А) 8000–500*n
б) через три минуты
8000–500*3=6500
через восемь минут
8000–500*8=4000
в) на девятой минуте
составив пропорцию мы получим
![(a+1)x^2-2x+1-а=0 \\(a+1)x^2-2x+(1-a)=0 \\D=4-4(a+1)(1-a)=4(1+a^2-1)=4a^2](https://tex.z-dn.net/?f=%28a%2B1%29x%5E2-2x%2B1-%D0%B0%3D0%0A%5C%5C%28a%2B1%29x%5E2-2x%2B%281-a%29%3D0%0A%5C%5CD%3D4-4%28a%2B1%29%281-a%29%3D4%281%2Ba%5E2-1%29%3D4a%5E2)
1) при a+1=0; a=-1 уравнение обращается в линейное:
![-2x+1+1=0 \\-2x=-2 \\x=1](https://tex.z-dn.net/?f=-2x%2B1%2B1%3D0%0A%5C%5C-2x%3D-2%0A%5C%5Cx%3D1)
2) при D>0 и a≠-1 имеет 2 различных корня
![\left \{ {{4a^2\ \textgreater \ 0} \atop {a \neq -1}} \right. \Rightarrow \left \{ {{a \in (-\infty;0)\cup (0;+\infty)} \atop {a \neq -1}} \right. \Rightarrow a \in (-\infty;-1)\cup (-1;0)\cup (0;+\infty) \\x_1= \frac{2+\sqrt{4a^2}}{2(a+1)} = \frac{1+|a|}{a+1} \\x_2= \frac{1-|a|}{a+1}](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7B4a%5E2%5C+%5Ctextgreater+%5C+0%7D+%5Catop+%7Ba+%5Cneq+-1%7D%7D+%5Cright.+%5CRightarrow++%5Cleft+%5C%7B+%7B%7Ba+%5Cin+%28-%5Cinfty%3B0%29%5Ccup+%280%3B%2B%5Cinfty%29%7D+%5Catop+%7Ba+%5Cneq+-1%7D%7D+%5Cright.++%5CRightarrow+a+%5Cin+%28-%5Cinfty%3B-1%29%5Ccup+%28-1%3B0%29%5Ccup+%280%3B%2B%5Cinfty%29%0A%5C%5Cx_1%3D+%5Cfrac%7B2%2B%5Csqrt%7B4a%5E2%7D%7D%7B2%28a%2B1%29%7D+%3D+%5Cfrac%7B1%2B%7Ca%7C%7D%7Ba%2B1%7D+%0A%5C%5Cx_2%3D+%5Cfrac%7B1-%7Ca%7C%7D%7Ba%2B1%7D+)
3) при D=0 и a≠-1 имеет 2 совпадающих корня:
![4a^2=0 \\a=0 \\x_1=x_2= \frac{2}{2(a+1)} = \frac{1}{a+1}=\frac{1}{1}=1](https://tex.z-dn.net/?f=4a%5E2%3D0%0A%5C%5Ca%3D0%0A%5C%5Cx_1%3Dx_2%3D+%5Cfrac%7B2%7D%7B2%28a%2B1%29%7D+%3D+%5Cfrac%7B1%7D%7Ba%2B1%7D%3D%5Cfrac%7B1%7D%7B1%7D%3D1+)
4) при D<0 и a≠-1 не имеет корней
![4a^2\ \textless \ 0 \\a \in \varnothing](https://tex.z-dn.net/?f=4a%5E2%5C+%5Ctextless+%5C+0%0A%5C%5Ca+%5Cin+%5Cvarnothing)
дальше не рассматриваем этот случай
Ответ:
![a\in \{-1\} \cup \{0\} \Rightarrow x=1 \\a \in (-\infty;-1)\cup (-1;0)\cup (0;+\infty) \Rightarrow x_1=\frac{1+|a|}{a+1};\ x_2= \frac{1-|a|}{a+1}](https://tex.z-dn.net/?f=a%5Cin+%5C%7B-1%5C%7D+%5Ccup+%5C%7B0%5C%7D+%5CRightarrow+x%3D1+%5C%5Ca+%5Cin+%28-%5Cinfty%3B-1%29%5Ccup+%28-1%3B0%29%5Ccup+%280%3B%2B%5Cinfty%29+%5CRightarrow+x_1%3D%5Cfrac%7B1%2B%7Ca%7C%7D%7Ba%2B1%7D%3B%5C+x_2%3D+%5Cfrac%7B1-%7Ca%7C%7D%7Ba%2B1%7D)
1)75-30=45°-АОС
2)75-45=30°-СОВ
Ответ:30°