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.
Answers
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.