1.
[tex]\frac{x+2}{x-1}\leq\frac{5}{2x-2}\\5(x-1)\leq(x+2)(2x-2)\\5x-5\leq2x^2-2x+4x-4\\0\leq2x^2-2x+4x-5x-4+5\\0\leq2x^2-3x+1\\2x^2-3x+1\geq 0\\\Delta=(-3)^2-4*2*1\\\Delta=9-8\\\Delta=1\\\\\sqrt{\Delta}=1\\x_1\frac{3-1}4=\frac24=\frac12\\x_2=\frac{3+1}4=\frac44=1\\x\in (-\infty; \frac12>U<1;\infty)[/tex]
2.
[tex]ctg(90-\alpha)=tg\alpha\\tg\alpha=\frac34\\tg\alpha=\frac{sin\alpha}{cos\alpha}\\\frac34=\frac{sin\alpha}{cos\alpha}\\3cos\alpha=4sin\alpha\\\frac34cos\alpha=sin\alpha\\sin^2\alpha+cos^2\alpha=1\\(\frac34cos\alpha)^2+cos^2\alpha=1\\\frac9{16}cos^2\alpha+cos^2\alpha=1\\\\\frac{25}{16}cos^2\alpha=1 /*16\\25cos^2\alpha=16/:25\\cos^2\alpha=\frac{16}{25}\\cos\alpha=\sqrt{\frac{16}{25}}\\cos\alpha=\frac45\\sin\alpha=\frac34*\frac45=\frac35[/tex]
[tex]tg\alpha=\frac34\\ctg\alpha * tg\alpha = 1\\ctg\alpha*\frac34=1/*4\\3ctg\alpha=4/:3\\ctg\alpha=\frac43[/tex]
3.
a = 4cm
b = 10cm
c = 5cm
b=a+2d
10=4+2d
6=2d
d=3
[tex]cos\alpha=\frac{d}c\\cos\alpha=\frac{3}5\\sin\alpha=\frac{h}5\\sin^2\alpha+cos^2\alpha=1\\(\frac{h}5)^2+(\frac35)^2=1\\\frac{h^2}{25}+\frac9{25}=1 /-\frac9{25}\\\frac{h^2}{25}=\frac{16}{25} /*25\\h^2=16\\h=\sqrt{16}=4[/tex]
[tex]cos\alpha=\frac35=\frac6{10}=0,6\\\alpha=53\\P=\frac{(a+b)*h}{2}\\P=\frac{(4+10)*4}{2}=14*2=28[/tex]
