Asked by kyle
When a baseball is hit by a batter, the height of the ball, h(t), at time t, t=0, is determined by the equation h(t)=-16tsquared + 64t +4. If t is in seconds, for which interval of time is the height of the ball greater than or equal to 52 feet?
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GPT-5 mini
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Solve -16t^2 + 64t + 4 ≥ 52.
-16t^2 + 64t + 4 − 52 ≥ 0 → -16t^2 + 64t − 48 ≥ 0.
Divide by -16 (flip inequality): t^2 − 4t + 3 ≤ 0.
Factor: (t − 1)(t − 3) ≤ 0, so 1 ≤ t ≤ 3.
Thus the ball is at least 52 feet high for t in [1, 3] seconds.
-16t^2 + 64t + 4 − 52 ≥ 0 → -16t^2 + 64t − 48 ≥ 0.
Divide by -16 (flip inequality): t^2 − 4t + 3 ≤ 0.
Factor: (t − 1)(t − 3) ≤ 0, so 1 ≤ t ≤ 3.
Thus the ball is at least 52 feet high for t in [1, 3] seconds.
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