ >x,(1/3+log2 (x))/log2(x)>0°0+2^(-1/3)°-° 1+>x;{x(0;1)U(2¹/³;∞),x(0;2-¹/³)U(1;∞);x (0;2-¹/³)U(2²/³;∞)
    1
  3089. ln(1-2x²/(1+x²))=-2x²/(1+x²)+.. limx->0+ -2√(x¹/³+1)=-2
    1
  3090. 2(7*14²⁹⁴-x/2)=0mod45 45=3²*5 45(1-1/3)(1-1/5)=24 294/24=12ost.6 7*14⁶=31*22= 7 2(7-x/2)=0 x=14✓
    1
  3091. А зачем он примерял эту роль?
    1
  3092. {m+n=-m,mn=n;{[m=0,n=-2;[n=0,m=1;×{2m-8}
    1
  3093. 0,5кг/км²=4,9мкПа 7*10-¹²/(4,9*10-⁶)= 1,4*10-⁶м²=1,4мм²
    1
  3094. {51х+49у=1,49х+51у=2;{х=-47/200, у=53/200.
    1
  3095. 1771/69=25 345=460-
    1
  3096. $(0;1/dxe^x$(0;3)e^3ydy=(e-1)(e^9-1)/3
    1
  3097. S=7,5²=56,25
    1
  3098. t=v0/u/g s=v0t-ugt²/2=v0²/u/g/2
    1
  3099. (2n-1-2n/|x|)/|x|^(2n-1) q=1/|x|²>1 расходится
    1
  3100. А можно узнать хотя бы как её зовут, эту самую активную?
    1
  3101. 2f(x)+f(1-x)=3x²,f(1-x)+0,5f(x)=1,5 (1-x)² f(x)=x²+2x-1✓ f(5)=34
    1
  3102. f(x)+f((1-x)/x)=1+x,f(1/x-1)+f(-2+1/(1-x)) =1/x,f(-1/(x-1)-2)+f(-1,5+0,25/(x-0,5))=-1/(x-1)-1,f(x)-f(0,25/(x-0,5)-1,5)=x-1/x-1/(x-1) y=-1+1/x
    1
  3103. {a=±2/3√15,b=±√15,c=±2√15.
    1
  3104. √3/2BC/sin60°=BC/sinx sinx=1 x=90°
    1
  3105. (x+1/x)²+x+1/x-12=0 x+1/x=(-1± √49)/2=3;-4[x²-3x+1=0,x²+4x+1=0; x=(3±√5)/2;-2±√3
    1
  3106. (x-1)((x+1/x+1)³-8(x+x-¹+1)-8)=0 x=1,x+1/x+1=(4+4√(1-32/27))¹/³+(..-..)..=2√(8/3)cos(1/3arccos(√(2 7/32))+2/3πn) x²+(1-2√(8/3)cos(1/3arccos(√(27/32))+2/3πn))x+1=0 x=(-1+2√(8/3)cos(1/3arccos√(27/32)+2/3πn)±√((1-2√(8/3)cos(1/3arc cos√(27/32)+2/3πn))²-4))/2, n=0;1;2✓
    1
  3107. (4,875+5cos(60°+6x)-1,5cos(30°+ 3x)-1,5sin(9x)+0,125cos(120°+12 x))⁴
    1
  3108. 18√3=0,5√3a² a=6(cm) B)
    1
  3109. (x-2/3)³+5/3(x-2/3)+7 11/27=0 x=2/3+(-100+45√5)¹/³/3+(..-..)..
    1
  3110. {x=-3/4z+15/4,y=-5/4z+25/4; z=4z1+1 (-3z1+3;-5z1+5;4z1+1)
    1
  3111. {у³-4у<3(х-3)²-1,у³-4у>-(х-4)²+2;(х-4)(х- 2,5)>0+°2,5-°4+>х хє(-∞;2,5)U(4;≠) {(y-4√3/3cis(1/3arccos(3√3/8)))(y-4√3/3 cis(1/3arccos(3√3/8)+2/3π))(y-4√3/3cis (1/3arccos(3√3/8)+4/3π))>0-°+°-°+>y, (y-4√3/3cis(1/3arccos(-3√3/16)))(y-4√3/3 cis(1/3arccos(-3√3/16)+2/3π))(y-4√3/3cis (1/3arccos(-3√3/16)+4/3π))<0-°+°-°+>y;{y(4√3/3cos(1/3arccos(3√3/8)+2/3π);4√3/3cis(1/3arccos(3√3/8)+4/3π))U(4√3/3cis(1/3arccos(3√3/8));∞),y(-∞;4√3/3cis(1/3arccos(-3√3/16)+2/3π))U(4√3/3cis(1/3arccos(3√3/8)+4/3πn);4√3/3cis(1/3arccos(3√3/8)));°-2,11°-1,67°-0,53°°0,25°1,86° 2,21>y 0/
    1
  3112. х+х/√(х²-1)>35/12 1-1/(х²-1)¹,⁵=0 х=±√2 +•-•+>х Макс=-2√2,мин=2√2 1152<1225 [{x≥35/12,(х²-1)⁰,⁵>-х/(x-35/12);{x(1;35/1 2),(x-35/24)⁴-1567/496(x-35/24)²+35*276 25/192/18/31(x-35/24)+35²*19408/24²/144/31<0; +*+*-=- z³-1567/992z²+(1567²*81-1225*1 9408*31)/81/256/16/31²z-(35*27625/19 2/18/31)²/64=0
    1
  3113. a(bcd-1)≥2bcd-2?b+c+d b(2cd-1)≥4cd-2?2+c+d c(4d-1)≥8d-2?4+d 7d≥14≥6✓
    1
  3114. √(x⁷+1)+√(1-x⁵)=8,x[-1;1]{-1/16x⁷-1/16x⁵+ 4=√(1-x⁵),-63⁰,²≤x;
    1
  3115. Tg(a/2)=1/9,tg(45°-a/2)=0,8=4/(h-4),h=9
    1
  3116. $(-1;1)x5/(x¹⁰⁰+4)dx=$(1;-1)-x⁵/(x¹⁰⁰+4)* -dx=-$(-1;1)x⁵/(x¹⁰⁰+4)dx, 2$(-1;1)x5/(x¹⁰⁰ +4)dx=0,$(-1;1)x5/(x¹⁰⁰+4)dx=0
    1
  3117. {y=7,x=-7.
    1
  3118. {|х-4|+3|у|=2,9у²+х²-8х+4(а+3)=0;{[{х-4+3у=2,х-4≥0,у≥0,{х-4-3у=2,х≥4,у<0,{-х+4+3у=2,х<4,у≥0,{-х+4-3у=2,х<4,у<0;(х-4)²+(3у)²=-4а+4;≥0 {[{у=2-х/3,х≥4,у≥0,{у=-2+1/3х,х≥4,у<0,{у=х/3-2/3,х<4,у≥0,{у=-1/3х+2/3,х<4,у<0;(х-4)²+(3у)²=-4а+ 4;а≤1 x≤6,y≤2/3 (6-4)²+(2/3-0)²=4+4/9=r², r=2√10/3 2√10≤-4a+4,a≤-0,5√10+1,R=2, 2≥-4a+4,a≥0,5, aє[0,5;-0,5√10+1]
    1
  3119. √(2tg(3π/2-x)sin(3π-2x))=-tg(2π/2)=-tgπ= 0, 2sin(3π/2-x)/cos(3π/2-x)*2sin(3π/2-x) cos(3π/2-x)=0,sin²(3π/2-x)=0,3π/2-x=πn, nєZ x=3π/2-πn,nєZ
    1
  3120. 2,74млн рублей на охрану Путина в день?
    1
  3121. limx->π/2-sin(x-π/2)/(x-π/2)=-1
    1
  3122. $(0;∞)(x-sinx)/x³dx=$(0;∞)(x^-2-sinx/x³)dx=x^-1/-1-$sinxdx/x³|(0;∞)=-1/x-x^ -2/-2sinx+0,5x^-1cosx+0,5$x^-1*sinxdx(0;∞)=0+0+0,5π/2=π/4
    1
  3123. (1,25)²/³/(3/2)⁴/⁵=(3125/11664)²/¹⁵
    1
  3124. lnp*cosф+фsinф+(фcosф-lnpsinф)i =pi{p=е^(-фtgф),ф/cosф=е^(-фtgф); ф=0,57;1,91;.. р=0,69;224;.. z=0,69(cos0,57+isin0,57);224(cos1,91+isin1,91);..
    1
  3125. a>b a=(a-b)²,b=8НОД(a,b) {a-√a=b,a-√a= √a*8; a-9√a=0,[a=0,a=81;a=81,b=81-9=72 HOK(81,72)=81*72/9=648
    1
  3126. (3^х-3)/(3^х-9)/(3^х-6)≤0-*1+°log3(6)-°2 +>х x(-∞;1]U(log3(6);2)
    1
  3127. ln²2-ln²3+2ln(2/3)*lnx+ln²x=0 lnx=-ln(2/ 3)±√(2ln1,5*ln3) x=2/3e^(±√(2ln1,5*ln3))
    1
  3128. {y=(10-x³)/9/x²,(x³-67)³-13392(x³-67)-596 376=0; x³-67=(298188+√(298188²+(-133 92)³/27))¹/³+(298188-4√(74547²-1121²* 4484))¹/³=4√1121cos(1/3arccos(74547 /1121/√4484)+2/3πn) x=(67+4√1121cos (1/3arccos(74547 /1121/√4484)+2/3π n))¹/³
    1
  3129. 3(10+6/n+3)=39
    1
  3130. (x+y)/2/cos2a (x+y)/2/cos2a-x x=y/(4cos²2a+2cos2a-1) y=√((x+y)²/2/cos2a-x(x+y)/2/cos 2a+x²) 0=(cos2a+1/8)⁴-27/32(cos2a+1/8)²-3/64(cos2a+1/8)+333/64² (z-9/64)³-9/16²(z-9/64)-9/16³=0 z-9/64=(9/2+√(81/4-27))¹/³/16+(..-..)..=1/8√3cos(10°+2/3πn) z=9/64+1/8√3cos(10°+2/3πn) cos2a+1/8=√(9/64+1/8√3cos10°)+√(9/64-1/8√3cos50°)+√(9/64-1/ 8√3cos70°);-√-√+√;-√+√-√;√-√-√ a=0,5arccos(-1/8+√(9/64+1/8√3cos10°)+√(9/64-1/8√3cos50°)+√(9/ 64-1/8√3cos70°);-1/8-√-√+√;-1/8-√ +√-√;-1/8+√-√-√),(0;45°) a=20°;60°×;80°×;40°{20°;40°}
    1
  3131. 3х³-5/7х²-6/7х=0,[х=0,х²-5/21х-2/7=0;х= (5/21±√(25/441-4*-2/7))/2=5/42±23/42 [х=2/3,х=-3/7;{0;2/3;-3/7}
    1
  3132. A≥0 a[0;1/3] min=-1+3a max=2a¹,⁵ a(1/3;1],min=0,max=2a¹,⁵ a>1,max=-1+3a min=0
    1
  3133. 6а=60°-0,5а а=120/13мин 1:50 10/13мин✓
    1
  3134. 5,5-10cos2x+cos²2x=0,sin2x≠0 x=±0,5arccos(5-√19,5)+πn
    1
  3135. {y=(a+2)x²+2ax+a-1,x=(a+2)y²+2ay+a-1;{y=(a+2)x²+2ax+a-1,x=(a+2)((a+2)x²+2a x+a-1)²+2a((a+2)x²+2ax+a-1)+a-1;x=(a+2)³x⁴+4(a+2)x²+(a-1)²(a+2)+4(a+2)²ax³+2(a +2)²(a-1)x²+4a(a-1)(a+2)x+(2a²+4a)x²+4a ²x+2a²-2a+a-1,-(a+2)x⁴-4(a+2)²x³+(-2a³-8 a²-8a)x²+(-4a³-8a²+8a+1)x-a³-2a²+4a-1=0, a+2=0,a=-2=>(-2*8-8*4-8*-2)x²+(-4*-8-8 4+8-2+1)x-(-8)-2*4+4*-2-1=(16-32+16)x²+(32-32-16+1)x+8-16-8-1=-15x-15=0,x=-1,x⁴+4(a+2)x³+2a(a+2)x²-(-4a³-8a²+8a+1)x/(a+2)+a²-4+9/(a+2)=0,(x²+2(a+2)x-6a 8)²+(28a²+80a+52+15/(a+2))x-35a²-9a- 68+9/(a+2)=0,\>*/>
    1
  3136. $2¹/⁶x¹/⁶dx=6*2¹/⁶x⁷/⁶/7+c
    1
  3137. 2320=2⁴+2⁸+2¹¹{(4;8;11)}
    1
  3138. -х^(1-х)=log(x)2^8,1-x=log(x)-8log(x)2,x=1-log(x)(-8log(x)2) e^((1-x)lnx)'=x^(1-x)*(-lnx+(1-x)/x)=0, =>x=1, ----->x max=1^(1-1)=1, 1=∞ неверно, 1 \> ∞/> неверно. Пустое множество. +1-
    1
  3139. 1+n-1+..+C(n-[n/2];[n/2])=((1/2+√5/ 2)^(n+1)-(-1/2-√5/2)^(-n-1))/√5
    1
  3140. ax=log²x≥0,a=0 1 решение,2logx*1/x=a, x=1,-*+>x logx0(2-logx0)=0,[x0=1,x0=e^2; a=4/e²,ає{0}U(4/e²;∞) 1 решение,ає{4/е²} 2 решения,ає(0;4/е²) 3 решения,а<0 0 решений
    1
  3141. Нормальной совести пожелать
    1
  3142. y^(6)=0,y^(5)=c1,y=c1x⁵/120+c2x⁴/24 +c3x³/6+c4x²/2+c5x+c6
    1
  3143. Ek=1;n1/4(1/(k+0,5)-1/(k+1,5))=0,25(1 /1,5-1 /2,5+...+1/(n+0,5)-1/(n+1,5))=1/6-1/ 4/(n+1,5)
    1
  3144. 4,74*10⁶/150'000=31,6 32 чел.✓
    1
  3145. (3/8)^(2√2)
    1
  3146. F(p)=3/(p-3)³,f(t)=1,5e^3t*t²
    1
  3147. a=(b+127)/(2b-1)=0,5(1+255/(2b- 1)) b=1;0;2;-1;3;-2;8;-7;9;-8;26;-25;43;-42;128;-127 a=128;-127;43;-43;26;-25;8;-8;8;-7;3;-2;2;-1;1;0
    1
  3148. S=250π-125arccos(91/1250-54/3125√10-3√(358358,5+9828√10)/625/√10)-90
    1
  3149. S=50/a²+10-50/a²=10
    1
  3150. [x+0,5]+[x]=x⁶,{2x+0,5≥x⁶,2x-1,5≤x⁶; {X⁶-2x-0,5≤0,x⁶-2x+1,5≥0;-5/3(1/3)¹/⁵-0,5<0,min=(54+19/26)/357>0 1,5⁶-3,5=7+57/64>0 x(-1;-0,5),x(1;1,5)[{x[-1;-0,5),×;{x[-0,5;0),×;{x[0;0,5),x=0;{x[0,5;1),x=1;{x[1;1,5),x=±2¹/⁶;{(0;2¹/⁶)}
    1
  3151. d=(a+b)/c 0=c²-abc+(a+b) c=(ab±√(a²b²-4 a-4b))/2 a≤c≤d≤b c=1,a=1,{d=b,1=(b±√((b 2-√8)(b-2+√8)))/2;b(-∞;2-√8]U[2+√8;∞) 4≠-4 b(-∞;(2-2√(1+a³))/a²]U[(2+2√(1+a ³))/a²;∞) (3a²-4√(1+a³)-4-4a³)/a³=0 0=a²(a⁴-3/2a³+9/16a²+a-1,5),a≤1/4-(31/64-√(31²/64²+(-3/16)³/27))^(1/3)-(31+8√ 15)^(1/ 3)/4=-71/96[a=0,(a²-3/4a)²+a-1,5 =0;\0(-1,5)*/3/8(-1 351/4096)*\3/4(-3/ 4)*/ a=-1,5;1,5 -1,50-*1,5->a,b≥1 b[5;∞)
    1
  3152. 18600+210∆t+1050(80-∆t)=0,∆t=122°C?×
    1
  3153. (xSin(1/x)-cos(1/x))/x=±∞ производной нет
    1
  3154. (√2+1)^x=(√2±1)⁴ x=±4
    1
  3155. 2^(6√3*√3/12)=2^1,5
    1
  3156. (n-1)/24(n³-n²-5n-3) 4 степень
    1
  3157. (8+h)/2*(8-h)+(12+h)/2*(12-h)=79 h=5(feet)
    1
  3158. 2x/(x-2),x f(2x/(x-2))-xf(x)=x², f(x)=-x²(x³-4x²+4x+4)/(x-2)²/(x²-1)
    1
  3159. 1,072..<1,264..
    1
  3160. r'(t)=acost*i->-asint*j->+bk-> r''(t)=-asint*i->-acost*j-> |i->. j-> k->|. -basintJ->-a²k->+ |acost -asint b|=abcost*i-> |-asint -acost 0| a√(b²+a²)/|√(a²+b²)|³=a/(a²+b²)
    1
  3161. 4√r,r,4-r 16r+r²=16-8r+r² r=2/3 S=14/9π
    1
  3162. x=(bc-10a-1)/(-a-b-c+10) {b=-10+1/(c+10),a=-b-c+10;c+10=±1 c=-9;-11 b=-10+1/1=-9;-10+1/-1=-11 a=-9-11 +10=-10{(-10;-9;-11)(-10;-11;-9)}
    1
  3163. S=7,8*26*0,5-46=65,4
    1
  3164. (-3log(x+1)(2x+5)+log²(x+1)(2x+5) +2)/log(x+1)(2x+5)=0 log(x+1)(2x+5)=(3±1)/2=2;1 [2x+5=(x+1)²,2x+5=x+1;[x=2,x=-2×,x=-4×.{2}
    1
  3165. Ельцину и Горбачеву поставят памятник в 2065 и 2079 гг..
    1
  3166. 0,0223=E✓
    1
  3167. $(-a;a)(1-x²/a²)b²dx=4a/3b² 4/3ba²✓
    1
  3168. [x=5,(x-5)²(x²-x+7)³+9(x-5)(x²-x+7)²+ 27(x-5)(x+4)+728=0;{5}
    1
  3169. 4^log2(x²)+4^log2(2/x²)=4, x⁴+4/x⁴=4,(x⁴)²-4x⁴+4=0,x⁴=(4±√(4²-4*4))/2=2 x=±2 ⁰,²⁵
    1
  3170. (3x³+2)³=x/3-2/3,x=-1:x⁶(x²-x+1)+x³(x²-x +1)+1/3(x²-x+26/27)≥0,188,а других решений нет
    1
  3171. {z=-4(x+y)/x/y,(y+z)/x/y/z=-1/24,(x+z)/x/y/z=1/24;{z=-4(x+y)/x/y,10x³-24,5x²+171 x-108+190/x=±(8 1/3x+15-60/x)√(25/36 x⁴-5/3x³+17x²-8x+16) y=(5/2x²-3x+12±3 √(25/36x⁴-5/3x³+17x²-8x+16))/x;{[x=-0,7 43,x=0,714;[y=-43,92,y=1,912,y=33,678,y= -2,494;[z=5,475,z=3,292,z=-5,721,z=-3,99 8;
    1
  3172. 8¹⁰*4/(4¹⁰*2)=2¹¹
    1
  3173. [x=0,2x-1=2^(2-2x);=>x=1{0;1}
    1
  3174. {а²-10a+18=0,b=10-a;a=5±√7 b=5-+√7 S=9-π
    1
  3175. P=4/5π√2g¹,⁵ph²,⁵D мощность ведра для сбора мусора в воде
    1
  3176. x⁴:16=0;1 15 x1;..;x7=1,x8..x14=0×
    1
  3177. √((9+r)²-(9-r)²)=6√r √((9-r)²-r²)=√(81-18r) 6√r=√(81-18r)+9 r-3=√(9-2r),r[3;4,5] r²-4r=0 r=0×;4✓{16π}
    1
  3178. ln(1+7t)e^(5t)/t
    1
  3179. /_2=arctg(a/b/3) /_1=arctg(1/3a/b) /_2=/_1✓
    1
  3180. ctg39°/cos/_ADE ctg39°tg/_ADE sin(39° +/_ADE)=sin51° [39°+/_ADE=51°+2πn,39°+/_ADE=129°+2πn;[/_ADE=12°+2πn,/_ADE =90°+2πn;/_ADE(0;39°) /_ADE=12°
    1
  3181. Y'=(1-x²)-⁰,⁵/2
    1
  3182. 0,5/sin70°,0,5/cos20° x=80°✓
    1
  3183. abcd=50(a+b+c+d),1≤50≤9⁴/9/4=9³/4=729/4=182,25 a=1,bcd=50(1+b+c+d),9³/28=729/28=26 1/28,0/ 2*9³/29=2*72 9/29=1458/29=50 8/29,2b9²/(2+b+18)= 162b/(b+20)≥50,162b≥50b+1000,b≥100 0/112=8 104/112,1*9³=729,50*28=1400, 3b9²/(3+b+2*9)=243b/(b+21)≥50,243b≥ 50b+1050,b≥1050/193=5 85/193,3*6cd= 50(3+6+c+d),d(18c-50)=450+50c,d=(50c+460)/(18c-50)=2+(14c+560)/(18c-50)\ >2 2/9 2+(14c+560)/(18c-50)=3,(14c+56 0)/(18c-50)=1,14c+560=18c-50,c=-610/-4 =152,5>9,≥2+686/122=7 76/122,2+(14c +560)/(18c-50)=8,(14c+560)/(18c-50)=6, 14c+560=108c-300,c=-860/-94=9 14/94 3*6*9²/27=18*81/27=54,3*7cd=50(3+ 7+c+d),d=(500+50c)/(21c-50)=2 8/21+ (500+2500/21)/(21c-50)\>2 8/21 200+350/9=238 8/9
    1
  3184. А что за музыка на заставке?
    1
  3185. AB√(2+(√6+√2)/2) /_ADC=atcsin ((√6+√3+1)/2/√(4+√6+√2))=67,5°
    1
  3186. a²√3/2=4,5√3 a=3(m) R=3(m) S=36-9π(m²)
    1
  3187. π/2(n+1)-Ek=0;narctg(x/(1+k(k+1)x ²))=π(n+1)/2-arctg((n+1)x) 2X,3x,.. S10(x)=11π/2-arctg(11x)
    1
  3188. (v(t)+k1/2/(kpS))'+kpS/m(v+k1/2/(kpS))²= k1²/4/(kpS)/m (v+k1/2/(kpS))-¹/-1+kpS/mt=c v=1/(kpS/mt-c)-k1/2/(kpS) c1=±k1 /2/(kpS) v=0;-k1/(kpS)[v=1/(kpS/mt-c)-k1 /2/(kpS),v=0,v=-k1/(kpS);[s=m/(kpS)ln|t-c m/(kpS)|-k1/2/(kpS)t+c1,s=c1,s=-k1/(kp S)t+c1.∆s=m/(kpS)ln|t-cm/(kpS)|-k1/2/(k pS)t-m/(kpS)ln|cm/(kpS)| t=cm/(kpS)-2m/k1 ∆s=m/(kpS)ln|2kpS/c/k1|-cmk1/(kpS) ²/2+m/(kpS)
    1
  3189. 2π*0,5/2*2*4=4π
    1
  3190. {-0,25a(n+1)+0,25an=bn,a(n+2)=-6a(n+1)-9an; a1=-1,b1=2 a3=-6a2-9a1=-6a2+9, 0,25a2-0,25=2,a2=-9,a3=63,q=-6-9/q q²+6q+9=0,q=-3,a4=81*-3 2/3 an=(-3)^n (1/3-2/3-2/7-2 8/21..),bn=(-3)^n(1/3-2/3 2/7-2 8/21+...+0,75..)
    1
  3191. а=9/4✓ х=(3±√(9-4а))/2 √(9-4a)/2 (0,5;1,5] 9-4a(1;9],a[0;2) a[0;2)U{9/4}
    1
  3192. ((9x&10)/(x-1))¹/⁷-((7x-8)/(x-1))¹/⁷=2 ((9x&10)/(x-1))¹/⁷((7x-8)/(x-1))¹/⁷ (32+2((9x&10)/(x-1))¹/⁷((7x-8)/(x-1))¹/⁷(8+((9x&10)/(x-1))¹/⁷((7x-8)/(x-1))¹/⁷))=-18 ((9x&10)/(x-1))¹/⁷ ((7x-8)/(x-1))¹/⁷=a (a+1)(a²+7a+9)=0 a=-1;(-7±√13)/2 x=9/8,(63-((-7±√13)/2)⁷)x²+(-142+2((-7±√13)/2)⁷)x+80- ((-7±√13)/2)⁷=0 D=4(1-((7-+√13)/2)⁷)<0{9/8}
    1
  3193. x(n+1)=n(1+n)/2+2+...+2cos(2πx(n-1)/3)+2cos(2π(x(n-1)+n-1+2cos(2πx(n-1)/3))/3) y(n+1)=n+1-1,n=3m-1;+0,m=3m;+1,n=3m+1 {x(n+1)-y(n+1)}={...2cos (2πx(3m-2)/3)+2cos(π*2/3+4/3π(1+....+cos(2πx(3m-2)/3)))}
    1
  3194. 0,25(-S0/S√(2g)t+c)²=h c=2√H h=0,25(-S0/S√(2g)t+2√H)² T=10(ч) (S0/S)²g*648*10⁶=H h'/(S0/S√(2g)* 18*10³-√h)=S0/S√(2g) √h=z,h=z², h'=2zz' √h+S0/S√(2g)*18*10³ln|√h- S0/S√(2g)*18*10³|=-S0/S√(0,5g)t+ S0/S√(2g)*18*10³ln|S0/S√(2g)*18 *10³|, h=(S0/S)²g*648*10⁶, 36*10³(-1+∞+ln|S0/S√(2g)*18*10 ³|)=t,t=86,3ч(?)
    1
  3195. 25³>1,08²⁰=3,816..
    1
  3196. En=1;∞(1/(n-3)!+3/(n-2)!+1/(n-1)!)= e+3e+e=5e
    1
  3197. U+4$tg(u/2)/(1+tg²(u/2))/(tg(u/2)-1-√2)/(tg(u/2)-1+√2)dtg(u/2) z=A*2z(z²-2z-1)+D(z²-2z-1)+B(1+z²)(z-1+√2)+C(1+z²)(z-1-√2){A=-(2√2+1)/28,B=(2√2+1)/28, C=(2√2+1)/28,D=(-2√2-1)/14; u-(2√2+1)/28ln|1+tg²(u/2)|-(2√2+1)/28u+(2√2+1)/28ln|tg(u/2)-1-√2|+(2√2+1)/28ln|tg(u/2)-1+√2|+c=-(2√2+1)/28ln|1+(1-√(1-x²))²/x²|+(27-2√2)/28arcsinx+(2√2+1)/28ln|(1-√(1-x²))/x-1-√2|+(2√2+1)/28ln|(1-√(1-x²))/x-1+√2|+c
    1
  3198. 2^9,599=770
    1
  3199. (√((√(b²+a²)x+a)²+b²(1-a²))-√((√(b²+a²)x-a)²+b²(1-a²)))/a=?
    1
  3200. 7920руб.
    1
  3201. log(x+1)=logx+1,{x+1=x*10,x+1>0;{x=1/9, x>-1;{1/9}
    1
  3202. F(p)=0,5(1+i)(p²-2i)/(p⁴-4)
    1
  3203. {x'+x-y=e^t
    1
  3204. [11x²-122x+11=0,x=-1;x=(61±60)/11=11;1/11{11;1/11;-1}
    1
  3205. a(n+1)=1/(2-an)=(n+c)/(n+c+1) an=(n+c-1)/(n+c) 0,5(-1/(n+c+1)+1/(n+c-1)) 0,5(1/c+1/(c+1))✓
    1
  3206. 1(cm) R-1,1,2√R 4R+1=R²-2R+1 R²-6R=0 R=6(cm) S=1/2π(6/2)²=4,5π(cm²)
    1
  3207. -√5+√7 A)
    1
  3208. [x=±arctg5+πn,x=πn.
    1
  3209. 0,5^(1/8)=0,92✓
    1
  3210. a/sin(o+a)=2/sina=√(a²/2-2)/sino a=2sin(o+a)/sina,o(0;30°] a=-0,5o+0,5arcsin(2sino);0,5π-0,5arcsin(2sino)≤π/2-o/2 a/2/sin(2a+2 o)=1/sino 2sino=2sino x=1✓
    1
  3211. X^n,2x^(n-1)+x^(n-2),x^(n-3)(5x+2),..,anx+bn {a1=2,b1=1,[m:2,a(2k+1)=2+2k,m:/2, a(2k+2)=5+2k;bm=a(m-1);{(2k;1+2k)(3+2k;2k)}
    1
  3212. |(-π/6;π/6)0,25(f+sin(6f)/6)=π/12
    1
  3213. {x>0,y>0,y=(2x²+1)/(x-1);x>1,y=(2x²+1)/(x-1)
    1
  3214. a1³+a2³+..+an³=2S²n,a1³=2a1²,[a1=0, a1=2;[a2=0,a2=2;a2=0,a2=4,a2=-2[an=0, 1 число =2, остальные 0,an=-a(n-1),an=2 a(n-1),an=0;
    1
  3215. √((4√2-1)²-1) V=8/3√(8-2√2)(cm³)
    1
  3216. {c=-a-b,a<1/2,b<1/2,-a-1/2<b,x²+(b-1)/ax-1-b/a≥0,x²+b/(a-0,5)x+(- a-b-0,5)/(a-0,5)≥0,a>0;(a+b/2)²≤b/2-1/4,{b=1/2,a=-1/4;2/3>0 -4040ab=505
    1
  3217. 103/2+3*9,5=51,5+28,5=80
    1
  3218. S=50/3π-25√3/2
    1
  3219. x=(1±√(4y²-3))y/2/(y²-1)≤(y/2+y²)/(y²-1)= 1+(0,5y+1)/(y²-1)(-0,5y²-0,5-2y)/(y²-1)²=0, y=-2±√3-+>y max=1-0,25(√3+2)=-0,2 5√3+0,5=0,..1+√3/4-0,5=√3/4+0,5=0,8..\> (y/2-√(4y²-3)y/2)/(y²-1)'=-0,5((y²+1)√(4y ²-3)-5y²+3)/(y²-1)²=0,(y²+1)√(4y²-3)=5y²-3,(y²+1)²(4y²-3)=(5y²-3)²,y≥√(3/5),y≤-√0,6; 4y⁶-3y⁴+8y⁴-6y²+4y²-3-25y⁴+30y²-9=0,4y⁶-20y⁴+28y²-9=0,(y²-5/3)³-4/3(y²-5/3)+50 3/108=0,y²-5/3=(-503/216+√(503²/216²+(-4/3)³/27))^(1/3)+(-503/216-√(439*7)/24)^(1/3),y=±√(5/3+(-503/216+√(503²/216²+(-4/3)³/27))^(1/3)+(-503-9√(439* 7))^(1/3)/6)*-1+*1->y max=0/0=(0,5-(4y ²-3)^-0,5*2y²-(4y²-3)⁰,⁵*0,5)/2/y=(0,5-2*1 -0,5)/2=-2/2=-1,min=0/0=(0,5-2-0,5)/2/-1 =-2/-2=1 учитывая значения экстремумов функции,получаем, что других корней нет.
