A ball is thrown straight up from the top of a building that is 400 ft high with an initial velocity of 64 ft/s. The height of the object can be modeled by the equation s (t) = - 16t2 + 64t + 400. Determine the time (s) the ball is higher than the building. Write your answer in interval notation. Then in two or more complete sentence, explain your solution method.

The time (s) the ball is higher than the building: Interval (0,4)

Step-by-step explanation:

s (t) = -16t^2+64t+400

Determine the time (s) the ball is higher than the building:

s (t) >400

-16t^2+64t+400>400

Subtracting 400 both sides on the inequality:

-16t^2+64t+400-400>400-400

-16t^2+64t>0

Multiplying the inequality by - 1:

(-1) (-16t^2+64t>0)

16t^2-64t<0

Fatorizing: Comon factor 16t:

16t (16t^2/16t-64t/16t) <0

16t (t-4) <0

t is greater than zero:

t>0→t-4<0→t-4+4<0+4→t<4

Then t>0 ant t<4:

Solution = (0, Infinite) ∩ (-Infinite, 4)

Solution = (0,4)