Question

What is the rate of change from x = 0 to x =pi over 2 ? (6 points)

Answer 1

6 over pi

This is because after using the slope formula, you get 3/(pi/2), which when simplified is your answer

Answer 2

Answer:

$\frac{6}{\pi}$.

Step-by-step explanation:    

We have been given the graph of sine function and we are asked to find the rate of change from $x=0$ to $x=\frac{\pi}{2}$.

We will use slope formula to find the rate of change for our given values.

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

We can see from our graph that at x equals 0, y is 0 and at x equals $\frac{\pi}{2}$, y is 3.

Upon substituting these values in slope formula we will get,

$\text{Slope}=\frac{3-0}{\frac{\pi}{2}-0}$

$\text{Slope}=\frac{3}{\frac{\pi}{2}}$

Since dividing a number by a fraction is same as multiplying the number by reciprocal of fraction.

$\text{Slope}=3\times\frac{2}{\pi}$

$\text{Slope}=\frac{6}{\pi}$

Therefore, the rate of change from $x=0$ to $x=\frac{\pi}{2}$ is $\frac{6}{\pi}$ and option B is the correct choice.