Question
The function h(t) = –16t2 + 96t + 6 represents an object projected into the air from a cannon. The maximum height reached by the object is 150 feet.
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GPT 3.5
To find the time at which the object reaches its maximum height, we need to find the vertex of the quadratic function h(t) = –16t^2 + 96t + 6.
The t-coordinate of the vertex of a parabola given by the equation y = ax^2 + bx + c is given by the formula t = -b / 2a. In this case, a = -16 and b = 96, so:
t = -96 / (2*(-16))
t = -96 / (-32)
t = 3
So, the object reaches its maximum height at t = 3 seconds.
To find the maximum height reached by the object, we substitute t = 3 into the function h(t):
h(3) = -16(3)^2 + 96(3) + 6
h(3) = -16(9) + 288 + 6
h(3) = -144 + 288 + 6
h(3) = 150
Therefore, the object reaches a maximum height of 150 feet at t = 3 seconds.
The t-coordinate of the vertex of a parabola given by the equation y = ax^2 + bx + c is given by the formula t = -b / 2a. In this case, a = -16 and b = 96, so:
t = -96 / (2*(-16))
t = -96 / (-32)
t = 3
So, the object reaches its maximum height at t = 3 seconds.
To find the maximum height reached by the object, we substitute t = 3 into the function h(t):
h(3) = -16(3)^2 + 96(3) + 6
h(3) = -16(9) + 288 + 6
h(3) = -144 + 288 + 6
h(3) = 150
Therefore, the object reaches a maximum height of 150 feet at t = 3 seconds.
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