    1
  3220. log6(4/=2/log2(3)=2/(x-3)
    1
  3221. f(coso)=coso(2(2cos²o-1)²-1+4(cos²o-1)(2cos²o-1)) f(x)=16x⁵-20x³+5x
    1
  3222. a1=1,5a1-1 a1=2 -0,5a2=-4,a2=8 an=2n+2 En=1;n-1an=2n+2²(n-1)+...2^n*1+2^(n-1) a1=(2n-1)2^n+2 3(2n-1)2^n+9+4*16^(n-1):13=3(2nmod13-1)2^(nmod12)+9+4*3^(nmod12-1)=3;6;5;7';9;1;12;'0;10;1';11;7;10 n=156n1+7
    1
  3223. (x-1)³-8(2x¹/³+1)=0 3((x⁴/³-x¹/³)²-16/ 9)x-²/³=0 x⁴/³-x¹/³-+4/3=0 min=-3/4(1/4)¹/³+4/3>0 z³+1/3z-1/64=0 z=(1/128+√(1/128²+1/27²))¹/³+(..-..)..;-(1/128+√(1/128²+1/27²))¹/³/2-(..-..)..±√(3/4((1/128+√(1/128²+ 1/27²))¹/³+(..-..)..)²+1/3)i x¹/³=-√((1/128+√(1/128²+1/27²))¹/³+(..-..)..)±2√(((1/128+√(1/128²+1/27 ²))¹/³+(..-..)..)²+1/3)-(1/128+√(1/128 ²+1/27²))¹/³/4-(..-..)..) x=(-√((1/128+√(1/128²+1/27²))¹/³+(..-..)..)±2√(((1/128+√(1/128²+1/27 ²))¹/³+(..-..)..)²+1/3)-(1/128+√(1/128 ²+1/27²))¹/³/4-(..-..)..))³+*-*+>x max=((-√((1/128+√(1/128²+1/27²))¹/³+(..-..)..)-2√(((1/128+√(1/128²+1/27 ²))¹/³+(..-..)..)²+1/3)-(1/128+√(1/128 ²+1/27²))¹/³/4-(..-..)..))³-1)³-16(-√((1/128+√(1/128²+1/27²))¹/³+(..-..)..)-2√(((1/128+√(1/128²+1/27 ²))¹/³+(..-..)..)²+1/3)-(1/128+√(1/128 ²+1/27²))¹/³/4-(..-..)..))-8>0,min<0 x=4,24;-1
    1
  3224. y=9+36/(x-4) x-4=1;-1;2;-2;3;-3;4;-4; 6;-6;9;-9;12;-12;18;-18;36;-36 x=5;3;6; 2;7;1;8;0;10;-2;13;-5;16;-8;22;-14;40;-32 x+y=50;-24;33;.. ну,в общем,сами все прдсчитаете
    1
  3225. √(25+а²)+а=√(144-а²)+√(49-а²) 49-193/144а²=0 а=84/√193 х=√193
    1
  3226. 7*8+4*3+3*4=80
    1
  3227. (x+y)(x-y)=49{(25;24)}
    1
  3228. X≥0 (x+x-¹)²-5(x+x-¹)+4=0 x+x-¹=(5±√9)/2=4;1 x²-4x+1=0 x=2±√3
    1
  3229. b≥4 0=b²-8b+7 b=(8±6)/2=7;1 {7}
    1
  3230. {x=-5/12z+13/12,y=13/12z-5/12; x²-y²+z²= 1
    1
  3231. [10²⁰'⁰⁰⁰/(10¹⁰⁰+3)]=10¹⁹'⁹⁰⁰-3*10¹⁹'⁸ ⁰⁰+..-3¹⁹⁹+[9¹⁰⁰/(10¹⁰⁰+3)] -3¹⁹⁹=-3³=1mod10✓ 10(1-1/2)(1-1/5)=4
    1
  3232. а=3/4√15,b=11/4+5 1/4=8{6√15}
    1
  3233. 11*12*23/6=506
    1
  3234. 45-3*6=27 x=√(3*6-2/3√27*1/3√27) =2√3
    1
  3235. X=10+3(n-1), (20+3(n-1))n/2=275 n=-17/6+83/6=11{40{ K
    1
  3236. 200/x=240/(x±10)-3 3x²-10x+2000=0×,3x²-70x-2000=0 x=(70±170)/6=40;-50/3×{40;30;5;8}
    1
  3237. 1/4x²-2|x-1|=1/2x-17/4[{x≥1,1/4x²-2,5x+6 1/4=0;{x<1,1/4x²+1,5x+2 1/4=0;[{x≥1,x=5;{x<1,x=-3;[x=5,x=-3.
    1
  3238. 6039π✓
    1
  3239. -1/3х=-4/3 х=4.
    1
  3240. 3sino/(3coso-5)'=-15(coso-3/5)/(3coso-5)²=0 csio=±arccos(3/5)+2 πn-*arccos(3/5)+•2π-arccos(3/5)->o min=3*4/5/(3*3/5-5)=-3/4 max=- 12/(-16)=3/4 o[π;2π]\>(-)•\>(-)=/> (+) />(-)•\>(-)=?(+) f(1,5π)=-3/-5=0,6 -3√(1-cos²o)/(3coso-5)≤b sin(o+arccos(1/√(1+b²)))≤5b/3/√ (b2+1)) b=±3/4≥0{3/4} />(+)*/>(-) =? \>(+)*/>(-)=/>(-) sin(o-arccos(1/√(b²+1)))≤-5b/3/√(b²+1)=1 b=-3/4 ✓ графически доказывается,что Макс=3/4,мин=-3/4.
    1
  3241. En=1;∞(-1)^(n-1)/2/n(lnx|∞+ Em=1;°(-n)^mx^(2m)/2/m/m!(=))=∞
    1
  3242. 89C=I+10A≤99,≥0 C=1 89=I+10A A=8,I=9 1+8+9=18
    1
  3243. 4²+b²=5^2 b=3 k=8/3 A)
    1
  3244. 4^(n-4)*4! P=4^(n-4)*4!/n!
    1
  3245. (√18+4)*2-(7√2-7√2)⁵=2√18+8✓
    1
  3246. s/(0,5s/12+0,5s/4)=24/4=6км/ч
    1
  3247. 5(7⁶-1)(7⁶+1):(5*2*3)=30
    1
  3248. (1+2m-1)/2*m=m², (2+2m)/2*m=(1+m)m
    1
  3249. {(0;666)(22;28)(28;22)(666;0)(-2;-668)(-24;-30)(-30;-24)(-668;-2)}
    1
  3250. {х+у=1,ху=-12;х⁵+у⁵=(х+у)((х+у)⁴-5 ху((х+у)²-ху))=781
    1
  3251. S∆=4(√2-1)
    1
  3252. 2<(log2(5))
    1
  3253. x=1,5±√17,25
    1
  3254. {(4/3у-4 1/3а)²+(у-2а-1)²=а-2, Х=4/3у+2/3а+1;25/9у²+(-140/9а-2)у+22 7/9а²+3а+3=0 у=(70а+9±3√(-25а²+65а -66))/25,х=22/5а+1,48±4√(-25а²+65а-66)/25 //
    1
  3255. (х-х0)²+(у-у0)²=R²,{√(40-8x0+2x0²)=R,y0= -2+x0; (x-x0)²+(y+2-x0)²=2x0²-8x0+40
    1
  3256. y'/x+y'²-y/x=0 (2(y+1/x)⁰,⁵)'+(1/x+1/x²)/√(y+1/x)=±x-⁰,⁵ (y+1/x)⁰,⁵=u 2uu'-+x-⁰,⁵u=- 1/x-1/x² [u=0,u=±x⁰,⁵+c; n?0,5,n=-0,5[{a(- 1,5)=0,a(-0,5)=-1,..,{a(-1,5)=0,a(- 0,5)=1,..; u=-+x-⁰,⁵[y=-1/x,y=x±2cx⁰,⁵-1/x+c2,y=0;
    1
  3257. X(-∞;-1]U[0;1] 0=-x²-x+1 x=(-1±√5)/2{(-1+√5)/2;(-1-√5(/2}
    1
  3258. 66(tg2a-tga)=55 (tga+5/18)³+83/108(tga+5/18)-3115/18²/9=0 tga=-5/18+(3115+√(3115²+83³))¹/³/18+(..-..)..=1/2 132/sin(3a)*sina= 60
    1
  3259. y=(x+1)²-2 y=a(x+b/2/a)²-b²/4/a+c (2;7)(4;5)(3;2){33=c,-25=b,a=4; y=4x²-25x+33 3x²-27x+34=0 x=(27+√321)/6✓
    1
  3260. y''-6y'+8y=x y0=c1e^kx+... k²-6k+8=0 k=(6±√(6²-4*8))/2[k=4,k=2;y0=c1e^4x+c2 e^2x yp=k1x+b 0-6(k1)+8(k1x+b)=x{8k1 =1,-6k1+8b=0;{k1=1/8,b=3/32;yp=1/8x+ 3/32 y=c1e^4x+c2e^2x+1/8x+3/32
    1
  3261. 60°-2/3о-2/3а=о+а о+а=36° х=60°-2/3*36°=36°D)
    1
  3262. Z²-(2¹/³(cos(60°+120°n)+isin(60°+120°n))-1)z-1=0 z=(2¹/³(cos(60°+120°n)+isin(60°+120°n))-1±(√(0,5 √(((-2⁴/³-2²/³)cos(60°+120°n)+5)²+ (2²/³-2⁴/³)²sin²(60°+120°n))+0,5((-2 ⁴/³-2²/³)cos(60°+120°n)+5))+i√(0,5√ (0,5√(((-2⁴/³-2²/³)cos(60°+120°n)+5) ²+(2²/³-2⁴/³)²sin²(60°+120°n))-0,5((-2 ⁴/³-2²/³)cos(60°+120°n)+5)))/2
    1
  3263. x/3=1/(√(x²+9)/2) x²+4,5=±7,5 x²=3;-12×,x=√3
    1
  3264. (3+√2+√3+√5)/(3+√2+√3+√5+√2 (3+√2+√3+√5))=1/(1+√2)=√2-1
    1
  3265. {0,5log|x|2>1,x²>0,x²≠1;{(0,5-log(2)|x|)/log(2)|x|>0,x≠0,x≠±1;{(log(2)|x|-0,5)/log(2)|x|<0,+1°2⁰,⁵-°+>|x| |x|є(-∞;1)U(2⁰,⁵;+∞) хє(-∞;-2⁰,⁵)U(-1;1)U(2⁰,⁵;+∞) хє(-∞;- 2⁰,⁵)U(-1;0)U(0;1)U(2⁰,⁵;+∞)
    1
  3266. 2021^(sin⁴x+cos⁴(x-π/4))=(2020+(sinx+ cosx)²-sin2x)⁰,²⁵ 2021^(sin⁴x+(cosx√2/2 +sinx√2/2)⁴)=(2020+sin²x+2sinxcosx+cos²x-2sinxcosx)⁰,²⁵ 2021^(sin⁴x+0,25(cos x+sinx)⁴)=2021⁰,²⁵,(sin²x+0,5(cosx+sin x)²)²-sin²x(cosx+sinx)²=0,25,(sin²x+0,5 (cos²x+2cosxsinx+sin²x))²-sin²xcos²x-2cosxsin³x-sin⁴x-0,25=0,(0,5+sin²x+sin2x)²- sin²x+sin⁴x-sin2xsin²x-sin⁴x-0,25=0,0,25+sin⁴x+sin²2x+sin²x+sin2x+2sin²xsin2x-sin²x-sin2xsin²x-0,25=0,sin⁴x+4sin²x(1-sin²x)+sin²x+sin2x*(cos²x+2sin²x)=0,[sinx=0, sin³x+4sinx-4sin³x+sinx+2cosx(1+sin²x)=0,[x=πn,-3sin³x+5sinx+2cosx+2cosxsin ²x=0;sin²x(-3sinx+2cosx)+√29sin(x+arc cos(5/√29))=0,-3sin³x+5sinx=±2√(1- sin²x)(1+sin²x),9sin⁶x-30sin⁴x+25sin²x=4 (1-sin²x)(1-2sin²x+sin⁴x),9sin⁶x-30sin⁴x +25sin²x-4(1-2sin²x+sin⁴x-sin²x+2sin⁴x-sin⁶x)=0,sin⁶x-30sin⁴x+25sin²x-4+12sin²x- 12sin⁴x+4sin⁶x=0,5sin⁶x-42sin⁴x+37sin²x-4=0,sin²x=y,y³-8,4y²+7,4y-0,8=0,(y-2,8)³-16,12(y-2,8)-23,984=0,y-2,8=(23,984/2+√(11,992²+(-16,12)³/27))^(1/3)+(1 1,992-√(-12,665'734))^(1/3), поэтому у нас 3 корня,y=2,8+√(16,12³/27)^(1/3) cos(arccos(11,992/√(16,12³/27))/3+2πn/3)*2,[y=7,41..>1,y=0,1258..≤1,≥0,y=0,85 7..≤1,≥0;[sin²x=0,1258,sin²x=0,857..;[sinx =±√0,1258,sinx=±√0,857;[x=arcsin±√0 ,1258+2πn,x=π-arcsin±√0,1258+2πn,x=arcsin±√0,857+2πn,x=π-arcsin±√0,857+2πn; 3224 259,8544 4188,842928/27= 1612. *16,12 =155 240183/2 9672. 5197088 7/62500 1612 2598544 259,8544 15591264 2598544 4188,842928
    1
  3267. [x=0,log²/³6(3)=x.
    1
  3268. Дорогой Бондаренко! А правда ли, что капитализм умрёт в 2100- 2160гг.?
    1
  3269. 33³*10³=35'937'000
    1
  3270. x=±2√5a/5
    1
  3271. [{a(-1-√11,5;-1+√11,5),x=a+7;{x=-a+2,a(-1,5-√10,25;-1,5+√10,25).
    1
  3272. ​ @zaurmagomedov5181  m=1✓
    1
  3273. (3-√5)(3-2√5)/-11=9/11√5-19/11
    1
  3274. x+1=2,x=1 x=log5(25)=2
    1
  3275. $(1;2)log2(x³+1)dx-$(1;2)3/(y³+1)/ln2dy-3/ln2=2ln9/ln2-1-6/ln2 X=log2(y³+1),dx=3y²/(y³+1)/ln2dy
    1
  3276. $(-π;π)f(t)dt=c f(0)=0 f'(x)=sinx+c f(x)=-cosx+cx+c1 0=-1+c1 c1=1 f(x)=-cosx+cx+1 -sinx+cx²/2+x(-π; π)=2π=c f(x)=-cosx+2πx+1
    1
  3277. (2 -5 3|2). (1 -2,5 1,5|1) (7 1 -2|12)(0 1 -25/37|10/37) (9 -2 5|52)(0 0 1|7) y=185/37=5 x=-9,5+12,5=3 (3;5;7)
    1
  3278. P=P/S=1/3*a²*apg/a²=1/3*apg, поэтому максимум напряжения будет внизу.И там показано, что максимум будет зелёный.
    1
  3279. √(3+2cos40°),l=√(2+2sin20°) x=arccos(√(1+cos70°)/√2)=35°
    1
  3280. 42 г азота и 46 г натрия NH4NO3,NaNO3 m1(N)=m(NH4NO3)*7/20 m2(N)=m(NaNO3)*14/85 m(Na)=m(NaNO3)*23/85=46 m(NaNO3)=170(г) m(NH4NO3)=40(г) 210 г 1)
    1
  3281. $(0;2a)(4a²x²-4ax³+x⁴)dx=16/15a⁵ $(0;a)4a√(a²-ay)dy=8a³/3 ry=√(16/15a⁵/(4a²/3))=√0,8a¹,⁵ rx=√(2a)
    1
  3282. (cosz+isinz)(cos(-z+π/2)+sin(-z+π/2)i)=i
    1
  3283. 2^(6x)=2^2,75 x=11/24✓
    1
  3284. X=shu,dx=chudu 0=e^(2u)-2/√3e^u-1 u=ln√3 $(0;ln√3)(e^1,5u+e^-0,5u)/2 du=e^(1,5u)/3-e^(-0,5u)(0;ln√3)=2/3
    1
  3285. x,2-x 5/x,-12-x 5/x*(-12-x)=1 -60-5x=x x=60/-6= -10, -10,12;-0,5, -2
    1
  3286. (lnz+1)z'=(-lnx-1) z'(x)'(y)=-z'(x)Z'(y)/z/lnz=-(lny+1)/(lnz+1)²/x=-1/x/(1+lnx)=-(xln(ex))-¹
    1
  3287. -4sin³x+2sin²x+2sinx-1<0
    1
  3288. -4sin³x-2sin²x+2sinx&1<0
    1
  3289. {c=±√(-a²-b²),f=±√(121-d2-e²/;
    1
  3290. E!,5-W(e⁵)=x
    1
  3291. (x-1)-¹Ei=0;nC(n;i)(-1)^in^(i+1)(x+n) ^-i~0 q=0 сходится
    1
  3292. Мужской, женский,м,ж,ж,ж,ж,ж.
    1
  3293. {z=1/(4-x),y=1-1/x,(-4/3x²+20/3x-25/3))/(x-4)/(x-1)=0;x=2,5 (2,5;0,6;2/3) 2,5*0,6* 2/3=1
    1
  3294. 2xcosx²'=2cosx²-sinx²*4x²
    1
  3295. AH=AEcos/_A AB=2AEcos/_A /_D =180°-/_A x=/_A/3 2AE/sin(180°-/_ A)2=AEcos/_A/sin(2/3/_A) ±45°+1,5 πn=/_A(0!180°) /_A=45°,x=15° A)
    1
  3296. √-x=u,x²=u⁴ u⁴+u-18=0 z³+9/2z-1/64=0 z=(1/2+√55297/2)¹/³/4+(..-..)..;-(1/2+√55297/2)¹/³/8-(.. ..)..±√(3/4((1/2+√55297/2)¹/³/4+(..-..)..)²+9/2)i u=-√((1/2+√55297/2)¹/³/4+(..-..)..)+2√(0,5√(((1/2+√55297/2)¹/³/4+(..-..)..)2+4,5)-(1/2+√55297/2)¹/³/16 (..-..)..) x=-(-√((1/2+√55297/2)¹/³/4+(..-..)..)+2√(0,5√(((1/2+√55297/2)¹/³/4+(..-..)..)²+4,5)-(1/2+√55297/2)¹/³/16-(..-..)..))²
    1
  3297. 3x/11+2/13*y=1,*11*13 39x+22y=143, 143-22*13*2=143-572=-429:39=-11 x= 11+22n y=26+39m |11+22n+26+39m|=|37+22n+39m|=0,
    1
  3298. cos1-e-⁰,⁵+$e^((x²-1)/2)sinxdx(0;1) e-¹,⁵*0,5√2$(0;1)e^(0,5z²-0,5)sinzdz 1/(e-¹,⁵*0,5√2)=√2e¹,⁵
    1
  3299. 2-4*10³+6*10⁶-4*10⁹+2*10¹² 2-2*10³+2*10⁶ (10⁶-10³+1)²/(10⁶-10³+1)=999'001
    1
  3300. 16/(2√(a²-12²)+2)=12/a (2a-3)²=(a²-12²)•9,a≥12 -5@²-12a+9*145=0 a=15,S=(2+20)/2*12=132
    1
  3301. (((x-1)²-3)(x+2)⁰,⁵-(x-1)²)(x-1)-²(x+2) ⁰,⁵=0 x(1+√3;∞), x⁵-3x⁴-4x³+2x²+24x+7=0 5((x-0,6)⁴-3,36(x-0,6)²-2,368(x-0,6)+4,4592)=0 (z-0,56)³-1,25(z-0,56)-1,371'194=0 z=0,56+(0,685597+√(0,685597²-1,25³/27))¹/³+(..-..)..;0,56-(0,685597+√ (0,685597²-1,25³/27))¹/³/2-(..-..)..±√ (3/4((0,685597+√(0,685597²-1,25 ³/27))¹/³+(..-..)..)²-1,25)i x=0,6+√(0,56+(0,685597+√(0,685597²-1,25³/27))¹/³+(..-..)..)±2√(0,5√( 0,9364-0,56((0,685597+√(0,685597²-1,25³/27))¹/³+(..-..)..)+((0,685597 +√(0,685597²-1,25³/27))¹/³+(..-..)..) ²)+0,28-(0,685597+√(0,685597²-1,2 5³/27))¹/³/4-(..-..)..)+*1,24..-2,80..*+>x max=28,..>0 min=-10,..<0 x=✓3,3;×2,4;-0,3×-*3,3+>x min=4,6-2*2,3=0✓{(3,3;3,3;3,3)}
    1
  3302. {2х1+х2+8х3=-11,3х1-19х2+23х3=36,х1+4х2-3х³=5;{2х1+х2+8х3=-11,41/3х2-22/3 х3=-35,-7х2+14х³=-21;{2х1+х2+8х3=-11, 41/3х2-22/3х3=-35,20х³=-76;{х1=9,6,х2= -4,6, х3=-3,8;
    1
  3303. (х-7/3)³-26 1/3(х-7/3)-24 26/27≤0 (х-7/3-(337+√(-379470))¹/³/3+..)(..)(..)≤0 (х-7/3-2/3√79cos(1/3arccos(337/79/√79))(х-7/3-2/3√79cos(1/3arccos(337/ 79/√79)+2/3π))(х-7/3-2/3√79cos(1/3arc cos(337/79/√79)+4/3π)≤0-+-*+>x x(-∞;7/3+2/3√79cos(1/3arccos(337/79/√79)+2/3π)]U[7/3+2/3√79cos(1/3arccos(337/79/√79)+4/3π);7/3+2/3√79cos(1/3 arccos(337/79/√79)] (x+1/3)³+2/3(x+1/ 3)+29 20/27≥0 x+1/3-(-14 47/54+√(803² +32)/54)¹/³-(-14 47/54-√(803²+32)/54)¹/³≥0 x[-1/3+(-14 47/54+√(803² +32)/54)¹/³+(-14 47/54-√(803²+32)/54)¹/³;∞) x[-1/3+(-14 47/54+√(803² +32)/54)¹/³+(-14 47/54-√(803²+32)/54)¹/³;7/3+2/3√ 79cos(1/3arccos(337/79/√79)+2/3π)]U [7/3+2/3√79cos(1/3arccos(337/79/√79) +4/3π);7/3+2/3√79cos(1/3arccos(337/ 79/√79)] xmax=8
    1
  3304. ​{x1=πn,e^2x2=-3;0/
    1
  3305. 36г объемом -4 мл×
    1
  3306. ln²x=1+lnx lnx=(1±√5)/2 x=e^((1±√5)/2)
    1
  3307. cos2x+cos(2/3π)=-1 cos2x=-0,5 x=±1/3π+πn
    1
  3308. {[x=π/2+πn,x=±π/4+2πn,x=πn;x[-π+2πm;2π m];[x=-π/2+2πn,x=-π/4+2πn,x=πn.
    1
  3309. 6x/(x-2)-2(12x/(x-2))¹/⁴-(12x/(x-2))¹/²>0 (12x/(x-2))¹/⁴=y (y-(2+10√3/9)¹/³-(2-10√3/ 9)¹/³)y>0+°0-°(2+10√3/9)¹/³+(2-10√3/9)¹/³+>y y(-∞;0)U((2+10√3/9)¹/³+(2-10√3/9)¹/³;∞) (x+((2+10√3/9)¹/³+(2-10√3/9)¹/³)⁴/6/(1-((2+10√3/9)¹/³+(2-10√3/9)¹/³)⁴/12))/(x-2)<0+°-°+>x x(((2+10√3/9)¹/³+(2-10√3/ 9)¹/³)⁴/6/(1-((2+10√3/9)¹/³+(2-10√3/9)¹/³) ⁴/12);2)
    1
  3310. X[10;90] 26=x✓
    1
  3311. 2^(-0,5n+1)cos(45°n)
    1
  3312. En=1;∞(1/(n+1)²-1/(n+1)+1/n)=π²/6+1
    1
  3313. ±1=y'y-⁰,⁵ ±x+c=y⁰,⁵ y=(±x+c)²
    1
  3314. 4*183/7/60=1,74 км/ч
    1
  3315. X=1+3(n-1) (-1+3n)/2*n=1717 n=1/6+203/6=34{100}
    1
  3316. (3x-8)/(x-2)-(x-2)/(x+2)=(2x²-6x+44)/(x²-4) (8x-64)/(x-2)/(x+2)=0,x=8;≠±2
    1
  3317. 5^(√x/2)-5^(√y/2)=625-25{√x/2=4, √y/2=2;{x=64,y=4.(64;4)
    1
  3318. 5√2=a*1,5+1,5√2 a=7/3√2{98/9}
    1
  3319. Y:7 x²+35y1²=51 y1=0;±1 y1=±1,x=±4 {(±4;±7)}
    1
  3320. а*√3/2*(2-а)/2+0,5*(1-а)*(√3/6-а√3/2)/(0,5-0,5а)*...=√3/2*а-√3/4а²+√3/6..-√3/2а..=0,5,а=0,а=0,5,а=1,
    1
  3321. limn->∞(1/9)=1/9
    1
  3322. {х<-1,(х+1)(х+3)х≥0--3+-1-*0+>х; хє[-3;-1)
    1
  3323. (√(x²-ax+8)+√(x²-ax+6))^x+(2/(√(x²-ax +8)+√(x²-ax+6)))^x=2^1,5x,(√(x²-ax+8 )+√(x²-ax+6))^2x-2^1,5x(√(x²-ax+8)+√(x²-ax+6))^x+2^x=0,(√(x²-ax+8)+√(x²-ax+6))^x= (2^1,5x±√(2^3x-4*2^x))/2,[(√(x²-ax+8)+ √(x²-ax+6))^x=2^(1,5x-1)+2^(x/2-1)√(2 ^2x-4),(√(x²-ax+8)+√(x²-ax+6))^x=2^(1,5x- 1)-2^(x/2-1)√(2^2x-4)>0;[{a=-((0,5(2^(1,5x-1)+2^(x/2-1)√(2^2 x-4))^(2/x)-x²-7)²-x⁴-14x²-48)/(2x³+14x+ 0,5x(2^(1,5x-1)+2^(x/2-1)√(2^2x-4))^(2/x)-x³-7x),a≥-0,5(2^(1,5x-1)+2^(x/2-1)√(2^2 x-4))^(2/x)/x+x+7/x,x≥1,{a=-0,25(((2^(1,5x-1)-2^(x/2-1)√(2 ^2x-4))^(2/x)-2x²-14)²-x⁴-14x²-48)/x/(2x²+14+2^(1,5x-1)-2^(x/2-1)√(2^2x-4)),a≥-2^(1-4/x)(2^x-√(2^2x-4))^(2/x)/x+x+7/x,x≥1;
    1
  3324. 4√2=2R(1+√2) R=2(2-√2) S=16-8π(6-4√2)
    1
  3325. Декабрь,дека,каре,бар,раб,дар,краб,брак,кеда,река,бак
    1
  3326. (5х+6)/30=(5х+2)/30 0=-4,0/
    1
  3327. х(ху-1)+у(ху-1)=(ху-1)(х+у)
    1
  3328. {d=2-a-b-c,c=(-a-b+2±√(4-2ab+4a+4b-3a²-3b²))/2, b³-4ab-2a²-2b²+a³+ab²+a²b+2ab-2=0,ab(&2a+ab+a²&2b+b²)=4; {a+b=x,ab=y;{[y=1,(x³-2x²-2)/(2x-2)= y;[x=0,x=1±√3,(x-1 1/3)³-20/3(x-1 1/ 3)-3 5/27=0;x-1 1/3=(43+√(43²-20³)) ¹/³/3+(..-..)..=2/3√20cos(1/3arccos (43/200√5)+2/3πn) x=4/3+2/3√20cos(1/3arccos(43/ 200√5)+2/3πn),y=((4/3+2/3√20cos(1/3arccos(43/200√5)+2/3πn))³-2 (4/3+2/3√20cos(1/3arccos(43/200 √5)+2/3πn))²-2)/(1/3+2/3√20cos (1/3arccos(43/200√5)+2/3πn))/2 {a=2/3+1/3√20cos(1/3arccos(43/ 200√5))-+√((17/18-2/3√20cos(1/3arccos(43/200√5))+40/9cos²(1/3 arccos(43/200√5))))/(1/3+2/3√20 cos(1/3arccos(43/200√5)))), b=2/3+1/3√20cos(1/3arccos(43/2 00√5))±√((17/18-2/3√20cos(1/3ar ccos(43/200√5))+40/9cos²(1/3arc cos(43/200√5)))/(1/3+2/3√20cos (1/3arccos(43/200√5)))); c=(2/3-2/3√20cos(1/3arccos(43/ 200√5)+2/3πn)±√(-4(17/18-2/3√20 cos(1/3arccos(43/200√5)+2/3πn)+ 40/9cos²(1/3arccos(43/200√5)))/(1/3+2/3√20cos(1/3arccos(43/20 0√5)))+28/3+8/3√20cos(1/3arcco s(43/200√5)))-8(2/3+1/3√20cos (1/3arccos(43/200√5)))²))/2, d=(2/3-2/3√20cos(1/3arccos(43/ 200√5)+2/3πn)-+√(-4(17/18-2/3√20cos(1/3arccos(43/200√5)+2/3πn)+40/9cos²(1/3arccos(43/200√5)))/(1/3+2/3√20cos(1/3arccos(43/20 0√5)))+28/3+8/3√20cos(1/3arcco s(43/200√5)))-8(2/3+1/3√20cos (1/3arccos(43/200√5)))²))/2
    1
  3329. -(1+x²)-¹,⁵x+(1+xy)-¹,⁵y=0+*->x [x=y,{x=0,y=0;{x=y,x=±√2; {-y⁷/9-((7/54y³+ 1,5/y+√((7/54y³+1,5/y)²+8/27²y⁶))¹/³ +(..-..)..)²y⁵+(2/3y⁶+3y²+1)((7/54y³+1 ,5/y+√((7/54y³+1,5/y)²+8/27²y⁶))¹/³+(..-..)..)-y³+2/3y=0,x=-y/3+(7/54y³+1, 5/y+√((7/54y³+1,5/y)²+8/27²y⁶))¹/³ +(..-..)..; max=0✓
    1
  3330. (n+1)²/n!=1/(n-2)!+3/(n-1)!+1/n! 5e
    1
  3331. На счёт этой дичи: Я ее тоже когда-то смотрел, слава богу ее уже давно не смотрю.
