![\begin{cases} \frac{x+3}{5}-\frac{x-2}{4}\leq1\\5x+8\leq38 \end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D+%5Cfrac%7Bx%2B3%7D%7B5%7D-%5Cfrac%7Bx-2%7D%7B4%7D%5Cleq1%5C%5C5x%2B8%5Cleq38+%5Cend%7Bcases%7D)
![\begin{cases} \frac{4(x+3)-5(x-2)-20}{20}\leq0\\5x\leq30 \end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D+%5Cfrac%7B4%28x%2B3%29-5%28x-2%29-20%7D%7B20%7D%5Cleq0%5C%5C5x%5Cleq30+%5Cend%7Bcases%7D)
![\begin{cases} 4x+12-5x+10-20\leq0\\x\leq6 \end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D+4x%2B12-5x%2B10-20%5Cleq0%5C%5Cx%5Cleq6+%5Cend%7Bcases%7D)
![\begin{cases} -x+2\leq0\\x\leq6 \end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D+-x%2B2%5Cleq0%5C%5Cx%5Cleq6+%5Cend%7Bcases%7D)
![\begin{cases} x-2\geq0\\x\leq6 \end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D+x-2%5Cgeq0%5C%5Cx%5Cleq6+%5Cend%7Bcases%7D)
![\begin{cases} x\geq2\\x\leq6 \end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D+x%5Cgeq2%5C%5Cx%5Cleq6+%5Cend%7Bcases%7D)
Выпишем все целые решения системы: 2,3,4,5,6
Ответ: 4
26 каминов с трубой(320+64=384 | 10000/384=26,01| )
Ордината - ось у
значит все точки имеют координату у=-6, график параллелен оси х, угловой коэффициент k=0, соответственно b=-6
Ответ: k=0, b=-6
![1)\; \; sin\frac{\pi (x+9)}{4}=-\frac{\sqrt2}{2}\\\\\frac{\pi (x+9)}{4}=-\frac{\pi }{4}+2\pi k\quad ili\quad \frac{\pi (x+9)}{4}=-\frac{3\pi }{4}+2\pi k\; ,\; k\in Z\\\\x+9=-1+8k\quad ili\quad x+9=-3+8k\; ,\; k\in Z\\\\x_1=-10+8k\qquad ili\qquad x_2=-12+8k\; ,\; k\in Z\\\\k=0:\; \; x_1=-10<0\; \; ;\; \; x_2=-12<0\\\\k=1:\; \; x_1=-2<0\; \; ;\; \; x_2=-4<0\\\\k=2:\; \; x_1=6>0\; \; ;\; \; x_2=4>0\\....................................................................](https://tex.z-dn.net/?f=1%29%5C%3B%20%5C%3B%20sin%5Cfrac%7B%5Cpi%20%28x%2B9%29%7D%7B4%7D%3D-%5Cfrac%7B%5Csqrt2%7D%7B2%7D%5C%5C%5C%5C%5Cfrac%7B%5Cpi%20%28x%2B9%29%7D%7B4%7D%3D-%5Cfrac%7B%5Cpi%20%7D%7B4%7D%2B2%5Cpi%20k%5Cquad%20ili%5Cquad%20%5Cfrac%7B%5Cpi%20%28x%2B9%29%7D%7B4%7D%3D-%5Cfrac%7B3%5Cpi%20%7D%7B4%7D%2B2%5Cpi%20k%5C%3B%20%2C%5C%3B%20k%5Cin%20Z%5C%5C%5C%5Cx%2B9%3D-1%2B8k%5Cquad%20ili%5Cquad%20x%2B9%3D-3%2B8k%5C%3B%20%2C%5C%3B%20k%5Cin%20Z%5C%5C%5C%5Cx_1%3D-10%2B8k%5Cqquad%20ili%5Cqquad%20x_2%3D-12%2B8k%5C%3B%20%2C%5C%3B%20k%5Cin%20Z%5C%5C%5C%5Ck%3D0%3A%5C%3B%20%5C%3B%20x_1%3D-10%3C0%5C%3B%20%5C%3B%20%3B%5C%3B%20%5C%3B%20x_2%3D-12%3C0%5C%5C%5C%5Ck%3D1%3A%5C%3B%20%5C%3B%20x_1%3D-2%3C0%5C%3B%20%5C%3B%20%3B%5C%3B%20%5C%3B%20x_2%3D-4%3C0%5C%5C%5C%5Ck%3D2%3A%5C%3B%20%5C%3B%20x_1%3D6%3E0%5C%3B%20%5C%3B%20%3B%5C%3B%20%5C%3B%20x_2%3D4%3E0%5C%5C....................................................................)
