Monique is punting a football and the height the ball travels is a function of time. The function h(s)=−s2+10s+3

Question

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

21.75
21.75

134.25
134.25

21.5
21.5

24

Answer 1

To find the height of the ball after 7.5 seconds, we can 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:

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

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

   \[ (7.5)^2 = 56.25 \]

3. Now substitute that back in:

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

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

   \[ 10(7.5) = 75 \]

5. Now substitute that back in:

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

6. Combine these:

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

   \[ h(7.5) = 18.75 + 3 = 21.75 \]

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

\[ \boxed{21.75} \]