2) (-7/5)^-1 = -5/7
4) (7/8)-² =(8/7)² =64/49 =1 15/49(одна целая пятнадцать сорок девятых)
6) (-3/5)^-3 =(-5/3)^3 =(-125/27) = -4 17/27
2) (0.3)^-4 =(3/10)^-4 =(10/3)^4 =10000/81 =123 37/81
4) (-0.7)-² =(-7/10)-² =(-10/7)² =100/49 =2 2/49
6) -(-0.9)-² = -(-9/10)-² = -(-10/9)² = -100/81 = -1 19/81
8) (2.1)-² =(21/10)-² =(10/21)² =100/441
2) (-3)^-3. -(1/2)^-4 =(-1/3)^3 -2^4 = -1/27 -16 =(-16 -27*16) /27*16 = -448 /432
4) (2/7)^-3 +(-2)^-5 =(7/2)^3. -(1/2)^5 =343/8 -1/32 =(343*4 -1)/32 =1371/32 =42 27/32
2) =5x^4*6.2x²y^5 /y^3 =31x^6*y²
4) =1.5y*y. /x^3*6.2x^4 =1.5y² /6.2x^7
6) =4m^3 /0.2*1*n^3*n^3 =4m^3 /0.2n^6 =20m^3 /n^6; (m^0=1)
<span>1/4(2y+1)=8
</span><span>2y+1=8:1/4
</span><span>2y+1=32
2y=32-1
2y=31
y=31/2
y= 15,5
</span>
1. Определяем область определения функции
D(f) = R - все действительные числа
2. Определяем производную функции
![f'(x)=(-x^3)'+(9x^2)'+(21x)=-3x^2+18x+21](https://tex.z-dn.net/?f=f%27%28x%29%3D%28-x%5E3%29%27%2B%289x%5E2%29%27%2B%2821x%29%3D-3x%5E2%2B18x%2B21)
3. Производная равна нулю
![-3x^2+18x+21=0|:(-3) \\ x^2-6x-7=0 \\ D=b^2-4ac=(-6)^2-4*1*(-7)=36+28=64 \\ \sqrt{D}=8 \\ x_1= \frac{-b+ \sqrt{D} }{2a} = \frac{6+8}{2} =7 \\ x_2= \frac{-b- \sqrt{D} }{2a} = \frac{6-8}{2} =-1](https://tex.z-dn.net/?f=-3x%5E2%2B18x%2B21%3D0%7C%3A%28-3%29%0A+%5C%5C+x%5E2-6x-7%3D0+%5C%5C+D%3Db%5E2-4ac%3D%28-6%29%5E2-4%2A1%2A%28-7%29%3D36%2B28%3D64+%5C%5C++%5Csqrt%7BD%7D%3D8+%5C%5C+%0Ax_1%3D+%5Cfrac%7B-b%2B+%5Csqrt%7BD%7D+%7D%7B2a%7D++%3D+%5Cfrac%7B6%2B8%7D%7B2%7D+%3D7+%5C%5C+x_2%3D+%5Cfrac%7B-b-+%0A%5Csqrt%7BD%7D+%7D%7B2a%7D+%3D+%5Cfrac%7B6-8%7D%7B2%7D+%3D-1)
Убывает
![(-\infty;-1)U(7;+\infty)](https://tex.z-dn.net/?f=%28-%5Cinfty%3B-1%29U%287%3B%2B%5Cinfty%29)
ОДЗ:
3x-1>0 x>1/3 x>1/3
x+3>0 x>-3
x+1>0 x>-1
log3(3x-1)-1=log3(x+3)-log3(x+1)
log3((3x-1)/3)=log3((x+3)/x+1))
(3x-1)/3=(x+3)/x+1
(x+1)*(3x-1)=3*(x+3)
3x^2-x+3x-1=3x+9
3x^2-x-10=0
D=1+120=121=11^2
x1=12/6=2
x2=-10/6 (не подходит по ОДЗ).
Ответ: x=2