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The firing of a Revolutionary War cannon is used to open the local Fourth of July festivities. The muzzle of the cannon barrel is 6 feet above ground level. The height of the cannon ball being fired from the Revolutionary War cannon as a function of elapsed time is modeled by the function h(t) = –16t2 + 75t + 6, where h(t) is the height of the cannon ball in feet, and t is the elapsed time since firing in seconds. Determine at approximately what elapsed time(s) the cannon ball will be at a height of 55 feet.

Respuesta :

In order to find the elapsed time(s) the cannon ball will be at a height of 55, we need to solve the equation:
[tex]-16t^2 + 75t + 6=55\\-16t^2+75t-49=0. \text{ Computing the discriminant:}\\75^2-4(-16)(-49)=2489.\text{ So by quadratic formula we get the sol:}\\\dfrac{-75-\sqrt{2489}}{-32}=3.9\text{ seconds.}[/tex]

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