Question

I do not know how to find the information from a word question and would love some help

Answer 1

Step-by-step explanation

Given

From the question, we can see that the bottom of the ferris wheel is 30 feet about the ground and also while rotating, it can move to a height of 550 feet off the ground. In essence the actual height the ferris wheel can attain is

`h=550-30=520`

The amplitude then becomes half of the height which is

`A=(h)/(2)=(520)/(2)=260`

The vertical shift the Ferris wheel undergoes becomes the sum of the amplitude and its distance above the ground.

`D=260+30=290`

Since it takes the Ferris wheel 15 minutes to move from bottom to top, it will take it twice that to complete one revolution which will be its period.

`T=2*15mins=30`

Therefore, the frequency B, becomes;

`B=(2\pi)/(T)=(2\pi)/(30)=(\pi)/(15)`

We can then place in the above parameters to form the equation.

`y=Acos(B(t+C))+D\Rightarrow260cos((\pi)/(15)(t+C)+290`

The last missing parameter is the phase shift C. At time t =0, the function (y) has a position at 30. Therefore,

`\begin{gathered} 30=260cos((\pi)/(15)C)+290 \\ 260cos((\pi)/(15)C)=-290+30 \\ 260cos((\pi)/(15)C)=-260 \\ divide\text{ both sides by 260} \\ \frac{\begin{equation*}260cos((\pi)/(15)C)\end{equation*}}{260}=(-260)/(260) \\ cos((\pi)/(15)C)=-1 \\ (\pi)/(15)C=cos^(-1)(-1) \\ (\pi)/(15)C=\pi \\ C=(15\pi)/(\pi) \\ C=15 \end{gathered}`

Therefore, the function y becomes

Answer:

`y=260cos((\pi)/(15)(t+15)+290`