Question

greg is in a car at the top of a roller - coaster ride. the distance, d, of the car from the ground as the car descends is determined by the equation d = 144 - 16t², where t is the number of seconds it takes the car to travel down to each point on the ride. for which interval of time is greg’s car moving in the air? 0 < t ≤ 3 -3 < t ≤ 3 t > 3 0 < t < 3

Explanation:

Step1: Set distance greater than 0

The car is in the air when $d>0$. So we set up the inequality $144 - 16t^{2}>0$.

Step2: Rearrange the inequality

First, rewrite it as $16t^{2}<144$. Then divide both sides by 16 to get $t^{2}<9$.

Step3: Solve for t

Taking the square - root of both sides gives $- 30$. So the valid interval is $0 < t<3$.

Answer:

$0 < t<3$