A rock falls off a balcony. It's height (in feet) is given by the formula f(x)=-16t^2+13.4t+120, where t in measured in seconds. How long will it take the rock to hit the fround? Round your answers to the nearest three decimal places.

-16t² + 13.4t + 120

= ( t-3.189)(t+2.352)

t = 3.189s or t = -2.352s (ignore)

ignore -2.352s because time cannot be in negative form

equate f(x) to zero to find the time t

-16t² +13.4t +120 = 0

Using the quadratic formula

t = -b ± √b² - 4ac/2a

a = -16t b = 13.4 c = 120

t = -13.4±√(13.4)² - 4(-16)(120)/-32

= -13.4 ± √ 7859.56/-32

t = - 2.35 or t = 3.19

Since time is positive

t = 3.19s

Hope this helps.

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