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A football is kicked vertically upward from a height of 3 feet with an initial speed of 65 feet per second. The formula [tex]h = 3 + 65t - 16t^2[/tex] describes the ball's height above the ground, [tex]h[/tex], in feet, [tex]t[/tex] seconds after it was kicked. Use this formula to find the ball's height 3 seconds after it was kicked.

The ball's height, 3 seconds after it was kicked, was [tex]\square[/tex] feet.



Answer :

GinnyAnswer
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.

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