Answer:
![Rate = 9(t+1)](https://tex.z-dn.net/?f=Rate%20%3D%209%28t%2B1%29)
Step-by-step explanation:
Given
![f(x) = 9x^2 - 2](https://tex.z-dn.net/?f=f%28x%29%20%3D%209x%5E2%20-%202)
![Interval = [1,t]](https://tex.z-dn.net/?f=Interval%20%3D%20%5B1%2Ct%5D)
Required
Determine the average rate of change
This is calculated using:
![Rate = \frac{f(b) - f(a)}{b - a}](https://tex.z-dn.net/?f=Rate%20%3D%20%5Cfrac%7Bf%28b%29%20-%20f%28a%29%7D%7Bb%20-%20a%7D)
Where
![[a,b] = [1,t]](https://tex.z-dn.net/?f=%5Ba%2Cb%5D%20%3D%20%5B1%2Ct%5D)
So, we have:
![Rate = \frac{f(t) - f(1)}{t - 1}](https://tex.z-dn.net/?f=Rate%20%3D%20%5Cfrac%7Bf%28t%29%20-%20f%281%29%7D%7Bt%20-%201%7D)
Solve for f(t) and f(1)
![f(t) = 9t^2 - 2](https://tex.z-dn.net/?f=f%28t%29%20%3D%209t%5E2%20-%202)
![f(1) = 9*1^2 - 2](https://tex.z-dn.net/?f=f%281%29%20%3D%209%2A1%5E2%20-%202)
![f(1) = 9 - 2](https://tex.z-dn.net/?f=f%281%29%20%3D%209%20-%202)
![f(1) = 7](https://tex.z-dn.net/?f=f%281%29%20%3D%207)
So, we have:
![Rate = \frac{9t^2 - 2 - 7}{t - 1}](https://tex.z-dn.net/?f=Rate%20%3D%20%5Cfrac%7B9t%5E2%20-%202%20-%207%7D%7Bt%20-%201%7D)
![Rate = \frac{9t^2 - 9}{t - 1}](https://tex.z-dn.net/?f=Rate%20%3D%20%5Cfrac%7B9t%5E2%20-%209%7D%7Bt%20-%201%7D)
Factorize:
![Rate = \frac{9(t^2 - 1)}{t - 1}](https://tex.z-dn.net/?f=Rate%20%3D%20%5Cfrac%7B9%28t%5E2%20-%201%29%7D%7Bt%20-%201%7D)
Apply difference of two squares
![Rate = \frac{9(t- 1)(t+1)}{t - 1}](https://tex.z-dn.net/?f=Rate%20%3D%20%5Cfrac%7B9%28t-%201%29%28t%2B1%29%7D%7Bt%20-%201%7D)
![Rate = 9(t+1)](https://tex.z-dn.net/?f=Rate%20%3D%209%28t%2B1%29)
Answer:
(2x - 5y)²
(2x - 5y)(2x - 5y)
2x(2x - 5y) - 5y(2x - 5y)
2x(2x) - 2x(5y) - 5y(2x) + 5y(5y)
4x² - 10xy - 10xy + 25y²
4x² - 20y + 25y²
The answer is B.
Step-by-step explanation:
Answer:
7.68
Step-by-step explanation: