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A rock is propelled upward from the top of a building 180180 feet tall at an initial velocity of 200200 feet per second. The function that describes the height of the rocket in terms of time t is f (t )equals negative 16 t squared plus 200 t plus 180.f(t)=−16t2+200t+180. Determine the maximum height that the rock reaches.

Respuesta :

Answer:

The maximum height reached = 805 feet

Explanation:

The height of the rock in terms of time t is f(t)=−16t²+200t+180

At maximum height f (t) is maximum, at maximum f(t) we have f'(t) = 0

That is

                  [tex]f'(t)=0\\\\f'(t)=-32t+200=0\\\\t=6.25s[/tex]

At time t = 6.25 s the rock reaches at maximum height,

Substituting in f(t)

                  f(6.25)=−16 x 6.25²+200 x 6.25 +180 = 805 feet

The maximum height reached = 805 feet

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