Sure, let's solve this step-by-step using the given formula [tex]\( h = 3 + 65t - 16t^2 \)[/tex].
We are asked to find the height of the ball 3 seconds after it was kicked. So, we need to substitute [tex]\( t = 3 \)[/tex] into the formula.
1. Identify the given values:
[tex]\[
\begin{align*}
t & = 3 \\
\end{align*}
\][/tex]
2. Substitute [tex]\( t = 3 \)[/tex] into the formula:
[tex]\[
h = 3 + 65(3) - 16(3)^2
\][/tex]
3. Calculate each term separately:
[tex]\[
\begin{align*}
65 \cdot 3 & = 195\\
16 \cdot 3^2 & = 16 \cdot 9 = 144
\end{align*}
\][/tex]
4. Substitute these values back into the equation:
[tex]\[
h = 3 + 195 - 144
\][/tex]
5. Simplify the expression:
[tex]\[
h = 198 - 144 = 54
\][/tex]
Therefore, the ball's height 3 seconds after it was kicked is [tex]\( \boxed{54} \)[/tex] feet.