    1
  3332. (cosx-1)/x²=-sinx/(2x)=-1/2
    1
  3333. tp,tж n N n^(tж/tp) Родилось n^(tж/tp)*0,5N,умерло N. Выросло N(0,5 n^(tж/tp)-1). В итоге N*0,5n^(tж/tp) через tж лет. N(t)=N*0,5^(t/tж)n^(t/tp)
    1
  3334. H=v0sinat-gt²/2,L=v0cosat {1,35(s)=t,arctg(2/3)(rad)=a, v0=5,33(m/s).
    1
  3335. х[1904;2024],у[0;120] у=a+b+c+d,999a+99b+9c=x x:9,x=9n,n[213;224]a=1,b=9,c=3;4;5;6;7;8;9 a=2,b=0,c=0;..;2 x[1930;2024]
    1
  3336. (2R)²=a²+b²,R=0,5√(a²+b²) a+b=a+b✓,arct g(a/b),r/a*√(a²+b²)+r/b*√(a²+b²)=√(a²+b ²),r=ab/(b+a)
    1
  3337. a=√(10,25+0,5AC²)/3 arccos((61+0,5AC²)/6/√(10,25+0,5AC²)) √(21+5/36-4AC²/9),√(-36 4/9-7/9AC²)× arccos((-7AC²/2-528,5)/√(41+2AC²)/√(190,25-4AC²))-arccos((1,5AC²-20)/√(41+2AC²)/AC)=180°-arccos((A C²+40)/22/AC)-arccos((-2-5/22AC ²)/√(-328-7AC²)){12}
    1
  3338. f(x)=10^(x/50)-4*10^(x/100)-3*10 ^(-x/100)+12*10^(-x/50) f'(x)=ln10(10^(x/25)+2*10^(3x/100)+1,5*10^(x/100)-12)*10^(-x/50)/50=0 (10^(x/100)+0,5)⁴-1,5 (10^(x/100)+0,5)²+2,5(10^(x/100) +0,5)-12 15/16=0 (z-0,25)³+51/16(z-0,25)+183/256=0 z=0,25+(-183+√357'921)¹/³/8+(.. ..)..;0,25-(-183+√357'921)¹/³/16-(.. -..)..±√(3/4((-183+√357'921)¹/³/8+(..-..)..)²+51/16)i x=100lg(-0,5-√(0, 25+(-183+√357'921)¹/³/8+(.. -..)..)+2√(0,5√(13/4-0,25((-183+√357'92 1)¹/³/8+(..-..)..)+((-183+√357'921)¹/³/8+(..-..)..)²)+1/8-(-183+√357'921) ¹/³/32-(..-..)..))*+>x min=(-0,5-√(0, 25+(-183+√357'921)¹/³/8+(.. -..)..)+2√(0,5√(13/4-0,25((-183+√357'92 1)¹/³/8+(..-..)..)+((-183+√357'921)¹/³/8+(..-..)..)²)+1/8-(-183+√357'921) ¹/³/32-(..-..)..))²-4*(-0,5-√(0,25+(-183 +√357'921)¹/³/8+(.. -..)..)+2√(0,5√(1 3/4-0,25((-183+√357'92 1)¹/³/8+(.. -..)..)+((-183+√357'921)¹/³/8+(.. -..)..)²)+1/8-(-183+√357'921)¹/³/32- (..-..)..)-3/(-0,5-√(0,25+(-183+√357'9 21)¹/³/8+(.. -..)..)+2√(0,5√(13/4-0,2 5((-183+√357'921)¹/³/8+(..-..)..)+((- 183+√357'921)¹/³/8+(..-..)..)²)+1/8- (-183+√357'921)¹/³/32-(..-..)..)+12/ (-0,5-√(0, 25+(-183+√357'921)¹/³/8 +(.. -..)..)+2√(0,5√(13/4-0,25((-183+ √357'92 1)¹/³/8+(..-..)..)+((-183+√3 57'921)¹/³/8+(..-..)..)²)+1/8-(-183+√ 357'921)¹/³/32-(..-..)..))² 0/
    1
  3339. √4444488889=(2*10⁵+1)/3=66'667
    1
  3340. 8/3R=4 R=1,5 2√(1,5r)+2r=3 2r+2√1,5√r-3=0 r=(9-3√5)/4
    1
  3341. En=0;bC(b;n)x^(b+a-n+1)(-1)^n/(b+a- n+1)(1;∞)+En=0;bC(b;n)(-1)^n/(n+1) =∞
    1
  3342. (√8+√5-√3)(-5+√40)=3√5+5√3-2√30
    1
  3343. 3х²-4|х²-1|+х-1=0,[{х²-1≥0,-х²+х+3=0;{х²-1<0,7х²+х-5=0;[{(х-1)(х+1)≥0+*+>х, х=(-1±√(1 -4-1*3))/-2;{(х-1)(х+1)<0+ **+>х,х=(-1±√(1-4*7 *-5))/14;[{хє(-∞;-1]U [1;∞),[x=1/2-0,5√13,x=0,5+0,5√13;{хє(& 1;1),[х=-1/14+√141/14,х=-1/14-√141/14;[х=0,5-0,5√13,х=0,5+0,5√13,х=-1/14+√141/14,х=-1/14-√141/14.
    1
  3344. a(n+1)=(an+c)/(1-anc)=(a(n-1)(1-c²)+2c)/(1-c²-2a(n-1)c)=(a0+tg ((n+1)arctgc))/(1-a0tg((n+1)arctg c)) (a0+tg(2025arctgc))/(a0-1/tg (2025arctgc))/tg(2025arctgc)>0
    1
  3345. X/(1-x)=$f(x)dx f(x)=1/(x-1)²
    1
  3346. Было это не на Куликовом поле,а на Куличковом.
    1
  3347. X=1;5 $(1;5)(2x²-12x+10)dx=2x³/3 -6x2+10x(1;5)=-21 1/3{21 1/3}
    1
  3348. {x=-3|y|-5,(x-a)²+y²
    1
  3349. 1/4/(1/2*±1)⁶=16
    1
  3350. 1/3/(7/9)=3/7 Sм=1/21S∆ S0=2/3S∆-6/21S∆-5/21S∆=1/7S∆=1/7*√(21(8)(7)*6)=12
    1
  3351. [5;5,5) 9-4=5✓[4,5;5,5)
    1
  3352. (2+S1)/(3+S2),S2/3+S1=1,S1+S2=3 {S2=3,S1=0.
    1
  3353. πr²-4*9, 6²*5=3²*17+3²-2*3√17*3cosa,a=arccos-18/18/√17,(360°-2a)/2=180°-a,sin(180°-a)=r/(3√5), r=sin(arccos-1/√17)*3√5=√(1-(-1/√17)²)*3√5=4/√17*3√5, π(12√85/17)²-81=144π*85/17²-81=720π/17-81
    1
  3354. p(%)V/(m/h^(2;3)*k)=p(‰)
    1
  3355. (х³+у³)/(х²+у2-ху)+1=х+у+1
    1
  3356. N=49/3a+7/3b+1/3c,a+25/4b-5c=0;b:4,b=0;4 [{a=5,c=1;{c=6,a=5;(5;0;1;82)(5;4;6;93)
    1
  3357. 4x²-2x-56=0 x=(1±15)/4=4;-3,5✓
    1
  3358. -log(x/6)(lg√(6-x)/lgx)>lg(|x|/x),{x/6>0,x/6≠1,√(6-x)>0,x≠1,|x|/x>0;{x>0,x≠6,х≠1,x <6,x>0; хє(0;1)U(1;6) -log(x/6)(lg√(6-x)/lgx)>0,log(x/6)(lg√(6-x)/lgx)<0,lg√(6-x)/lgx>0,1-°+°5->x хє(1;5),=>хє(1;5)
    1
  3359. (47-21√5)(3-√5)/4=(123-55√5)/2 (47-21√5)/2,85-38√5✓
    1
  3360. y,4-y, 10/y,1,8y 4-y+1,8y=6,y=2,5 x=1,5*4=6
    1
  3361. (-2х+9)³=(х+3)², -8х³+3(-2х)²*9+3(-2х)*9²+9³-х²-6х-9=0, х³-107/8х²+492/8х-9*10=0, (х-107/24)³+(61,5-3*107²/24²)(х-107/24)-90+107³/24³+(61,5-59 1 21/192)*107/24=0, х-107/24=(45-107³/24³/2-107/48*1 167/192+√((45-1073/24³/2-107/48*1 167/192)²+(1 167/192)³/27))^(1/3)+(45-107³/24³/2-107/48*1 167/192-√((45-1073/24³/2-107/48*1 167/192)²+(1 167/192)³/27))^(1/3), х=4 11/24+(45-107³/24³/2-107/48*1 167/192+√((45-1073/24³/2-107/48*1 167/192)²+(1 167/192)³/27))^(1/3) 107+(45-107³/24³/2-107/48*1 167/192-√((45-1073/24³/2-107/48*1 167/192)²+(1 167/192)³/27))^(1/3),+*- Макс. √(4 11/24+(45-107³/24³/2-107/48*1 167/192+√((45-1073/24³/2-107/48*1 167/192)²+(1 167/192)³/27))^(1/3) 107+(45-107³/24³/2-107/48*1 167/192-√((45-1073/24³/2-107/48*1 167/192)²+(1 167/192)³/27))^(1/3)+3)+(9-2(4 11/24+(45-107³/24³/2-107/48*1 167/192+√((45-1073/24³/2-107/48*1 167/192)²+(1 167/192)³/27))^(1/3) 107+(45-107³/24³/2-107/48*1 167/192-√((45-1073/24³/2-107/48*1 167/192)²+(1 167/192)³/27))^(1/3)))^(1/4)>√3, корни существуют, минимальное значение:х=-3, 0+√√(9-2(-3))>√√9=√3, х=4,5, √(4,5+3)=√7,5>√3, хє[-3;4,5] 107 749 107 11449|192 960 59 1849 1728 121
    1
  3362. √29/√π S=π*29/π•0,5=14,5✓
    1
  3363. Y=x±4√(x+c/8)✓
    1
  3364. arcsin((n-1)/2/n)=π/6
    1
  3365. y²-yx-x²=0 y=(1±√5)/2*x
    1
  3366. y=4/(x±ic)+c1
    1
  3367. π²/8-π/2(0,5ln2+4π/3/√3)+3,09
    1
  3368. X=0;1, 4=x✓
    1
  3369. Arccos(1/2)=60° √(a²+x²-ax)+√(b²+x ²-bx)=√(a²+b²+ab),x≥-b(a+2b)/(a-b) (A²+2ab+b²)x²-2abx(a+b)+b²a²=0 x=(1+√2)ab/(a+b)
    1
  3370. -W(-x)=y=f-¹(x)
    1
  3371. Arccos(23/27) tg(0,5arccos(23/27))*12=√((4/27)/(50/27))*12=12√2/5 S=288/25π
    1
  3372. √(2^x-9^x)=√2^x x=0
    1
  3373. 24En=1;∞1/n!/n(-1)^nx^n(1-24^n) (=)-23 сходится
    1
  3374. ab(a+b+2)/(ab-1) b(ba²-2a-b-2)/(ab-1)²= 0,a=(2±√(4-4b(-b-2)))/2/b=(1±√(b²+2b+ 1))/b[a=(b+2)/b,a=-1;+*+>a min=(b+2)/b*b(1+2/b+b+2)/((b+2)/b*b-1)=(b+2)(b²+3b+2)/b*(b+2-1)=(b+2)(b+1)(b+2)/b*(b+1)=b³+13b+4/b+6b²+12,3b²+13+4 b^-2+12b=0,3b⁴+12b³+13b²-4=0,b=-1,3b³+9b²+4b-4=0,(b+1)³-5/3(b+1)-2/3=0,b+ 1=(1/3+√(1/9+(-5/3)³/27))^(1/3)+(1/3- √(-44/3⁶))^(1/3),b=-1+2√(5/9)cos(arccos(9/√(125))/3+2πn/3),+*-1-*-√3/2;-0,5+ *0;-0,5-*√3/2;1+>b min=(-1+2√(5/9)co s(arccos(9/√(125))/3)³+13(-1+2√(5/ 9)cos(arccos(9/√(125))/3)+4/(-1+2√ (5/9)cos(arccos(9/√(125))/3)+6(-1 +2√(5/9)cos(arccos(9/√(125))/3)²+12
    1
  3375. y'=(1-x-y)/(x-y)=-5/-2=2,5 y'=-1/2
    1
  3376. S∆=0,5*4,5*36=81 1/√(1+3cosx)* √(1-cosx)/(1+2cosx) π²/4-$dx*x/√ (1+3cosx)*√(1-cosx)/(1+2cosx)(0; π/2)=π²/4-0,41
    1
  3377. 2^(х+1)=3 х=log2(3/2)✓
    1
  3378. [x²+x-16=0,x²-x-15=0;[x=(-1±√65)/2, x=(1±√61)/2.
    1
  3379. 19>680/36=18 8/9
    1
  3380. $sin√xdx/√x=$sinu/u*2udu=2$sinudu=2* -cosu+C=-2cos√x+C √x=u,x=u²,dx=2udu
    1
  3381. x/(1-x)+x²/(1-x)+..=x/(1-x)²
    1
  3382. 3(x+√3/3y+7√3/6)²-30,25≥-30,25
    1
  3383. S1+5+S3-S2-S4=x,S1/2=x/S2,(x+S2)/S4=3/S3 {S1+5+S3-S2-S4=x,-S2S1/2+S1+5+S3-S2=S4,S3=(3S1+6)/(S2S1/2+S2- 3)-3;x=S2S1/2 (S2-10/S1)/(S2-6/(S 1+2))<0 20>-4S1 S2(6/(S1+2);10/S1) x<5 A)
    1
  3384. (|x|-2+log6(5))*|x|≤0 +-2+log6(5)*-0-*2-log6(5)+>x x[-2+log6(5);2-log6(5)]
    1
  3385. 3x=x¹/²/3[x=0,x=1/81.
    1
  3386. -√3/27✓
    1
  3387. $x³e^-xdx=x³e^-x/-1-$3x²*-e^-Xdx=-x³e^-x+3x²e^-X/-1-$6x*-e^-xdx=-x³e^-x-3x²e^-x+6xe^-x/-1-$6*-e^-xdx=(-x³-3x²-6x)e^-x+6e^-x/-1+C=(-x³-3x²-6x-6)e^-x+C
    1
  3388. a²+b²=100,a+6=b+4 {b²-2b-48=0,a=b-2;b=8 a=6 S∆=30√3
    1
  3389. 2yy'(x)=y²+y'²
    1
  3390. diva=2xy-2xy+x²+y²=x²+y² $(-R;R)dx$(-√(R²-x²);√(R²-x²))dy$(0;H)(x²+y²)dz=$(-R; R)dx√(R²-x²)(2/3R²+4/3x²)H=R²(0,5R²arcs in(x/R)+x√(R²-x²)/2)-1/3x(R²-x²)¹,⁵(-R;R)=R² (0,5R²π/2)-R²(0,5R²*-π/2)=0,5πR⁴
    1
  3391. х≥1,х≤0 -1/(1+(3x-2)(3x-1))=-1 x=2/3×;1/3×
    1
  3392. 333=333✓
    1
  3393. $(-1;1)dx$(0;1)(1+yx)/√(1-x²)dy=$(-1;1) dx/√(1-x²)/xln|x+1|=-∞-$arcsinx/(x+1)/xdx(-1;1)-0,5/0=-∞
    1
  3394. UKL=15π(mm) UHN=9π UKL-UHN=6π(mm)
    1
  3395. 1/9/4=1/? ?=36
    1
  3396. a^(1/72)
    1
  3397. y=x^a^a+a^x^a+
    1
  3398. √(50^x-2³)<7-(5√2)^x,{x<log(5√2)7,x≥log(5√2)(2√2),log(5√2)(57/14)>x;x[log(5√2)(2√2);log(5√2)(57/14))
    1
  3399. А Ирина Пелихова говорила, что это иезуиты пытались присоединить Украину к России.
    1
  3400. f=333/2/3,14√(π•0,015²/0,25/(π•0, 05²*0,2+π*0,015²*0,05))=1,95Гц
    1
  3401. limx->0(sinx)/x=1
    1
  3402. 2f(x)=f(2x/(1-x²)),x=tga,2f(tga)=f(tg2a), f(tga)=ca f(x)=carctgx
    1
  3403. (R-6)²+18²=R² R=30
    1
  3404. ∆g=8π²l/T⁴b
    1
  3405. (1+√11)^x-+x=0 (1+√11)^xln(1+√11)-1=0 x=log(1+√11)(1/ln(1+√11))-*+>x min=log(1+√11)(eln(1+√11))>0 x=-0,49✓
    1
  3406. Ортодоксальные марксисты не марксисты,а мраксисты.
    1
  3407. tgx=tg(π/2-x-1) x=π/4-0,5+πn/2
    1
  3408. u'+6ut²=t²,u'/(1-6u)=t²,-1/6ln|u-1/6|=t³/3+c,u=±e^(-2t³-6c)+1/6
    1
  3409. x^x-¹=(2x)^(1/(2x)) x=0;2
    1
  3410. 16x⁵+31x-16=0,/>x=0,5(0=0)
    1
  3411. x=-i
    1
  3412. x≥0,x≤16 8=16-8√x x=1✓
    1
  3413. √(17-12√2)=3-2√2 a^x=±(√2-1) (a^3x+a^-3x)/(a^x-a^-x)=10√2/(√2-1 -(√2+1))=-5√2
    1
  3414. V/t=const D=√(const/v)
    1
  3415. {x=4-3y,[y=1,y=(1±√5)/2;{(1;1)((5-+3√5)/2;(1±√5)/2)}
    1
  3416. √(a²-4²) h=4√(a²-16)/a √(a²-3²) √(a²-16)/a=3/a a=5 4√(5²-16)/5=2,4 ..=3²/5=1,8 x=√(2,6²+1,8²)=√10
    1
  3417. 5x²+x+1
    1
  3418. S=14,75-1,25π
    1
  3419. 40(x+1)⁴-26(x+1)²+3=0 (x+1)²=(13±7)/40=1/2;3/20 x=-1±√0,5;-1±√(3/20)
    1
  3420. (y"')'/siny"'+1=0,-ln|cos(y"'/2)|+ln|sin(y"'/2)|+x=C,tg(y"'/2)=±e^(-x+C),y"'=2arctg(Ce^ -x)+2πn,y"=$2arctg(Ce^-x)dx+2πnx+C1,y '=$dx$2arctg(Ce^-x)dx+πnx²+C1x+C2,y=$dx$dx$2arctg(Ce^-x)dx+πnx³/3+C1x²/2+ C2x+C3,
    1
  3421. 7(7⁵⁰-1)/6, 259*25=6475
    1
  3422. y^(a+1):3^(a+1)=3^(a+1)/3^(a+1)=1
    1
  3423. log(y¹,⁵x¹,⁵/z¹,⁵)+log1,2=3/2 2,5log(1,2)=3/ 2 1,2^(5/3)=a
    1
  3424. Х²+(-2а-2)х+2а²+3а-6=0 х=а+1±√(-а²-а+7),ає[(-1-√29)/2;(-1+√29)/2]
    1
  3425. cosa=1/2 a=60° S=2*4*√3/2=4√3
    1
  3426. $(0;π/2)dx/(a²cos²x+b²sin²x)=$(0; =)dt/b²/((a/b)²+t²)=b-¹arctg(t/(a/b))/a(0;=)=π/2/(ab) tgx=t,x=arctgt,dx=dt/(1+t²)
    1
  3427. sin(wt+π/3)-sin(wt+1/3π)=0
    1
  3428. sin(x+arccos(2/√4,25))>-0,5/√4,25 [x+arccos(2/√4,25)>-arcsin(0,5/√4,25)+2π n,x+arccos(2/√4,25)<π-arcsin(-0,5/√4,25) +2πn;[x>-π/2+2πn,x<π/2+2arcsin(0,5/√4,2 5)+2πn.
    1
  3429. (c²-(b-a)²)(a+b-c)=-c³+c²(a+b)+c(b²-2ba +a²)-(b-a)²(b+a)≤abc c(c²-b²+3ab-a²)≥(b+ a)(c²-(a-b)²)
    1
  3430. h=1/(1+2+√3)=(3-√3)/6 h2=(3+√3)/6 l=hctg15°=(3-√3)/6(2+√3)=(3+√ 3)/6 l1=l-1/3=1/6+√3/6 ctga=l1/h2 =(1+√3)/6/((3+√3)/6)=1/√3 a=60° ?=15+60=75°
    1
  3431. 2)x²+1)⁰,⁵+ln(x+√(x²+1))(0;2)=2√5 +ln(2+√5)-2
    1
  3432. у"-ху'+у=0,
    1
  3433.  @snowmaiden3048  у"-ху'-у=0, (e^u*u'²+e^uu'u'')-xе^u*u'-e^u=0,u'²+u'u''-xu'-1=0, u'=-$(u'-x-1/u')dx=-u+x²/2+$dx/u'+c, u'+u-$dxu^(-1)(u')'=x²/2+c, u=ax²+bx+c, 2ax+b+ax²+bx+c-$dx/(2ax+b)=0,5x²+c, ax²+(2a+b)x+b+c-ln|x+b/2/a|/2/a=0,5x²+c, a=0,5, b=-2*0,5=-1,y=e^(0,5x²-x+c)
    1
  3434. x²+4x-4=0 x=-2±√8 (x-2)((x-1)²+(x-1)+3)=0 x=2 1 7/8<2
    1
  3435. P(x)=2x²-3x+4 A=(-1 2 0) (2 1 -3) (0 -1 2) P(A)=2(5 0 -6)-3(-1 2 0)+4(1 0 0)= (2 8 -9). (2 1 -3). (0 1 0) (-2 -3 7) (0 -1 2). (0 0 1) (10 0 -12)+(3 -6 0)+(4 0 0)=(17 -6 -12) (4 16 -18). (-6 -3 9).(0 4 0). (-2 17 -9) (-8 -12 28) (0 3 -6). (0 0 4). (-8 -9 26)
    1
  3436. [(x²+1)/10]+[10/(x²+1)]=1,[{x²/10+1/10≥ 1,<2;10/(x²+1)<1;{x²/10+1/10<1,10/(x² +1)≥1,<2;[xє(-√19;-3)U(3;√19),{x<3,x>- 3,x[-3;3],(x-2)(x+2)/(x2+1)>0+°-2-°2+>x;[xє(-√19;-3)U(3;√19),0/;xє(-√19;-3)U(3;√ 19)
    1
  3437. (x+m)³-3mx-m³+1,5n-1,5f(x)=0 D=(-m³+1,5n-1,5f(x))²/4-m³<0 (n-2/3m³-f(x)-4/3m¹,⁵)(n-2/3m³-f(x)+4/3m¹,⁵)<0 n(2/3m³+f(x)-4/3m¹,⁵; 2/3m³+f(x)+4/3m¹,⁵)
    1
  3438. dC/(C-Cy)=-v/Vst ln|C-Cy|=-v/Vt+c C=e^(-v/Vt)c+Cy
    1
  3439. AD/sin62°sinx,AD/sin(x+62°)=BD/sin56° ±86°-31°+πn=x x(0;62°) x=55°C)
    1
  3440. Уважаемый Сигизмунд! Почему на Вашей футболке написана зима?
    1
  3441. 2*8/3+5/3=7
    1
  3442. X≥0,[[x=3,x=-1;×.{3}A)
    1
  3443. (a-6)√5=a*2/√5 a=10 S=a*(a-6)*2=10*4*2=80
    1
  3444. {c=2-a-b,a=-b/2+1±√(-3/4b²+b); b(b-4/3)≤0 b=0;1 a=1;1;0 c=1;0;1{(1;0;1)(1;1;0)(0;1;1)}
    1
  3445. a=4,(0,5(9-8x+7cos(2x))-⁰,⁵(-8-14sin (2x))-b)/(2x)=(-1-b)/0 b=-1,-1,875✓
    1
  3446. Потому что только он катализирует органические вещества.
    1
  3447. 2^(7x/8+3/8)+(2^(7/8x+3/8))³=520 2^(7/8x+3/8)=8 7/8x+3/8=3 x=3
    1
  3448. 4+6=0 7+6=3✓
    1
  3449. 16/25=S/(S+9) 16=S
    1
  3450. $(-1;1)(2-2x²)dx=2x-2x³/3(-1;1)=2* 2-2/3*2=8/3
    1
  3451. 12,5+0,5*7,5*10=50(cm²)
    1
  3452. {x²+y²=6,x³+y³=14;{x+y=a,xy=b;{b=a²/2-3,a³-18a+28=0;a=(-14+√ (196-6³))¹/³+(..-..)..=2√6cos(1/3ar ccos(-14/36√6)+2/3πn),b=12cos²(1/3ar ccos(-14/36√6)+2/3πn)-3 {y=2√6cos(1/3arccos(-14/36√6)+ 2/3πn)-x,x²-2√6cos(1/3arccos(-14/ 36√6)+2/3πn)x+12cos²(1/3arccos (-14/36√6)+2/3πn)-3=0;x=√6cos(1/3arccos(-14/36√6)+4/3π)±√(-3cos (2/3arccos(-14/36√6)+8/3π)) n=2 y=√6cos(1/3arccos(-14/36√6)+4/3π)-+√(-3cos(2/3arccos(-14/36√6)+ 8/3π))✓
    1
  3453. {a²+b²=13,a²+c²=29,b²+c²=34;{a²=4,b²=9,c²=25;(±2;±3;±5)a³+b³+c³ =±8±27±125=±160;±90;±106;±144
    1
  3454. {x=1/2log3(32),y=1/5log2(25); xy=log2(5)/log2(3)=log3(5) 5^(3x-¹y-¹)=27
    1
  3455. (x-2)!=2(x+1) x-2=4,x=6 4!=14×
    1
  3456. X²-x-1 ax¹⁷+bx¹⁶+1=(2584a+1597b)x+1597a+987b+1=0 {a=-1597,b=2584.
    1
  3457. 2a√(16-a²)=2√(64-(a²-8)²)≤16
    1
  3458. $(0;∞)|sint|e^-tdt=e^-t(-0,5sint-0,5cost)|(2πn;π+2πn)+e^-t(0,5sint+0,5cost)|(π+2π n;2π+2πn)=e^(-π-2πn)(0-0,5*1)-e^(-2πn)(0-0,5*1)+e^(-2π-2πn)(0+0,5)-e^(-π-2πn)(0+0,5*-1)=(e^-π+0,5+0,5e^(-2π))/(1-e^( 2π)),n≥0 e^-t(c1sint+c2cost)'=-e^-t(c1sint+c2cost)+e^-t(c1cost-c2sint){-c1-c2=1,-c2+c1=0;{c1=-0,5,c2=-0,5;{-c1-c2=-1,-c2+c1=0;{c1=0,5,c2=0,5.
    1
  3459. 13/e<8 2⁵>25
    1
  3460. -sinxcos(2x)..cos(nx)+cosx((-2sin (2x)cos(3x)-3cos(2x)sin(3x))..cos(nx)+..)=-cosxcos(2x)..cos(nx)(tgx+2t g(2x)+..+ntg(nx))=0,x=π/2+πm;..;(π/2+πm)/n;?+*0->x f''(x)=cosxcos(2x)..cos(nx)((tgx+2t g(2x)+..+ntg(nx))²-cos-²x-cos-²(2x) -..-cos-²(nx))=0 f''(0)=-n n>2023
    1
  3461. x⁵-5x³+5x=a⁵+1/a⁵ x³(x²-5)+5x-a⁵-1/a⁵=0, 5x⁴-15x²+5=0,x²=(15±√(15²-4*5*5))/10 [x²=1,5+0,5√5,x²=1,5-0,5√5;[x=±√(1,5+0,5 √5),x=±√(1,5-0,5√5);+*√(1,5+0,5√5)--√(1 ,5-0,5√5)*+*√(1,5-0,5√5)-√(1,5+0,5√5)*+>x max=-2,5√5-5,5+2,5√5+7,5=2,min=( √1,25+0,5)⁵-5(-√1,25+0,5)³+5(-√1,25+0,5)=5/2√5+11/2,max=-2,5√5-5,5,min=-2 a⁵+ 1/a⁵є(-∞;-2]U[2;∞), 1реш.,если а⁵+1/а⁵>2,5√5+5,5 (а¹⁰-(2,5√5+5,5)а⁵+1)/а⁵>0,(а⁵-(1,25√5+2,75+√(57,5+27,5√5)/2))(а⁵ (1,25√5+2,75-√(57,5+√5*27,5)/2))/а⁵>0, 0°+°..-√-°...+√+>а ає(0;(1,25√5+0,75-√(5 7,5+√5*27,5)/2)⁰,²)U((1,25√5+0,75+√(5 7,5+√5*27,5)/2)⁰,²;∞),2реш.а{(1,25√5+0 ,75-√(5 7,5+√5*27,5)/2)⁰,²;(1,25√5+0,75+ √(57,5+√5*27,5)/2)⁰,²},3 реш.а⁵+1/а⁵>-2, 5√5-5,5,(а¹⁰+(2,5√5+5,5)а⁵+1)/а⁵>0,(а⁵-(- 1,15√5-2,75+√(57,5+27,5√5)/2))(а⁵-(-1, 25√5-2,75-√(57,5+27,5√5)/2))/а⁵>0,(а-(-1, 25√5-2,75-√(57,5+27,5√5)/2)⁰,²)(а-(-1, 25√5-2,75+√(57,5+27,5√5)/2)⁰,²)/а⁵>0 ..-√..-°-..+√..+°0-°+>а ає((-1,25√5-2,75-√ (57,5+27,5√5)/2)⁰,²;(-1, 25√5-2,75+√(57 ,5+27,5√5)/2)⁰,²)U(0;∞),ає(-∞;0)U((1, 25√5+2,75-√(57,5+27,5√5)/2)⁰,²;(1,25√ 5+2,75+√(57,5+27,5√5)/2)⁰,²),ає((-1,25 √5-2,75-√(57,5+27,5√5)/2)⁰,²;(-1,25√5 2,75+√(57,5+27,5√5)/2)⁰,²)U((1,25√5+ 2,75-√(57,5+27,5√5)/2)⁰,²;(1,25√5+2,75+ √(57,5+27,5√5)/2)⁰,²),4реш.a⁵+1/a⁵=-2,5 √5+5,5,a¹⁰+(2,5√5-5,5)a⁵+1=0,a⁵=(-2,5√5+5,5±√((2,5√5-5,5)²-4*1))/2=-1,25√5+2,75 ±√(57,5-27,5√5)/2 aє{(-1,25√5+2,75±√(5 7,5-27,5)/2)⁰,²},5реш.a⁵+1/a⁵є(-2;2) 0/.
