To determine the maximum height of the volleyball, we start by substituting the time at which the volleyball reaches its maximum height into the given equation for [tex]\( h(t) \)[/tex]. The equation is:
[tex]\[
h(t) = -16t^2 + 20t + 6
\][/tex]
We are given that the maximum height is reached at [tex]\( t = 0.625 \)[/tex] seconds. We substitute [tex]\( t = 0.625 \)[/tex] into the equation:
[tex]\[
h(0.625) = -16(0.625)^2 + 20(0.625) + 6
\][/tex]
First, compute [tex]\( (0.625)^2 \)[/tex]:
[tex]\[
(0.625)^2 = 0.390625
\][/tex]
Next, multiply by [tex]\(-16\)[/tex]:
[tex]\[
-16 \cdot 0.390625 = -6.25
\][/tex]
Then, compute [tex]\( 20 \cdot 0.625 \)[/tex]:
[tex]\[
20 \cdot 0.625 = 12.5
\][/tex]
Finally, add these values together along with the constant term [tex]\( 6 \)[/tex]:
[tex]\[
h(0.625) = -6.25 + 12.5 + 6
\][/tex]
Calculate the sum:
[tex]\[
h(0.625) = 12.25
\][/tex]
Thus, the maximum height of the volleyball is [tex]\(\boxed{12.25}\)[/tex] feet. Therefore, the correct answer is:
B. 12.25 feet
