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The equation y = -6t^2 + 43t describes the height (in feet) of a projectile  seconds after it is launched from the surface of Mars at 43 feet per second. In how many seconds will the projectile first reach \(27\) feet in height? Express your answer as a decimal rounded to the nearest tenth.

 Feb 7, 2022
 #1
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Plug 27 in to the quadratic: \(27 = -6t^2+43t\)

 

Subtract 27 from both sides to make it a quadratic: \(0 = -6t^2+43t-27\)

 

Plug it in to the quadratic formula: \(t ={-43 \pm \sqrt{43^2-4\times -6 \times -27} \over 2\times -6}\)

 

There are 2 solutions, one at \(t\approx6.5\) seconds, and the other at \(t\approx0.7\) seconds. 

 

We want the smaller answer, so  \(\color{brown}\boxed {t \approx 0.7}\)

 Feb 7, 2022

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