    1
  3462. 3,2;4,5;6,8;9,11;12,14 12N
    1
  3463. E^(-e^((1-х)lnx)lnx)e^((1-x)lnx)(lnx+1)(lnx-1/x)=0[x=1/e,x=e^W(1). +*1/e-*e^W(1)+>x max=e^e^(-1+1/e)<2⁸ min=e^(-1/e)<2⁸×
    1
  3464. I=M/10R²
    1
  3465. (n+p)(m+p)(m+n)=0 [n=-p,m=-p,m=-n;1/m²⁰²³-1/m²⁰²³=0
    1
  3466. R=v0²/g/cosa
    1
  3467. (x²-6x+a²+2a)/(2x²-ax-a²)=0,2 разл.реш. {х=(6±√(36-4(а²+2а)))/2,2х²-ах-а²≠0;{х=3 ±√(-а²-2а+9),х≠(а±√(а²-4*2*а²))/4=а/4± √9а/4;{х=3±√(-а²-2а+9),[х≠а,х≠-0,5а;-а²-2 а+9>0,(а-(2+√(4-4*-1*9))/-2)(а-(2-√4 0)/-2)<0,-1-√10+°-1+√10-°+>а,ає(-1-√10; 1+√10),3+√(-а²-2а+9)=а,√(-а²-2а+9)=-3 +а,{-а²-2а+9=9-6а+а²,-3+а≥0;{-2а²+4а=0, а≥3;{-2а(а-2)=0,а≥3;{[а=0,а=2,а≥3;0/3+√ (-а²-2а+9)=-0,5а,√(-а²-2а+9)=-3-0,5а≥0,{-а²-2а+9=9+3а+0,25а²,-3-0,5а≥0;{-1,25а²-5а=0,а≤-6;{[а=0,а=-4;а≤-6;0/ 3-√(-а²-2а+9)=а,√(-а²-2а+9)=3-а,а=0;2 3-√(-а²-2а+9)=-0,5а,√(-а²-2а+9)=3+0,5а,а=0;-4 ає(-1-√10;-4)U(-4;0)U(0;2)U(2;-1+√1 0)
    1
  3468. $(1;∞)e^(-(p-2)t)(t+1)dt=e^(-(p-2)t)(t+1)/-(p-2)-e^(-(p-2)t)(t+1)/(p-2)² (1;∞)=-2e^(-p+2)/(p-2)+2e^(-(p-2))/(p-2)²
    1
  3469. 1/n³-3/n²+6(1/n-1/(n+1))-3/(n+ 1)²-1/(n+1)³ 10-π²✓
    1
  3470. a+a+2a+0,5a=4,5a=4 a=8/9(cm) S=2²+4²+1²+(4/9)²+(8/9)²+(2/9)²=22 1/27(cm²)
    1
  3471. 6/√(10²-6²)=3/4 0,5*10*10*3/4=75/2
    1
  3472. a^(k+k²-2023*1011)=a^1<0
    1
  3473. (X+1,5(y+1))²-2,25(y+5)²=(x-6)(x+3y +9)
    1
  3474. х²+2а=х+|х²-а|,[{х²-а≥0,х²+2а=х+х²-а;{х²-а<0,х²+2а=х-х²+а;[{(х-√а)(х+√а)≥0,+*+>х х=3а;{(х-√а)(х+√а)<0,+*+>х 2х²-х+а=0;[{хє(-∞;-√а]U [√a;+∞),x=3a;{xє(-√а;√а),х=(1±√(1-4*2 а))/4;[{а≥0,хє[√a;+∞),x=3a;{а<0,х=3а;{хє(-√а;√а),х=1/4±√(1-8а)/4,а ≥0,1-8а≥0,а≤1/8,√а>1/4+√(1-8а)/4,√а -1/4>√(1-8а)/4,а-0,5√а+1/16>(1-8а)/16, 1,5а-0,5√а>0,√а(√а-1/3)>0,0°-°1/9+>а ає(1/9;+∞),ає(1/9;1/8],{1/4-√(1-8а)/4>-√а,1/4-√(1-8а)/4<√а;{√(1-8а)/4<1/4+ √а,[{1/4-√(1-8а)≥0,1/16-√(1-8а)/8+(1-8а)/16<а;{1/4-√(1-8а)/4<0,а≥0; {-1,5а<√а/2,[{15/128≤а,√(1-8а)/8>-1,5а+1/8;{а<0,а≥0;-13/256 {а>0,[а>15/128;0/;ає(15/128;+∞) 3а≥√а,√а(3√а-1)≥0,√а(√а-1/3)≥0+*0-*1/9+>а [{ає{0}U[1/9;+∞),x=3a;{а<0,х=3а;[х=1/4+√(1-8а)/4,ає(1/9;1/8]; х=1/4-√(1-8а)/4,ає(15/128;1/8];\*0*|1/9/*|15/128/'*1/8/>a ає(15/128;1/8] 0/
    1
  3475. (ln(2π)/2+0,5lnn)/n^n+(lnn-1)/n^(n- 1),q=0✓
    1
  3476. a²+b²-0,5ab=c² cosC=0,25 sinC=√15/4 B)
    1
  3477. 697/150=4 97/150 5 человек!
    1
  3478. (1+m)m(3n-4m-2)=12144 m=1;-2;2;-3;3;-4;11;-12;22;-23;23;-24 2⁴*3*11*23 n=2029;×;678;×;354;×;46;×;38;-22;×;-24{(1;2029)(678;2)(354;3)(46;11)(46;22)(38;22)(-23;-22)(-24;-24)}
    1
  3479. (x-y)(1+i)=7(1+i) x=y+7 z=y+7+yi
    1
  3480. (0;±1)(±4;±3) х²-2у²=-2,хє[√2у-1/√2/у;√2 у],
    1
  3481. (1+n)/2*n*(π/n)²=π²(1+n)/2/n=π²/2
    1
  3482. 7-А+9-А=7,А=4,5
    1
  3483. S=25/2(π/2-1)+12=25π/4-0,5 S=75π/4+0,5 1/4(75π+2) 77✓
    1
  3484. limn->∞((4n/e)/n)=4/e
    1
  3485. 33:20 Бедность.
    1
  3486. Sin80°/sin60°,0,5/sin80° 0,5/sin80°/sinx=sin80°/√3*2/sin(150°-x) Arctg(cos10°/(1+√3cos10°))=x {20°}
    1
  3487. √5>1 199/294
    1
  3488. S=√3/2-1/4π
    1
  3489. a[1;n-1],b[0;n-1] 318=(an²+b)(n+1) ≤n⁴-1 n≥319¹/⁴=4,.. 0≥(n+1/3)³-1/3(n+1/3)-317 25/27 n+1/3≤(158 26/27+√((158 26/27)² -1/27²))¹/³+(..-..)..=7 n≤6 2/3 318=2*3*53 n=5 a*25+b=53 a=2,b=3 2+3+5=10
    1
  3490. f:Z=>Z, f(2a)+2f(b)=f(f(a+b)), f(x)=€m=0 n amx^m, €m=0 n am(2a)^m+2€m=0 n amb^m=€m=0 n am(€m=0 n am(a+b)^m)^m, a0+a1*2a+..+an(2a)^n+2 a0+2a1b+..+2anb^n=a0+a1(€m=0 n am(a+b)^m)+...+an(€m=0 n am(a+b)^m) ^n, 2a0+2a1(a+b)+..+2an(2^(n-1)a^n+b ^n)-a0-a1(a0+a1(a+b)..+an(a+b)^n)-..-a n(a0+a1(a+b)+...+an(a+b)^n)^n=0, {a0-a1 a0-...-ana0^n=0, 2a1-a1²-..-an(n-1)na0a1= 0,..., -an*an^n=0, {{a0=0, 1-a1-..-ana1^ (n-1)=0; {a1=0, 2-a1-...-an(n-1)a0^ (n-1)=0; ...{an=0; {{a0=0, 1-a1-..a(n-1)^n=0; {a1=0, 2-a1-...-a(n-1)(n-2)(n-1)a0=0; ...{-a(n-1)*a(n-1)^(n-1)=0,{an=0;[a1,..,an=0; f(x)=0,
    1
  3491. x⁰,²⁵(√(x⁰,⁵+1)²-√(x-1)-1,5)=0[x=0,x=1,5625;
    1
  3492. 37'505✓
    1
  3493. xy=-12,5±6,5=-6;-19[{x=y+5,y=-2,5±0,5;{x=y+5,y=-2,5±√-12,75;{(3;-2)(2;-3)}13✓
    1
  3494. sin((2n+1)x)/(2n+1)/(sin((2n-1)x)/(2n-1)) =(2n+1)/(2n-1)=1,xє(-1;1) сходится,x=1: En=1∞sin(2n+1)/(2n+1)->$(1;∞)sin(2n +1)/(2n+1)dn=конеч. числ.,а следовате льно,ряд сходится,х=-1:En=1∞-sin(2n+ 1)/(2n+1) сходится,хє[-1;1].
    1
  3495. $(1;x)f(x)dx=y y'-1/xy=-x-x² y=cx-x-x²/2 f(x)=c-1-x
    1
  3496. Yx²-x+y³-3y=0 x=(1±√(-4y⁴+12y²+1))/2/y ±√(-4y⁴+12y²+1)=3y y=±1 x=(1±3)/±2=2;1{(2;1)(1;-1)}
    1
  3497. 24/35(cm)
    1
  3498. {d=(ab-16)/c,a=(c+16b)/(c²+b²);{(1;0;1;-16)(-1;0;-1;16)(1;16;1;0)(-1;-16;-1;0)}
    1
  3499. S=8(π/6-0,5)+4=4/3π
    1
  3500. 0,25/√(0,5+0,5√17)(1/((x+2-√(0,5+0,5√17))²+0,5√17-0,5)-1/((x+2+√(0,5+0,5√17))²+0,5√17-0,5)) 0,25/√(0,5+0,5√17)(arctg((x+2-√(0, 5+0,5√17))/√(0,5√17-0,5))/√(0,5√17 -0,5)-arctg((x+2+√(0,5+0,5√17))/√(0, 5√17-0,5))/√(0,5√17-0,5))+c
    1
  3501. 6!*8(cos(4πn/7)cos(6/7πn)cos(2/7πn) +cos(4πn/7)cos(6/7πn)+cos(4/7πn)co s(2/7πn)+cos(4/7πn)+cos(6/7πn)cos (2/7πn)+cos(6/7πn)+cos(2πn/7)+1)=57 60(1 1/8+cos(2π/7)-cos(3/7π));5760(1 1/8+2cos(2/7π)-cos(1/7π)-2cos(3/7π));5760(1 1/8-0,5cos(3/7π}+0,5cos(2/7π)-c os(1/7π));5760(1 1/8-2,5cos(1/7π)+1,5c os(2/7π)-cos(3/7π))...
    1
  3502. (1+√(0,5√17+0,5)+i√(0,5√17-0,5))/2
    1
  3503. -Xcosx+sinx(-π;π)=2π
    1
  3504. √((AE+41)15*26AE)=(AE+41)*15 (AE+41) *15(26AE-(AE+41)15)=0,[AE=-41,AE=55 10/11;AE=55 10/11 S=96 10/11*15= 1453 7/11
    1
  3505. 0=(x-7-2)((x-7)²+2(x-7)+3) x=9
    1
  3506. x=(-AB+AC)/2 y=√((AB+AC)²AB²A C²/(-AB²-AC²+10/3ABAC)/(AB²+ AC²-2ABAC)*4/9-1/2ACAB) √(284/81(ABAC)²+(AB²+AC²-20/9 ABAC)²)√(ACAB)/√(-(AB-3AC)(AB- 1/3AC))/(-AB+AC)²√2=tg(/_A/2-90°+/_B)=-(AB-AC)/√(-(AB-3AC)(AB-A C/3)) При некоторых условиях да.
    1
  3507. 6En=0;∞1/6^((3n+n²)/2) Т.к. НОК всех чисел =∞,то числитель и знаменатель =∞,но при этом взаимно просты. Следовательно, число иррациональное.
    1
  3508. 4/3=x/(5-x), 20/3-4/3*x=x, x=-20/3/(-7/3?=20/7, 5-20/7=15/7 4²=CO²+(20/7)²-2C O*20/7*cos/_AOC, 3²=CO²+(15/7)²-2CO 15/7*cos(180°-/_AOC), cos/_AOC=(CO² +400/49-16)/CO/40*7, cos/_AOC=(9-CO ²-225/49)/30*7/CO, (CO² +400/49-16)/CO/40*7=(9-CO ²-225/49)/30*7/CO, CO²+(400-490-294)/16=(-CO²+216/49) 4/3, CO²+(-90-294)/16+4/3*CO²-72/49 4=0,CO²=(384/16+288/49)/(7/3)= (192/8+288/49)/7*3=(24+288/49)/7*3=(216+960+288)/343*3=1464/343*3 =4392/343, CO=√(4392/343) R=√(4392 /343)/√2=√(2196/343) x=15/7-2√(549 7)/49=15/7-2*3/49*√(61*7)
    1
  3509. 0=n²+n(-4k-1)+4k²-2 n=2k+(1±√(8k+9))/2 n[2;20],k[1;n-1] 0≤k(-2+k) k[4;12] k[1;7] √(8k+9)≥-2k+1✓ k=5,n=7 k=9,n=14 k=2,n=7 k=5,n=14{(5;7)(9;14)(2;7)(5;14)}
    1
  3510. √40/(4/3√3+6)=(-2√30+9√10)/23
    1
  3511. {b=(5-ax)/y,y=(10-ax²)/(5-ax), x=(6a²+6 15a+300)(7a-15)/a/(101a³-564a²+595a+ 75),[a=0,a=-205,12,a=-50,6,a=-1,76,a=-0,49, a=4,63*10-⁵,a=2,14; {(-205,12;2,29;-0,001; 2,09)(-50,6;2,90;0,0077;1,86)(-1,76;3,91; 3,63;2,91)(-0,49;2,50;-0,0094;2)(4,63*10-⁵; -5,43*10-⁵;-1295515,49;-1195'833,26)(2,14;2,37;0,063;2,05)} ax⁵+by⁵=91,32;64, 56;-293,38;80;3,02*10²⁶;85,81
    1
  3512. $(0!3)dx*e^x²x/3=e^x²/6(0;3)=e⁹/6-1/6
    1
  3513. y=1+(5x+5)/(x²+x+1) y'=-5x(x+2)/(x² +x+1)²=0 x=-2;0-+->x min=-2/3 max=6
    1
  3514. Прямая калька с Джорджа Оруелла "1984".
    1
  3515. log4(n)/2=√log4(n)[n=1,n=4^4.
    1
  3516. (1 0|-1/18√3) (0 1|16/9√3) A+b=31/18√3
    1
  3517. limx->0(6*cos²(2x²-x)/(4x-1))=-6
    1
  3518. 2²⁰²¹:100 25=5²,ф()=25(1-1/5)=20 2019:2 0=19(по 20) 4*2¹⁹=32*56²=32*36=..52
    1
  3519. Arctg(ctg9°)=81°
    1
  3520. a(n+1)=10an/(5+an) a1=1/13, an=5/(64/2^(n-1)+1)
    1
  3521. 2/log(2)(2x-2)+3/log(2)(4x-4)≤8/(log(3) 27+log(2)(x-1)),{2x-2>0,4x-4>0,x-1>0;{x>1,x>1,x>1;хє(1;+∞) 2/(log(2)(x-1)+1)+ 3/(log(2)(x-1)+2)-8/(3+log(2)(x-1))≤0, (2(log(2)(x-1)+2)(log(2)(x-1)+3)+3(log(2)(x-1)+1)(log(2)(x-1)+3)-8(log(2)(x-1)+1)(log(2)(x-1)+2))/(log(2)(x-1)+1)/(log(2)(x-1)+2)/(log(2)(x-1)+3)≤0,(2log²(2)(x-1)+10log(2)(x-1)+12+3log²(2)(x-1)+12 log(2)(x-1)+9-8log²(2)(x-1)-24log(2)(x-1)-16)/(log(2)(x-1)+1)/(log(2)(x-1)+2)/(log(2)(x-1)+3)≤0,(-3log²(x-1)-2log(2)(x-1) +5)/(log(2)(x-1)+1)/(log(2)(x-1)+2)/(log (2)(x-1)+3)≤0,(log(2)(x-1)-(2+√(4-4*3* 5))/-6)(log(2)(x-1)-(-1/3+√64/6))/(log(2)(x-1)+1)/(log(2)(x-1)+2)/(log(2)(x-1)+3)≥ 0,-°-3+°-2*-1 2/3+°-1-1*+>log(2)(x-1) log(2)(x-1)є(-3;-2)U[-1 2/3;-1)U[1;+∞) [x-1 >1/8,x-1<1/4;x-1≥1/2/4^(1/3),x-1≤1/2;x-1≥2;[x>1 1/8,x<1 1/4,x≥1+2^(-1 2/3),x≤1,5, x≥3;хє(1 1/8;1 1/4)U[1+2^(-1 2/3);1,5]U [3;+∞)
    1
  3522. -√(R²-(4-√(R²-20,25))²)+√(R²-0,5²)=2 R≥4,25,(R²-40,5)⁴-4760(R²-40,5)²+3'404'608(R²-40,5)+131'298'532=0 z³-2380z²-31'386'033z-425'576²=0 z=8539;-3080±3024i R=√(40,5-√8539+4√(7√5941-385))
    1
  3523. $(-0,5cos((n+1)x)+0,5cos((n-1)x)) dx=-0,5sin((n+1)x)/(n+1)+0,5sin((n -1)x)/(n-1)+c
    1
  3524. 2√х=1,5х[х=0,16/9=х.
    1
  3525. 1/((a+1/a)²-3)=1/2022
    1
  3526. y'=z,z"+2z'+z=0,k²+2k+1=0,k=-1,×2 z=c1 e^-x+c2xe^-x,y=-c1e^-x+c2x*-e^-x-c2^-x+c3=c1e^-x+c2xe^-x+c3
    1
  3527. Sinx1chy+cosx1Sh(y)i=1+i(π+2πn) {sinx1chy=1,e^2y-2(π+2πn)/cosx1 e^y-1=0;e^y=(π+2πn)/cosx1+√((π+ 2πn)²/cos²x1+1) sin²x1±sinx1(π+2πn)-1=0,x1(2πm;π+2πm) x1=arcsin((-|π+2πn|+√((π+2πn)²+ 4))/2)(-1)^k+πk y=ln(±√2/2√((π+2πn)²+|+π+2πn|√((π +2πn)²+4))+(|π+2πn|+√((π+2π)²+ 4))/2) x=arcsin((-|π+2πn|+√((π+2π n)²+4))/2)+2πk+ln(±√2/2√((π+2πn)² +|π+2πn|√((π+2πn)²+4))+(|π+2πn|+√ ((π+2π)²+4))/2)i;π-arcsin((-|π+2πn|+ √((π+2πn)²+4))/2)+2πk+ln(±√2/2√ ((π+2πn)²+|π+2πn|√((π +2πn)²+4))+(|π+2πn|+√((π+2π)²+ 4))/2)i
    1
  3528. х^(1/3/√х)=9^(1/9),х=9:9^(1/3/√9)=9 ^(1/9) е^(1/3*х^-0,5lnx)'=е^(1/3*х^-0, 5lnx)(-1/6x^-1,5lnx+1/3x^-0,5*1/x)=0, x^-1,5lnx-2x^-1,5=0,lnx-2=0,x=e^2 +*->x max=(e^2)^(1/3/e)=e^(2/3/e),e²<9,x=2^ (1/2/√2)=1+√2/4*1+√2/4(√2/4-1)/2!+... =1,35..+0,35*-0,325+...=1,24>9^(1/9)=(1, 3..)^(1/3)=1,1.. 7^(1/3/√7)=7^(1/3/2,65)= 7^(1/7,95)=1,32..^(1 1/159)>1,1..x=6,141 175 70 105 0,11375
    1
  3529. (х-13/4)⁴+106 5/8(х-13/4)²+663 3/8(х-13/4)+919 47/256=0 х=13/4 -√(-853/12+2(927953411/55296+11√12712992520699/6144)¹/³+ 716771/(576(927953411/55296+ 11√12712992520699/6144)¹/³))/2±√(-853/6-2(927953411/55296+ 11√12712992520699/6144)¹/³- 716771/(576(927953411/55296+ 11√12712992520699/6144)¹/³)+ 5307/(4√(-853/12+2(927953411/ 55296+11√12712992520699/6144)¹/³+716771/(576(927953411/ 55296+11√12712992520699/6144)¹/³))))/2
    1
  3530. √(а²+9) 1/(0,5√(а²+9))=а/3 3⁰,⁵=а S=3√3
    1
  3531. (h-x/2)/(x-2/3h)=0,5 h=3/4x 69=11/24x² x=6√(46/11)
    1
  3532. x²e^(2x),(2x+2x²)e^(2x),f^(n)(x)=(cn+ bnx+anx²)e^(2x) {bn=2^n*n,an=2^n,cn=2^n*(n-1)n/4; y^(20)=(2¹⁸*19*18+2²⁰*20x+2²⁰x²)e^(2x)
    1
  3533. X=(17/2±13/2)/10=1,5;0,2
    1
  3534. 3x=x¹/³/3 [x=0,x=±1/27.{0;±1/27}
    1
  3535. 2R2-4R+4=100 R²-2R-48=0 R=1±7=8 S=16π-24
    1
  3536. БЕЛСАТ NEWS,1:18 у Nexta не своё тело.
    1
  3537. х²-2у²=1, (±1;0)(±3;±2) а больше нет? (х²-1)/у²=2, х/у>√2=x/y-0,5/x/y+..., (±17;±12) y последняя цифра 0,2,3,5,7,8.
    1
  3538. X=-√a a√3/2,a/2 (a√3/2-√a)²=a²/4 a=0,a-2a⁰,⁵√3+2=0 a⁰,⁵=√3±1 a=4±2√3≥4/3 a=4+2√3
    1
  3539. x,y,z>0,(x+y+z)(1/x+1/y+1/z)=1+x/y+x/z++y/x+1+y/z+z/x+z/y+1=3+(x²+y²)/x/y+(x²+z²)/x/z+(y²+z2)/y/z≥9 ч.т.д.
    1
  3540. X=yt(y) -1/y=t'sint ±yarccos(ln|y|-c) =x +✓,c=0 x=yarccos(ln|y|) cosx(2)=2ln²2-1 (2)✓
    1
  3541. B=2A-E,A²=A B=(a11 a12...an1) (... ) (am1... amn) A*A=(a1 a12..an1)*(a1 a12..an1)=(a1²+a (... ). (... ). (... (am1... amn). (am1... amn). (am1a 12+..an1am1 ... a1an1+...an1amn)=(a1.. ). (... 1+...amnam1....am1an1+..+amn²). (am1.. an1){a1²+a12a21+...+an1am1=a1, ) ... amn)a1an1+...+an1amn=an1,*a1/an1 ... am1a1+...amnam1=am1, ... am1an1+...+amn²=amn; (1 0...0)(0 0..0)B=(2 0...0)-(1 0..0)=(1 0..0) (... )(.........). (..........). (.........). (..........) (0 0...1),(0 0..0). (0 0...2). (0 0..1) (0 0..1) B=(0 0..0)-(1 0...0)=(-1 0...0) (..........). (.........). (...........) (0 0...0). (0 0..1). (0 0..-1)
    1
  3542. x->'=(3 -1;-1 3)x->+(4;4)e^2t x->(0)=(1 1) x->0'=(3 -1;-1 3)x-> (A-лI)x->0=0,|3-л -1;-1 3-л|=0,(3-л)²-(-1)²=0,[3-л=1,3-л=-1;[л=2,л= 4;(1 -1;-1 1)*(a b)=0,{a-b=0,-a+b=0;{a=b,a= b;(1;1)(-1 -1;-1 -1)(a b)=0,{-a-b=0,...;a=-b (1;-1) х->0=С1(1;1)е^2t+C2(1;-1)e^4t x-> p=(A;B)e^2t,2(A;B)e^2t=(3 -1;-1 3)(A B)e ^2t+(4;4)e^2t,(2A;2B)=(3A-B+4;-A+3B+4) {2A=3A-B+4,2B=-A+3B+4;{-A-B=4,A-B=4;{A=0,B=-4; xp->=(0;-4)e^2t x->=С1(1;1)е^ 2t+C2(1;-1)e^4t+(0;-4)e^2t (1 1)=C1(1;1) +C2(1;-1)+(0;-4)=(C1+C2;C1-C2-4){C1+ C2=1,C1-C2-4=1;{C1+C2=0,C1-C2=5;{C1=2,5,C2=-2,5; x->=(2,5;-1,5)e^2t+(-2,5; 2,5)e^4t
    1
  3543. 4x=|3x-|x+a||+9|x-3|≥0,x≥0[{x≥a/2,x≥-a,x≥ 3;a/7+27/7=x;{x≥a/2, x≥-a,x<3,x=-a/11+ 27/11;{x≥-a/4,x<-a,x≥3, a/7-27/7=x;{x≥-a/4,x<-a,x<3,x=a/9+3;{x<a/2,x≥-a,x≥3,-a/3+9 =x;{a>54/13,a<18,x=a/15+9/5;{a<-108/5, a≥-24,a+27=x;{a<-8 4/13,a>-24,x=-a/17+2 7/17;
    1
  3544. X(ctgo-1)/(1+ctgo)=y coso+sino=x y=coso-sino x²+y²=2 D)
    1
  3545. -0,5/n+1/3/(n-1)+1/6/(n+2) -0,5/2+1/3/1+1/3/2=1/4
    1
  3546. 0,x,(x-1)³/3+1/3[0;1/3],.. f(n+1)x[0;1]✓(-1)^n$(0;x)(fn(x)- 1)²dx≥(-1)^nfnx limn->≠$(0;a)(f(n) x-1)²dx=0 f(n)a=1-1/(a+c)
    1
  3547. (-1)^[m/2-1/2](m-1)!!(m:/2,1;m:2,(n-1)!!/n!!(N:/2,1;n:2,π/2))(n-1)!!/(n-1+2[m/2-1/2])!!
    1
  3548. ((x-8)²/³+3x¹/³(x-16)¹/³)(x-8)¹/³=0 [x=8,x=8±√48;{8;8±√48}
    1
  3549. x²+1+2/(x²+1)+1≥2√2+1 x=±√(√2-1)
    1
  3550. {a=-d,b=-1/3d,c=2/3d;a/b+b/c+c/d+d/a=- d/(-1/3d)-1/3d/(2/3d)+2/3d/d+d/(-d)=2 1/ 6
    1
  3551. (1+√5)/4-(-1+√5)/4=0,5
    1
  3552. (4^x-4)(2^x-1)=0[x=1,x=0
    1
  3553. (1/5+2/5)/(1-1/5*2/5)=15/23 π-arctg(15/23)
    1
  3554. -3b/2+1±√(-3/4b²+b) 1,5±(-3/4b²+b)-⁰,⁵(-3/4b+1/2)=0 0=b²-1 1/3b+1/9 b=2/3±√3/3 +*2/3-√3/3->b*2/3+√3/3+>b max=2√3/3 min=-1/8 min=-2√3/3 max=1 2/3 [-2√3/3;5/3]
    1
  3555. kctga/(5k)=tga arctg(1/√5)=a √6*1/√6=1 A)
    1
  3556. f(x)=x-¹f(0)-f(0)
    1
  3557. cosa+cos2a+..+cosna=ncos((n+1)/2a)cos (n/4a)..cosa?
    1
  3558. 8√6/5*5√6*0,5=24
    1
  3559. (х-1)⁵+(х+3)⁵=242(х+1),(х-1+х+3)((х-1)⁴ -(х-1)³(х+3)+..+(х+3)⁴)-242(х+1)=0,2(х+1)((х-1)³(х-1-х-3)-4(х-1)(х+3)+х⁴+4х³*3+4!/2!/2!х²*3²+4х*3³+3⁴-121)=0,[х=-1,-4(х³-3х ²+3х-1)-4х²-12х+4х+12+х⁴+12х³+54х²+108х-40=0,-4х³+12х²-12х+4+х⁴+12х³+50х²+100х-28=0,х⁴+8х³+62х²+88х-24=0,(х²+4х +23)²-96х-553=0,240=240,х=-2,х³+6х²+50х-12=0,(х+2)³+38(х+2)-96=0,х+2=(48+2 √(87810)/9)^(1/3)+(48-2√(87810)/9)^ (1/3),х=-2+(48+2√(87810)/9)^(1/3)+(48 -2√(87810)/9)^(1/3){-2;-1;-2+(48+2√(8 7810)/9)^(1/3)+(48 -2√(87810)/9)^(1/3)}
    1
  3560. 0=x✓
    1
  3561. ​ @Vestnik_Buri ,у меня было 1200!
