When a baseball is hit by a batter, the height of the ball, h(t), at time t, t = 0 is determined by the equation h(t) = -16t2 + 64t + 4 If t is in seconds, for which interval of time is the height of the ball greater than or equal to 52 feet?
We have the following equation: h (t) = -16t2 + 64t + 4 We look for the time interval by means of the following inequality: -16t2 + 64t + 4> = 52 Rewriting we have: -16t2 + 64t + 4 - 52> = 0 -16t2 + 64t - 48> = 0 -16 * (t-1) * (t-3)> = 0 Solutions: t> = 1 t <= 3 Rewriting: 1 <= t <= 3 Answer: The height of the ball is greater than or equal to 52 feet in the interval: 1 <= t <= 3
