для этого нужно найти среднее сумм каждых координат
AB={-3-1/2 ; 5+3/2 ; 12+6/2 } = {-2;4;9}
1-2sin^2(45°+1,5a)=cos(2(45°+1,5a))=cos(90°+3a)=-sin(3a)=-(3sina-4sin^3a)=4sin^3a-3sina
Общий вид уравнения касательной:
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Найдем значение функции в точке
, получим
![f(1)=3-\sqrt{1}-\frac{2}{\pi}\sin\pi =3-1-0=2](https://tex.z-dn.net/?f=f%281%29%3D3-%5Csqrt%7B1%7D-%5Cfrac%7B2%7D%7B%5Cpi%7D%5Csin%5Cpi%20%3D3-1-0%3D2)
Найдем производную функции
![f'(x)=(3-\sqrt{x}-\frac{2}{\pi}\sin \pi x)=(3)'-(\sqrt{x})'-\frac{2}{\pi}\cdot(\sin\pi x)'=\\ \\ =-\frac{1}{2\sqrt{x}}-\frac{2}{\pi}\cdot \cos\pi x\cdot(\pi x)'=-\frac{1}{2\sqrt{x}}-\frac{2}{\pi}\cdot \cos\pi x\cdot \pi =-\frac{1}{2\sqrt{x}}-2\cos\pi x](https://tex.z-dn.net/?f=f%27%28x%29%3D%283-%5Csqrt%7Bx%7D-%5Cfrac%7B2%7D%7B%5Cpi%7D%5Csin%20%5Cpi%20x%29%3D%283%29%27-%28%5Csqrt%7Bx%7D%29%27-%5Cfrac%7B2%7D%7B%5Cpi%7D%5Ccdot%28%5Csin%5Cpi%20x%29%27%3D%5C%5C%20%5C%5C%20%3D-%5Cfrac%7B1%7D%7B2%5Csqrt%7Bx%7D%7D-%5Cfrac%7B2%7D%7B%5Cpi%7D%5Ccdot%20%5Ccos%5Cpi%20x%5Ccdot%28%5Cpi%20x%29%27%3D-%5Cfrac%7B1%7D%7B2%5Csqrt%7Bx%7D%7D-%5Cfrac%7B2%7D%7B%5Cpi%7D%5Ccdot%20%5Ccos%5Cpi%20x%5Ccdot%20%5Cpi%20%3D-%5Cfrac%7B1%7D%7B2%5Csqrt%7Bx%7D%7D-2%5Ccos%5Cpi%20x)
Значение производной функции в точке ![x_0=1](https://tex.z-dn.net/?f=x_0%3D1)
![f'(1)=-\frac{1}{2\cdot \sqrt{1}}-2\cos\pi=-0.5-2\cdot(-1)=-0.5+2=1.5](https://tex.z-dn.net/?f=f%27%281%29%3D-%5Cfrac%7B1%7D%7B2%5Ccdot%20%5Csqrt%7B1%7D%7D-2%5Ccos%5Cpi%3D-0.5-2%5Ccdot%28-1%29%3D-0.5%2B2%3D1.5)
Уравнение касательной:
![y=1.5(x-1)+2=1.5x-1.5+2=\boxed{1.5x+0.5}](https://tex.z-dn.net/?f=y%3D1.5%28x-1%29%2B2%3D1.5x-1.5%2B2%3D%5Cboxed%7B1.5x%2B0.5%7D)
![\left \{ {{y+2x=9} \atop {3x-5y=4}} \right. \left \{ {{y=9-2x} \atop {3x-5y=4}} \right. \left \{ {{y=9-2x} \atop {3x-5(9-2x)=4}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7By%2B2x%3D9%7D+%5Catop+%7B3x-5y%3D4%7D%7D+%5Cright.+%5Cleft+%5C%7B+%7B%7By%3D9-2x%7D+%5Catop+%7B3x-5y%3D4%7D%7D+%5Cright.+%5Cleft+%5C%7B+%7B%7By%3D9-2x%7D+%5Catop+%7B3x-5%289-2x%29%3D4%7D%7D+%5Cright.+)
3x-5(9-2x)=4
3x-45+10x=4
13x=49
![x=3\frac{10}{13}](https://tex.z-dn.net/?f=x%3D3%5Cfrac%7B10%7D%7B13%7D)
![y=9-2*\frac{49}{13}\\ y=9-\frac{98}{13}\\ y=9-7\frac{7}{13}\\ y=\frac{117}{13}-\frac{98}{13}=\frac{19}{13}=1\frac{6}{13}\\](https://tex.z-dn.net/?f=y%3D9-2%2A%5Cfrac%7B49%7D%7B13%7D%5C%5C+y%3D9-%5Cfrac%7B98%7D%7B13%7D%5C%5C+y%3D9-7%5Cfrac%7B7%7D%7B13%7D%5C%5C+y%3D%5Cfrac%7B117%7D%7B13%7D-%5Cfrac%7B98%7D%7B13%7D%3D%5Cfrac%7B19%7D%7B13%7D%3D1%5Cfrac%7B6%7D%7B13%7D%5C%5C+)
Получаем, что данная система уравнения имеет решения