(5^(n+5)*2^(2n+5))/(20^(n+5))=(5^(n+5)*2^(2n+5))/(5^(n+5)*4^(n+5))=2^(2n+5)/4^(n+5)=2^(2n+5)/2^(2*(n+5))=2^(2n+5)/2^(2*n+10)=2^(2n+5-2n-10)=2^(-5)=1/(2^5)=1/32
![(2^3 \sqrt{x^2-1}+4\sqrt{x^3-6x^2})'=2^3 (\sqrt{x^2-1})' + 4(\sqrt{x^3-6x^2})'](https://tex.z-dn.net/?f=%282%5E3+%5Csqrt%7Bx%5E2-1%7D%2B4%5Csqrt%7Bx%5E3-6x%5E2%7D%29%27%3D2%5E3+%28%5Csqrt%7Bx%5E2-1%7D%29%27+%2B+4%28%5Csqrt%7Bx%5E3-6x%5E2%7D%29%27)
Далее по правлилу производных от сложной функции:
![2^3 (\sqrt{x^2-1})' + 4(\sqrt{x^3-6x^2})'= 2^3 \frac{1}{2} \frac{(x^2-1)'}{\sqrt{x^2-1}}+ 4 \frac{1}{2} \frac{(x^3-6x^2)'}{\sqrt{x^3-6x^2}} = \newline = 2^3 \frac{1}{2} \frac{2x}{\sqrt{x^2-1}}+ 4 \frac{1}{2} \frac{3x^2-12x}{\sqrt{x^3-6x^2}} = 2^3 \frac{2x}{\sqrt{x^2-1}}+2\frac{3x^2-12x}{\sqrt{x^3-6x^2}}](https://tex.z-dn.net/?f=2%5E3+%28%5Csqrt%7Bx%5E2-1%7D%29%27+%2B+4%28%5Csqrt%7Bx%5E3-6x%5E2%7D%29%27%3D+2%5E3++%5Cfrac%7B1%7D%7B2%7D++%0A%5Cfrac%7B%28x%5E2-1%29%27%7D%7B%5Csqrt%7Bx%5E2-1%7D%7D%2B+4++%5Cfrac%7B1%7D%7B2%7D++%0A%5Cfrac%7B%28x%5E3-6x%5E2%29%27%7D%7B%5Csqrt%7Bx%5E3-6x%5E2%7D%7D+%3D+%5Cnewline%0A%3D+2%5E3++%5Cfrac%7B1%7D%7B2%7D++%5Cfrac%7B2x%7D%7B%5Csqrt%7Bx%5E2-1%7D%7D%2B+4++%5Cfrac%7B1%7D%7B2%7D++%0A%5Cfrac%7B3x%5E2-12x%7D%7B%5Csqrt%7Bx%5E3-6x%5E2%7D%7D+%3D+2%5E3+%0A%5Cfrac%7B2x%7D%7B%5Csqrt%7Bx%5E2-1%7D%7D%2B2%5Cfrac%7B3x%5E2-12x%7D%7B%5Csqrt%7Bx%5E3-6x%5E2%7D%7D)
Ответ:
А)Скорость (V) = S : T = 20 : 1 = 20 км/ч
Б)Расстояние (S) = V × T = 20 × (1 ×2) (по условию) = 40 км
В) 3 часа (по графику)