    1
  3562. (-3b;b;-2b;-b)-5b≤-5✓
    1
  3563. (1-x^2^n)/(1-x),x≠1,2^n,x=1
    1
  3564. 7000*16,38=114660кг=114,66т
    1
  3565. 50*120*24+60*40*24=6000*24+2400*24=144000+57600=201'600
    1
  3566. 5-a²+1+2√(5-a²)a/√5=5 0=2,25a⁴-7,5a²+1,25,a[1;√5] a=√((5+√20)/3) S∆=(5+√5)/6
    1
  3567. F(x)(f(0)-1)/f(3)=f(3-x) F(3-x)=f(x)f(3)/(f(0)-1) f(3)=±(f(0)-1) f(6-x)=±f(-3)
    1
  3568. 10ctg20°=b arctgctg20°=70°✓
    1
  3569. k(-1;0)U(0;∞),ln((2-3k)/(1+k))/ln(1+k)<0 1/4=k°-1-°0+°1/4-°2/3>k k(-1;0)U(1/4;2/3)
    1
  3570. 8*0,5*0,625²√2/2=√2*25/32m²
    1
  3571. y'+2x-¹y=x² y=cx-²+x⁵/5
    1
  3572. А сколько Вам лет-то?
    1
  3573. (2+√2)⁹=901*2⁵+1393*16*√2
    1
  3574. (2^(-1/(х+1))-1/2)(2^(-1/(х+1))+4/ 9)≥0 2^(-1/(х+1))≥0,5 х/(х+1)]0 хє(-=;-1)U[0;=)
    1
  3575. (1;2)(2;1) х²(у-1)+ху²-у²-1=0 х=(-у²±√(у⁴+4у³-4у²+4у-4))/2/(у-1) (у²+2y-4)²+20у-20=n² {0≤(y-4-9,5)(y-4+√9,5),0≤(y+6-√50,5)(y+6+√50, 5);y(-∞;-6-√50,5]U[4+√9,5;∞) y[-13;7] y=2,n=6 y=-5,n=1 x=(-4±6)/2=1;-5 x=(-25±1)/-12=2;×{(-5;2)(2;-5)}
    1
  3576. (х+1)/х<0 хє(-1;0)
    1
  3577. (√6+√2)/2/sin(135°-x)=1/sinx x=30°
    1
  3578. f(x)=a+b/x f(2009)=9,5*10⁶ f'(2015)=-0,00 35 f'(x)=-bx-² {a=-56,7*10⁶,b=133*10⁹; f(1994)=10,0*10⁶.
    1
  3579. -6sin²x+7sinx-2=0 sinx=(-7±1)/-12=0,5; 2/3 [x=π/6+2πn,x=5/6π+2πn,x=arcsin(2/ 3)+2πn,x=π-arcsin(2/3)+2πn;x≠±arccos(±√5/3)+2πn {π/6+2πn;5/6π+2πn}
    1
  3580. y+1/2±√(8y+1)/2=x y≥0, y=(n²-n)/2, x=(n²+n)/2;(n²-3n+2)/2,nZ
    1
  3581. 3/5mg=5F F=3/25mg
    1
  3582. (1/3(27+x)-²/³+1/3(27-x)-²/³)/(1+ 8/3x¹/³)=2/3/3²=2/27
    1
  3583. (1+cos1-cos(n+1)-cosn)/2/sin1
    1
  3584. 10√(3x-√(72(x-2)))>3x-12 x≥2 10(√(3/2x+ 3|x-4|/2)-√(1,5x-1,5|x-4|))>3x-12[x(-10√6/ 3+62/3-√(-√6*1000/9+377 7/9); -10√6/ 3+62/3+10√(-√6*10+34)/3); x[2;4); -√6*4000/9+1511 1/9>0 x[2;4)U(-10√6/ 3+62/3-√(-√6*1000/9+377 7/9); -10√6/ 3+62/3+10√(-√6*10+34)/3)
    1
  3585. {x≤-√3,-2≠x;x(-∞;-2)U(-2;-√3]
    1
  3586. log(-x²+4x-3)(√3sin(π/x)+cos(π/x))=0,{-x²+4x-3>0,-x²+4x-3≠1,√3sin(π/x)+cos(π/x)>0;{(x-(-4+√(16-4*-1*-3))/-2)(x-(-4-√4)/ -2)<0+°-1°3+>x,-x²+4x-4≠0,sin(π/x+π/6)>0;{xє(1;3),х≠(-4±√(16-4*-1*-4))/-2,π/х+π/6є(2πn;π+2πn);{хє(1;3),х≠2,хє(1/(5 /6+2n);1/(-1/6+2n));хє(1;2)U(2;3).2sin(π/x+π/6)=1,sin(π/x+π/6)=1/2,[π/x+π/6=π/6+2πn,π/x+π/6=5/6π+2πn;[x=1/2/n,x=1/(2/3+2n);[0/,0/;0/
    1
  3587. (√2cos25°cos10°+cos50°)/cos5°
    1
  3588. -cos4t=2/3-2/3cos²4t 2/3cos²4t-cos4t -2/3=0 cos4t=(3±5)/4[cos4t=2,cos4t= -0,5;4t=±2/3π+2πn t=+π/6+πn/2
    1
  3589. 36^50/48^25=(3³)²⁵=3⁷⁵
    1
  3590. x⁰,⁵=(5±3)/2=4;1 [x=16,x=1.
    1
  3591. S=(-1/3+4/3√3)π-4√3/3
    1
  3592. L^-1{1/(s³+s)}=L^-1{1/s/(s²+1)}=1-cost A/s+B2s/(s²+1)+C/(s²+1)=1/s/(s²+1),A (s²+1)+2sBs+Cs=1,As²+A+2Bs²+Cs=1,{A+2B=0,C=0,A=1;{A=1,C=0,B=-1/2.
    1
  3593. S∆=11x²/16=80 x=16√(5/11)(cm)
    1
  3594. 3/8+0,25En=0;=(-1)^n/(2n)!(-2*2^(2 n)+0,5*4^(2n))x^(2n)
    1
  3595. X+6=3(x-4(,x=6 A)
    1
  3596. {√2021x+√2019y=2,√2019x+√2021y=1;{x=√2021-√2019/2,y=-√2019+√2021/2;x²-y²=(√2021-√2019/2)²-(-√2019+√2021/2)²=2021-√(2021*2019)+2019/4-(2019-√(2019*2021)+2021/4)=2525,75-√(2021*2019)-2019+√(2021*2019)-505,25=1,5
    1
  3597. √2sin85°-1,√2cos85°,1-√2cos85° tgA=(1 -√2cos85°)/(√2sin85°-1)=16sin10°cos 20°*cos²25°,A=65°
    1
  3598. $(0;1)√2√(x/(x+1))dx-1+√2ln|1+√2|=1 x=sh²u dx=2shuchudu 2-ln(1+√2)√2
    1
  3599. x+1=±x;±xi x=-0,5;-0,5-+i/2
    1
  3600. x=2^log(6√3)3
    1
  3601. 90°-1,5x+2*2x=180° x=36°.
    1
  3602. 0=(x+√7)²+(y-√7/2)²≥0{x+√7=0,y-√7/2=0;{-√7;√7/2}
    1
  3603. 3(3⁴-5(3²-1))=123 3(3⁶-7(81-2(3²-1/2)))=843
    1
  3604. {x+y=5,3x+4y=18;{x=2,y=3;
    1
  3605. En=1;∞(-1)^(n-1)x^n(4^n-1)/n/n!*4(=)-3 сходится
    1
  3606. Sз=(6/5√5)²-3-1/5=4
    1
  3607. Председатель СНТ, это перевиранме фактов в угоду себе.
    1
  3608. {y=x²-1,[x=0,x=-1,x=(1±√5)/2;{(0;-1)(-1;0)((1±√5)/2;(1±√5)/2)}
    1
  3609. abcdabcd b=b=7✓
    1
  3610. x=-2;-2cos²0,65✓
    1
  3611. (x⁴+x²+1)/(x-1)=x³+x²+2x+2+3/(x-1) x⁴/4+x³/3+x²+2x+3ln|x-1|+c✓
    1
  3612. y²-1=y,y²-y-1=0 y=(1±√(1-4*-1))/2=(1±√5)/2
    1
  3613. 2|3d.|6000l 2|10d.|20'000l 5|25d.|20'000l{25 дней}
    1
  3614. 121,77/(5/6)=146,12 150✓!
    1
  3615. {ad²+bd+c-k=0,[d=e,e=-b/a-d; 2ade-c+2k=-2bd-3c+4k;c B)
    1
  3616. r²+(r+√2/2)²=1 r²*2+√2r-1/2=0 r=(-√2+√6)/4{(2-√3)/8π}
    1
  3617. X≥7 (x-2)³-100(x-2)+288=0 x-2=(-144+8√(18²-25³/27))¹/³+(..-..)..=20/3¹/²cos(1/3arccos(-54/ 125√3)+2/3πn) x=2+20/3¹/²cos (1/3arccos(-54/125√3)),n=0 54√3<125,5 21/173×
    1
  3618. 3+х кг 1/3(3+х)=1+х/3 х=2+2/3х х=6 9кг.
    1
  3619. A=3/5(B+1)-1,A=7/12(B-1)+1 B=49,A=29
    1
  3620. 2arcsin(1/3)
    1
  3621. x->∞(x+1,5-(3x-1/3)-(5x+2/5)+7x+4/7)=2 1/210
    1
  3622. (R/2+8/R)²π/2+π/2(8/R)²-R²π/2-π/2(2/R)²=π/2(-3R²/4+8+124/R²) 8/R=R R=√8 S=π*35/4
    1
  3623. π/4(x+x³/3)(0;1)=π/3
    1
  3624. 25*0,2*2=10г 69/14=4,9л 10*10-³/4,9= 2,04‰
    1
  3625. x=1,61;-0,61;1,27
    1
  3626. 16^((x-1)/x)*5^x=100 (x-1)/x+xlog(16)5= log(16)100 x-1+x²log(16)5-xlog(16)100= 0, x²log(16)5+x(1-log(16)100)-1=0, x=(-1+log (16)100±√((-1+log(16)100)²-4 *log(16)100*(-1)))/2/log(16)100=(-1+log (16)100±√(1-2log(16)100+log²(16)100+4 *log(16)100))/2/log(16)100=(-1+log (16)100±√(1+2log(16)100+log²(16)100)/2/log(16)100 x=1,x=-2/2/l0g(16)100=-lo g(100)16
    1
  3627. a≥b y=b√(1-X²/A²) x=±ab/√(a²+b²) $(-ab/√(a²+b²);ab/√(a²+b²))b√(1-x²/a²)dx=b/a (0,5a²arcsin(x/a)+x√(a²-x²)/2)|(-ab/√(a²+ b²);ab/√(a²+b²))=baarcsin(b/√(a²+b²))+a²b²/(a²+b²) S∆=0,5(ab/√(a²+b²))²=0,5a ²b²/(a²+b²) S=baarcsin(b/√(a²+b²)) $..=4 abarcsin(b/√(a²+b²))
    1
  3628. Максимум 50*98=4900.
    1
  3629. х/2(100-2)=49x=1000×
    1
  3630. 8sin15°=1,5a a=8(√1,5-√0,5)/3 S=52/3 (√6-√2)(√6+√2)=208/3
    1
  3631. $(0,75sinx-0,25sin3x)dx=-0,75cosx+1/12cos3x+c
    1
  3632. {y=(1-x³)^(1/3),x⁵+(1-x³)⁵/³=1;(1-x)((1-x)²/³ (1+x+x²)⁵/³-1-x-..-x⁴)=0,[x=1,x=0,1+10x+5,4 x²+6,2x³+5,4x⁴+3x⁵+x⁶=0;x=-1,85,x=-0,11;(1;0)(0;1)(-1,85;(1+1,85³)¹/³)(-0,11;(1+0,11 ³)¹/³)
    1
  3633. S=25/2π-9/2π+4π/2=10π
    1
  3634. 2sint(1/cos³t/(1-3tg²t)-2)=0[sint=0,0= cos³t-3/4cost-1/8;[t=πn,cost=(1/16+√(1/ 256+(-3/4)³/27))^(1/3)+(1-√-3)^(1/3)/16 ^(1/3)=1/2cos(π/9+2πn/3);[t=πn,t=±arcco s(0,5cos(π/9+2πn/3))+2πm.
    1
  3635. Х+у=8,6х+8у=54 х=5,у=3
    1
  3636. 3log(1/3)8=x
    1
  3637. 6²=2r*4r,r=3√0,5,2arcsin(2√2/3)+arcsin(2/3√2)=3arcsin(2√2/3)≠180°3/3
    1
  3638. 90°-a/2 45°-a/4=a a=36° x=108
    1
  3639. $e^cosx*((1-2sin²x)cossinx-2sinxcosxsinsinx)dx=e^cosx*2cosxsinsinx-e^cosx*2sinsinx+...+c
    1
  3640. Y'-Y=X y=ce^x-xe^-x-e^-x
    1
  3641. x≥9,√(x-9)=9-√x,x≤81 25=x{25}
    1
  3642. [х+2=0,0=(х+2)⁴+90(х+2)²+810;{-2}
    1
  3643. {b=12/√a-a/3,(a¹,⁵-9)³-226(a¹,⁵-9)-226*9=0;a=(9+(113*9+113√(1283/27))¹/³+(..-..)..)²/³ b=12/(9+(113*9+113√(1283/27)) ¹/³+(..-..)..)¹/³-(9+(113*9+113√(128 3/27))¹/³+(..-..)..)²/³/3
    1
  3644. 6sin(90°-2arctg0,5)*2=36/5✓
    1
  3645. |х-х²-1|=|2х-3+х²|,{-х²+х-1=х²+2х-3,-х²+х-1 =-х²-2х+3;{-2х²-х+2=0,3х-4=0;{х=(1±√(1-4* -2*2))/-4,х=4/3;{-1/4±√17/4;4/3}
    1
  3646. √(49-9x²) 4x/7=3x/√(49-9x²) x=7√7/12 S=1225/96√7
    1
  3647. 1,06⁵⁰=18,403'8*1,1236=20,68
    1
  3648. B=sin70°/sin30°*a ..=2sin80°a a(1+2sin70°)/sin110°=2sin80°a/sin? 40°=?
    1
  3649. a³/6-4a²+7a-10 1/3=S(a) a²/2-8a +7=0 a=16±11√2+*-*+>a max=728 1/3-1562/3√2 min=-56 2/3
    1
  3650. $(2,5/(x-2)²+0,25/x-0,25/(x-2))dx= -2,5(x-2)-¹+0,25ln|x|-0,25ln|x-2|+c
    1
  3651. {±2/3√3=x,y=±√3/3;{(2/3√3;√3/3)(-2/3√3;-√3/3)}
    1
  3652. y=log0,5(loga(3/x)(√x-√a)) loga(3/x)(√x- √a)>0,[a>3,-3°+°a->x;a=3,-°3->x;a<3,-a°+°3->x;[a>3,x(0;a);a(1;3),x(0;3);a(0;1),x(0;a) U(3;∞);
    1
  3653. х=±2√55
    1
  3654. х=2(107*27*107²)¹/³=642
    1
  3655. (a+2 -b+1|33) (A-1 2b+1|9) {A=1,y=9/(2b+1),x=11+3(b-1)/(2b+1);{a≠1,x=(b(-25a-50)-8a-16)/(b(-a-1)-1)/(a+2),y=(8a-17)/(b(-a-1)- 1). 11+3*3/9=12×{[a=-2,-24a²-133a+357=0;(8a-16)/(-a-1)=b; a=(-133±√51961)/48{(-2;32/3)((-133±√51961)/48;(-1354±6√51961)/233)}
    1
  3656. x=(√3±i)/2 x⁶=-1 ((-1)⁷-1)/-2=1
    1
  3657. Хє(-1;0) сходится условно х=0,-//- //-,х(-=;-1)U(0;=) расходится -// 1-2/(х+1) расходится абсолютно х(-≠;-1)U[0;1), сходится -// х(-1;0)U[1;=)
    1
  3658. 32°-0,5a,2bcos(180°-a),2bsin(180°-a) tg(3 2°-0,5a)=(tg32°-tg0,5a)/(1+tg32°tg0,5a)= -tg0,5a(3-tg²0,5a)/(1-3tg²0,5a) tg³0,5a+2/(2-tg32°)tg0,5a+tg32°/(2-tg32°)=0 tg0,5a =(-tg32°/(2-tg32°)/2+√(tg²32°/(2-tg32°)²/4+(2/(2-tg32°))³/27))^(1/3)+(-0,5tg32°/(2-tg32°)-√(81(tg²32°-2tg32°)²+192-96tg3 2°)/(2-tg32°)²/18)^(1/3),a=2arctg((-tg32°/(2-tg32°)/2+√(tg²32°/(2-tg32°)²/4+(2/(2-t g32°))³/27))^(1/3)+(-0,5tg32°/(2-tg32°)-√ (81(tg²32°-2tg32°)²+192-96tg32°)/(2-tg32 °)²/18)^(1/3))+2π
    1
  3659. 0,5a*11√2/2=22 a=4√2,b=√(32+121-2*4 √2*11sin45°)=√65 (4√2)²+c²-2*4√2ccos 135°=65,c²+8c-33=0 c=-4±7,[c=3,c=-11;c>0 c=3.
    1
  3660. f(x)=x2+kx+kf(x-1) f(0)? f(x)=(-2x²k^(x+ 2)+(2x²+2x-1)k^(x+1)+(2x²+2x-3)k^(x+2)-x²(k³-k²+k+1)+(-k²-k-2)x+k³+k²-k+3)/(k-1)²+k^xf(0) f(0)=(k²-k-3)(k-1)+f(0),k²- k-3=0,k=(1±√(1-4*-3))/2=0,5±√13/2
    1
  3661. w²+w+1=0 w⁸+w⁴+1=-w³+1=0
    1
  3662. [x²-x-10=0,x²+x-9=0;[x=(1+√41)/2, x=(-1-√37)/2.
    1
  3663. |(0;π)2022x=2022π
    1
  3664. CP->=-5/3AP->-4/3BP->
    1
  3665. 0,5xarcsin²x+arcsinx*(1-x²)⁰,⁵-x(-1;1)=π²/4-2
    1
  3666. 1,75 95, 75х=95,х=1,2(6), 1,75*1,2(6)=1,75*19/15=2,21(6)м 1575 175 33,25
    1
  3667. 80-8a+a²=a² a=10 S=10*8-16=64
    1
  3668. {x+y=a,xy=b;{b=-72,a=1;{y=1-x,x(1-x)=-72;-x²+x+72=0 x=(-1±√289)/-2=-8;9 y=9;-8{(-8;9)(9;-8)}
    1
  3669. √6-√3+√6+√3=2√6
    1
  3670. √(х+8)=8 х=56✓
    1
  3671. А почему этот историк в очках?
    1
  3672. $ln((x+1)(x³+4x²+7x+4))dx=$(ln(x+1)+ln ((x+1)(x²+3x+4))dx=2(x+1)ln(x+1)-2x+$ln((x+1,5)²+1,75)dx=2(x+1)ln(x+1)-2x+((x+1,5)²+1,75)/2/(x+1,5)ln²((x+1,5)²+1, 75)/2-$(0,15-0,4375/(x+1,5)²)ln²((x+1, 5)²+1,75)dx+C 5,11,11,4
    1
  3673. 2(2-5x)²,⁵/125-4(2-5x)¹,⁵/75+c
    1
  3674. 2019+2=2021
    1
  3675. 2²(7*17:25)=76
    1
  3676. En=1;∞(-1)^(n-1)(n-5/3)!(-1/3)!/(N-2)! n!m!/(m+n)!
    1
  3677. (kx-1)/(x+k)=y dx/(1+x²)?dy/(1+y²) =dx/(x²+1)✓
    1
  3678. g(x)=14/(x+4)-3
    1
  3679. 7/18a²-2/9a²=1/6a²=1 a²=6✓
    1
  3680. √(-a²+2a+3)=-√2-1+a≥0,a≥√2+1 a²+(-2-√2) a+√2=0 a=1+0,5√2±√6/2≥√2+1 {1+0,5√2+ √6/2} S=a²=3+√2+√6+√3
    1
  3681. [{x[1;3],f(x)=-x²+4x-5;{x>3,f(x)=-4+2 x;{x<1,f(x)=4-2x.
    1
  3682. (m-5-√8)(m-5+√8)≥0 m(-≠;5-√8]U[5+√8;∞) x=(m+1±√(m²-10m+17))/2,mZ (m-5-n)(m-5+n)=8[{m=8,n=1;{..=2,..=1;x=(9±1)/2=5;4 x=(3±1)/2= 2;1{2;8}
    1
  3683. a+b±√(1000-a²-b²) 1-a(1000-a²-b²)-⁰,⁵=0 √(1000-b²)/√2=a +*>a max=b+2√(500 b²/2) 1+(500-b²/2)-⁰,⁵*-b=0 ±10√(10/3)=b +*10√(10/3)->b max=30√(10/3) min=-30 √(10/3)
    1
  3684. 8*10⁹/8000=10⁶(c)=11 31/54(дн.)
    1
  3685. (x+2y)²-y²+z²=1-98²+102²=801
    1
  3686. f(a)=±4a²(a+1) f(2)=±48
    1
  3687. (x•(y••z•••-z••y•••)+y•(z••x•••-x••z•••)+z•(x••y•••-y••x•••))/(x•²x••²+y•²y••² +z•²z••²)
    1
  3688. n≥5,n²+4n+2=47 n=±7-2=5;-9×{5}
    1
  3689. $(-1;1)f(x)dx=c $(0;2)f(x)dx=c1 f(x)=x²+cx+c1 x³/3+cx²/2+c1x(-1;1) =2/3+2c1=c x³/3+cx²/2+c1x(0;2)= 8/3+2c+2c1=c1 {c=-14/15,c1=-0,8; f(x)=x²-14/15x-0,8
    1
  3690. z³+1/2z-9/64=0 z=(9/2+11√105/18)¹/³/4+(..-..)..; -(9/2+11√105/18)¹/³/8-(..-..)..±√(3/ 4((9/2+11√105/18)¹/³/4+(..-..)..)²+ 1/2)i x=-√((9/2+11√105/18)¹/³/4+(..-..)..)±2√(0,5√(((9/2+11√105/18) ¹/³/4+(..-..)..)²+1/2)-(9/2+11√105/ 18)¹/³/16-(..-..)..)
    1
  3691. 1200/0,75/2/(122+3*31+28+30-28)*7/5=800/245*1,4=3,21*1,4=4,494 года. А остальное время просто повторяем? 1284 321 4,494
    1
  3692. E^x=y,x=lny,dx=dy/y $arctgy/y³dy= arctgy*y-²/-2+0,5(-arxtgy-y-¹)+c=arctge^x*e^(-2x)/-2+0,5(-arxtge^x-e^(-x))+c
    1
  3693. Li3(-e)+Li3(-1/e)+2n(3)-1/2=° -e^(2n-1)((12n²-6n+1)/(2n-1)³+1-e)/8/n³
    1
  3694. limn->∞(1/3+1/n)=1/3
    1
  3695. (sin8x+sin2x)sinx=0[sin8x+sin2x=0,sinx=0;[sin8x=-sin2x,x=πn;[x=0,2πn,x=π/6+1/3π n,x=πn;{0,2πn;π/6+1/3πn}
    1
  3696. 1,16*10¹²$ Ещё 1,82*10¹²$.
    1
  3697. B/м²=кг*м/с²/Кл=кг²× ф=I(кг*м²)
    1
  3698. 31*481:900=511
    1
  3699. 2*30/c*√(c²-30²)/c=12/√(c²-30²) C=15√5 S=80/2*30=1200 A)
    1
  3700. Arcsin(a/2)+arcsin(b/2)=60° a√(1-b²/4)=-√(1-a²/4)b+√3 0=b²-2√3√(1-a²/4)b-a²+3 b=√3√(1-a²/4)±a/2 A3B=√(1)=1
    1
  3701. са^х=log(a)с*2012+2013х,0/
    1
  3702. (cos(x/2)+1/2)cos(x/2)=0[cos(x/2) =0,cos(x/2)=-1/2;[x=π+2πn,x=±4/3π +4πn.
    1
  3703. (373,15К;101325Па)(647,3К;22,1МПа)(273,16К;610Па) P=aT²+bT+c {a*373,15²+ 373,15b+c=101325,373,15b+1,576c=(101325-22,1*576²)/0,424, -0,79c=(101325-22, 1*576²)/0,424+(101325-610*1,3660²)/0,3 66;
    1
  3704. (lnx-ln(x+1))²/2(2;8)=ln²(8/9)/2-ln²(2/3)/2
    1
  3705. 0,52*36/(23+35,5)/(0,1)=3,2°С
    1
  3706. 6(a+b)(a+c)(b+c)-(a²+4ab+4ac+b² +4bc+c²)(a+b+c)≤3abc Если взять а=0,то решается просто.
    1
  3707. 55,8¹/³=3,83 (2√2)³+6√2b=22√2 b=1 3*2² *2*1+1³=25✓ 1+2√2+2(3-√2)=7.
    1
  3708. $W(x)dx=xW(x)-x+$dx/(W(x)+1)+c
    1
  3709. (5m)^5m=3125^5⁵ 5m=3125{625}
    1
  3710. $sinsinxdx*cosx/cosx=sinsinx/cosx-$si nsinx*cos^-2x*sinxdx=sinsinx/cosx-sins inx*sinx/cos³x+$sinsinx*(-2cos²x+3)/cos⁴xdx=sinsinx/cosx-sinsinx*sinx/cos³x +...+C
    1
  3711. $(0;π/2)0,25(0,5sin(3x)+sinx-0,5sin (5x))dx=0,25(-cos(3x)/6-cosx+0,1 cos(5x))(0;π/2)=2/15
    1
  3712. x^x^b+x^b^x+b^x^x'=e^(x^blnx)x^(b-1)(b lnx+1)+e^(lnx*b^x)b^x(1/x+lnx*lnb)+b^x^x e^(xlnx)(lnx+1)lnb
    1
  3713. x=(3-y)/(1+y) 3(1-y)/(3+y²)+(y²-3y)/(1+y)=max=-8 7467/17700;-1,19 min=-7,98;22,57 (-∞;-8 7467/1770 0]U[22,57;∞) (-48,25-23,5y-40,25y²+(y³+y²+2,5y+ 3,5)²)/(3+y²)²/(1+y)²=0 y=1,55;-2,77;-2,64;1,76 +-2,77*-2,64-+1,55-1,76*+>y
    1
  3714. √((10/2-1)(5-2)(5-3)(5-4))=2√6
    1
  3715. limn->∞0,5(4+1/n)-⁰,⁵=0,25.
    1
  3716. (3-4*(5/7)^n)/-5=-3/5.
    1
  3717. {c=2050-ab,a=(2050b-2051)/(b²-1); b=0,a=2051 b:2,b:10=ost.0;2;8 b=2,a=683 b=-8,a=-18451/63×{(2051;0;2050)(683;2;684)}
    1
  3718. 1/6+5/6(1/5+4/5()))=1✓
    1
  3719. [{а≥0,х[а(1-√2/2);2а];{а<0,х[а(1+√2/2);0]; а(1+√2/2)=2+√2 а=2 а(-1-√2/2)=2+√2 а=-2{±2}
    1
  3720. Y'=-2x+2 (x0;-x0²+2x0+15) (-x0²+2x0+15)|-2x0+2|+x0=1 [x0=1,x0²-2x0-15,5=0;x0=1+√16,5 a=√((x0-1)²+(-x0²+2x0+15)²)=√67/2 a(-15;-√67/2]U[√67/2;15)
    1
  3721. $(0;2)dx$(x²;4)dy=4x-x³/3(0;2)=16/3
    1
  3722. |B|=-1*-4-5*1=-1≠0 B-¹=(1 -1;-5 4) B-¹*A=(1 -1;-5 4)*(2 1;3 2)=(-1 -1;2 3) ..*B²=(-1 -1;2 3)*(6 -25;5 21)=(-11 4;27 13) ..+6E=(-5 4;27 19) (-5 27;4 19)
    1
  3723. 3/4/(1-9/16)=12/7
    1
  3724. 1180/1600=0,7375=73,75%
    1
  3725. -1/3(9-x²)¹,⁵+3x²-2x³/3(0;3)=18(cm³) X=8/(4+π)(cm) Y=(20+6π)/(4+π)(cm³)
    1
  3726. √(50-h²) (√(50-h²)-2)²+h²=BC², BC=√(50-h²-4√(50-h²)+4+h²)=√(54-4√(5 0-h²)) 2*(2√(50-h²)-2)=6*.., ...=(4√(50- h²)-4)/6=2/3*√(50-h²)-2/3 (1/3*√(50-h ²)-1/3+3)²+(√(50-h²)-2)²=50, (50-h²)/9+2 /3*2 2/3√(50-h²)+(2 2/3)²+50-h²-4√(50-h²)+4=50, √(50-h²)(16/9-4)=-5 5/9+h²/9-64/9-50+h²-4+50≤0, (50-h²)*20²/9²=(1 1/9h²-16 6/9)²,h²≤16 2/3/(1 1/9)=(144+ 6)/10=150/10=15, h≤√15 20'000/81-40 0/81*h²-100/81*h⁴-(16 2/3)²+20/9*h²*16 2/3=0, h²=x, -100/81*x²+(-400+1000*3)/81 *x+20'000/81-125'000/27=0, x=(-2600/81±√(2600²/81²-4*(-100/81)*(20'000-125'000*3)/81))/(-200/81)=13±√(169+400*(20'000 -375'000)/40000)=13±√(169-355'000 /100)=13±√(169-3550)=13±√-3381 x≥0, h=√(13+√-3381) BC=√(54-4√(50-(13+ √-3381)))=√(54-4√(37-√-3381)) √((37+√(37²+3381))/2)=√(18,5+√(1369 +3381)/2)=√(18,5+√2750/2)=√(18,5+5 √110/2)
    1
  3727. {2019x+2020y=1,-2/2021y=4036/2021;{x=2019,y=-2018.
