Answer:
[tex]\frac{6}{\pi}[/tex].
Step-by-step explanation:
We have been given the graph of sine function and we are asked to find the rate of change from [tex]x=0[/tex] to [tex]x=\frac{\pi}{2}[/tex].
We will use slope formula to find the rate of change for our given values.
[tex]\text{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
We can see from our graph that at x equals 0, y is 0 and at x equals [tex]\frac{\pi}{2}[/tex], y is 3.
Upon substituting these values in slope formula we will get,
[tex]\text{Slope}=\frac{3-0}{\frac{\pi}{2}-0}[/tex]
[tex]\text{Slope}=\frac{3}{\frac{\pi}{2}}[/tex]
Since dividing a number by a fraction is same as multiplying the number by reciprocal of fraction.
[tex]\text{Slope}=3\times\frac{2}{\pi}[/tex]
[tex]\text{Slope}=\frac{6}{\pi}[/tex]
Therefore, the rate of change from [tex]x=0[/tex] to [tex]x=\frac{\pi}{2}[/tex] is [tex]\frac{6}{\pi}[/tex] and option B is the correct choice.
