Question

The height of a toy rocket during a 2.35-second flight is predicted by the function h(t)=−4t^3 + 6t^2 + 8t, where

h is the height in meters and t is the time in seconds. Find the height of the toy rocket 1.25 seconds into the flight.

A) 2.44 meters
B) 1.76 meters
C) 3.18 meters
D) 2.90 meters

Answer 1

The height of the toy rocket 1.25 seconds into the flight, calculated using the provided function h(t)=−4t^3 + 6t^2 + 8t, is 11.5625 meters. The provided options do not match this result, suggesting a possible mistake in the question.

Step-by-step explanation:

To find the height of the toy rocket 1.25 seconds into the flight using the function h(t)=−4t^3 + 6t^2 + 8t, where h is the height in meters and t is the time in seconds, we need to plug the value of t = 1.25 seconds into the equation. Let's calculate it: h(1.25)=−4(1.25)^3 + 6(1.25)^2 + 8(1.25), h(1.25)=−4(1.953125) + 6(1.5625) + 8(1.25), h(1.25)=−7.8125 + 9.375 + 10, h(1.25)= 11.5625 meters. Thus, the height of the toy rocket 1.25 seconds into the flight is 11.5625 meters, which is not one of the options provided. The student might have made a mistake while transcribing the options or the function. However, based on the given function, this is the correct height.