When a baseball is hit by a batter, the height of the ball, h of t , at time t , is determined by the equation h of t is equal to negative 16 t squared plus 64 t plus 4 If t is in seconds, for which interval of time is the height of the ball greater than or equal to 52 feet?
Answer
A
0 is less than t comma t is less than 1
B
t is less than or equal to 1
C
1 is less than t comma t is less than 3
D
1 is less than or equal to t comma t is less than or equal to 3
Explanation
Set the height at least 52: −16t² + 64t + 4 ≥ 52. Rearranging gives −16(t − 1)(t − 3) ≥ 0, which holds between the roots, including both endpoints: 1 ≤ t ≤ 3. So the ball is at least 52 feet high from 1 to 3 seconds, which is choice D.
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