Альбом р руб
цветные карандаши b руб
5%=0,05
3%=0,03
2(p+0,05)+b+0,03=2p+0,1+b+0,03=2p+b+0,04
А. 13%, все кто записались, а 35% это часть уже из записанных
![\left\{{{x^2-y^2=-5}\atop{x^2+y^2=13}}\right.](https://tex.z-dn.net/?f=%5Cleft%5C%7B%7B%7Bx%5E2-y%5E2%3D-5%7D%5Catop%7Bx%5E2%2By%5E2%3D13%7D%7D%5Cright.)
Сложим эти уравнения:
![x^2-y^2+x^2+y^2=-5+13](https://tex.z-dn.net/?f=x%5E2-y%5E2%2Bx%5E2%2By%5E2%3D-5%2B13)
![x^2+x^2=-5+13](https://tex.z-dn.net/?f=x%5E2%2Bx%5E2%3D-5%2B13)
![2x^2=8](https://tex.z-dn.net/?f=2x%5E2%3D8)
![x^2=8:2](https://tex.z-dn.net/?f=x%5E2%3D8%3A2)
![x^2=4](https://tex.z-dn.net/?f=x%5E2%3D4)
![x_1=-\sqrt{4}=-2](https://tex.z-dn.net/?f=x_1%3D-%5Csqrt%7B4%7D%3D-2)
![x_2=\sqrt{4}=2](https://tex.z-dn.net/?f=x_2%3D%5Csqrt%7B4%7D%3D2)
Подставим значение х вo второе уравнение ![x^2+y^2=13.](https://tex.z-dn.net/?f=x%5E2%2By%5E2%3D13.)
![1)x_1=-2;=>(-2)^2+y^2=13;=>y^2=13-4](https://tex.z-dn.net/?f=1%29x_1%3D-2%3B%3D%3E%28-2%29%5E2%2By%5E2%3D13%3B%3D%3Ey%5E2%3D13-4)
![y^2=9](https://tex.z-dn.net/?f=y%5E2%3D9)
![y_1=-\sqrt{9}=-3](https://tex.z-dn.net/?f=y_1%3D-%5Csqrt%7B9%7D%3D-3)
![y_2=\sqrt{9}=3](https://tex.z-dn.net/?f=y_2%3D%5Csqrt%7B9%7D%3D3)
![2)x_2=2;=>2^2+y^2=13;=>y^2=13-4](https://tex.z-dn.net/?f=2%29x_2%3D2%3B%3D%3E2%5E2%2By%5E2%3D13%3B%3D%3Ey%5E2%3D13-4)
![y^2=9](https://tex.z-dn.net/?f=y%5E2%3D9)
![y_3=-\sqrt{9}=-3](https://tex.z-dn.net/?f=y_3%3D-%5Csqrt%7B9%7D%3D-3)
![y_4=\sqrt{9}=3](https://tex.z-dn.net/?f=y_4%3D%5Csqrt%7B9%7D%3D3)
Ответ: (-2; -3); (-2; 3); (2; -3); (2; 3).
1)Sin5x = -sinx
Sin5x + sinx = 0
2*[sin(5x + x)/2]*[cos(5x - x)/2] = 0
[sin(6x)/2]*[cos(4x)/2] = 0
[sin(3x)]*[cos(2x)] = 0
a) sin3x = 0
3x = πn, n∈Z
x1 = πn/3, n∈Z
b) cos2x = 0
2x = π/2 + πk, k∈Z
x2 = π/4 + πk/2, k∈Z
2) sin(x/2)*sinx = 0
a) sin(x/2) = 0
x/2 = πk, k∈Z
x1 = 2πk, k∈Z
b) sinx = 0
x2 = πn, n∈ Z