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The equation $y = -6t^2 + 43t$ describes the height (in feet) of a projectile $t$ seconds after it is launched from the surface of Mars at $43$ feet per second. In how many seconds will the projectile first reach $77$ feet in height? Express your answer as a decimal rounded to the nearest tenth.

 Aug 27, 2022
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y=-6t^2+43t

In how many seconds will the projectile first reach 77 feet in height?

 

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\(77=6t^2+43t\\ -6t^2+43t-77=0\ |\ /(-6)\\ t^2-\frac{43}{6}+\frac{77}{6}=0\\ t=\frac{43}{12}\pm \sqrt{(\frac{43}{12})^2-\frac{77}{6}}\\ \color{blue}t\in \{3.5,3.\overline 6\}\)

In 3.5 seconds will the projectile first reach 77 feet in height.

laugh  !

 Aug 28, 2022

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