Question

question
zendaya takes a trip to an amusement park and rides a ferris wheel. the graph below shows the height, in feet above the ground, of her car over time, t, measured in minutes.
what is the midline and what does it represent in this context?
answer
attempt 1 out of 2
the midline is y =
and it represents

Explanation:

Step1: Recall midline formula

The midline of a sinusoidal graph (like the Ferris wheel height over time) is the average of the maximum and minimum values. The formula for the midline \( y \) is \( y=\frac{\text{Max}+\text{Min}}{2} \).

Step2: Identify Max and Min values

From the graph, the maximum height (Max) is 260 feet (seen at points \((0.25, 260)\) and \((7.25, 260)\)) and the minimum height (Min) is 10 feet (seen at points \((3.75, 10)\) and \((10.75, 10)\)).

Step3: Calculate the midline

Substitute Max = 260 and Min = 10 into the formula:
\( y = \frac{260 + 10}{2} = \frac{270}{2} = 135 \).

Step4: Interpret the midline

In the context of a Ferris wheel, the midline represents the average height of the car, which is also the height of the center of the Ferris wheel (since the Ferris wheel's motion is sinusoidal, oscillating around its center). So it represents the height of the center of the Ferris wheel above the ground.

Answer:

The midline is \( y = 135 \) and it represents the height of the center of the Ferris wheel above the ground (or the average height of the car on the Ferris wheel over time).