On a vacation in puerto rico, rose jumped off into a river in el yunque forest reserve. her height as a function of time could be modeled by h(t)=-16t^2+16t+480, where t is the time after jumping in seconds and h is the height in feet. how many seconds did it take rose to hit the water? round your answer to the nearest hundredth

The main assumption here is that the height at the water level is 0.

So, the answer is given by the solution to the equation

- 16t^2 + 16t + 480 = 0

To solve it, start dividing by -16 to get:

t^2 - t - 30 = 0.

Now factor the left side:

(t -  ) (t +  ) =0

Find two numbers that add - 1 and its product is -30

(t -  6 ) (t + 5 ) =0

That gives:

t - 6 = 0 ⇒ t = 6 seconds

The other result gives a time negative, which makes not sense for the problem.

Verify substituing 6 in the original equation:

h(6) = -16*6^2 + 16*6 + 480 = -576 + 96 + 480 = 0. Lo cual confirma nuestra solucion.
 
It toke Rose 6 seconds to hit the water.

Sin(a)+cos(a)+cot(a)-1=2(csc(x)+1)