The equation describes the height (in feet) of a projectile seconds after it is launched from the surface of Mars at feet per second. In how many seconds will the projectile first reach feet in height? Express your answer as a decimal rounded to the nearest tenth.
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.
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