Answer:
25%
Step-by-step explanation:
The quarter is 25%
sorry if wrong.
8+8+10+2+2+(8-2)=36
The perimeter is 36ft
You could divide all of them by 6, which would give you 3:5:12
Answer:
![f(126) \approx 5.01333](https://tex.z-dn.net/?f=f%28126%29%20%5Capprox%205.01333)
Step-by-step explanation:
Given
![\sqrt[3]{126}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B126%7D)
Required
Solve using differentials
In differentiation:
![f(x+\triangle x) \approx f(x) + \triangle x \cdot f'(x)](https://tex.z-dn.net/?f=f%28x%2B%5Ctriangle%20x%29%20%5Capprox%20f%28x%29%20%2B%20%5Ctriangle%20x%20%5Ccdot%20f%27%28x%29)
Express 126 as 125 + 1;
i.e.
![x = 125; \triangle x = 1](https://tex.z-dn.net/?f=x%20%3D%20125%3B%20%5Ctriangle%20x%20%3D%201)
So, we have:
![f(125+1) \approx f(125) + 1 \cdot f'(125)](https://tex.z-dn.net/?f=f%28125%2B1%29%20%5Capprox%20f%28125%29%20%2B%201%20%5Ccdot%20f%27%28125%29)
![f(126) \approx f(125) + 1 \cdot f'(125)](https://tex.z-dn.net/?f=f%28126%29%20%5Capprox%20f%28125%29%20%2B%201%20%5Ccdot%20f%27%28125%29)
To calculate f(125), we have:
![f(x) = \sqrt[3]{x}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Csqrt%5B3%5D%7Bx%7D)
![f(125) = \sqrt[3]{125}](https://tex.z-dn.net/?f=f%28125%29%20%3D%20%5Csqrt%5B3%5D%7B125%7D)
![f(125) = 5](https://tex.z-dn.net/?f=f%28125%29%20%3D%205)
So:
![f(126) \approx f(125) + 1 \cdot f'(125)](https://tex.z-dn.net/?f=f%28126%29%20%5Capprox%20f%28125%29%20%2B%201%20%5Ccdot%20f%27%28125%29)
![f(126) \approx 5 + 1 \cdot f'(125)](https://tex.z-dn.net/?f=f%28126%29%20%5Capprox%205%20%2B%201%20%5Ccdot%20f%27%28125%29)
![f(126) \approx 5 + f'(125)](https://tex.z-dn.net/?f=f%28126%29%20%5Capprox%205%20%2B%20f%27%28125%29)
Also:
![f(x) = \sqrt[3]{x}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Csqrt%5B3%5D%7Bx%7D)
Rewrite as:
![f(x) = x^\frac{1}{3}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20x%5E%5Cfrac%7B1%7D%7B3%7D)
Differentiate
![f'(x) = \frac{1}{3}x^{\frac{1}{3} - 1}\\](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%20%5Cfrac%7B1%7D%7B3%7Dx%5E%7B%5Cfrac%7B1%7D%7B3%7D%20-%201%7D%5C%5C)
Using law of indices, we have:
![f'(x) = \frac{x^\frac{1}{3}}{3x}](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%20%5Cfrac%7Bx%5E%5Cfrac%7B1%7D%7B3%7D%7D%7B3x%7D)
So:
![f'(125) = \frac{125^\frac{1}{3}}{3*125}](https://tex.z-dn.net/?f=f%27%28125%29%20%3D%20%5Cfrac%7B125%5E%5Cfrac%7B1%7D%7B3%7D%7D%7B3%2A125%7D)
![f'(125) = \frac{5}{375}](https://tex.z-dn.net/?f=f%27%28125%29%20%3D%20%5Cfrac%7B5%7D%7B375%7D)
![f'(125) = \frac{1}{75}](https://tex.z-dn.net/?f=f%27%28125%29%20%3D%20%5Cfrac%7B1%7D%7B75%7D)
So, we have:
![f(126) \approx 5 + f'(125)](https://tex.z-dn.net/?f=f%28126%29%20%5Capprox%205%20%2B%20f%27%28125%29)
![f(126) \approx 5 + \frac{1}{75}](https://tex.z-dn.net/?f=f%28126%29%20%5Capprox%205%20%2B%20%5Cfrac%7B1%7D%7B75%7D)
![f(126) \approx 5 + 0.01333](https://tex.z-dn.net/?f=f%28126%29%20%5Capprox%205%20%2B%200.01333)
![f(126) \approx 5.01333](https://tex.z-dn.net/?f=f%28126%29%20%5Capprox%205.01333)
Vertex= (6,-5)
y-intercept=(0,175)
(x-6)^2-5=0
(x-6)^2=5
x-6=+- square root 5
x=6+- square root 5
x=8.24, x=3.76
x-intercepts= 8.24 and 3.76