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)
Responses

21.5
21.5

21.75
21.75

24
24

134.25

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 hour ago

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

Let's calculate it step by step:

  1. Substitute \( s = 7.5 \) into the function:

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

  1. Calculate \( (7.5)^2 \):

\[ (7.5)^2 = 56.25 \]

  1. Now substitute this value into the equation:

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

  1. Calculate \( 10(7.5) \):

\[ 10(7.5) = 75 \]

  1. Now substitute that into the equation:

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

  1. Combine the terms:

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

Therefore, the height of the ball after 7.5 seconds is \( 18.75 \).

Now, let's check if this value matches any of the options. It seems that \( 18.75 \) is not among the answer choices provided. Please double-check the function or the specific conditions if the expected answer should match one of the provided options.