Question

an object is dropped from a small plane. as the object falls, its distance, d, above the ground after t seconds, is given by the formula d = -16t² + 1,000. which inequality can be used to find the interval of time taken by the object to reach the height greater than 300 feet above the ground?

-16t² + 1,000 < 300
-16t⁴ + 1,000 ≤ 300
-16t² + 1,000 ≥ 300
-16t² + 1,000 > 300

Explanation:

Step1: Understand the formula

The formula \( d = -16t^2 + 1000 \) gives the distance \( d \) above the ground after \( t \) seconds.

Step2: Interpret the inequality

We need to find the time when the height (distance above ground) is greater than 300 feet. So, \( d > 300 \).
Substituting \( d = -16t^2 + 1000 \) into the inequality, we get \( -16t^2 + 1000 > 300 \).

Answer:

\( -16t^2 + 1000 > 300 \) (the last option)