Question

Dau coroana celui mai bun răspuns!

Answer 1

$1.\vec{a},\vec{b}->coliniari=>\frac{x}{1}=\frac{-2}{4}<=> \frac{x}{1}=\frac{-1}{2}<=>2x=-1=>x=-\frac{1}{2}\\ \\2.cos135^o=cos(90^o+45^o)=cos90^ocos45^o-sin90^osin45^o=0*\frac{\sqrt2}{2}-1*\frac{\sqrt2}{2}=-\frac{\sqrt2}{2}=>cos135^o=\frac{\sqrt2}{2}$

$3.25^x-6*5^x+5=0<=>5^{2x}-6*5^x+5=0\\t=5^x,t>0\\t^2-6t+5=0\\\Delta=(-6)^2-4*1*5=36-20=16\\t_{1,2}=\frac{-(-6)\pm\sqrt{16}}{2}=\frac{6\pm4}{2}=3\pm2\\ t_1=3+2=5\\t_2=3-2=1\\Pt.t_1=5=>5^x=5=>x_1=1\\Pt.t_2=1=>5^x=1=>x_2=0\\x\in\{0,1\}$

$4.f:R->R\\f(x)=(m-3)x+4\\A(1,2m)\in G_f=>f(1)=2m\\f(1)=(m-3)*1+4=m-3+4=m+1\\f(1)=2m=>m+1=2m=>m=1$