![3)\; \; y(x)=\frac{x-2}{3+x}\\\\y'(x)=\frac{(3+x)-(x-2)}{(3+x)^2}=\frac{5}{(3+x)^2}\; \; \to \; \; y'(-2)=\frac{5}{(3-2)^2}=5\\\\\\4)\; \; sin(\frac{\pi}{2}+a)-cos(\pi +a)=cosa-(-cosa)=2cosa](https://tex.z-dn.net/?f=3%29%5C%3B%20%5C%3B%20y%28x%29%3D%5Cfrac%7Bx-2%7D%7B3%2Bx%7D%5C%5C%5C%5Cy%27%28x%29%3D%5Cfrac%7B%283%2Bx%29-%28x-2%29%7D%7B%283%2Bx%29%5E2%7D%3D%5Cfrac%7B5%7D%7B%283%2Bx%29%5E2%7D%5C%3B%20%5C%3B%20%5Cto%20%5C%3B%20%5C%3B%20y%27%28-2%29%3D%5Cfrac%7B5%7D%7B%283-2%29%5E2%7D%3D5%5C%5C%5C%5C%5C%5C4%29%5C%3B%20%5C%3B%20sin%28%5Cfrac%7B%5Cpi%7D%7B2%7D%2Ba%29-cos%28%5Cpi%20%2Ba%29%3Dcosa-%28-cosa%29%3D2cosa)
![5)\; \; a_1=1\; ,\; a_3=9\; ,\; \; a_2=?\\\\a_2=a_1+d\\\\a_3=a_1+2d\; \; \to \; \; a_3=1+2d=9\; ,\; \; 2d=8\; ,\; d=4\\\\a_2=1+4=5\\\\ili\\\\\frac{a_1+a_3}{2}=a_2\; \; \to \; \; a_2=\frac{1+9}{2}=5](https://tex.z-dn.net/?f=5%29%5C%3B%20%5C%3B%20a_1%3D1%5C%3B%20%2C%5C%3B%20a_3%3D9%5C%3B%20%2C%5C%3B%20%5C%3B%20a_2%3D%3F%5C%5C%5C%5Ca_2%3Da_1%2Bd%5C%5C%5C%5Ca_3%3Da_1%2B2d%5C%3B%20%5C%3B%20%5Cto%20%5C%3B%20%5C%3B%20a_3%3D1%2B2d%3D9%5C%3B%20%2C%5C%3B%20%5C%3B%202d%3D8%5C%3B%20%2C%5C%3B%20d%3D4%5C%5C%5C%5Ca_2%3D1%2B4%3D5%5C%5C%5C%5Cili%5C%5C%5C%5C%5Cfrac%7Ba_1%2Ba_3%7D%7B2%7D%3Da_2%5C%3B%20%5C%3B%20%5Cto%20%5C%3B%20%5C%3B%20a_2%3D%5Cfrac%7B1%2B9%7D%7B2%7D%3D5)
6) В коробке 6 белых шариков и "k" чёрных.
Вероятность того, что выбран 1 белый шарик равна
.
Значит,
![6\cdot 5=3\cdot (6+k)\; \; \to \; \; 30=18+3k\; ,\; \; 3k=12\; ,\; \; k=4](https://tex.z-dn.net/?f=6%5Ccdot%205%3D3%5Ccdot%20%286%2Bk%29%5C%3B%20%5C%3B%20%5Cto%20%5C%3B%20%5C%3B%2030%3D18%2B3k%5C%3B%20%2C%5C%3B%20%5C%3B%203k%3D12%5C%3B%20%2C%5C%3B%20%5C%3B%20k%3D4)
В коробке 4 чёрных шарика.
7) 1 -Д , 2 - Г , 3- В , 4 - Б .
![8)\; \; y=\frac{1}{5sinx+7}\\\\-1\leq sinx\leq 1\; \; \to \; \; -5\leq 5sinx\leq 5\; \; \to \; \; 2\leq (5sinx+7)\leq 12\\\\\frac{1}{12} \leq \frac{1}{5sinx+7}\leq \frac{1}{2}\\\\y(naibol)=\frac{1}{2}](https://tex.z-dn.net/?f=8%29%5C%3B%20%5C%3B%20y%3D%5Cfrac%7B1%7D%7B5sinx%2B7%7D%5C%5C%5C%5C-1%5Cleq%20sinx%5Cleq%201%5C%3B%20%5C%3B%20%5Cto%20%5C%3B%20%5C%3B%20-5%5Cleq%205sinx%5Cleq%205%5C%3B%20%5C%3B%20%5Cto%20%5C%3B%20%5C%3B%202%5Cleq%20%285sinx%2B7%29%5Cleq%2012%5C%5C%5C%5C%5Cfrac%7B1%7D%7B12%7D%20%5Cleq%20%5Cfrac%7B1%7D%7B5sinx%2B7%7D%5Cleq%20%5Cfrac%7B1%7D%7B2%7D%5C%5C%5C%5Cy%28naibol%29%3D%5Cfrac%7B1%7D%7B2%7D)
![9)\; \; \sqrt[3]{5+2\sqrt6}\cdot \sqrt[6]{49-20\sqrt6}=\sqrt[6]{(45+2\sqrt6)^2}\cdot \sqrt[6]{49-20\sqrt6}=\\\\=\sqrt[6]{49+20\sqrt6}\cdot \sqrt[6]{49-20\sqrt6}=\\\\=\sqrt[6]{49^2-(20\sqrt6)^2}=\sqrt[6]{2401-2400}=1](https://tex.z-dn.net/?f=9%29%5C%3B%20%5C%3B%20%5Csqrt%5B3%5D%7B5%2B2%5Csqrt6%7D%5Ccdot%20%5Csqrt%5B6%5D%7B49-20%5Csqrt6%7D%3D%5Csqrt%5B6%5D%7B%2845%2B2%5Csqrt6%29%5E2%7D%5Ccdot%20%5Csqrt%5B6%5D%7B49-20%5Csqrt6%7D%3D%5C%5C%5C%5C%3D%5Csqrt%5B6%5D%7B49%2B20%5Csqrt6%7D%5Ccdot%20%5Csqrt%5B6%5D%7B49-20%5Csqrt6%7D%3D%5C%5C%5C%5C%3D%5Csqrt%5B6%5D%7B49%5E2-%2820%5Csqrt6%29%5E2%7D%3D%5Csqrt%5B6%5D%7B2401-2400%7D%3D1)
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0,01ab × 100a = a²b
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Возводи в квадрат все.
Решается устно. Ответ 35.
Николай может купить 8 дисков, решение:
х*6=(кол-во денег у Вити)
х=2руб. (к примеру)
2*6=12
12*2=24
2руб.*1.5=3руб.
24/3=8 дисков (ответ) (( всё элементарно, Ватсон :D ))