Наименьший положительный корень х=4 .
![2)\; \; cos\frac{\pi (2x+9)}{3}=\frac{1}{2}\\\\\frac{\pi (2x+9)}{3}=\pm \frac{\pi }{3}+2\pi n\; ,\; n\in Z\\\\2x+9=\pm 1+6n\; ,\; n\in Z\\\\2x=-9\pm 1+6n\; \; \Rightarrow \; \; 2x=-10+6n\; \; \; ili\; \; \; 2x=-8+6n\\\\x_1=-5+3n\quad ili\quad x_2=-4+3n\\\\n=0:\; \; x_1=-5<0\; \; ;\; \; x_2=-4<0\\\\n=-1:\; \; x_1=-8<0\; \; ;\; \; x_2=-7<0\\\\n=1:\; \; x_1=-2<0\; \; ;\; \; x_2=-1<0\\\\n=2:\; \; x_1=1>0\; \; ;\; \; x_2=2>0\\.................................................................](https://tex.z-dn.net/?f=2%29%5C%3B%20%5C%3B%20cos%5Cfrac%7B%5Cpi%20%282x%2B9%29%7D%7B3%7D%3D%5Cfrac%7B1%7D%7B2%7D%5C%5C%5C%5C%5Cfrac%7B%5Cpi%20%282x%2B9%29%7D%7B3%7D%3D%5Cpm%20%5Cfrac%7B%5Cpi%20%7D%7B3%7D%2B2%5Cpi%20n%5C%3B%20%2C%5C%3B%20n%5Cin%20Z%5C%5C%5C%5C2x%2B9%3D%5Cpm%201%2B6n%5C%3B%20%2C%5C%3B%20n%5Cin%20Z%5C%5C%5C%5C2x%3D-9%5Cpm%201%2B6n%5C%3B%20%5C%3B%20%5CRightarrow%20%5C%3B%20%5C%3B%202x%3D-10%2B6n%5C%3B%20%5C%3B%20%5C%3B%20ili%5C%3B%20%5C%3B%20%5C%3B%202x%3D-8%2B6n%5C%5C%5C%5Cx_1%3D-5%2B3n%5Cquad%20ili%5Cquad%20x_2%3D-4%2B3n%5C%5C%5C%5Cn%3D0%3A%5C%3B%20%5C%3B%20x_1%3D-5%3C0%5C%3B%20%5C%3B%20%3B%5C%3B%20%5C%3B%20x_2%3D-4%3C0%5C%5C%5C%5Cn%3D-1%3A%5C%3B%20%5C%3B%20x_1%3D-8%3C0%5C%3B%20%5C%3B%20%3B%5C%3B%20%5C%3B%20x_2%3D-7%3C0%5C%5C%5C%5Cn%3D1%3A%5C%3B%20%5C%3B%20x_1%3D-2%3C0%5C%3B%20%5C%3B%20%3B%5C%3B%20%5C%3B%20x_2%3D-1%3C0%5C%5C%5C%5Cn%3D2%3A%5C%3B%20%5C%3B%20x_1%3D1%3E0%5C%3B%20%5C%3B%20%3B%5C%3B%20%5C%3B%20x_2%3D2%3E0%5C%5C.................................................................)
Наибольший отрицательный корень х= -1 .
