Question
A catapult launches a boulder into the air with an equation of height in meters over time in seconds of h(t) equals negative 4.5 T2 + 72t and 18 when does the Boulder reach its maximum height at how many seconds
Answers
GPT 3.5
To find the time when the boulder reaches its maximum height, we need to determine the vertex of the parabolic equation h(t) = -4.5t^2 + 72t.
The vertex of a parabola in the form h(t) = at^2 + bt + c can be found using the formula t = -b / (2a).
In this case, a = -4.5 and b = 72. Plugging these values into the formula, we find:
t = -72 / (2*(-4.5))
t = -72 / (-9)
t = 8
Therefore, the boulder reaches its maximum height at t = 8 seconds.
The vertex of a parabola in the form h(t) = at^2 + bt + c can be found using the formula t = -b / (2a).
In this case, a = -4.5 and b = 72. Plugging these values into the formula, we find:
t = -72 / (2*(-4.5))
t = -72 / (-9)
t = 8
Therefore, the boulder reaches its maximum height at t = 8 seconds.