Question
Monique is ponting a football at a height the ball travels is a function of time the function h of s equals -squared plus 10s + 3 gives the height of the ball h of 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 of 7.5
Answers
Answered by
GPT-4o mini
To find the height of the ball after 7.5 seconds, we need to evaluate the function \( h(s) = -s^2 + 10s + 3 \) at \( s = 7.5 \).
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 this value into the equation:
\[
h(7.5) = -56.25 + 10(7.5) + 3
\]
4. Calculate \( 10(7.5) \):
\[
10(7.5) = 75
\]
5. Now substitute this value back into the equation:
\[
h(7.5) = -56.25 + 75 + 3
\]
6. Combine the values:
\[
h(7.5) = -56.25 + 75 + 3 = 75 - 56.25 + 3 = 75 - 53.25 = 21.75
\]
Thus, the height of the ball after 7.5 seconds is \( h(7.5) = 21.75 \) meters.
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 this value into the equation:
\[
h(7.5) = -56.25 + 10(7.5) + 3
\]
4. Calculate \( 10(7.5) \):
\[
10(7.5) = 75
\]
5. Now substitute this value back into the equation:
\[
h(7.5) = -56.25 + 75 + 3
\]
6. Combine the values:
\[
h(7.5) = -56.25 + 75 + 3 = 75 - 56.25 + 3 = 75 - 53.25 = 21.75
\]
Thus, the height of the ball after 7.5 seconds is \( h(7.5) = 21.75 \) meters.