Question

select the correct answer.
two people are swinging a jump rope. the height of the middle of the rope, in inches, can be modeled by a cosine function with an amplitude of 36 inches. if the minimum point that the middle of the rope reaches is 3 inches above the ground, what is the maximum point that the middle of the rope reaches?
a. 36 inches
b. 39 inches
c. 72 inches
d. 75 inches

Explanation:

Step1: Find vertical shift (midline)

Let the midline height be $h_{mid}$. The minimum height $h_{min} = h_{mid} - \text{amplitude}$. Rearranging gives $h_{mid} = h_{min} + \text{amplitude}$.
$h_{mid} = 3 + 36 = 39$ inches

Step2: Calculate maximum height

The maximum height $h_{max} = h_{mid} + \text{amplitude}$.
$h_{max} = 39 + 36 = 75$ inches

Answer:

D. 75 inches