    1
  3728. $(х2-1)/(х²+х+1)²*dx=arctg (x+0,5)/(√3/ 2)/(√3/2)-0,5(x²+x+1)^(-1)-0,5(ln|(x+0,5 -√-3/2)|/√-3-1/√-3ln|x+0,5+√-3/2|)=2√3/ 3*arctg (2√3/3x+√3/3)-0,5/(x²+x+1)-0,5(-∞(x+0,5-0,5√-3)^(-1)/-1+∞(x+0,5+0,5√-3)^(-1)/-1)=2√3/ 3*arctg (2√3/3x+√3/3)-0,5/(x²+x+1)-0,5∞/(x+0,5-0,5√-3)+0,5∞/(x+0,5+0,5√-3)= 2√3/3*arctg (2√3/3x+√3/3)-0,5/(x²+x+1)-0,5∞(-√-3)/(x²+x+1)=∞ (x²-1)(x²+x+1)²=(2Ax+A)/(x²+x+1)+B/(x²+x+1)+(2Cx+C)/(x²+x+1)²+D/(x²+x+1)² x²-1=(2Ax+A)(x²+x+1)+B(x²+x+1)+2Cx+ C+D, 2A=0, 2A+A+B=1, 2A+A+B+2C=0, A+ B+C+D=-1, A=0, B=1, C=-1/2 D=-1/2 a(x+0,5+√-3/2)²+b(x+0,5+√-3/2)(x+0,5-√-3/2)²+c(x+0,5-√-3/2)²+d(x+0,5-√-3/2)(x+0,5+√-3/2)²=1, b+d=0, a+b(1-√-3+0,5+√-3/2)+c+d(1+√-3+0,5-√-3/2)=0, a(1+√-3)+b((0,5-√-3/2)²+(0,5+√-3/2)(1-√-3))+c(1-√-3)+d((0,5+√-3/2)²+(0, 5-√-3/2)(1+√-3)=0,*1/(1-√-3) a(0,5+√-3 /2)²+b(0,5+√-3/2)(0,5-√-3/2)²+c(0,5-√-3 /2)²+ d(0,5+√-3/2)²(0,5-√-3/2)=1,*1/(-0,5+0,5√-3) d=-b, a+b(1,5-0,5√-3)+c+d(1,5+0,5√-3)=0, b(1,5-0,5√-3-(-0,5-√-3/2+0,5-0,5√-3+0,5√-3+1,5)/(1-√-3))+d(1,5+0,5√-3-1/(1-√-3)(-0,5-0,5√-3+0,5+0,5√-3-0,5√-3+1,5))=0, b(1,5-0,5√-3-1/(-0,5+0,5√-3)(0,5+0,5√-3)(-0,5-0,5√-3))+c(1-(-0,5-0,5√-3)/(-0,5+0,5√-3))+d(1,5+0,5√-3-(-0,5+0,5√-3)(0,5-0,5√-3)/(-0,5+0,5√-3))=-1/(-0,5+0,5√-3),*(1,5-0,5√-3-(1,5-0,5√-3)(1+√-3)/4)/(1,5-0,5√-3+(-0,5+0,5√-3)/(-0,5+0,5√-3)) d=-b, a+b(1,5-0,5√-3)+c+d(1,5+0,5√-3)=0, b(1,5-0,5√-3-(1,5-0,5√-3)/(1-√-3))+d(1,5+0,5√-3-(1,5-0,5√-3)/(1-√-3))=0, -(1-0,25-0,75)(1,5-0,5√-3-1,5/4-1,5√-3/4 +0,125√-3+0,125*(-3))/(2,5-0,5√-3)c+((1,5+0,5√-3-(1,5-0,5√-3)(1+√-3)/4)-(1,5+0,5√-3-0,5+0,5√-3)(0,75-0,75√-3)/(2,5-0,5√-3))d=1/(-0,5+0,5√-3)*(0,75-0,7 5√-3)(2,5+0,5√-3)/7, d=-b, a+c=0, b(0,75+0,25√-3-(0,75+1,25√-3))=0,b=0,d=0 c=(1,5-1,5√-3)(2,5+0,5√-3)/7/(-1+√-3)/0=(3,75+0,75√-3-3,75√-3-0,75(-3))(1+√-3)/-28/0=(6-3√-3)(1+√-3)/0=(6+6√-3-3√-3-3(-3))/0=(12+3√-3)/0=∞, a=-∞, -∞/(x+0,5-√-3/2)²+∞/(x+0,5+√-3/ 2)²
    1
  3729. 34=32+1+1=16+16+2 (5;0;0)(1;2;1) 5/4;2 1/4
    1
  3730. (-x²+2x-5)e^-x+(-2x+2)e^-x-2e^-x+c
    1
  3731. √3/2=3/l*√(1-16/l²)+√(1-9/l²)*4/l 9/16l⁴-37,5l²+481=0,l≥4,(l²-6)²≥-156 ✓l²=(25±12)/(3/2)=74/3;26/3≥16 l=√(74/3)
    1
  3732. √loga(x)+1/√log(a)x+|√loga(x)-1/√log(a)x|=2a[{a≥1,x=a^a²;{a>1, x=a^(1/a²).
    1
  3733. (A+6-2r)²=a²+(6-a)²,r[0;3]U[6;=) a=-2r+12±√(8(r-4,5)²-18) (a+6)r=-2r² +18r±r√(8(r-4,5)²-18)=12 +✓,r⁴-57r²+108r-36=0 z³-57/2z²+212 1/16z-27²/4=0 z=√ 313*sin(±atan(24√28653/3763)/3+ π/6)/2+19/2;-√313* cos(atan(24√28653/3763)/3)/2+ 19/2 r=√+√-√=6,40✓
    1
  3734. X(4/57)=200 x=2850
    1
  3735. e/2-3~n n~-1,64 ln((n+1)/n)/(n-1)= ln(2n+6)/(n-1) 0=2n²+5n-1 n=(-5±√33)/4×
    1
  3736. √(R²+5) R²/√(R²+5)=4 R=20⁰,⁵ S=10π
    1
  3737. z=cx+c1, где с,с1 не зависит от х
    1
  3738. 4/150/10⁶=(4-h)/s=h/(150*10⁶-s), s=37,5*10⁶(4-h),s=100,h=3'999,997(m)
    1
  3739. 1/4/11/../13<1/5
    1
  3740. X=cos(π/5+2πn/5)+sin(π/5+2πn/5), n=0;..;4
    1
  3741. z=-xy/(x+y) (x+y)/z+(x+z)/y+(y+z)/x=-(x² +2xy+y²)/(xy)+(x²-xy+y²)/x/y=-3xy/x/y=-3
    1
  3742. (x-1/2y-1/2z)²+3/4(y-z)²≥0✓ (x+k/2y+k/2 z)²+(1-k²/4)(y+0,5k/(1+k/2)z)²-(k-2)(k+1)/(2+k)z²≥0✓
    1
  3743. tgxlncosx-tgx+x+c
    1
  3744. √(x-1)=1+(x-2)¹/³ [1=x,x=2.
    1
  3745. (224-80√6)/2=112-40√6
    1
  3746. А только мне в детстве казалось, что Соболь и Собчак одно и то же лицо?
    1
  3747. x=-0,5arcsin(2/3);0,5π+0,5arcsin(2/3)+πn x=-0,5arcsin(2/3)+4π;0,5arcsin(2/3)+3,5π 1,5/(sinx+cosx)=±1,5√3
    1
  3748. {y=(-x²-x+2)/4/x,[x=1,x=-1+(-3+2√214/9)¹/³+(-3-2√214/9)¹/³;{(1;0)(-1+(-3+2√214/9)¹/³+(-3-2√214/9)¹/³;((-3+2√214/9)²/³+(-3-2√ 214/9)²/³-2(127/3)¹/³/3+4-3(-3+2√214/9) ¹/³-3(-3-2√214/9)¹/³)/4/(-1+(-3+2√214/9) ¹/³+(-3-2√2 14/9)¹/³)}
    1
  3749. 25¹³<27¹³ ²/³
    1
  3750. 0,5sinB(casB-cos(2A+B))≤0,25sin2B≤0,25 A=π/2-B/2,B=45°
    1
  3751. Ну я отношусь к поколению Z, хотя и не очень похож на описанный Вами портрет.
    1
  3752. a√3/2 a/6√3,a(-2+4/3√3) a²√3/6=32 a=8*3¹/⁴ S∆=a²/6(-√ 3+2)=32(-3+2√3)/3
    1
  3753. C=(1+a)/(ab)+1(1;1;3)(2;2;2)
    1
  3754. 21+9i-14i-6(-1)=27-5i
    1
  3755. {2a²-13a-28=0,b=a-14; a=(13±√393)/4, b=-10,75±√393/4(13/4±√393/4;-10,75±√393/4)
    1
  3756. $2du/(1+u)¹,⁵/√(1-u)=-2√(1-u)/√(u +1)+c=-2√(1-√x)/√(√x+1)+c
    1
  3757. {x(0;3),[x=π/4+πn/2,x=±π/3+2πn; n[0;1],n[0],×{π/4;3/4π;π/3}
    1
  3758. h=√3/4AB=cos(90°-a),a=45° AB=2√(2/3)
    1
  3759. x1²-4(p+x1²)>0, -3x1²>4p, x1²<-4p/3, x1e(-√(-4p/3);√(-4p/3)) (-q/2+√(q²/4+p³/27))^(2/3)-2p/3+(-q/2+√(q²/4+p³/27))^(2/3)<-4p/3, (q²/2+p³/27-q√(q²/4+p³/27))^(1/3)+(q²/2+p³/27+q√(q²/4+p³/27))^(1/3)<-2p/3, q²/2+p3/27-q √(q²/2+p³/27)<-8p³/27-3(-2p/3)²(q²/2+p³/27+q√(q²/4+p³/27))^(1/3)+3(-2p/3)(q²/2+p³/27+q√(q²/4+p³/27))^(2/3)-q²/2-p³/27-q√(q²/4+p³/27),q²+10p³/27<-4p²/3(q²/2+p³/27+q√(q²/4+p³/27))^(1/3)-2p (q²/2+p³/27+q√(q²/4+p³/27))^(2/3)=-2p ((q²/2+p³/27+q√(q²/4+p³/27))^(1/3)+p/3)²+2p*p²/9,p<0 (q²/4+p³/27),√(-0,5q²/p-2p²/27)<(q²/2+p³/27+q√(q²/4+p³/27))^(1/3)+p/3,-0,5q²/p-2p²/27>=0, q²+4p³/27≥0,(√(-0,5q²/p-2p2/27)-p/3)³<q²/2+p³/27+q√(q²/4+p³/27), (-0,5q²/p-2p²/27)¹,⁵+3(-0,5q²/p-2p²/27)(-p/3)+3(-0,5q²/p-2p²/27)⁰,⁵p²/9-2p³/27-0,5q²<q√(q²/4+p3/27), 0,5q²/p+2p²/27-2p³/27-0,5q²<(√(-2/p)(0,5q²/p+2p²/27)-3√(-2/p)p²/9+q)√(q²/4+p3/27), (0,5q²+2p³/27)²(1/p-1)²<(√(-2/p)0,5q²/p-7p²/27*√(-2/p)+q)²(q²/4+p3/27), D<0,-<+ D>0,p<0
    1
  3760. $(0;π)2πxsinxdx=2π(-xcosx+sinx)(0; π)=2π(π)=2π²
    1
  3761.  @Vaska.Uticha  -0,5x²+0,5ax+9>0 (x-(0,5a-√(0,25a²+18))(x-(0,5a+√(0,25a ²+18)))<0,x(0,5a-√(0,25a²+18);0,5a+√(0, 25a²+18)),x[0;a]{0,5a<√(0,25a²+18), √(0,25a²+18)<0,5a;0/.
    1
  3762. 1+2+3+..+9=45
    1
  3763. 66,8/1,6=41 3/4 мин=42 профессии
    1
  3764. 645/8000=0,080625
    1
  3765. (3p-14)*(2^x)²+(29p-154)*2^x+11p-41=0 p=14/3,x=log2(31/56) p≠14/3,x=log2((-29p+154±√(709p²-7824p+21420))/2/(3p-14)) 709p²-7824p+21420≥0 p=4254/709;3570/709 p(-∞;3570/709]U[6;∞),(-29p+154±√(709p²-7824p+21420))/(p-14/3)>0-(-)°41/11-(+)°14/3+(+)°6-(-)>x p(14/3;3570/709],p(41/11;14/3)U(14/3;3570/709]
    1
  3766. F=SndW/dn F=yRT/l n=yRT/V/W'(n) вязкость у газов увеличивается с ростом температуры.
    1
  3767. $(0;π)dx*xsin1=π²/2sin1
    1
  3768. e^(En=0;∞(-1)^n(2n+1)^(-k+1)Ek=1;∞(-1)^(k-1)/k(4π)^k)=e^(8G/π)((1-e^(-π/2))/(1+e^(-π/2)))²
    1
  3769. {x²-2x-1=±(x-1), x²-3x=0, x=0, x≥1, [x²-x-2=0,x=3, x<1, {x≥1,. [x=(1±√9)/2, 0/. {x≥1, x=3, x=2,
    1
  3770. (2+i)(2-i)(10+11i)(10-11i)=5*221 {(±31;±12)(±32;±9)}
    1
  3771. {x²+3ax+3≥0,0=(x+1,5a)⁴+(-4,5a²-1)(x+1,5a)²+3a(x+1,5a)+81/16a⁴-9/4 a²;(z-0,75a²-1/6)³+(-27/16a⁴+3/8a²+1/48)(z-0,75a²-1/6)+(-9/8a⁴+5/8a²+7/144)(0,75a²+1/6)-9a2/64=0 z-0,75a2-1/6=((9/16a⁴-5/16a²-7/288)(0,75a²+1/6)+9a²/128+√(((-9/8a ⁴+5/8a²+7/144)(0,75a²+1/6)-9a²/64)²/4+(-27/16a⁴+3/8a²+1/48)³/27))¹/³+(..-..)..=1/2√(9a⁴-2a²-1/9)c os(1/3arccos((27a⁶-9a⁴-7/27)/(9a ⁴-2a²-1/9)¹,⁵)+2/3πn) z=0,75a²+1/6+1/2√(9a⁴-2a²-1/9)c os(1/3arccos((27a⁶-9a⁴-7/27)/(9a ⁴-2a²-1/9)¹,⁵)+2/3πn){|a|≥√(1+√2)/3,a⁶-17/54a⁴-2/243a²-25/9⁴≥0;a∈(-inf;-√((√267665/(59049*2√2)+14849/4251528)^(1/3)+361/26244/(√267665/(59049*2√2)+14849/4251528)^(1/3)+17/162)]⋃[sqrt((√267665/(59049*2√2)+14849/4251528)^(1/3)+361/26244/(√267665/(59049*2√2)+14849/4251528)^(1/3)+17/162);inf),а(-∞;(-1-√2)/3]U[(1 +√2)/3;∞),x=-1,5a+|a|/a)-√(0,75a²+1/6+1/2√(9a⁴-2a²-1/9)c os(1/3arccos((27a⁶-9a⁴-7/27)/(9a ⁴-2a²-1/9)¹,⁵)))+√(0,75a²+1/6+1/2√(9a⁴-2a²-1/9)c os(1/3arccos((27a⁶-9a⁴-7/27)/(9a ⁴-2a²-1/9)¹,⁵)+2/3π))+√(0,75a²+1/6+1/2√(9a⁴-2a²-1/9)c os(1/3arccos((27a⁶-9a⁴-7/27)/(9a ⁴-2a²-1/9)¹,⁵)+4/3π)));-1,5a+|a|/a(√ -√+√);-1,5a+|a|/a(√+√-√);..+(-√-√-√) -√(0,75a²+1/6+1/2√(9a⁴-2a²-1/9)cos(1/3arccos((27a⁶-9a⁴-7/27)/(9a⁴-2a²-1/9)¹,⁵)))√(0,75a²+ 1/6+1/2√(9a⁴-2a²-1/9)cos(1/3arcc os((27a⁶-9a⁴-7/27)/(9a⁴-2a²-1/9)¹, ⁵)+2/3π))-√(0,75a²+1/6+1/2√(9a ⁴-2a²-1/9)cos(1/3arccos((27a⁶-9a⁴-7/27)/(9a⁴-2a²-1/9)¹,⁵))))√(0,75a²+ 1/6+1/2√(9a⁴-2a²-1/9)cos(1/3arcc os((27a⁶-9a⁴-7/27)/(9a⁴-2a²-1/9)¹, ⁵)))+√(0,75a²+1/6+1/2√(9a⁴-2a² -1/9)cos(1/3arccos((27a⁶-9a⁴-7/27)/(9a⁴-2a²-1/9)¹,⁵)+2/3π))√(0,75a²+ 1/6+1/2√(9a⁴-2a²-1/9)cos(1/3arcc os((27a⁶-9a⁴-7/27)/(9a⁴-2a²-1/9)¹, ⁵)+4/3π)))>=-1,75 A>=b=>c,a(-1)≤-c,
    1
  3772. F(p)=6/(p²+2p+5),ft=3e^-t*sin2t
    1
  3773. 20ab²x²(y+1)³
    1
  3774. (81/35x-36/7)/(x-1)=2 x=10
    1
  3775. 1/2=y'/(y²+2c)[{c>0,tg(1/2√(2c)x+c1√(2c))√(2c)=y;{c=0,-2/(x+2c1)=y;{c<0,-2√(-2c)/(e^√ (-2c)x*2c1√(-2c)-1)-√(-2c)=y.
    1
  3776. 7x-5=-2(x-1),9x=7,x=7/9.
    1
  3777. limx->1(x^x-x)/(lnx-x+1)=0/0=limx->1(e ^ (xlnx)(lnx+x*1/x)-1)/(1/x-1)=(1(0+1)-1)/(1/1-1)=0/0=limx->1(1/x/-1)=-1
    1
  3778. f(x)³/g(x)³/3+c C)
    1
  3779. (2³)(3x-5)=2^(3x+6),9x-15=3x+6,x=21/6= 3,5
    1
  3780. $(0;1)y²dy/4=y³/12(0;1)=1/12
    1
  3781. 2sin0,5o(cos(-π/2+0,5o)+isin(-π/2+0,5o)) ln(2sin0,5o)+i(-π/2+0,5o+ 2πn),o(4πm;2π+4πm);ln(-2sin0,5o)+i(π/2+0,5o+2πn),o(2π+4πm;4π+4 πm)
    1
  3782. 111-81=30 30-27=3{(4;3;1)}8✓
    1
  3783. (x-8)(x+8)/(x-4)/(x²+4x+16):((x+8)²/4/(x²+4x+16)=4(x-8)/(x+8)/(x-4)
    1
  3784. max(0,24)=1,13..
    1
  3785. (a-b)/2 S=π(54-ab)~22π
    1
  3786. En=1;∞1/5/n²(e^(-15n)-e^(-10n))
    1
  3787. 90°-x/2+8x=180° x=12°
    1
  3788. {х=2,у=1,а+2=±3;{1;-5} {(1;2;1)(-5;2;1)}
    1
  3789. у=(5а+10(15-а)х)/((10х+а)²+25) Еу[0;1] у'=1000((15-а)(х+0,1а-1)²-11,25+2,75а-0,2 а²))(х+0,1а))/((10х+а)²+25)²=0 х=-0,1а+1 ±√((11,25-2,75а+0,2а²)/(15-а))а<15+**+ >х мин=(а²-20а+150+10(15-а)√((11,25-2, 75а+0,2а²)/(15-а)))/(8√((11,25-2,75а+ 0,2а²)/(15-а))+(1170-161а+5,8а²)/(15-а) ²)/25≥0, (а²-20а+150+10√((11,25-2,75а+ 0,2а²)(15-а)))/(8√((11,25-2,75а+0,2а²)(15 а))(15-а)+1170-161а+5,8а²)≥0 Макс=(а²-20а+150+10(а-15)√((11,25-2, 75а+0,2а²)/(15-а)))/(-8√((11,25-2,75а+0, 2а²)/(15-а))+(1170-161а+5,8а²)/(15-а)²)/25≤1
    1
  3790. $sin(x-π/4)/cos(x-π/4)dx=-ln|cos(x- π/4)|+c
    1
  3791. (3 4 -2|0) (2 -3 4|11) (1 -2 3|7) (1 0 0|422/347) (0 1 0|27/347) (0 0 1|687/347)
    1
  3792. -2sinx/cos7x/cos8x=2cos15xsinx [sinx=0,-5=cos30x+cos16x+cos14x; x=πn
    1
  3793. En=1;∞(-1)^(n-1)(-(-a/p)^n+(-b/p)^ n)/n=-ln(1-a/p)+ln(1-b/p)
    1
  3794. -1/2(3/2)(1/2)=-3/8
    1
  3795. (√6+√2)*(√6-√2)/2=2 S∆=0,5*2(2√3+2)sin120°=3+√3
    1
  3796. aZ,a:3 a=3n+1✓ a=3n+2 1=2×{3n;3n+1,nZ}
    1
  3797. 2¹⁹⁹⁵>5⁸⁵⁴,1995/854=2 287/854 4⁹⁹⁷*2= 8⁶⁶⁵=128^(285)>125²⁸⁵>125²⁸⁴(²/³)
    1
  3798. (х²+27/2х+77)х=0 х=0;(-27±√503i)/4{0}
    1
  3799. у/x=z,z+xz'=z+1/z,zz'=1/x,z²/2=ln|x|+c, z=±√(2ln|x|+2c),y=±x√(2ln|x|+2c)
    1
  3800. f'(x)=(-2x*2e^x²-(-x²-1)e^x²*4x)/2/e^(2x²)
    1
  3801. √(x+4)=2(1-i) x=-4-8i
    1
  3802. Cos²x=(a-2±(a+4))/2=a+1;-3× a[-1;0],x=±0,5arccos(2a+1)+πn
    1
  3803. (K²-1)x²+(-6k+2c+6)x-c²-6c=0 {k=±1,[c=0,c=-6;[c=0,c=-6;(0;1)(-6;-1)
    1
  3804. 1,5t+0,5=√(t²+3),t≥0 1,25t²+1,5t-2,75=0 t=(-1,5±4)/2,5= 1;-11/5≥0 √(x+6)=1,x=-5✓
    1
  3805. S=13*8-33=71(cm²)
    1
  3806. {y=x²/4-13x/4,[x=0,x=17,x=12,x=-3;{(0;0)(17;17)(12;-3)(-3;12)}
    1
  3807. {у=(3-х²)/х,х=±(√7±1);{(±(√7±1);±(-+9-3√7)/6)}
    1
  3808. {x<a-4,x≥-3a-8,a≥-1,x≤√(25-(a+1)²),x≥-√(25-(a+1)²);(a+1)(a+4)≥0,(a+1)(a-4)≤0✓,x[-3a-8;a-4],∆=4a+4=2 a=-0,5
    1
  3809. y²=x±√(-0,5(x²-1)²) x²-1=0 x=±1 y2=±1 y=±1 (1;±1)
    1
  3810. tgx(cosx+√3/2)=0[x=πn,x=±5/6π+2πn;
    1
  3811. x=(-5a+8±3a)/4=-0,5a+2;-2a+2 {(x+0,5a-2)(x+2a-2)≤0+*-*+>x,x≤a+2,≥a-1;[{a[0;1],x[-2a +2;-0,5a+2];{a[1;2], x[a-1;-0,5a+2];{a<0, x[-0, 5a+2;a+2];
    1
  3812. {3|x-2|+|ax+2a+2|=3,ax+2a+2=y;(a+0,5)/a?0+°-°+>a [{a[0;1/4],x=(-2a+7)/(a+3),(15a+ 6)/(a+3)=y;{a[0;1/4)U(3;∞),x=(-2a-5)/(a-3),(-9a-6)/(a-3)=y;{a[-5/4;-0,5),x=(2a+11)/(-a+3),(15a+6)/(-a+3)=y;{a(-3;-2/3],x=(-2a+1)/(a+3),(19a+6)/(a+3)= y;{a<-0,5,x=(-2a-5)/(a-3),(3a-6)/(a-3)=y;{a[-0,5;-0,4),x=(2a+11)/(3-a),(15a+6)/(3-a) =y;{@(-0,4;0),x=(-2a+7)/(3+a),(15a+6)/(a+ 3)=y;{a[-0,5;0),x=(-2a-5)/(-3+a),(-9a-6)/(a- 3)=y;
    1
  3813. S=0,5*4*2+2(π*2²/4-0,5*2²)=2π
    1
  3814. S=(3√3+3)/2*(3√3-3)+π•6²•30/360-0,5*6² sin30°=3+3π
    1
  3815. S=xy/2+(12-y)*(x-3)/2+(18-x)*(16-y)/2+(y-4)(15-x)/2=96
    1
  3816. T=5/8с l=150 t=240/24=10с
    1
  3817. y'-2/xy=2x³ y=cx²+x⁴✓ (n-2)x^(n-1)c1=2x³
    1
  3818. (x²+a²/16)-√(x²+a²/16)+xa/4-√(xa)/2=0 √(x²+a²/16)=(1±√(-xa+2√(xa)+ 1))/2≥0,[{x²+a²/16=(1+√(-xa+2√(xa)+1))²/4,xa[0;3+2√2];{x²+a²/16=(1-√(- xa+2√(xa)+1))²/4,xa{0}U[4;3+2√2];х=±1,а=0
    1
  3819. f(x,1)-f(x,x)=xf(1) n=2 f(x,y)=ax²+bx+c+a1y²+b1y {a1=0,{b1=0,-c=a+b;f(x,y)=ax²+bx-a-b✓
    1
  3820. 1-(1-tg37°)tg37°=(-sin74°+2)/(1+cos 74°) arctg((-sin74°+2)/(1+cos74°))
    1
  3821. DF=a-btg(45°-arctg(21/a)),b/cos(45 °-arctg(21/a))-a=7,a>21, b=(7+a)√2/2*(a+21)/√(a²+441) DF=a-(7+a)√2/2*(a-21)/√(a²+441) (a+7)⁴+686(a+7)²-28*539(a+7)+20*49²>0 (z+343/3)³-109*49²/12(z+34 3/3)-7⁶*1175/54=0,1190,95>0 z=-343/3+(2350+√(2350²-109³))¹/³*7²/6+(..-..)..;-343/3-(2350+√(2350²-109³))¹/³*7²/12-(..-..)..±√(3/4((2350+√(2350²-109³))¹/³*7²/6+(..-..)..)²-109*49²/12)i a=-7+√(-343/3+(2350+√(2350²-109³))¹/³*7²/6+(..-..)..)+2√(0,5√(-49²*131/36+343/3((2350+√(2350²-109³))¹/³*7²/6+(..-..)..)+((2350+√(2350²-109³))¹/³*7²/6+(..-..)..)²)-343/6-(2350+√(2350²-109³))¹/³*7²/24-(..-..)..) a>-7+√(-343/3+(2350+√(2350²-109³))¹/³*7²/6+(..-..)..)+2√(0,5√(-49²*131/36+343/3((2350+√(2350²-109³))¹/³*7²/6+(..-..)..)+((2350+√(2350²-109³))¹/³*7²/6+(..-..)..)²)-343/6-(2350+√(2350²-109³))¹/³*7²/24-(..-..)..)😢😤😣🤬
    1
  3822. s{An/\{2,3,5,7}}=2,s{An/\A{2,3,5}}=2 An={2,3};{2,5};{3,5} 2^a1*3^a2 (a1+1)(a2+1)<100 99=3*33=9*11 4+4+..
    1
  3823. (х²-х-20)/4/х=х/4-5/х-1/4 х/4-5/х+1/4 х/4-5/х=у 2у²+1/8=1/4 у=±1/4 [х²/4-1/4х-5=0,х²/4+1/4х-5 =0;[х=5,х=-4,Х=4,Х=-5.✓
    1
  3824. X²=A(2x-1)(x²+x+1)+B(x²+x+1)+c(2x+1)(x²-x+1)+D(x²-x+1){A=1/4,B=1/4,c=-1/4,D=1/4;1/4ln|x²-x+|+1/2/√3arctg((x-1/2)*2/√3)-1/4ln|x²+x+1|+1/2/√3arctg((x+1/2)*2/√3)+c
    1
  3825. √(117-108cos2a),6sina,6cosa,9²=6²+117- 108cos2a-2*9√(117-108cos2a)cos/_C,/_C=arccos((4-6cos2a)/3/√(13-12cos2a)) arccos((4-6cos2a)/3/√(13-12cos2a))-90 °+a MH=√(35,25-15cos2a-18cos²2a-9√(1 67 2/9-306 2/3cos2a+140cos²2a)sin2a)
    1
  3826. Y=b-bx/a b²-c²-2b²/ax+x²(b²/a²+1) =0 x=(b²/a±√(b²/a²c²-b²+c²))/(b²/a²+1),y=b/a(a-+√(b²c²/a²-b²+c²))/(b²/a²+1) AB=2√((b²+a²)c²-a²b²)/√(b²+a²)
    1
  3827. cos²x(​2cos⁴x-3cos²x+1)=0[x=π/2+ πn,x=πn,x=π/4+πn/2.{π/4n}
    1
  3828. 62°+a+a=180° a=59°
    1
  3829. (х-19/3)³-334/3(х-19/3)-451 2/27=0 х-19/3=(6089,5+√(6089,5²-334³))¹/³/3+(..-..)..=2/3√334cos(1/3arccos(60 89,5/√334³)+2/3πn) x=19/3+2/3√334cos(1/3arccos(60 89,5/√334³)+2/3πn) 77,5<92 7/9
    1
  3830. AC=AB/sin(2a) AB=10sin(2a) MN=0,5AB(ctga-ctg(2a))=5sin(2a)/sin(2a)=5 C)
    1
  3831. P(x)=Ei=1;nai*x^i Ei=1;nai*(x^2-1)^i=(Ei=1;nai*x^i)²+1 a1;2+..a(n-2)+an=(-1)^n,0=a(n-1), 0=a(n-3),..,[n:2,a1=0;n:/2,a2=0; an=-2a(n-2)=(-2)^[n/2]a(2{n/2})= [(-2)^((n-1)/2)a1,n:/2;(-2)^((n-2)/2) a2,n:2; P(x)=a1((-2)^((n-1)/2)x^n+(- 2)^((n-3)/2)x^(n-2)+..+x),n:/2;a1((- 2)^((n-2)/2)x^n+(-2)^((n-4)/2)x^(n-2) +..+x²),n:2
    1
  3832. a=(-b³/2+√(b⁶/4+b³/27))^(1/3)+(-b³/2-b√(27b³+4b)/6/√3)^(1/3),1 корень: b(-∞;-4^(1/3)/3)U(0;∞),2 корень:b{0}U{-4^(1/3)/3} 3 корень:b(-4^(1/3)/3;0).
    1
  3833. 3/a=√(a²-2²)/a a=13⁰,⁵
    1
  3834. Я бы точно такое же сказал про корейский язык.
