You can turn 5 into 10/2 and add to x/2
then you need to use simple algebra to left the x alone in the equation so you need to multiply both sides by 2 so you get
2y=10+x
then you need to subtract both sides a 10 so
2y-10=x
now change the x to f'(x) and y to x so:
f'(x)=2x-10
The LCD of 24 and 23 is 552, so 276/552 - 240/552 = 36. After simplifying 36/552, you get 3/46 and that is your answer.
If I remember My geometry correctly
you add GH AND EF then divide 2
The numbers of visits a member could go is 82 visits.
The average rate of change for the function f(x) can be calculated from the following equation
![\frac{f( x_{2})-f( x_{1} )}{ x_{2} - x_{1} }](https://tex.z-dn.net/?f=%20%5Cfrac%7Bf%28%20x_%7B2%7D%29-f%28%20x_%7B1%7D%20%29%7D%7B%20x_%7B2%7D%20-%20x_%7B1%7D%20%7D%20)
By applying the last formula on the given equations
(1) the first function f
from the table f(3π/2) = -2 and f(2π) = 0
∴ The average rate of f =
![\frac{f(2 \pi)-f( \frac{3 \pi}{2} )}{2 \pi - \frac{3 \pi}{2} } = \frac{0-(-2)}{ \frac{\pi}{2} }= \frac{2}{ \frac{\pi}{2} } = \frac{4}{\pi}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bf%282%20%5Cpi%29-f%28%20%5Cfrac%7B3%20%5Cpi%7D%7B2%7D%20%29%7D%7B2%20%5Cpi%20-%20%20%5Cfrac%7B3%20%5Cpi%7D%7B2%7D%20%7D%20%3D%20%20%5Cfrac%7B0-%28-2%29%7D%7B%20%5Cfrac%7B%5Cpi%7D%7B2%7D%20%7D%3D%20%20%5Cfrac%7B2%7D%7B%20%5Cfrac%7B%5Cpi%7D%7B2%7D%20%7D%20%20%3D%20%20%5Cfrac%7B4%7D%7B%5Cpi%7D%20)
(2) the second function g(x)
from the graph g(3π/2) = -2 and g(2π) = 0
∴ The average rate of g =
![\frac{g(2 \pi)-g( \frac{3 \pi}{2} )}{2 \pi - \frac{3 \pi}{2} } = \frac{0-(-2)}{ \frac{\pi}{2} }= \frac{2}{ \frac{\pi}{2} } = \frac{4}{\pi}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bg%282%20%5Cpi%29-g%28%20%5Cfrac%7B3%20%5Cpi%7D%7B2%7D%20%29%7D%7B2%20%0A%5Cpi%20-%20%20%5Cfrac%7B3%20%5Cpi%7D%7B2%7D%20%7D%20%3D%20%20%5Cfrac%7B0-%28-2%29%7D%7B%20%5Cfrac%7B%5Cpi%7D%7B2%7D%20%7D%3D%20%20%5Cfrac%7B2%7D%7B%20%0A%5Cfrac%7B%5Cpi%7D%7B2%7D%20%7D%20%20%3D%20%20%5Cfrac%7B4%7D%7B%5Cpi%7D%20)
(3) the third function h(x) = 6 sin x +1
∴ h(3π/2) = 6 sin (3π/2) + 1 = 6 *(-1) + 1 = -5
h(2π) = 6 sin (2π) + 1 = 6 * 0 + 1 = 1
∴ The average rate of h =
By comparing the results, The <span>function which has the greatest rate of change is h(x)
</span>
So, the correct answer is option <span>
C) h(x)</span>