Given:
Consider the function is:
![f(x)=\dfrac{x^2}{3}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdfrac%7Bx%5E2%7D%7B3%7D)
To find:
The average rate of change over the interval 2 ≤ x ≤ 4.
Solution:
We have,
![f(x)=\dfrac{x^2}{3}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdfrac%7Bx%5E2%7D%7B3%7D)
At
,
![f(2)=\dfrac{2^2}{3}](https://tex.z-dn.net/?f=f%282%29%3D%5Cdfrac%7B2%5E2%7D%7B3%7D)
![f(2)=\dfrac{4}{3}](https://tex.z-dn.net/?f=f%282%29%3D%5Cdfrac%7B4%7D%7B3%7D)
At
,
![f(4)=\dfrac{4^2}{3}](https://tex.z-dn.net/?f=f%284%29%3D%5Cdfrac%7B4%5E2%7D%7B3%7D)
![f(4)=\dfrac{16}{3}](https://tex.z-dn.net/?f=f%284%29%3D%5Cdfrac%7B16%7D%7B3%7D)
The average rate of change of a function f(x) over the interval [a,b] is:
![m=\dfrac{f(b)-f(a)}{b-a}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7Bf%28b%29-f%28a%29%7D%7Bb-a%7D)
So, the average rate of change over the interval 2 ≤ x ≤ 4 is:
![m=\dfrac{f(4)-f(2)}{4-2}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7Bf%284%29-f%282%29%7D%7B4-2%7D)
![m=\dfrac{\dfrac{16}{3}-\dfrac{4}{3}}{2}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7B%5Cdfrac%7B16%7D%7B3%7D-%5Cdfrac%7B4%7D%7B3%7D%7D%7B2%7D)
![m=\dfrac{\dfrac{16-4}{3}}{2}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7B%5Cdfrac%7B16-4%7D%7B3%7D%7D%7B2%7D)
On further simplification, we get
![m=\dfrac{12}{3\times 2}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7B12%7D%7B3%5Ctimes%202%7D)
![m=\dfrac{12}{6}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7B12%7D%7B6%7D)
![m=2](https://tex.z-dn.net/?f=m%3D2)
Therefore, the average rate of change over the interval 2 ≤ x ≤ 4 is 2.
264=8x+48
the 48 is derived from 8x6, since eight people (the seven friends AND chuck) paid six dollars each for the rodeo
Answer:
X=2.5
Step-by-step explanation:
4+6+4+7+X+(X+1)+8+2/8=5
31+X+(X+1)/8=5
40=31+X+(X+1)
9=X^2+X
X=2.5
Answer:
Explanation
Step-by-step explanation:
Angles 2 and 6 are corresponding angles in a transversal meaning they have the same measure.
Answer:
Radius: 18
Area of Circle: 1017 or 1018(depends on whether you used the pi function or 3.14)
Step-by-step explanation:
Formula for the circumference and area:
C= 2πr
A= πr^2