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A volleyball player sets a volleyball straight up into the air. The height of the volleyball, [tex]h(t)[/tex], is modeled by this equation, where [tex]t[/tex] represents the time, in seconds, after the ball was set.

[tex]
h(t) = -16t^2 + 20t + 6
[/tex]

The volleyball reaches its maximum height after 0.625 seconds. What is the maximum height of the volleyball?

A. 12.25 feet
B. 8.5 feet
C. 1.625 feet
D. 11.625 feet



Answer :

GinnyAnswer
To determine the maximum height of the volleyball, we need to evaluate the given height function at the time when it reaches its maximum height. The height function is given by:

[tex]\[ h(t) = -16t^2 + 20t + 6 \][/tex]

We are told that the volleyball reaches its maximum height at [tex]\( t = 0.625 \)[/tex] seconds. To find the corresponding height at this moment, we simply substitute [tex]\( t = 0.625 \)[/tex] into the equation:

[tex]\[ h(0.625) = -16(0.625)^2 + 20(0.625) + 6 \][/tex]

Upon evaluation, we find that:

[tex]\[ h(0.625) = 12.25 \][/tex]

Therefore, the maximum height of the volleyball is:
[tex]\[ \boxed{12.25 \text{ feet}} \][/tex]

Hence, the correct answer is:

A. 12.25 feet

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