1) 800; 2) 450; 3) 50; 4) 600; 5) 0,5; 6) 1800.
Привет,
решим систему методом сложения
для этого домножим первое уравнение на -4
-8х-4у=8
+
3х+4у=2
-------------
-5х=10
х=-2
2*(-2)+у=-2
-4+у=-2
у=2
Дано:
- арифметическая прогрессия;
![c_5=8,2\\\\c_{10}=4,7\\\\c_1-?;d-?](https://tex.z-dn.net/?f=c_5%3D8%2C2%5C%5C%5C%5Cc_%7B10%7D%3D4%2C7%5C%5C%5C%5Cc_1-%3F%3Bd-%3F)
Решение.
![\left\{{{c_5=c_1+4d}\atop{c_{10}=c_1+9d}}\right.\\\\\left\{{{8,2=c_1+4d}\atop{4,7=c_1+9d}}\right.\\\\\left\{{{c_1+4d=8,2}\atop{c_1+9d=4,7}}\right.\\\\\left\{{{c_1=8,2-4d}\atop{4,7=c_1+9d}}\right.\\\\\left\{{{c_1=8,2-4d}\atop{4,7=8,2-4d+9d}}\right.\\\\4,7=8,2-4d+9d\\\\5d=4,7-8,2\\\\5d=-3,5\\\\d=-3,5:5\\\\d=-0,7\\\\\\c_1=8,2-4*(-0,7)=8,2+2,8=11\\\\c_1=11](https://tex.z-dn.net/?f=%5Cleft%5C%7B%7B%7Bc_5%3Dc_1%2B4d%7D%5Catop%7Bc_%7B10%7D%3Dc_1%2B9d%7D%7D%5Cright.%5C%5C%5C%5C%5Cleft%5C%7B%7B%7B8%2C2%3Dc_1%2B4d%7D%5Catop%7B4%2C7%3Dc_1%2B9d%7D%7D%5Cright.%5C%5C%5C%5C%5Cleft%5C%7B%7B%7Bc_1%2B4d%3D8%2C2%7D%5Catop%7Bc_1%2B9d%3D4%2C7%7D%7D%5Cright.%5C%5C%5C%5C%5Cleft%5C%7B%7B%7Bc_1%3D8%2C2-4d%7D%5Catop%7B4%2C7%3Dc_1%2B9d%7D%7D%5Cright.%5C%5C%5C%5C%5Cleft%5C%7B%7B%7Bc_1%3D8%2C2-4d%7D%5Catop%7B4%2C7%3D8%2C2-4d%2B9d%7D%7D%5Cright.%5C%5C%5C%5C4%2C7%3D8%2C2-4d%2B9d%5C%5C%5C%5C5d%3D4%2C7-8%2C2%5C%5C%5C%5C5d%3D-3%2C5%5C%5C%5C%5Cd%3D-3%2C5%3A5%5C%5C%5C%5Cd%3D-0%2C7%5C%5C%5C%5C%5C%5Cc_1%3D8%2C2-4%2A%28-0%2C7%29%3D8%2C2%2B2%2C8%3D11%5C%5C%5C%5Cc_1%3D11)
Ответ: ![c_1=11;d=-0,7](https://tex.z-dn.net/?f=c_1%3D11%3Bd%3D-0%2C7)
Решение
<span>Sin7x+sin6x+sin5x = (sin7x + sin5x) + sin6x =
</span>= 2*[sin(7x + 5x)/2 * cos(7x - 5x)/2] + sin6x =
= 2*sin6x * cosx + sin6x = sin6x*(2cosx + 1)