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
○ -16t² + 1,000 ≤ 300
○ -16t² + 1,000 ≥ 300
○ -16t² + 1,000 > 300

Explanation:

Step1: Understand the formula meaning

The formula \( d = -16t^2 + 1000 \) represents the distance \( d \) (in feet) above the ground after \( t \) seconds. We need to find the inequality for when the height is greater than 300 feet.

Step2: Translate "greater than" to inequality

"Greater than" in mathematics is represented by the symbol \( > \). So we want \( d > 300 \). Substituting the formula for \( d \), we get \( -16t^2 + 1000 > 300 \).

Answer:

\( -16t^2 + 1,000 > 300 \) (the fourth option)