![3)\; \; tg\frac{\pi (x+2)}{3}=-\sqrt3\\\\\frac{\pi (x+2)}{3}=-\frac{\pi }{3}+\pi n\; ,\; n\in Z\\\\x+2=-1+3n\; ,\; n\in Z\\\\x=-3+3n\; ,\; n\in Z\\\\n=0:\; x=-3<0\\\\n=-1:\; x=-6<0\\\\n=1:\; x=0\\\\n=2:\; x=3>0\\..................................................................................](https://tex.z-dn.net/?f=3%29%5C%3B%20%5C%3B%20tg%5Cfrac%7B%5Cpi%20%28x%2B2%29%7D%7B3%7D%3D-%5Csqrt3%5C%5C%5C%5C%5Cfrac%7B%5Cpi%20%28x%2B2%29%7D%7B3%7D%3D-%5Cfrac%7B%5Cpi%20%7D%7B3%7D%2B%5Cpi%20n%5C%3B%20%2C%5C%3B%20n%5Cin%20Z%5C%5C%5C%5Cx%2B2%3D-1%2B3n%5C%3B%20%2C%5C%3B%20n%5Cin%20Z%5C%5C%5C%5Cx%3D-3%2B3n%5C%3B%20%2C%5C%3B%20n%5Cin%20Z%5C%5C%5C%5Cn%3D0%3A%5C%3B%20x%3D-3%3C0%5C%5C%5C%5Cn%3D-1%3A%5C%3B%20x%3D-6%3C0%5C%5C%5C%5Cn%3D1%3A%5C%3B%20x%3D0%5C%5C%5C%5Cn%3D2%3A%5C%3B%20x%3D3%3E0%5C%5C..................................................................................)
Наибольший отрицательный корень х= -3 .
![4)\; \; sin\frac{\pi (2x-3)}{6}=-0,5\\\\\frac{\pi (2x-3)}{6}=-\frac{\pi }{6}+2\pi n\; \; \; \; \; ili\; \; \; \; \frac{\pi (2x-3)}{6}=-\frac{5\pi }{6}+2\pi n\; ,\; n\in Z\\\\2x-3=-1+12n\; \; \; ili\; \; \; 2x-3=-30+12n\; ,\; n\in Z\\\\2x=2+12n\qquad ili\qquad 2x=-27+12n\; ,\; n\in Z\\\\x_1=1+6n\qquad ili\qquad x_2=-13,5+6n\; ,\; n\in Z\\\\n=0:\; \; x_1=1>0\; \; ;\; \; x_2=-13,5<0\\\\n=-1:\; \; x_1=-5\; \; ;\; \; x_2=-19,5\\\\n=1:\; \; x_1=7>0\; \; ;\; \; x_2=-7,5<0\\............................................................................](https://tex.z-dn.net/?f=4%29%5C%3B%20%5C%3B%20sin%5Cfrac%7B%5Cpi%20%282x-3%29%7D%7B6%7D%3D-0%2C5%5C%5C%5C%5C%5Cfrac%7B%5Cpi%20%282x-3%29%7D%7B6%7D%3D-%5Cfrac%7B%5Cpi%20%7D%7B6%7D%2B2%5Cpi%20n%5C%3B%20%5C%3B%20%5C%3B%20%5C%3B%20%5C%3B%20ili%5C%3B%20%5C%3B%20%5C%3B%20%5C%3B%20%5Cfrac%7B%5Cpi%20%282x-3%29%7D%7B6%7D%3D-%5Cfrac%7B5%5Cpi%20%7D%7B6%7D%2B2%5Cpi%20n%5C%3B%20%2C%5C%3B%20n%5Cin%20Z%5C%5C%5C%5C2x-3%3D-1%2B12n%5C%3B%20%5C%3B%20%5C%3B%20ili%5C%3B%20%5C%3B%20%5C%3B%202x-3%3D-30%2B12n%5C%3B%20%2C%5C%3B%20n%5Cin%20Z%5C%5C%5C%5C2x%3D2%2B12n%5Cqquad%20ili%5Cqquad%202x%3D-27%2B12n%5C%3B%20%2C%5C%3B%20n%5Cin%20Z%5C%5C%5C%5Cx_1%3D1%2B6n%5Cqquad%20ili%5Cqquad%20x_2%3D-13%2C5%2B6n%5C%3B%20%2C%5C%3B%20n%5Cin%20Z%5C%5C%5C%5Cn%3D0%3A%5C%3B%20%5C%3B%20x_1%3D1%3E0%5C%3B%20%5C%3B%20%3B%5C%3B%20%5C%3B%20x_2%3D-13%2C5%3C0%5C%5C%5C%5Cn%3D-1%3A%5C%3B%20%5C%3B%20x_1%3D-5%5C%3B%20%5C%3B%20%3B%5C%3B%20%5C%3B%20x_2%3D-19%2C5%5C%5C%5C%5Cn%3D1%3A%5C%3B%20%5C%3B%20x_1%3D7%3E0%5C%3B%20%5C%3B%20%3B%5C%3B%20%5C%3B%20x_2%3D-7%2C5%3C0%5C%5C............................................................................)
Наименьший положительный корень х=1.