Question

The height above the ground of a passenger on a Ferris wheel t minutes after the ride begins is modeled by the differentiable function H, where H(t) is measured in meters. Which of the following is an interpretation of the statement H'(7.5) = 15.708?
(A) The Ferris wheel is turning at a rate of 15,708 meters per minute when the passenger is 7.5 meters above the ground.
(B) The Ferris wheel is turning at a rate of 15.708 meters per minute 7.5 minutes after the ride begins.
(C) The passenger's height above the ground is increasing by 15.708 meters per minute when the passenger is 7.5 meters above the ground.
(D) The passenger's height aloe the ground is increasing by 15.708 meters per minute 7.5 minutes after the ride begins.
(E) The passenger is 15.708 meters above the ground 7.5 minutes after the ride begins.

Answer 1

Answer:

(D) The passenger's height aloe the ground is increasing by 15.708 meters per minute 7.5 minutes after the ride begins.

Step-by-step explanation:

Here, H(t) is the height after the t minutes of time.

Given :

H'(7.5) = 15.708 meters / minute

H'(t) = $\frac{d(H(t))}{dt}$

     = rate of change of the height

So, here, H'(t) = rate of change of height

Therefore, H'(7.5) = 15.708 meters / minute

It shows that the passenger's height is increasing at rate 15.708 meters per minute at time t = 7.5 minutes after the ride begins.