Comments by "Fhf Fhf" (@fhffhff) on "MyGap" channel.

  1. 7:24 это не парабола, а нормальное распределение.
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  2. 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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  3. 2√3^ncos(30n°),2√3^ncos(30°n)
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  4. $(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)
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  5. Ei=0;n-1 2(π²(i+1)²-2)/n³=(π²(n+1)(2n+1)/3-(n-1))/n²=2/3π²
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  6. $(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
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  7. 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
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  8. 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)
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  9. 2a²/(6a²)=1/3 D)
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  10. (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]
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  11. y'=xy²++y+1/x²,y1=-1/x
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  12. S=1/(2,5×0,5^2×1,5)^0.5=4/15×15^0,5
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  13. x=log3(y),y=3^x=3⁴⁹
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  14. CD/DB=1/2 CD=0,5DB S∆ABC=666, S∆DEC=0,5*DB*h1/2*0,5=0,5*666=333
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  15. 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✓
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  16. (R-1)²+2²=R² -2R+5=0,R=2,5
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  17. S1+S2+S4+S5+20+14++=
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  18. I+J=π/2-1/2 I=J I=π/4-1/4
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  19. {x≤20/3,[x=4,x=-100/7;{-100/7;4}
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  20. 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]
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  21. (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)
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  22. √(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
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  23. 2а+2b,3b a=0,5b
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  24. 6(а+2b-2c)+c,1,a+2b-2c=14(mod17),a+2 b-c=15(mod17),(a+2b-c):17
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  25. $(0,625/(0,625-0,5sin2x-0,125cos4x)- 0,5(-cos2x-0,25cos4x)/(0,625-0,5sin2x-0,125cos4x))dx
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  26. 666 комментариев.
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  27. (X+y/2+1)²-y²/4=(x+1)(x+y+1)
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  28. f(40y)=30/y f(x)=1200/x f(50)=24
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  29. (2x³-12x)/(x²-9)=2x+6x/(x²-9)
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  30. 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.
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  31. d=-a-b-c 3(c²+c(a+b)+ab)/(ab+ca+cb+c²)= 3
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  32. x=2±√2,y=2-+√2,x>y,(2+√2;2-√2) √2-1
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  33. (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)
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  34. 5n=15*ab*3367 b:/2
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  35. 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)}
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  36. $(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)
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  37. {(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;
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  38. $(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)
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  39. А почему такое название?(Моя пустота,щель,пробел и т.д.)
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  40. (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]
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  41. Хуже.
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  42. 328=256+64+8 (8;3;1)(6;4;1)(3;8;4)
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  43. √((-10+√170)/14)
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  44. {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)
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  45. 1/cos24,37°=1/0,916=1,09
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  46. ~~`~ ~`~ ~~~`~ ~~`~ ~`~ ~~~`, ~` ~`~ ~ ~`~ ~`~, ~ ~`~ ~~` ~~`? 4 8 18 4 9 50, 4 2 600 4? 500 1 600 700?
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  47. 40^2a=40⁴ 2a=4{2}
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  48. Ek=1;nak=(b+1)^(n-1)a
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  49. 31/32=0,96875<0,97312<0,992
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  50. (11⁵+12)/(
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  51. 22000/6,06/2,44/2,56=36,3/4,2464=8,7кг/м^3 1818 3820 3636 184 1464 1220 288 42464
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  52. 1,5((1+x)-⁰,⁵+(1-x)-⁰,⁵)/((1+x)-²/³+ (1-x)-²/³)=1,5*2/2=1,5
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  53. 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)}
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  54. /_1=180°-25°-115°=40° 65°,1,2sin25° √(1+4sin²25°-4sin25°cos65°)=1{65°}
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  55. √3/2BC/sin60°=BC/sinx sinx=1 x=90°
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  56. 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.
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  57. 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.
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  58. [x=0,log²/³6(3)=x.
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  59. √(3+2cos40°),l=√(2+2sin20°) x=arccos(√(1+cos70°)/√2)=35°
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  60. 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
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  61. 13/e<8 2⁵>25
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  62. 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/
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  63. 21+9i-14i-6(-1)=27-5i
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  64. {2a²-13a-28=0,b=a-14; a=(13±√393)/4, b=-10,75±√393/4(13/4±√393/4;-10,75±√393/4)
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  65.  @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/.
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  66. 65+8√2✓
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  67. 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;∞)
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