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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.

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