    1
  3835. 4+а,5+а-1,8+а-4 а=7✓ 7 напротив 4, 6 - 5, 3 - 8
    1
  3836. -x+0,5=1,5-2(x-1) x=3✓
    1
  3837. lnx=-(ln5+ln2) x=1/10
    1
  3838. 1/9;2/3;9 (2/3-1/9)*1+(9-2/3)*2+(10-9)*3=20 2/9{182}
    1
  3839. 2032/8=254
    1
  3840. √(8/3gpR/c/р(г))=v v=10,4(м/с)
    1
  3841. √(a²+b²-ab) a²+b²-ab=4/√3≥ab S∆=3√3/4ab+1≤4,≥1
    1
  3842. 2acos(|f|/2)/(π-f) (2acos(|f|/2)/(π-f)cos(|f|/2+π/2);2acos(|f|/2)/(π-f)sin(|f|/2+π/2))
    1
  3843. a(cosx-1)+b²=cos(ax+b²)-1≤0,≥-2,(0;0) {b≤√-a(cosx-1),b≥-√(a(-cosx+1)),b²≥-2-a(cosx-1);[{bє[-√(a(-cosx+1));√(a(-cosx+1))],2/(1-cosx)>а;{a≥2/(-cosx+1),bє[-√(-2+a(- cosx+1));-√(-2a(-cosx+1))];{bє[-√(a(-cosx +1));√(a(-cosx+1))],0≤a<1;
    1
  3844. √(y'(t)²+x'(t)²)dt=a√(1+t²)dt
    1
  3845. S=4√3/4*√72²=72√3(cm²) V=1/3*72√(72-18-18)=144(cm³)
    1
  3846. tg⁴(x/2)+(2+√3)tg³(x/2)+(-2+√3)tg(x/2)-1 =0 (tg²(x/2)+(1+√3/2)tg(x/2)-7/8-√3/2)²+ (5/4+23/8√3)tg(x/2)-161/64-7√3/8=0 tg(x/2)=0,64;-3,73 x=2arctg0,64+2πn; 2arctg-3,73+2πn
    1
  3847. Решений нет.
    1
  3848. 4r1r2/(r1+r2)
    1
  3849. 0,5=h,y=a±√(1-(x-1)²) √0,75=x0-1 x0=√3/2+1,y0=-1/4 -+0,5-1/4=a a=0,25;-0,75 a[-2;0,25]
    1
  3850. 9¹/³*10-20=h1✓
    1
  3851. [{у≥1,х[0;1],y=1,x=1;{y≥1,x[-1;0), y=1+√(2-(x-1)²);{y≥1,x<-1,y=1+√(2- (x+1)²);
    1
  3852. 137-9n,n[9;∞) 9'999'995+999'999'995=1009'999'990 1+9*6=55
    1
  3853. 2sin68°sin67°/cos23°/cos22°=2
    1
  3854. 3'900'000,3,9*10⁶*1,5+x,3,9*10⁶*1,5⁴+x(1,5³+1,5²+1,5+1) 3,9*10⁶*1,5⁵+x(1,5⁴+1,5³+1,5²+1,5)=3,9*10⁶*8,25 x=210*10³(руб.)
    1
  3855. {х=(у²+3)/у,3(у²)²+14у²+18=0;у²=-7/3±√ -5/3,у=±6⁰,²⁵(√(-7√6+18)/6±i√(18+7√6)/6) х=±(-16√(-7√6+18)+√(90+35√6)±i(16 √(18+7√6)+√(-35√6+90)))6⁰,⁷⁵/108 xy= 6⁰,²⁵(117√6±i(-8√30+18√5))/324 Otvet:6⁰,²⁵(117√6±i(-8√30+18√5))/27=8.
    1
  3856. lnsinx(-∞;0] x=arcsine^y $(0;∞) arcsine^-y*dy=π/2/(1-1/e)
    1
  3857. ([x]-1)([x]+3)≤0 [x][-3;1],x[-3;2)
    1
  3858. $√(x²-9)/xdx=$3(-2e^u/(e^2u+1)+ch u)du=3(-2arctg(x/3±√(x²/9-1))±√(x²/9-1))+c x=3chu dx=3shudu 0=(e^u)²-2x/3 e^u+1 e^u=x/3±√(x²/9-1)
    1
  3859. {a+b²*3+c²*2=6,ab=-1/2,ac=-1,bc=1;abc=±1/√2 (±√2/2;-+√2/2;-+√2) 1/2+1/2*3+2*2=6✓ |√2/2-√6/2-2|=-√2/2+√6/2+2✓
    1
  3860. a=2x-x³ x³-2x+a=0 x=(-a/2+√(a²/4- 8/27))¹/³+(..-..).. cos(1/3arccos(-a/2/√(8/27))=3a/4√1,5 4√3/9=a
    1
  3861. 3333^(2x)=-0,5±3333,5=3333;-3334>0 x=1/2
    1
  3862. x²+4xy+y²+1/4=0, x=(-4y±√(16y²-4*(y²+ 1/4)))/2=-2y±√(16y²-4y²-1)/2=-2y±√(12y²- 1)/2,12y²-1≥0,(y-1/√12)(y+1/√12)≥0, +**+>y,yє(-∞;-1/√12]U[1/√12;+∞) √(1-4(-2y±√(3y²-1/4))²)-√(1-4y²)-2x -2y=0,√(2-28y²±16y√(3y²-1/4))-√(1-4y²)+2y-+2√(3y²-1/4)=0,2-28y²±16y√(3y²-1/4)-2√(2-28y²±16y√(3y²-1/4))√(1-4y²)+1-4y²=4y²±8y√(3y²-1/4)+4(3y²-1/4),±8y√(3y²-1/4)+4-48y²-2√(2-28y²±16y√(3y²-1/4)√(1-4y²)=0,64y²(3y²-1/4)±16y√(3y²-1/4)(4-48y²)+(4-48y²)²=4(2-28y²±16y√(3y ²-1/4)) 2496y⁴-288y²+8=±768y³√(3y²-1/ 4) 2496²y⁸+288²y⁴+8²-2*2496*288y⁶+ 2*2496*8y⁴-2*288*8y²=768²y⁶(3y²-1/4), (312²-96²*3)y⁸+(-624*36+96²/4)y⁶+(1296 +624)y⁴-72y²+1=0,y²=a,≥0,aє[1/12;1/4]144*(26²-64*3)a⁴+144(-52*3+16)a³+1920a²-72a+1=0,144*16*157a⁴-144*140a³+1920a²-72a+1=0, (а²-35/8/157а+0,00226..)² 7,28*10^-5а-4,29*10^-6=0,\>/> минимум а=35/8/157/2=35/16/157,-1,01*10^-6<0 поэтому есть 2 корня, а=0,014,а=0,010 у=±0,12..>0,289,<-0,289,у=±0,101>0,288,<-0,289 0/ 169-12=157
    1
  3863. 6/√5*2/√5=12/5 S∆=0,5*3*12/5=3,6(cm²)
    1
  3864. 4H=..T H≠0;6,T:2 500M+100A+29T/2+2H=555X -0,5T+2H:5 min=-2 max=18 ..=0;5;10;15 ..=0 T=4H,H=1;2 T=4;8 20A=11M+99;87≤180 M≤7;8 M=9×;3 A=6,X=4,H=2,T=8 T=4H-10 H=3;4 T=2;6 20A=11M+100;98 M=0×;2 A=6,X=3,H=4,T=6 T=4H-20 H=5;7× T=0;8× 20A=11M+109;85 M=1;5× A=6;7× X=2 T=4H-30 H=8;9 T=2;6 20A=11M+102;90 M=8;0× A=×✓ M+A+T+H-X=15×;15×;10✓{2}
    1
  3865. х³/3-3х2/2+7х|(-1;2)=2³-1,5*2²+7*2-(-1)³/3+1,5*1-7*-1=24 5/6
    1
  3866. е^(2х)/2|(0;1)=е²/2-1/2
    1
  3867. $(√3/4;3/4)dx/(9+16x²)=1/16arctg(x/(3/4))/(3/4)|(√3/4;3/4)=1/12arctg(3/4/3* 4)-1/12arctg(√3/4/3*4)=1/12*π/4-1/12 *π/6=π/144
    1
  3868. $(4;9)(2/3x+0,25x-⁰,⁵)dx=2/3x2/2+0,25 x⁰,⁵/0,5(4;9)=1/3*9²+0,5*9⁰,⁵-1/3*4²-0,5* 4⁰,⁵=22 1/6
    1
  3869. y'=xy/(x²-2y²),y'(-2y²+x²)=xy,-2(y³)'+x²y'-x y=0,y=ce^u,-6c³e^(3u)u'+x²ce^uu'-xce^u=0,(-6En=0∞(2u)^n/n!c²+x²)u'-x=0,u=(3c²W (-e^(k1/3/c²)x²/6/c²)-k1)/6/c² y=ce^(0,5 W(-e^(k1/3/c²)x²/6/c²)-k1/6/c²)
    1
  3870. √(a²-x²)=a+√(a²/4-(a-x)²),a²-x²=5/4*a²-a²+2ax-x²+2a√(-3/4*a²+2ax-x²),(3/4*a²-2ax)²=4a²(-3/4*a²+2ax-x²), 9/16*a⁴-3a³x+4a²x²+3a²-8a³x+4a²x²=0, 8a²x²-11a³x+9/16*a⁴+3a²=0, x=(11a³±√(121a⁶-32a²(9/16*a⁴+3a²)))/16/a²=11a/16±√(103a²-96)/16,/_а=arcsin(5/16*а±√(103а²-96)/16)/(0,5а) S=0,5arcsin(5/16*а±√(103а²-96)/16)/(0,5а)a²/4-0,5(a/2)²(5/8±√(412-384/a²)/8)+a²/2*arccos(11/16±√(103a²-96)/16)-0,5a²sin(arccos(11/16±√(103a²-96)/16)=0,125arcsin(5/8±√7/4)-0,125(5/8±√7/4)+0,5arccos(11/16±√7/16)-0,5√(1-(11/16±√7/16)²)=0,125arcsin(5/8±√7/4)-0,078125-+0,03125√7+0,5arccos(11/16±√7/16)-0,5√(43/128-+11√7/128) 256-121-49=86 А Карл Фридрих Гаусс тоже думал над геометрией Лобачевского, но только его бы просто не поняли.
    1
  3871. У меня такой же ноутбук, как у автора канала.
    1
  3872. x²+4x=y,(y-2 1/4)(y+1 3/4)<0 +-1,75°-°2,25+>y y(-1,75;2,25){(x+0,5)(x+3,5)>0+°-3,5-°-0,5+>x,(x-0,5)(x+4,5)<0+°-4,5-°0,5+>x; {x(-∞;-3,5)U(-0,5;∞),x(-4,5;0,5);x(-4,5;-3,5)U(-0,5;0,5)✓
    1
  3873. (2,5+a)²+(a/2)²=5² -18,75+5a+1,25a²=0 a=-2±√19≥0 a=-2+√19 S=23-4√19
    1
  3874. [{x[π/2;π],sinx;{x[0;π/2),sinx.
    1
  3875. √х=u,x=u²,dx=2udu $cosu*2du=2sin u+c=2sin√x+c
    1
  3876. y-²(1+y⁶)/y/(y⁶+1)=y-³
    1
  3877. Почему у того бородатого голос как у Понасенкова?
    1
  3878. c¿(a+b-2)/(ab-1) -(b²-b+1)/(Ab-1)²=0 ×->a min=-1+2/(b+1)\>0 c(-1;0)c<0 ?=>✓ Т.к. условие симметричное, то выбирает такую переменную, которая принадлежит промежутку (-1;0). Если таких нет,то с¿-b+2≥1 ?=>.Ч.т.д.
    1
  3879. х<97,х≥95 хє[95;97)руб.
    1
  3880. n=(1+2m)/(1/6+2k)
    1
  3881. 1/(n1+..+n2022+2)(ln(n1+..+n2022+ 3)+0,5-0,5/(n1+..+n2022+3))*0,5 конечное число,никак быстро не вычисляемое
    1
  3882. 150/7=21 3/7г. Для собаки слишком много!
    1
  3883. 5√10/2=R
    1
  3884. 1/(х+1)=f(x)✓
    1
  3885. 65+8√2✓
    1
  3886. A=1,BCD+BC+B=284,B=2 CD+C=62,C=5,D=7{1257}
    1
  3887. 100-25π/2✓
    1
  3888. [x=0,(2/3)^x=1+(4/3)^x;x=-1,3{0;-1,3}
    1
  3889. A=-B+90° (m;n)=)15;8)(8;15)
    1
  3890. X=3^n 6n*3^(6n)=3/> 6n=1 n=1/6 x=3¹/⁶✓
    1
  3891. (3/2-2/5x+1/6x²-7/3)/x³=0 x²/6-2/5x-5/6= 0 x=6/5±√161/5
    1
  3892. ∆=(9-n)*n,∆=3*6=18 10+18=28
    1
  3893. x²/45=25 x=15√5
    1
  3894. (x+1/x)²-3,5(x+1/x)-2=0 x+1/x=(3,5 ±√20,25)/2=4;-0,5× x=2±√3
    1
  3895. R1R2=4m² S=π/2(2R1R)=4π(m²)
    1
  3896. |(2x-3)²-36| x=2,35× x0=4,5;-1,5 x=4,11✓ x=5,13✓ x:3,9|(2x1-1)²-4|:3,>3 |(2x-9)(2x+ 3)|x>5×,x=-1 11✓,x=-2 13✓{-2;-1;4;5}
    1
  3897. {sin5x=1,cos2x=-1;{x=π/10+2/5πn,x=π/2+ πn. 2n=2+5m,n=5n1+1 x=π/2+2πn1
    1
  3898. o=-45°+360°n;105°+360°n tgo=-1;-2-√3
    1
  3899. h=3/(16√91/91)=3/16√91 EC=3/16√91 /(√0,91/5)=75/8 AE=-35/8
    1
  3900. sin²x(cosx-1)²/√(16-2^(x-5)²)≤0 {x=2πm, x(3;7);m(1,5/π;3,5/π)=1 x=2π
    1
  3901. ±х-2^(х/32)=0 1-2^(х/32)ln2/32=0 x=32log2(32/ln2)+*->x max=32log2(32/ln2/e)>0 x=256;1,03 x=-0,97{256;1,03;-0,97}
    1
  3902. X=3n+x1,y=3m+3-x1 x1=-1,5n+1,5m+1,5±√((n+m+1)³-15/4(n+m+1)²+3(n+m+1)+1-9m) n+m:2 -1,5n+1,5m+1,5±√((n+m+1)³-15/4(n+m+1)²+3(n+m+1)+1-9m)[0;2] (n;m)=(0;0)(0;-1)(1;-2)(2;-1)(1;3)(5;-1) (0;0)(0;-3)(3;-6)(6;-3)(3;9)(15;-3)
    1
  3903. √(144+(12-2a)²)/3/(12-a)=(12-2a)/√(144+(12-2a)²) 6-+√18=a≤6 a=6-√18 S∆=48-2a=36+6√2
    1
  3904. x((6,5+√9897/18)¹/³+(..-..)..;∞) (x-2,5)/(x³+2x-13)≥0 x(-∞;2,..]U[2, 5;∞) x[2,5;∞)
    1
  3905. 8:55 диктатор Португалии.
    1
  3906. Паша, о таких либералах писал ещё Ленин.
    1
  3907. √(7/3)=1,52..<log(2)3=1,59
    1
  3908. (Sin(π/2-x))²=sin(x-π/4)√2 (cosx+1)((cosx+1/3)³+2/3(cosx+1/3)-34/27)=0[x=π+2πn,x=±arccos(-1/3+(17+3√33)¹/³/3+(..-..)..)+2πn.cos²x-2ctgx=∞;(-1/3+(17+3√ 33)¹/³/3+(..-..)..)²-2(-1/3+(17+3√33) ¹/³/3+(17-3√33)¹/³/3)/√(1-(-1/3+(1 7+3√33)¹/³/3+(17-3√33)¹/³/3)²)
    1
  3909. a=-1±√31>0 a=-1+√31 1+√31.
    1
  3910. (x²-3x-5,5)²+25x-81,25=0 1,5+√31/2є/Q \1,5-√31/2(-25√31/2-43,75)*/1,5(16,312 5)*\*1,5+√31/2(12,5√31-43,75)/ x=-√31 -0,25;1,5-32,625/(119,565+25√31)
    1
  3911. S=12*0,5*4²sin30°=96*0,5=48
    1
  3912. Sж=27π-13,5π=13,5π
    1
  3913. 3^(6x)=3^9 x=1,5
    1
  3914. x(-∞;-2]U[0;2] 1/24=x(2=2)✓
    1
  3915. 0=(x+1)³-17(x+1)+4,x≥1 x+1=(-2+√(4-17³/27))¹/³+(..-..)..= 2√(17/3)cos(1/3arccos(-6/17/√(1 7/3))+2/3πn) x=-1+2√(17/3)cos(1/3arccos(-6/17/√(17/3))),n=0✓{3}
    1
  3916. 3,6/0,3=12 4²=1²+l²-2lcosa,4²=3²+l²-2*3lc os(180°-a),cosa=(l²-15)/2/l, 16=9+l²+6(l²-15)/2/l*l,-3l²+52=0,l=√(52/3) √(52/3)/13,√(52/3)*12/13 √((2√(13/3)/13+2*12√(13/3)/13+3)/2(√(13/3)+1,5 -2√(13/3)/13)(√(13/3)+1,5-2√(13/3)* 12/13)(√(13/3)+1,5-3))=√(√(13/3)+1,5)(11/13√(13/3)+1,5)(-11√(13/3)/13+1,5)(√(13/3)-1,5))=√((13/3-2,25)(2,25-121*1 3/3/169))=√(2 1/12*(-133/156))=5/2/6 √(133/13),√((2√(13/3)/13+24√(13/3)/13+4)/2(√(13/3)+2-2√(13/3)/13)(√(13/3)+2-24√(13/3)/13)(√(13/3)+2-4)=√((2√(13/3)+2)(11√(13/3)/13+2)(-11√(13/3)/13+2)(√(13/3)-2))=√((4*13/3-4)(4-121*13/3/1 69)=2√(10/3*35/39)=10/3√(14/13) √3/4*4²-4√3*1/4-5/12√(133/13)-10/3√(14/13)=3√3-5/12√(133/13)-10/3√(14/13)
    1
  3917. (2x-1)(3y+2)=33(2;3)
    1
  3918. x³-+ix-1=0 x=(1/2+√(1/4±i/27))¹/³+(..-..)..=(1/2+√(1/8(1+16/729)¹/²+ 1/8)±i√(1/8(1+16/729)¹/²-1/8))¹/³+(..-+..)..=(1/4+√(1/8(1 16/729)¹/²+ 1/8)+1/4(1 16/729)¹/²)¹/⁶(cos(1/3a rccos((1/2+√(1/8(1 16/729)¹/²+1/ 8))/√(1/4+√(1/8(1+16/729)¹/²+1/ 8)+1/4(1 16/729)¹/²))+2/3πn)+isin (1/3arccoa((1/2+√(1/8(1 16/729)¹/²+1/8))/√(1/4+√(1/8(1+16/729)¹/² +1/8)+1/4(1 16/729)¹/²))+2/3πn))+ (1/4-√(1/8(1 16/729)¹/²+ 1/8)+1/4(1 16/729)¹/²)¹/⁶(cos(1/3a rccos((1/2-√(1/8(1 16/729)¹/²+1/ 8))/√(1/4-√(1/8(1+16/729)¹/²+1/ 8)+1/4(1 16/729)¹/²))+2/3πn)-+isin (1/3arccoa((1/2-√(1/8(1 16/729)¹/²+1/8))/√(1/4-√(1/8(1+16/729)¹/² +1/8)+1/4(1 16/729)¹/²))+2/3πn))
    1
  3919. 2(x+1,5)⁴+3(x+1,5)²-16 7/8=0 (x+1,5)²=(-3±12)/4=9/4;-15/4≥0 x+1,5=±1,5 x=0;-3
    1
  3920. Rsin48°,R(1-cos48°) sin48°/(1-cos48 °)=ctg24°=tg66° 180°-a=66° a=114° B)
    1
  3921. 5^√x+√x=27/> √x=2 x=4✓
    1
  3922. a²=(a-b)²+(a-64/b)² 0=b²+(-a-+√128) b+64 b=(a±√128±√(a²±2√128*a-128))/2 a-64/b-∆x=∆x+b ∆x=a/2-32/b-b/2 x=8
    1
  3923. Р=0,25 кВт, v=15 км/ч,Р=Fv, F=250/4,17=60 H, m=61 кг
    1
  3924. х=-1/2✓
    1
  3925. S=22+(4)*2/3=24 2/3
    1
  3926. x=(x-0,5)(cos(2πn/2001)+isin(2πn/2001)),n=1..2000 x=-0,25/sin(πn/2 001)(-sin(πn/2001)+icos(πn/2001)) Ei=1;2001xi=500,25
    1
  3927. [x≤-7,x≥9;x(-∞;-7]U[7/9;∞)
    1
  3928. {x}=2024+2024²/([x]-2024) [-1;0] {x}=2024/2025;0 x=-1/2025;0
    1
  3929. 22,5*15=337,5=225*1,5✓ √(15²-9²)=12 22,5/15*12=18 h=18-12=6 a=22,5*9/15= 13,5 S=(13,5+9)/2*6=67,5.
    1
  3930. Объяснение такое же, почему солнечные сутки длиннее звездных.
    1
  3931. x+y±√(xy)=a,√y²±√x√y+x-a=0, x2+y²+xy=b2,√y=(-+√x±√(x-4(x-a)))/2, z=±√(xy),y=(x-3x+4a-+2√(x(-3x+4a)))/4, x²+(x-3x+4a-+2√(x(-3x+4a)))²/4²+x(x-3x+4a-+2√(x(-3x+4a)))/4=b²,16x²+(-2x+4a)²-+4(-2x+4a)√(-3x²+4ax)+4(-3x²+4ax)+4x(-2x+4a-+2√(-3x²+4ax))= 16b²,16a√(-3x³+4ax)=-20x²+16xa-16a²+12x²-16ax+8x²-16xa+16b²,|:4,16a²(-3x²+4ax)=(-4xa-4a²+4b²)²,|:16 -3x²a²+4a³x=x²a²+a⁴+b⁴+2xa³-2xab²-2a²b²,-4x²a²+2a³x-a⁴-b⁴+2xab²+2a²b²=0, x=(-2a³-2ab²±√((-2a³-2ab²)²-4*(-4a²)(-a⁴-b⁴+2a²b²)))/(-8a²)=0,25+0,25b²/a±√(1/16*a⁶+2/16a⁴b²+1/16a²b⁴-1/4*a⁶-1/4*a²b⁴+2/4*a⁴b²)=0,25+0,25b²/a±a√(-3/16*a⁴-3/16*b⁴+5/8a²b²),y=(-2(0,25+0,25b²/a±a√(-3/16*a⁴-3/16*b⁴+5/8 *a²b²))+4a-+2√(-3(0,25+0,25b²/a±a√(-3/16*a⁴-3/16*b⁴+5/8a²b²))²+4(0,25+0,25b²/a±a√(-3/16*a⁴-3/16*b⁴+5/8 *a²b²))a))/4,z=±√((0,25+0,25b²/a±a√(-3/16*a⁴-3/16*b⁴+5/8a²b²))(-0,5-0,5b²/a-+2a√(-3/16a⁴-3/16b⁴+5/8a²b²)+4a-+2√(-3(0,25+0,25b²/a)²-+6a(0,25+0,25b²/a)√(-3/16a⁴-3/16b⁴+5/8a²b²)-3(-3/16a⁴-3/16b⁴+5/8a²b²)+a+b²±4a²√(-3/16a4-3/16b4+5/8a²b²)))/4)
    1
  3932. $(1;∞)(lnx)²⁰¹¹x-²⁰¹¹dx=-(lnx)²⁰¹¹* x-²⁰¹⁰/2010-2011(lnx)²⁰¹⁰x-²⁰¹⁰/2010²-..-2011!x-²⁰¹⁰/2010^2012 (1;∞)=2011!/2010²⁰¹²
    1
  3933. -;--10*+;-*2+;+>х 3х-|х+10|-|х-2|≤-6 [x=2,x[-10;2);x<-10;x(-∞;2]
    1
  3934. 8 1/3=(15k+5)/(2k+6) k=-27.
    1
  3935. (R-10)²+8²=(R-8)² 25=R
    1
  3936. (х⁵+х+1)/(х²+х+1)=х³-х²+1
    1
  3937. (1+√(1+4x()/2=(x+√(x2+4x))/2 {x≥1/6;[x=0,20x²-19x+4=0;x=(19±√41)/40 {(19+ √41)/40} x+x/y=y 0=y²-xy-x y=(x+√(x²+4x))/2
    1
  3938. f(x²)=f(x)/2 x=2^2^n f(2^2^(n+1))=f(2)/2^(n+1) f(x)=f(2)/log2(x) f(xy)=f(2)/log 2(xy)=f(2)/(og2(yx)
    1
  3939. (19+6√2)²,⁵=(433+228√2)(3√2+1)= 1527√2+1801
    1
  3940. 2x+3y+9=x/3-1,5y+5/3=3x-y {x=-49/5,y=2.
    1
  3941. ..>n(m-1)/2-m+1,≤n(m-1)/2 ..=[n(m-1)/2]..
    1
  3942. 3^log0,6(log(3)5)-5^log0,6(log(3)5)≥3^x-5^x=4(x-0,75)²-2,25≥-2,25 1 koren x[0,75; ∞)х=1(-2=-2),хє[-log3(5);0,75)\>=\> х=0 x<log(0,6)log3(5),/>=\>x=-1,7 0/ {1;0}
    1
  3943. 2√r1+2√(r1(3-2√2))=2√(3-2√2) r1=1,5-√2.
    1
  3944. -√(x²-2)(x²-1)/2arcsin²(1/(x²-1))/2-x(3x²/2-2,5)(x²-1)/2*arcsin³(1/(x²-1))/6-...(√2; ∞)=√2(π/4)³/24+..
    1
  3945. E..≥-ln²n+2lnn/n,≤-ln²n+2lnn/n-0,5n-¹+0,5 lim[n^(2+2/n)/n^n;n^(2,5+2/n)/n^n/n^(0,5 n-¹)]=0
    1
  3946. (x-1)(x²-2x+4)=0[x=1,0/.
    1
  3947. a+b-2√(12/π)=√(a²+b²) a=(2√(12/π)b-24/π)/(b-2√(12/π)) tg(90°-2/_ 1)=b/a 1-2b/atg/_1-tg²/_1=0 tg/_1 =-b/a+√(b²+a²)/a r=((b-√(12/π))²+ 12/π)/((b+√(12/π))²-36/π)*√(12/π) S=36(?)
    1
  3948. A1=3,an=S(n-1)/(n-1)+n*2^n=1+(n+1)*2^n
    1
  3949. $√(x²+x+1)/(x+1)dx-х+ln|x+1|+c √(x²+x+1)=u,x=-0,5±√(u²-0,75) dx=±(u²-0,75)-⁰,⁵udu $(±0,5(u²-0,75)⁰,⁵±0,375(u²-0,75)-⁰, ⁵)/(1-u²)du+u+0,5ln|u-1|-0,5ln|u+1|
    1
  3950. z=(9+2i±(1+8i))*(2-i)/10=3+i;1-2i✓
    1
  3951. P*9²+q*9+r=q*6²+r*6+p P*80=q*27+r*5,q:5 q[0;5],q=0;5,q≠0 q=5,r[0;5],p[1;5],16p=27+r p=2,r=5 n=2*9²+5*9+5=212=11010100(2)
    1
  3952. х=(37±√169)/2[х=25,х=12.
    1
  3953. (x+2)²+5²=(x+3)² 10=x✓
    1
  3954. yMctga xM+yMctga,y=-tga*x+tgaxM+2yM y=tg/_Ax x=(tgaxM+2yM)/(tga+tg/_A) y=(tgaxM+2yM)tg/_A/(tga+tg/_A) S∆=0,5 (tgax²M+3yMxM+2yM²ctga)tg/_A/(tga+tg/_A) S∆'=0,5tg/_A(tg²a(x²Mtg/_A-3xMyM) 4yM²tga-2yM²tg/_A)/(tga+tg/_A)²/sin²a=0 tga=(2yM²±yM²√(4yM²+2x²Mtg²/_A-6xM yMtg/_A))/(xM²tg/_A-3xMyM)+**+>a min=yM(5xMyM+6yM²ctg/_A+3xM²tg/_A± √(4y M²+2x²Mtg²/_A-6xMyMtg/_ A)(2x M- 3yMctg/_A))(2yM²-3xMyMtg/_A+xM²t g²/_A-+yM√(4yM²+2x²Mtg²/_A-6xMy Mtg/_ A))/(-6yM³+11xMyM²tg/_A-6xM²yMtg²/_A+xM³tg³/_A)
    1
  3955. √(x/7)=-(1-x/7)^(1/6)+1{(-x/7+1)^(1/6)((-x/7+1)^(5/6)+(1-x/7)^(1/6)-2)=0,x≥0, x≤7;{(1-x/7)^(1/6)=0,(1-x/7)^(1/6)=1,/>;xє[0;7];{[х=7,х=0;Хэ[0;7];{0;7}.
    1
  3956. e^2x+e^-x=2
    1
  3957. L^-1{3/p+7/p³+4/(p²-7)}=3+7/2t²+4/√7 sh(√7t)
    1
  3958. X+5x²+4=5(-x-1)+x+4=-4x-1
    1
  3959. 44:07 Яшин?
