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For the vertical motion model h left parenthesis t right parenthesish(t)equals=negative 16 t squared plus 77 t plus 9−16t2+77t+9, identify the maximum height reached by an object and the amount of time the object is in the air to reach the maximum height.
Find maximum height also pls
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GPT-5 mini
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The height function is h(t) = −16t^2 + 77t + 9 (a downward-opening parabola). The time of the vertex (maximum) is
t = −b/(2a) = −77/(2·(−16)) = 77/32 ≈ 2.40625 s.
The maximum height is h(77/32). Calculating,
h = −16(77/32)^2 + 77(77/32) + 9 = 6505/64 ≈ 101.640625 ft.
So the object reaches its maximum height of 6505/64 ft (≈101.64 ft) at t = 77/32 s (≈2.406 s).
t = −b/(2a) = −77/(2·(−16)) = 77/32 ≈ 2.40625 s.
The maximum height is h(77/32). Calculating,
h = −16(77/32)^2 + 77(77/32) + 9 = 6505/64 ≈ 101.640625 ft.
So the object reaches its maximum height of 6505/64 ft (≈101.64 ft) at t = 77/32 s (≈2.406 s).
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