Comments by "Fhf Fhf" (@fhffhff) on "ВЫХОД ЕСТЬ!" channel.

  1. $$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
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  2. (x/4)^(x/4)=2² {8}
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  3. 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
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  4. {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
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  5. 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
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  6. 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.
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  7. 142000'000*0,998^(х-2022)=0,5 х=2022+500*19,505=11774,5г.
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  8. (1,5t;1,125t²) t=0,5t√(1+(1,25t)²) ±4/5√3=t≥0 t=4/5√3
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  9. 📅📆🗓️
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  10. 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
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  11. $(-1;1)x5/(x¹⁰⁰+4)dx=$(1;-1)-x⁵/(x¹⁰⁰+4)* -dx=-$(-1;1)x⁵/(x¹⁰⁰+4)dx, 2$(-1;1)x5/(x¹⁰⁰ +4)dx=0,$(-1;1)x5/(x¹⁰⁰+4)dx=0
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  12. {|х-4|+3|у|=2,9у²+х²-8х+4(а+3)=0;{[{х-4+3у=2,х-4≥0,у≥0,{х-4-3у=2,х≥4,у<0,{-х+4+3у=2,х<4,у≥0,{-х+4-3у=2,х<4,у<0;(х-4)²+(3у)²=-4а+4;≥0 {[{у=2-х/3,х≥4,у≥0,{у=-2+1/3х,х≥4,у<0,{у=х/3-2/3,х<4,у≥0,{у=-1/3х+2/3,х<4,у<0;(х-4)²+(3у)²=-4а+ 4;а≤1 x≤6,y≤2/3 (6-4)²+(2/3-0)²=4+4/9=r², r=2√10/3 2√10≤-4a+4,a≤-0,5√10+1,R=2, 2≥-4a+4,a≥0,5, aє[0,5;-0,5√10+1]
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  13. √(2tg(3π/2-x)sin(3π-2x))=-tg(2π/2)=-tgπ= 0, 2sin(3π/2-x)/cos(3π/2-x)*2sin(3π/2-x) cos(3π/2-x)=0,sin²(3π/2-x)=0,3π/2-x=πn, nєZ x=3π/2-πn,nєZ
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  14. a>b a=(a-b)²,b=8НОД(a,b) {a-√a=b,a-√a= √a*8; a-9√a=0,[a=0,a=81;a=81,b=81-9=72 HOK(81,72)=81*72/9=648
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  15. (3^х-3)/(3^х-9)/(3^х-6)≤0-*1+°log3(6)-°2 +>х x(-∞;1]U(log3(6);2)
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  16. b≥4 0=b²-8b+7 b=(8±6)/2=7;1 {7}
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  17. 4²+b²=5^2 b=3 k=8/3 A)
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  18. (√18+4)*2-(7√2-7√2)⁵=2√18+8✓
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  19. s/(0,5s/12+0,5s/4)=24/4=6км/ч
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  20. x=1,5±√17,25
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  21. cos1-e-⁰,⁵+$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
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  22. 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)
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  23. 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/
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  24. 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.
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  25. 3x=x¹/²/3[x=0,x=1/81.
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  26. 1/9/4=1/? ?=36
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  27. (R-6)²+18²=R² R=30
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  28. 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×
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  29. 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)
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  30. 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;+∞)
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  31. (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
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  32. 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)
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  33. 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
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  34. 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;
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  35. ((x-8)²/³+3x¹/³(x-16)¹/³)(x-8)¹/³=0 [x=8,x=8±√48;{8;8±√48}
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  36. 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.
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  37. 6²=2r*4r,r=3√0,5,2arcsin(2√2/3)+arcsin(2/3√2)=3arcsin(2√2/3)≠180°3/3
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  38. 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
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  39. (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;
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  40. $sinsinxdx*cosx/cosx=sinsinx/cosx-$si nsinx*cos^-2x*sinxdx=sinsinx/cosx-sins inx*sinx/cos³x+$sinsinx*(-2cos²x+3)/cos⁴xdx=sinsinx/cosx-sinsinx*sinx/cos³x +...+C
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  41. 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
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  42. 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×
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  43. {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)}
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  44. $2du/(1+u)¹,⁵/√(1-u)=-2√(1-u)/√(u +1)+c=-2√(1-√x)/√(√x+1)+c
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  45. 66,8/1,6=41 3/4 мин=42 профессии
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  46. 2¹⁹⁹⁵>5⁸⁵⁴,1995/854=2 287/854 4⁹⁹⁷*2= 8⁶⁶⁵=128^(285)>125²⁸⁵>125²⁸⁴(²/³)
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  47. 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)
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  48. f'(x)=(-2x*2e^x²-(-x²-1)e^x²*4x)/2/e^(2x²)
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  49. S=4√3/4*√72²=72√3(cm²) V=1/3*72√(72-18-18)=144(cm³)
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  50. 2sin68°sin67°/cos23°/cos22°=2
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