![4. ( 1+ ( x- \frac{3}{2} ):3)(-0,75)<0 \\ 1+ ( x- \frac{3}{2} ):3>0 \\ ( x- \frac{3}{2} ):3> -1 \\ x- \frac{3}{2}> - 3 \\ x> - 3 + \frac{3}{2} \\ x> - 3 + 1,5 \\ x> - 1,5 \\](https://tex.z-dn.net/?f=4.+++%28+1%2B+%28+x-+%5Cfrac%7B3%7D%7B2%7D+%29%3A3%29%28-0%2C75%29%3C0+%5C%5C+%0A+++++++1%2B+%28+x-+%5Cfrac%7B3%7D%7B2%7D+%29%3A3%3E0+%5C%5C+%0A%28+x-+%5Cfrac%7B3%7D%7B2%7D+%29%3A3%3E+-1+%5C%5C+%0Ax-+%5Cfrac%7B3%7D%7B2%7D%3E+-+3+%5C%5C+%0Ax%3E+-+3+%2B+%5Cfrac%7B3%7D%7B2%7D+%5C%5C+%0Ax%3E+-+3+%2B+1%2C5+%5C%5C+%0Ax%3E+-+1%2C5+%5C%5C+)
ОТВЕТ: ( - 1,5 ; + оо )
![5. (x- x^{2} )^{2}+5x-5x^{2}=6 \\ (x- x^{2} )^{2}+5(x-x^{2}) - 6=0 \\ x- x^{2}=t \\ t^{2}+5t - 6=0 \\ t_{1} = 1 , t_{2} = -6 \\ x- x^{2}= 1 ,, x- x^{2}= -6 \\ x^{2} - x +1 =0 ,, x^{2} - x -6 =0 \\ D= 1 - 4 < 0 ,, x_{1} = 3 , x_{2} = -2 \\ x_{1} +x_{2}= 3+(-2) = 1 \\](https://tex.z-dn.net/?f=5.++%28x-+x%5E%7B2%7D+%29%5E%7B2%7D%2B5x-5x%5E%7B2%7D%3D6+%5C%5C+%0A++%28x-+x%5E%7B2%7D+%29%5E%7B2%7D%2B5%28x-x%5E%7B2%7D%29+-+6%3D0+%5C%5C%0A+x-+x%5E%7B2%7D%3Dt+%5C%5C+%0At%5E%7B2%7D%2B5t+-+6%3D0+%5C%5C%0A+t_%7B1%7D+%3D+1+%2C+++t_%7B2%7D+%3D+-6+%5C%5C+%0A+x-+x%5E%7B2%7D%3D+1++%2C%2C+++x-+x%5E%7B2%7D%3D+-6+%5C%5C+%0Ax%5E%7B2%7D+-+x+%2B1+%3D0+%2C%2C++x%5E%7B2%7D+-+x+-6+%3D0+%5C%5C+%0AD%3D+1+-+4+%3C+0++++++%2C%2C+x_%7B1%7D+%3D+3+%2C+++x_%7B2%7D+%3D+-2+%5C%5C%0A++x_%7B1%7D+%2Bx_%7B2%7D%3D+3%2B%28-2%29+%3D+1+%5C%5C++)
ОТВЕТ: 1.
![9. \left \{ {{2 x^{2} +xy=40} \atop {3x-y=10}} \right. \\ 3x-y=10 => y=3x-10 \\ 2 x^{2} +xy=40 \\ 2 x^{2} +x(3x-10)=40 \\ 2 x^{2} +3 x^{2}-10x-40=0 \\ 5x^{2}-10x-40=0 \\ x^{2}-2x-8=0 \\ x_{1} + x_{2}=2 \\ x_{1}x_{2}=-8 \\ x_{1}=4, x_{2}=-2 \\](https://tex.z-dn.net/?f=9.+++%5Cleft+%5C%7B+%7B%7B2+x%5E%7B2%7D+%2Bxy%3D40%7D+%5Catop+%7B3x-y%3D10%7D%7D+%5Cright.++%5C%5C+%0A3x-y%3D10+%3D%3E+y%3D3x-10+%5C%5C+%0A2+x%5E%7B2%7D+%2Bxy%3D40+%5C%5C+%0A2+x%5E%7B2%7D+%2Bx%283x-10%29%3D40+%5C%5C+%0A2+x%5E%7B2%7D+%2B3+x%5E%7B2%7D-10x-40%3D0+%5C%5C+%0A5x%5E%7B2%7D-10x-40%3D0+%5C%5C+%0Ax%5E%7B2%7D-2x-8%3D0+%5C%5C+%0A+x_%7B1%7D+%2B++x_%7B2%7D%3D2+%5C%5C+%0Ax_%7B1%7Dx_%7B2%7D%3D-8+%5C%5C+%0A+x_%7B1%7D%3D4%2C++x_%7B2%7D%3D-2+%5C%5C+)
ОТВЕТ: 4; - 2.
10. По условию графики не пересекаются => уравнение
![a x^{2} - a x = a x - 4 \\](https://tex.z-dn.net/?f=a+x%5E%7B2%7D+-+a+x+%3D+a+x+-+4+%5C%5C+)
не будет иметь решений, т.е D < 0.
Найдём дискриминант:
![a x^{2} - a x = a x - 4 \\ a x^{2} - a x - a x + 4 =0\\ a x^{2} - 2a x + 4 =0\\ D= (-2a)^{2} - 4*a*4 = 4a^{2} - 16a \\ D < 0 => \\ 4a^{2} - 16a< 0 \\ 4(a^{2} -4a)< 0 \\ a^{2} -4a < 0 \\ a(a - 4) < 0 \\ ](https://tex.z-dn.net/?f=a+x%5E%7B2%7D+-+a+x+%3D+a+x+-+4+%5C%5C%0Aa+x%5E%7B2%7D+-+a+x+-+a+x+%2B+4+%3D0%5C%5C%0Aa+x%5E%7B2%7D+-+2a+x+%2B+4+%3D0%5C%5C%0AD%3D+%28-2a%29%5E%7B2%7D++-+4%2Aa%2A4+%3D+4a%5E%7B2%7D+-+16a+%5C%5C+%0AD+%3C+0+++%3D%3E++++%5C%5C+%0A4a%5E%7B2%7D+-+16a%3C+0+%5C%5C+%0A4%28a%5E%7B2%7D+-4a%29%3C+0+%5C%5C+%0Aa%5E%7B2%7D+-4a+%3C+0+%5C%5C+%0Aa%28a+-+4%29+%3C+0+%5C%5C+%0A)
0 4
______________о____________________о___________
+ - +
ОТВЕТ: а ∈ ( 0 ; 4)
Длина окружности С = 2*pi*r = 2 * 3.14 * 0.02 = 0.1256 (м) = 12.56 (см)
20 минут - треть часа. Значит, минутная стрелка проходит треть окружности. S = 12.56/3 = 4.18 (см)