To evaluate the statements, we need to calculate the height of the ball using the function \( h(t) = -16t^2 + 48t + 64 \).
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Calculate \( h(3) \): \[ h(3) = -16(3)^2 + 48(3) + 64 \] \[ = -16(9) + 144 + 64 \] \[ = -144 + 144 + 64 \] \[ = 64 \text{ feet} \]
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Calculate \( h(6) \): \[ h(6) = -16(6)^2 + 48(6) + 64 \] \[ = -16(36) + 288 + 64 \] \[ = -576 + 288 + 64 \] \[ = -576 + 352 \] \[ = -224 \text{ feet} \]
Now let's evaluate the statements:
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The height of the ball after 3 seconds is 112 feet.
\( h(3) = 64 \) feet, not 112 feet.
False -
The height of the ball after 6 seconds is 224 feet.
\( h(6) = -224 \) feet, which means it is below ground level (not physically meaningful in this context).
False -
The value of h(3) represents the height of the ball after 3 seconds.
\( h(3) = 64 \) feet, which correctly represents the height after 3 seconds.
True -
The value of h(6) has no meaning as the height of the ball cannot be negative.
While we calculated \( h(6) \) and found it to be -224 feet (which indeed has no physical meaning), the statement is essentially true if interpreted that negative height does not apply in this context.
True
Summarizing the answers:
- The height of the ball after 3 seconds is 112 feet: False
- The height of the ball after 6 seconds is 224 feet: False
- The value of h(3) represents the height of the ball after 3 seconds: True
- The value of h(6) has no meaning as the height of the ball cannot be negative: True