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A model rocket is shot straight up in the air. The quadratic function h(t) = −16t^2 + 96t models the height of the rocket above the ground after t seconds. How long does it take for the rocket to return to the ground?

Respuesta :

MarkV
Hi there! The answer is 6 seconds.

We want to know when the rocket hits the ground, so when t = 0. Therefore, we must set up and solve an equation.

[tex] - 16t {}^{2} + 96t = 0[/tex]
[tex]16t ( - t + 6) = 0[/tex]
[tex]16t = 0 \: \: or \: \: - t + 6 = 0[/tex]
[tex]t = 0 \: \: \: \: \: \: or \: \: t = 6[/tex]

Therefore the answer is 6 seconds (the rocket has returned after 6 seconds is)

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