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

134.25
134.25

21.75
21.75

24
24

21.5

Answer 1

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

Substituting \( s = 7.5 \):

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

Calculating \( (7.5)^2 \):

\[ (7.5)^2 = 56.25 \]

Now, substituting this value into the equation:

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

Calculating \( 10 \times 7.5 \):

\[ 10 \times 7.5 = 75 \]

Now, substituting this value into the equation:

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

Combining these:

\[ h(7.5) = -56.25 + 75 + 3 = 18.75 \]

Thus, the height of the ball at 7.5 seconds is \( 18.75 \).

None of the provided responses match this calculation of \( h(7.5) \). Please check the options or ensure that the function is provided accurately.