![A_1(9,5,5),\; \; A_2(-3,7,1)\\\\\overline {A_1A_2}=(-12,2,-4)\; \; \Rightarrow \; \; \overline{s}=-\frac{1}{2}\cdot \overline {A_1A_2}=(6,-1,2)\\\\A_3(x_0,y_0,z_0)](https://tex.z-dn.net/?f=A_1%289%2C5%2C5%29%2C%5C%3B+%5C%3B+A_2%28-3%2C7%2C1%29%5C%5C%5C%5C%5Coverline+%7BA_1A_2%7D%3D%28-12%2C2%2C-4%29%5C%3B+%5C%3B+%5CRightarrow+%5C%3B+%5C%3B+%5Coverline%7Bs%7D%3D-%5Cfrac%7B1%7D%7B2%7D%5Ccdot+%5Coverline+%7BA_1A_2%7D%3D%286%2C-1%2C2%29%5C%5C%5C%5CA_3%28x_0%2Cy_0%2Cz_0%29)
Прямая, параллельная А1А2 и проходящая через точку А3:
[/tex]
![\frac{x-x_0}{6}=\frac{y-y_0}{-1}=\frac{z-z_0}{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bx-x_0%7D%7B6%7D%3D%5Cfrac%7By-y_0%7D%7B-1%7D%3D%5Cfrac%7Bz-z_0%7D%7B2%7D)
ВОт
<span>2)Корень из 0,0025 </span>
1)√10*√20+√5*√20-5√8=√200+√100-5√8=√25*8+10-5√8=5√8+10-5√8=10
2)(√mn+n-n+m)/(√m+√n)
(√mn+m)/(√m+√n)=(√m*(√n+√m))/(√m+√n)=√m
Найдем пересечение линий:
9/x^2 = -4x+13
![x \neq 0 \\ 4x^{3}-13 x^{2} +9=0 \\ x=1 \\ 4x^{3}-13 x^{2} +9 / (x-1)=4x^2-9x-9 \\ 4x^2-9x-9=0 \\ D=81-4*4*(-9)=225 \\ x_{1}=3 \\ x_{2}=- \frac{3}{4}](https://tex.z-dn.net/?f=x+%5Cneq+0+%5C%5C+4x%5E%7B3%7D-13+x%5E%7B2%7D++%2B9%3D0+%5C%5C+x%3D1+%5C%5C+4x%5E%7B3%7D-13+x%5E%7B2%7D++%2B9+%2F+%28x-1%29%3D4x%5E2-9x-9+%5C%5C+4x%5E2-9x-9%3D0+%5C%5C+D%3D81-4%2A4%2A%28-9%29%3D225+%5C%5C+x_%7B1%7D%3D3+%5C%5C++x_%7B2%7D%3D-+%5Cfrac%7B3%7D%7B4%7D+++)
Т.к. нас интересует первая четверть, то подходят две абциссы
x1=1 и х2=3
Далее используем интеграл )
![\int\limits^3_1 {-4x+13 - \frac{9}{x^2} } \, dx =(-2x^2+13x+ \frac{9}{x})= \\ (-18+39+3)-(-2+13+9)=24-20=4](https://tex.z-dn.net/?f=+%5Cint%5Climits%5E3_1+%7B-4x%2B13+-++%5Cfrac%7B9%7D%7Bx%5E2%7D+%7D+%5C%2C+dx+%3D%28-2x%5E2%2B13x%2B+%5Cfrac%7B9%7D%7Bx%7D%29%3D+%5C%5C+%28-18%2B39%2B3%29-%28-2%2B13%2B9%29%3D24-20%3D4+)
Ответ: 4