    1
  3960. 2/а=1/n,n=m², a=2n, 1/a<1/n, a>n, 2017: 2=1008,5>n,<2n nє(504;1008) √nє[23;31]
    1
  3961. S=4+2√2-(2+√2)=2+√2
    1
  3962. an=(1-nan)/(n+3) an=1/3 a(n+1)=2/(n+ 2)/(n+3)...+6a/(n+3)/(n+2)/(n+1)
    1
  3963. xa(xz²+yz²+2)+iya(xz²+yz²+2)+i(2x²axz+2y²axz+xz)+yz(2xa²+2ya²+1)=0 {±xa(-2xa²-2ya²-1)√((2xa²+2ya²+1)²-4ya²yz²-8ya²)=2ya²yz²xa+2xaya²-2xa²yzya²-2yzya⁴-ya²yz-xa(-2xa²-2ya²-1)², xz=(-2xa²-2ya²-1±√((2xa²+2ya²+1)²-4ya²yz²-8ya²))/2/ya;
    1
  3964. sin(A-B)=3/5,sinA=2sinB ±√(1-4sin²B)sinB=sin2B-3/5 B=-0,5arccos(4/√41)+0,5arcsin (6,2/√41)(-1)^n+0,5πn(0;180°) B=-0,5arccos(4/√41)+0,5arcsin (6,2/√41);-0,5arccos(4/√41)+0,5π- 0,5arcsin(6,2/√41) A=π-arcsin(2sinB);arcsin(2sinB) (a+b)/c=3/(2cosB+cosA)=1/5√205; 3/√5✓ C)
    1
  3965. R=√48 h=2*4√3*√3/2=12 a=12√3 S∆=72√3 m²
    1
  3966. у=се^2х-0,5xe^-2x-0,25e^-2x
    1
  3967. lnx=1 8/17 x=e^(1 8/17)
    1
  3968. 6+(x+3)²=(x+5)²,{x+3>0,x+5>0;x²+6x+15- x²-10x-25=0,x>-3,x>-5;{-4x-10=0,x>-3;{x= -2,5,x>-3x=-2,5.;
    1
  3969. $xcos3xdx=xsin3x/3+cos3x/9+c
    1
  3970. (8-2a)²+(8-a)²=8² 64-48a+5a²=0 a=(24±16)/5=8×;8/5✓{64/25}
    1
  3971. $(0;1)sinlnx/lnx*dx=$(-∞;0)sinu/u*e^udu =sinu/u*e^u-(cosu*u-sinu)/u²e^u+.. (-∞;0)=1*1-(1*0-0)/0*1+...-0+0-...=-∞ lnx=u,x=e^u dx=e^udu
    1
  3972. (7+1)/)7-1)=4/3
    1
  3973. -2/25а³b✓
    1
  3974. 4=0,5(b-18/a)(a-10/b) 0=(ab)²-36ab+280 ab=18±√144≥18 ab=30
    1
  3975. 0=5(x-31,5)⁴+2,5(x-31,5)²-30,937'5 x-31,5=±1,5 x=33;30✓
    1
  3976. (b-√15)²+14√10-15=14√10-5
    1
  3977. (2-r2)²=(r1-r3)(r1+2r2+3r3) -r1²-2r1r3+3r3²+4+(-2r1+2r3-4)r2+ r2²=0 r2=r1-r3+2-√(2r1²+4r1-2r3²-4r3)<2 r1≥r3 S=π((-3r1+r3-4)√(2r1²+4r1-2r3²-4r 3)+4r1²-2r3²+10r1-6r3-r1r3+4)
    1
  3978. 0,25ln|t-1|-0,25ln(t+1)-0,25/(t-1)-0,25/(t+1)(2;x)=-0,25/(x-1)-0,25/(x+1)+0,25ln3+0,25+1/12 0,25ln3+1/3
    1
  3979. 23²+7²=578=2а² а=17≥0✓
    1
  3980. 0=(a1²+3da1+d²)²-4a1-d²-6d a1+1,5d=2 -836/169-42/13d+(3,25d²-10,5d+128/ 13)²=0
    1
  3981. 1¹8¹9¹6¹9*2=37938 6 цифр д[1;4], т[2;9] а≠0,р:2 а=9 д=1,т=3,м=6 (2;5;7)×(3;7;×(4;8;9)×
    1
  3982. A/r√(1-2πr/A)=h✓
    1
  3983. 12/(8*0,644)=2,33 раза
    1
  3984. bn=a(n-1)+6+(-3a²(n-1)-a(n-1)+1)/(a³(n- 1)+2a²(n-1)+a(n-1))≥2(n+1)>2n✓,a1=0,5 limn->∞(a1+a2+..+an)=limn->∞(0,5+2/9 +..+a(n-1)/(1+a(n-1))²)=0,5ln(n+1)/n=0
    1
  3985. (3/2)^(2/9)✓
    1
  3986. $(-∞;∞)f(x)(x²+4a)-⁰,⁵xdx=$(-∞;∞) f(x)dx
    1
  3987. Байер от bay - по-немецки залив, по-английски купить. А Шлецер никак не переводится,скорее всего от слёз.
    1
  3988. $x²sinπxdx=x²*-cosπx/π+2xsinπx/π²+ 2cosπx/π³+c
    1
  3989. (2+√-121)^(1/3)+(2-√-121)^(1/3)=2√125cos(arccos(2/√125)/3+2πn/3){10√5cos(a rccos(2/√125)/3);10√5cos(a rccos(2/√12 5)/3+2π/3);10√5cos(arccos(2/√125)/3+ 4π/3)}
    1
  3990. {0=-4,4+0,4x,y=x²+1;{x=11,y=122.
    1
  3991. $(π/4;π/3)(1-0,5/cos²0,5x)dx=x- tg(0,5x)(π/4;π/3)=π/12-√3/3+√2-1
    1
  3992. Arccos((2500-a²)/2400) √(2500-a²)/2/40=sin(45°-0,5arccos((2500-a²)/2400)) √6√(2500-a²)/2=√(4900-a²)-√ (-100+a²) (525+0,75a²)²=(4900-a2)(-100+a²) 765'625-8425/2a²+25/16a⁴=0 a²=4(337±288)=2500;196 a=×50;14 S∆=0,5*30*40*7/25=168
    1
  3993. $(0;2)dx$(0;4-x²)xe^(2y)/(4-y)dy=$(0;2)dx (e⁸/4/xe^(-4x²)-e⁸/4/x-xe⁸/16(e-¹⁶-1))=(-e⁸/32x-²+e⁸/32x-⁴..)*e^(-4x²)-e⁸/4ln|x|-x²/2*e ⁸/16(e-¹⁶-1)|(0;2)=(-1/128+1/512+..)e^-8 -e⁸(1/4ln2+1/8e-¹⁶-1/8)+∞=∞
    1
  3994. 1-1/3√3-2KE/3√3=BE=2-√3
    1
  3995. z=x²-xy+2y²+3x+2y+1 x=0,y=0,y=-x-5 z'(x)=2x-y+3=0 x=0,5y+1,5 z'(y)=-x+4y+2 =0 y=x/4-0,5 x=0,5(x/4-0,5)+1,5 x=1,25/(7/8)=10/7 y=-1/7 (10/7;-1/7) *+>x*+>y min(10/7;-1/7) z(0;0)=1,z(-5;0)=9 z(0;-5)= 41 4x²+26x+41=4(x+3,25)²-5/4≥-1,25
    1
  3996. $√tgxdx=$u/(u⁴+1)*2udu=$2u²/((u²+1) ²-2u²)du=$2u²/(u²+1+√2u)/(u²+1-√2u)*du =$(A(2u+√2)/(u²+√2u+1)+B/((u+√2/2)²+0,5)+C(2u-√2)/((u-√2/2) ²+0,5))+D/((u-√2/2)²+0,5))du=2arctg ((u+√2/2)/√0,5)/√0,5+C=2√2arctg(√2 √tgx+1)+C 2u²=A(2u+√2)(u²-√2u+1)+B((u-√ 2/2)²+0,5)+C(2u-√2)((u+√2/2)²+0,5))+D((u+√2/2)²+0,5)=2Au³-2√2Au²+2Au+√2Au²-2Au+√2A+Bu²-√2Bu+B+2Cu³+2√2Cu²+2Cu-√2Cu²-2Cu-√2C+Du²+√2Du+D=(2A+2C)u³+(-2√2A+2A+B+√2C+D)u²+(-√2B+√2D)u+√2A+B+D-√2C {2A+2C=0, (-2√2+2)A+B+√2C+D=2,|*2/(-2√2+2)-√2B+√2D=0, √2A+B-√2C+D=0|*√2;{2A+2C=0, (√2+1)B+(4+√2)C+(√2+1)D=2√2+2,-√2B+√2D=0,|*(√2+1)/ -√2 (-√2)B+4C-√2D=0;|•(√2+1)/-√2 {2A+2C=0, (√2+1)B+(4+√2)C+(√2+1)D=2√2+2,(4+√2)C+(2√2+2)D=0, (8+3√2)C=0;{A=0,B=2,C=0,D=0; √tgx=u, tgx=u², x=arctgu² dx=1/((u²)²+1)* 2udu
    1
  3997. √(16*4)=8
    1
  3998. f(x)=ca^x a^(a^x)=e^-x,c=1×
    1
  3999. -lnf(x)=f-¹(x) невозможно решить
    1
  4000. x=i)-i+2πn)=1+2πni
    1
  4001. Y=(15-ax)/b h=20/13√13 k=2/3 y=-1,5(x-x0)+(15-ax0)/b=2/3(x+1) +1 x=90/13/b-6/13x0(a/b-1,5)-10/ 13 ±20=45/b-x0(3a/b+2)-5 [x0=(-25-45/b)/(3a/b+2),x0=(15-45/b)/(3a/b+2).a≠-2/3b,b≠-9/5;3 5a+2b≠-4/3b=12/5;-4(4)
    1
  4002. (1 2). (-4 1 3) (-2 7 -1) (-3 2)*(1 3 -2)=(14 3 -13)
    1
  4003. |(0;8)√6/4(y³/6*π+y³,⁵/10,5lny-y³,⁵/10,5/3,5+(π/6+ln2/3)y²,⁵/1,5-ln2/ 10,5y³,⁵-y²,⁵/7,5lny+y²,⁵/7,5/2,5)= √6*64/3π+7'552√3/105ln2-37'756√3/49/75+(π/18+ln2/9)*128√3
    1
  4004. f(x+y)=xf(y)+yf(x),f(y)=yf(0),f(0)=0 f(y)=0
    1
  4005. (х⁰,⁵+х-⁰,⁵)⁷-5(х⁰,⁵+х-⁰,⁵)⁵-(х⁰,⁵+х-⁰,⁵)³+5(х⁰,⁵+х-⁰,⁵)=0[(х⁰,⁵)²-+√5х⁰,⁵+1=0;х⁰,⁵=(±√5±1)/2≥0 х=(3±√5)/2
    1
  4006. (n-1)(n²-7n+13) n=3✓ n=2;4✓ 5*(6-2+3)=..5×{2;3;4}
    1
  4007. BC=5/sin75°sin45° ∆S=25√3-175/4
    1
  4008. √((k+1)/2)-√((k-1)/2) √(2/2)-√0+√(3/2)-√(1/2)+..+√((n+1)/2)-√((n-1)/2)=-√0,5+√(n/2)+√((n+1)/2)
    1
  4009. 5/3..0,28(m) V=h³/64=0,000'343 (m³) n=2915
    1
  4010. 4²+r²=(8-r)² 3=r✓ S=9π
    1
  4011. {b=25/4-a,0=47,5-20,25(√a+0,5)-23/4(√a+0,5)²+(√a+0,5)⁴,a[0;25/4]; (z-23/24)³-9649/3/256(z-23/24)-971'407/27/2048=0 z=23/24+(971407+√(971407²-9649³))¹/³/48+(..-..)..;23/24-(971407+√(9 71407²-9649³))¹/³/96-(..-..)..±√(3/4 ((971407+√(971407²-9649³))¹/³/48 +(..-..)..)²-9649/768)i a=7/8+√22214/24-7√(√22'214/6-35/4)/4✓ 25805>9649*(-15/196) (155 3/4)/16/149 b=43/8-√22214/24+7√(√22'214/6-35/4)/4✓ ab=(504-11107/18-31/6√22214+(-126+7/3√22214)√(√22214/6-35/4))/16
    1
  4012. (k-1)²(K-2)=0 k=1;2 an=c1+c2*n+c3*2^n{4=c1,-11=c2,4=c3;an=4-11*n+4*2^n
    1
  4013. y''y'=y-³y',y≠c y'y/√(2cy²-1)=±1 {c>0,y=±√(0,5/c+(2cx±c1/2)²/2/c).
    1
  4014. 8*1.1111<9
    1
  4015. √(tg(x/2))=t x=2arctgt² dx=4t/(1+t⁴)dt $(0;π)sin(x/2)√sinxdx= $(0;∞)4√2t⁴/(t²-√2t+1)²/(t²+√2t+2) ²dt=4,218
    1
  4016. y²-3y+1=0 y=(3±√5)/2 √(√5*8*3*6/√5)=12
    1
  4017. $dx/((x-1/2)²+3/4)=arctg((x-1/2)/√3 *2)/√3*2+c
    1
  4018. Sг=14 1176,2177 14/53(?✓)
    1
  4019. х²у+х-ху=6 у=(6-х)/х/(х-1) х≠0;1 х=2,у=2 х=3,у=1/2 (6;0) (-12х+6+х²)/х²/(х-1)²=0,х= 6±√30 +**+>х минимум=-11+2√30=-0,.. максимум=-(√6+√5)²=-22 х=-1,у=3,5 х=-2,у=4/3 х=-3,у= 3/4 -*0+*1*6+>х
    1
  4020. a=8 x²+8²-16x*-4/5=17² x²+64/5x-225=0,x=-32/5±√6669/5≥0 x=-32/5+3√741/5 O1O2=8/5+3√741/5✓
    1
  4021. y=e^u,u'(1-e^-ucosx/x)=0,5/x+0,5tgx
    1
  4022. x≥40,x≤100 0=7-√x x=49✓
    1
  4023. 19²+17²-2*19*17cis60°=327 9²+11²-2*9 *11cosx°=327,cosx°=-125/198 x=arccos (-125/198)
    1
  4024. X=arctg(9(39√15+629+133√3+51√5)/6677)
    1
  4025. xctgb/(5x)=tga 1/5=tgatgb E=4/5
    1
  4026. 60°-2arctg0,219..
    1
  4027. S=112+arcsin(1/4)*16-√15-9,5π
    1
  4028. ((√3i+1)/(i-1))⁶=((√3i+1)(i+1)/-2)⁶=((-3+ √3i+i+1)/-2)⁶=((√3/2+1/2)i-1)⁶=((√3/2+1/2)²*-1-2(√3/2+1/2)i+1)³=(-√3/2+(-√3-1)i) ³=-3√3/8+3*3/4*(-√3-1)i+3*-√3/2*-(-√3-1)²+(-√3-1)3*-i=5 5/8√3+9+(-5,25√3-5,25)i
    1
  4029. 999=p1+p2 (2;997) n=1994
    1
  4030. 2arcsin((x-1)/2)+0,5(x-1)√(4-(x-1)²)+c
    1
  4031. R²+4=(R+1)² 1,5=R S=2m1,125π
    1
  4032. -Xe^-ax²/a/2+√(π/a)Ф(x/√(0,5/а))/2/a(-=;≠)=√(π/а)/2/а
    1
  4033. X1=cost y1=sint,x2=cos(t/5) y2=sin(t/5) ∆x=cos(t/5)-cost ∆y=sin(t/5)-sint l=√((cos(t/5)-co st)²+(sin(t/5)-sint)²)=√(2-2cos(4t/5)) =2sin(2t/5)≤2 t=5π/4
    1
  4034. $(sh-1;sh1)2ysiny*dy=-2ycosy+2sin y(-(e-e-¹)/2;(e-e-¹)/2)=-2(e-e-¹)cos((e- e-¹)/2)+4sin((e-e-¹)/2)
    1
  4035. (logx(3)-1)(logx(3)+1/3)/(logx(3)- 1/3)≤0-*-1/3+°1/3-*1+>logx(3) logx(3)(-∞;-1/3]U(1/3;1][x[1/27;1),[3;27];x[1/27;1)U[3;27]
    1
  4036. A³-26a-23=304/8-36=2 2⁷=128
    1
  4037. (1 0|7) (0 1|3){(7;3)}
    1
  4038. X=√((5x-1)/(x-3)/(x-2)),x≥0 (x-1,25)⁴-2,75(x-1,25)²-5 5/8(x-1,25) 4 3/64=0 (z-11/24)³+41/48(z-11/24)+3'397'741/27/2¹⁸=0 z=11/24+(-3397741/2 +√(3397741²+41³*2²⁶)/2)¹/³/192+(..-..)..;11/24-(-3397741/2+√(33977 41²+41³*2²⁶)/2)¹/³/384-(..-..)..±√(3/ 4((-3397741/2+√(3397741²+41³* 2²⁶)/2)¹/³/192+(..-..)..)²+41/48)i x=1,25+√(11/24+(-3397741/2+√ (3397741²+41³*2²⁶)/2)¹/³/192+(..-..)..)+2√(0,5√(121/24²-11/24(( 3397741/2+√(3397741²+41³*2²⁶)/2)¹/³/192+(..-..)..)+((-3397741/2+√ (3397741²+41³*2²⁶)/2)¹/³/192+(.. -..)..)²+41/48)+11/48-(-3397741/2+√(3397741²+41³*2²⁶)/2)¹/³/768-(.. -..)..)
    1
  4039. 2acos²(o+π/4)-2√2cos(o+π/4)+a= 0 o=-π/4±arccos((-√2±√(2+2a²))/2/a)+2πn o(0;π) o=-π/4+arccos((-√2± √(2+2a²))/2/a)>0 (-1-a±√(1+a²))/a< 0 a=0-°0->a(a≠0)+°0->a(a>0) (-1+√2a±√(1+a²))/a≥0 a²-2√2a=0 a=0;2√2+°0+2√2*+>a a≠0+°0*2√2 +>a a≥2√2 a(-∞;0)U(0;∞)
    1
  4040. F((7^(n+1)-1)/6)=49^(n+1)f(0) n+1=log7(6y+1) f(y)=(6y+1)²f(0) f(x)=(6x+1)²f(0)
    1
  4041. Sin(2t+32°)=-1/2 [t=-31°+πn,t=89°+πn.
    1
  4042. 1/2,2/3,26/33,173/206,...1 S(n)=S(n-1)+ (1+S(n-1)²)/(2n²-S(n-1))<0,5/n²(S(n-1)-n ²)²-0,5n²+0,5/n²
    1
  4043. (388-x²)¹/⁴+√x=5√2, (388-x²)¹/⁴x¹/²=50±38=88;12 [(x²-194)²=×194²-88⁴,x=18,x=8;{18;8}
    1
  4044. 4a-2b=14 a=0,5b+3,5 2ax+b=-7 b=-7,a=0 ax³-10b -8a-10b=14 3ax²=0× -14b-28=14 b=-3,a=2✓ 4x-3=-11,6x²=24
    1
  4045. xe^x²+c✓
    1
  4046. {2⁰,⁴⁶}
    1
  4047. 6πnr²v=$(L)F->•dr 6nrv=F✓
    1
  4048. S1=8√3-8π/3
    1
  4049. ±arccos(1/√5)+2πn-π/2+arcos(1/√5)=o coso=4/5;0 B)
    1
  4050. √(1-(2-DC/2)²) 1-(2-DC/2)²+DC²/4= 2² -3+2DC=4 DC=3,5
    1
  4051. 1,65*7=11,55
    1
  4052. 2⁷*3>5³
    1
  4053. ​2(√2+√3+2)/(√2+√3+2+√2(2+√3+√ 2))=2/(1+√2)=2(√2-1)
    1
  4054. 5³(5*4/2)²=5⁵*2²=12500
    1
  4055. (1+√3)*2/(2+2√3)=1
    1
  4056. 2¹⁵(4⁴-1)/3=2¹⁵*85
    1
  4057. x≥1,0=x²-6x[x=0,x=6.{6}
    1
  4058. 2,33(5)=2 151/450=1051/450
    1
  4059. (х-2)²(х+2)(х+3)(х+4)=0 х=±2;-3;-4
    1
  4060. √(a²-16) x²+a²=5²+a²-16 x=3≥0✓
    1
  4061. x=-0,5±√5,25 55±12√21 55±12√21+55-+12√21=110
    1
  4062. E(x)(-0,5^n+1)-0,5^n*(n+2)+2
    1
  4063. a(n+1)=2^(n-(0,5n-0,5)+0,5(n-2)-...(-1)^ (n-1)0,5)*√a1^(-1)^n=2^0,75n*a1^(0,5(-1)^n)=2^0,75n
    1
  4064. (5x³-x²+10x+3)/(5x-1)=x²+2+5/(5x-1)
    1
  4065. f(x)=-2cos(2(x+30°))+k*2sin(x+30°)=-2+4 t²+2kt,f(x)=4t²-2/√3t-2,t(-0,5;0,5) f(x)=4(t- 0,25/√3)²-2 1/3≥-2 1/3,≤1/√3-1 1/4 f(x)[-2 1/3;√3/3-1,25)
    1
  4066. 2*4/5/3=8/15
    1
  4067. -2x+1≥0,x≤1/2 [x=5/3,x=-3;{-3}
    1
  4068. 45°=arcsin(a/(4√5))+arcsin(√2/(2√5)) a=4√5sin(45°-arcsin(√2/2/√5))=4√5√(1/5)=4 S=16 D)
    1
  4069. 90°-1,5b=/_B=/_C 90°-1,5b-2o, 90°-1,5b-o AB/sin(2b+2o)sin(2b) AB/sin(b+o)sinb 2ABsin(1,5b) AB/sin(b+o)sinb/sin(90°-1,5b-2o)=AB/sin(2b+2o)sin(2b)/sin(90°-1,5b-o) 0,5b+2o=±0,5b+2πn[o=0,×.x=180°-b=120°A)(?)
    1
  4070. cosa=(3²+5²-7²)/2/3/5=-1/2 a=120°
    1
  4071. 200:46=4ost.16,2¹⁶:47=18✓
    1
  4072. [х=-(1+√5)/2,х⁸-(1+√5)/2х⁷+(3+√5)/2х⁶+(1-√5)х⁵+2х⁴+(-1-√5)х³+(11+√ 5)/2х²-(4+3√5)х-6,5+3,5√5=0;{-1/2-√5/2;0,134;1,20}
    1
  4073. {х1'=4х1-х2,х2'=3х1+х2-х3,х3'=х1+х3;{х2=4х1-х1',-5х1'+х1''+7х1=х3,х1"'-6х1''+12х1'-8х1=0;k³-6k²+12k-8=0,(k-2)³=0,k=2, x1=c1e^2t+c2te^2t+c3t²e^2t,x2=(2c1-c2)e^2t+(2c2-2c3)te^2t+2c3t²e^2t,x3=(c1-c2+2c3)e^2t+(c2-2c3)te^2t+c3t²e^2t.
    1
  4074. ?=y/a*x a?=a*yx/a=95(cm²) {(1;95)(5;19)(19;5)(95;1)}
    1
  4075. 2-3x-2x2-x-2=-2x²-4x=0,x=0, x=-2, -2x³/3-4x²/2|(-2;0)=2/3*(-8)+2*4=2 2/3
    1
  4076. (AL+BN)/BN=7/2 AL=4,5BN MN/BC=2/11
    1
  4077. limx->1(x-1)/(x-1)=0/
    1
  4078. S=1/6*2²π-0,5*1*√3=2/3π-√3/2
    1
  4079. y=x²+2/x y'=2x-2x^-2=0 x³-1=0,x=1-*+>x min=3
    1
  4080. 2((х-2/3)³+5/9(х-2/3)+1/6)/(х-1)²=0 х=2/3+(-1/12+√12561/12/81)¹/³+(..-..)..-*+>х у=х²+2х+2+3/(х-1) х=2;4 у=13;27{(2;13)(4;27)}
    1
  4081. {logx+(logx+8logy)/(log²x+log²y)=2,logy+ (8logx-logy)/(log²x+log²y)=0;{log³x+logx log²y+logx+8logy=2log²x+2log²y,log²xlogy-log³y+8logx-logy=0;{log²y(logx-2)+8logy +log³x-2log²x+logx=0,log²xlogy-log³y+8logx-logy=0;{logy=(-8±√(64-4(logx-2)(log³x 2log²x+logx)))/2/(logx-2),[log²x(-8+√(-4lo g⁴x+16log³x-20log²x+8logx+64)/(2logx-4) -(-8+√(-4log⁴x+16log³x-20log²x+8logx+64)³/(2logx-4)³+8logx-(-8+√(-4log⁴x+16log³ x-20log²x+8logx+64)/(2logx-4)=0; log²x(-8-√(-4log⁴x+16log³x-20log²x+8logx+64)/(2logx-4)-(-8-√(-4log⁴x+16log³x-20lo g²x+8logx+64)/(2logx-4)+8logx-(-8-√(-4lo g⁴x+16log³x-20log²x+8logx+64)/(2logx-4) =0;(log²x-2logx+1/2)²-16,25≤0,(log²x-2lo gx-√16,25+0,5)(log²x-2logx+0,5+√16,25) ≤0,(logx-(2+√(4-4(-√16,25+0,5)))/2)(logx (2-√(4√16,25+2))/2)≤0,+*-*+>logx logxє [1-√(√16,25+0,5);1+√(√16,25+0,5)],[logx=0,logx=1,logx=2,logx=3,12,logxє [1-√(√16,25+0,5);1+√(√16,25+0,5)];[logx=0,=1,=2,=3,12;[x=1,x=10,x=100,x=1 0³,¹²;[y=1,y=10000;y=1,y=10⁸,y=10^(-1/4), y=10^(-25/7+√81678,7456/224),y=10^(-25/7-√81678,224).
    1
  4082. h(10/3)=5 h=1,5(cm) S∆1=0,5*1,5*2=1,5(cm²) S2=2,5(cm²) S=4(cm²)
    1
  4083. 377,5/5-118/35*35/3=36 1/6
    1
  4084. 9/(x-5)/(x-3)+(x-5)(x-3)-4(x-5)+(x-3)³+2(x-3)²+8 Ответа тут нет,но выберу D).
    1
  4085. ∆S=2,45²-2,4²=0,2425(m²) e=4,21%
    1
  4086. 1402,701,700,350,175',174,87,86,43,42',21,20,10,5,4' 21+20(1/2^4-1)/(1/2-1)=60
    1
  4087. х+2=(х-4)*2 х=10
    1
  4088. (4/3)^4,5=512√3/243
    1
  4089. [m=√11,m²+√11m-√11=0;m=(-√11±√(11+4√11))/2{√11;(-√11±√(11+4√1 1))/2}
    1
  4090. a=√5/4-1/4±√(2,5+√5/2)i/2 a⁵=cos(5a rcxos(√5/4-1/4)±sin(5arxsin(√(2,5+√5/2)/2))
    1
  4091. {z=15-xy/4,[y=4,x=60/(y+4);[x=11,x=4,0=(y-7/3)³-120 1/3(y- 7/3)+491 25/27;y-7/3=(-(245*27+ 26)+√(6641²-(361*19)²)/27)¹/³/3+(..-..)..=38/3/3¹/²cos(1/3arccos(-66 41/19³)+2/3πn) y=7/3+38/3/3¹/²co s(1/3arccos(-6641/19³)+2/3πn){(11;4;4)(4;4;11)(180/(19+38/3¹/² cos(1/3arccos(-6641/19³)+2/3π n));7/3+38/3/3¹/²cos(1/3arccos (-6641/19³)+2/3πn);15-180/(19+ 38/3¹/²cos(1/3arccos(-6641/19³)+2/3πn))(7/3+38/3/3¹/²cos(1/3ar ccos(-6641/19³)+2/3πn))/4)} 6859×
    1
  4092. 54-3х=9х х=54/12=4,5
    1
  4093. (a+b)(3a+3c)=3
    1
  4094. y''+(1-2/t)y'+y/t=0 (u'+0,5-1/t)'+(u'+0,5-1/t)²=0,25-2/t+2/t² (u'+0,5-1/t)-¹/-1+t=c u'+0,5-1/t=1/(t-c) ..=c1t-¹+c2 -c1t-²+c1²t-² +2c1c2t-¹+c2²=2/t²-2/t+0,25{[c1=2, c1=-1; c1=-+2,c2=±0,5;{c1=2,c2=-0,5; u'+0,5-1/t=2t-¹-0,5 [u=-0,5t+ln|t|+ln|t-c|+c1,u=-t+3ln|t|+c1;[y=e^(-0,5t)t(t-c)c1, y=e^(-t)t³c1.
    1
  4095. (10-x)²+4x²=100 -20x+5x²=0 x=0×;4✓
    1
  4096. 3√(2(20-n)),n:2 6√(10-m),m=10-k², n=20-2k²✓
    1
  4097. (х⁴+1)(ax¹⁵⁷-ax¹⁰⁵+ax⁵³+b)-b/(x⁴⁸-x⁴⁴+..+1) b=0,a=3 3/2(3,5⁴+1)(3,5¹⁰⁴-3,5 ⁵⁴+1)*3,5⁵³ E)
    1
  4098. a(a+b)+b(b+1)=a²+ab+b²+b=(a+1/2b)²+ 3/4(b+2/3)²-3/4*(2/3)²≥-1/3
    1
  4099. {c=-4,d=-1,b=2,a=1;x-1=0 x=1
    1
  4100. h*√3/3+5√3=h√3 h=7,5
    1
  4101. Cosa=19/16× h=3 D)
    1
  4102. a[0;1] x=±(1±√(-a+1))
    1
  4103. l~√(2Rh)=√(2*6370*5,642)=268,155км Чёрное море можно увидеть (110<268,155), Каспийское - нет(400>268,155).
    1
  4104. x=2023/2/(2023/2024)=1012
    1
  4105. X[n;n+1),x=±√(10n-51/4),n≥2 {n[2;8],0<(n+2,5)(n+5,5);n[2;8],{√29/2;√189/2;√229/2;√269/2}
    1
  4106. $(0;2π)1/16(4,375-7cos2x+3,5cos4x-cos6x+0,125cos8x)dx=1/16(4,375x-7sin2x/2+3,5sin4x/4-sin6x/6+1/64 sin8x)(0;2π)=1/16(8,75π)=35/64π
    1
  4107. ((x+2)²+30)(x+2)²=0 x=-2
    1
  4108. Y=ax²+bx+c{4=c,6=b,1=a;f(1)=a+b+c=11
    1
  4109. у'lny/y=1 ln|lny|=x+c lny=e^xc y=e^(e^xc)
    1
  4110. А почему у Вас косоглазие?
    1
  4111. √(а²+1),а(2+√3)-1 а²(-3-2√3)+(2+√3)а+2=0 а=(√3+(2√3-3)√(31+20√3))/6 arctg(√(-30+48√3+(12-6√3)√(31+20√3))/12)
    1
  4112. y'=2xe^-x y=-2xe^-x-2e^-x+c✓
    1
  4113. 3/sin(arctg(3/2)+arctg(4/3))*sinar ctg(4/3)=12√13/13(c
    1
  4114. X=-arccos(2/√5)+arcsin(a/√5)(-1)^ n+πn X=-arccos(2/√5)+arcsin(a/√5);-arccos(2/√5)+π-arcsin(a/√5), x[π/4;3/4π] a[3/√2;√5],a[1/√2;√5]=>a[1,5√2;√5]
    1
  4115. -2sin²(x+30°)+2,5sin(x+30°)-2=0 sin(x+30°)=(2,5±√-9,75)/4×
    1
  4116. На кладбище тоже всё стабильно. А чем таким Делягин заболел?
    1
  4117. En=0;∞(-0,5)^n/(n/2+1)^(n+1)
    1
  4118. z=(1/2+2n)/(1+2m)
    1
  4119. {y=x¹,⁵,[x=0,x=1;[{y=0,x=0;{x=1,y=1.
    1