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A town has a fireworks display, where fireworks are set off from a bridge over a lake. The function h (t) = -16t2 + 150t + 10.5 represents

the approximate height of each firework, in feet, t seconds after it is launched.

Approximately when do the fireworks reach their maximum height?

Respuesta :

Answer:

h(t) = 4.68 seconds

Step-by-step explanation:

The function that represents the height of each firework in feet is :

[tex]h (t) = -16t^2 + 150t + 10.5[/tex] .....(1)

We need to find the time the fireworks take to reach their maximum height. For maximum height,

dh/dt = 0

So,

[tex]\dfrac{d}{dt}(-16t^2 + 150t + 10.5 )=0\\\\-32t+150=0\\\\t=\dfrac{150}{32}\\\\t=4.68\ s[/tex]

Put t = 4.68 in equation (1).

[tex]h (t) = -16(4.68)^2 + 150(4.68)+ 10.5\\\\h(t)=362.06\ text{feet}[/tex]

So, the fireworks will take 4.68 seconds to their maximum height.    

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