Question

алгебра срочно помогите пожалуйста ​

Answer 1

Ответ:

$31)\ \ \ \left\{\begin{array}{l}sinx+cosy=1\\sinx\cdot cosy=\dfrac{1}{4}\end{array}\right\\\\\\\Big(\ \dfrac{5\pi}{6} \ ;\ \dfrac{\pi}{3}\ \Big)\ \ \Rightarrow \ \ sin\dfrac{5\pi}{6}+cos\dfrac{\pi}{3}=\dfrac{1}{2}+\dfrac{1}{2}=1\ \ \ verno\\\\\\sin\dfrac{5\pi}{6}\cdot cos\dfrac{\pi}{3}=\dfrac{1}{2}\cdot \dfrac{1}{2}=\dfrac{1}{4}\ \ \ \ verno\\\\\\Otvet:\ \ B)\ .$

$32)\ \ \int\limits^{\pi /4}_{-\pi /2} \, cosx\cdot sinx\, dx=\dfrac{1}{2} \int\limits^{\pi /4}_{-\pi /2} \, sin2x\, dx=\dfrac{1}{2}\cdot \Big(-\dfrac{1}{2}\cdot cos2x\Big)\Big|_{-\pi /2}^{\pi /4}=\\\\\\=-\dfrac{1}{4}\cdot \Big(cos\dfrac{\pi}{2}-cos(-\pi)\Big)=-\dfrac{1}{4}\cdot \Big(0-(-1)\Big)=-\dfrac{1}{4}=-0,25\\\\\\-0,25\in [-1\ ;-0,25\ ]\ \ \ ,\ \ \ -0,25\in (-0,5\ ;\ 0,5\, )\ \ ,\ \ \ -0,25\in [-1\ ;\ 0\ ]\\\\Otvet:\ \ B)\ ,\ C)\ ,\ D)\ .$