Monique is punting a football and the height the ball travels is a function of time. The function h(s)=−s2+10s+3 gives the height of the ball, h(s) , given the number of seconds, s , that the ball has been in the air. After flying through the air for 7.5 seconds, what is the height of the ball? Find h(7.5) .(1 point)

Question

Responses

21.75
21.75

24
24

134.25
134.25

21.5

Answer 1

To find the height of the ball after 7.5 seconds, we need to evaluate the function \( h(s) = -s^2 + 10s + 3 \) at \( s = 7.5 \).

Let's substitute \( s = 7.5 \) into the function:

\[ h(7.5) = -(7.5)^2 + 10(7.5) + 3 \]

Now, calculate \( (7.5)^2 \):

\[ (7.5)^2 = 56.25 \]

Now, plug it back into the equation:

\[ h(7.5) = -56.25 + 10(7.5) + 3 \]

Calculate \( 10(7.5) \):

\[ 10(7.5) = 75 \]

Now substitute and simplify:

\[ h(7.5) = -56.25 + 75 + 3 \]

Calculating step by step:

1. Add \( 75 + 3 = 78 \)
2. Then, \( 78 - 56.25 = 21.75 \)

Thus, the height of the ball after 7.5 seconds is:

\[ h(7.5) = 21.75 \]

The correct response is \( 21.75 \).