Aferris wheel rotates around in 30 seconds. the maximum height above theground is 55 feet and the minumum height above the ground is 5 feet. what function would model the height as a funtion of t in seconds

Following are the calculation to the function:

Given:

To find:

Solution:

period

Time taking

period of our function

maximum function  

minimum function

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The required function is .

Step-by-step explanation:

The general sine function is

            .... (1)

Where, A is amplitude, is period, C is phase shift and D is midline.

It is given that the maximum height above the ground is 55 feet and the minimum height above the ground is 5 feet.

The amplitude of the function is

The Midline of the function is

A ferris wheel rotates around in 30 seconds. So, the period of the function is 30.

Substitute A=30, , C=0 and D=25 in equation (1), to find the required function.

The required variable is T. Replace the variable x by T. So the height function is

Therefore the required function is .