Question

Помогите с математикой

Answer 1

$5.\quad \frac{sina-5cosa}{3sina+cosa}=1\; \; \Big |\frac{:cosa}{:cosa}\\\\\frac{\frac{sina}{cosa}-5}{3\cdot \frac{sina}{cosa}+1}=1\\\\\frac{tga-5}{3tga+1}=1\\\\tga-5=3tga+1\\\\2tga=-6\\\\tga=-3\\\\6.\quad y=-2x^3+9x^2+3\\\\y'=-6x^2+18x=0\; |:(-6)\\\\x^2-3x=0\\\\x(x-3)=0\\\\x_1=0\; ,\; \; x_2=3\\\\znaki\; y':\quad +++(0)---(3)+++\\\\.\qquad \qquad \qquad \nearrow \; \; (0)\; \; \searrow \; \; (3)\; \; \nearrow \\\\x_{max}=0\; ,\; \; y_{max}=y(0)=3$