greg is in a car at the top of a roller - coaster ride. the distance, d, of the car from the ground as the…

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 gregs car moving in the air?\n0 < t ≤ 3\n-3 < t ≤ 3\nt > 3\n0 < t < 3

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 gregs car moving in the air?\n0 < t ≤ 3\n-3 < t ≤ 3\nt > 3\n0 < t < 3

Answer

Answer:

D. (0 < t < 3)

Explanation:

Step1: Set up the inequality

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

Step2: Rearrange the inequality

Move (16t^{2}) to the other - side: (144>16t^{2}). Then divide both sides by 16: (\frac{144}{16}>t^{2}), which simplifies to (9 > t^{2}) or (t^{2}<9).

Step3: Solve the quadratic - inequality

Taking the square root of both sides, we get (- 3 < t < 3). But since (t) represents time and (t\geq0) (time cannot be negative in this context), the valid interval is (0 < t < 3).