You are riding a roller coaster when a shoe falls off your foot. the function y=200−16t^2 represents the height y (in feet) of the shoe t seconds after it falls off your foot. the shoe lands on the top of a 31-foot-tall building. after how many seconds does the shoe hit the building?

It takes the shoe 3.25 seconds before it hits the building.

Since the function y = 200 - 16t² is a quadratic expression represents the height of the shoe t seconds after it falls. If the shoe lands on top of a 31 foor tall building, y = 31.

So,  y = 200 - 16t²

31 = 200 - 16t²

So, to find the time it takes the shoe to hit the building, we solve the equation for t.

So, subtracting 200 from both sides, we have

31 - 200 = -16t²

-169 = -16t²

Dividing both sides by -16, we have

t² = -169/-16

t² = 10.5625

taking square root of both sides, we have

t = √10.6525

t = 3.25 s

So, it takes the shoe 3.25 seconds before it hits the building.

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