[latex]1.\k:y=2x-3\\l:y=ax+b\\kperp lLeftrightarrow 2a=-1Rightarrow a=-frac{1}{2}\\l:y=-frac{1}{2}x+b; A(4;-1)\\-frac{1}{2}cdot4+b=-1\\b=-1+2\\b=1\\l:y=-frac{1}{2}x+1[/latex] [latex]2.\2x^3+2x^2-8x-8=0\\2x^2(x+1)-8(x+1)=0\\(x+1)(2x^2-8)=0\\x+1=0 vee 2x^2-8=0\\x=-1 vee x=-2 vee x=2[/latex] [latex]3.\cgtalpha=frac{7}{12}; alphain(0^0; 90^0)\\ctgalpha=frac{cosalpha}{sinalpha}\\ left{egin{array}{c}frac{cosalpha}{sinalpha}=frac{7}{12}\sin^2alpha+cos^2alpha=1end{array} ight\\left{egin{array}{c}cosalpha=frac{7}{12}sinalpha\sin^2alpha+cos^2alpha=1end{array} ight\\sin^2alpha+(frac{7}{12}sinalpha)^2=1\\sin^2alpha+frac{49}{144}sin^2alpha=1[/latex] [latex]frac{193}{144}sin^2alpha=1 /cdotfrac{144}{193}\\sin^2alpha=frac{144}{193}\\sinalpha=sqrtfrac{144}{193}\\sinalpha=frac{12sqrt{193}}{193}\\cosalpha=frac{7}{12}cdotfrac{12sqrt{193}}{193}=frac{7sqrt{193}}{193}\\cosalpha-sinalpha=frac{7sqrt{193}}{193}-frac{12sqrt{193}}{193}=-frac{5sqrt{193}}{193}[/latex] ©DRK
