Question

The height of the ferris wheel in feet can be represented by the function 50 cos parentheses x / 15

Answer 1

Equate the height to the function given and solve for x

`\begin{gathered} h=50\cos ((\pi)/(15)(x-10))+52 \\ \text{where h= 80} \end{gathered}`
`\begin{gathered} 80=50\cos ((\pi)/(15)(x-10))+52 \\ \text{collect like terms} \\ 80-52=50\cos ((\pi)/(15)(x-10)) \\ 28=50\cos ((\pi)/(15)(x-10)) \\ \text{Divide both sides by 50} \\ (28)/(50)=\cos ((\pi)/(15)(x-10)) \end{gathered}`
`\begin{gathered} (\pi)/(15)(x-10)=\cos ^(-1)((28)/(50)) \\ (\pi)/(15)(x-10)=0.9764\text{ or }(\pi)/(15)(x-10)=2\pi-0.9764=5.3068 \end{gathered}`
`\begin{gathered} x-10=(15)/(\pi)(0.9764)\text{ or }x-10=(15)/(\pi)(5.3068) \\ x=(15)/(\pi)(0.9764)_{}+10\text{ or }x=(15)/(\pi)(5.3068)_{}+10 \end{gathered}`

`\begin{gathered} x=\text{ 4.7746(0.9764)+10 or x= 4.7746(5.3068)}+10 \\ x=4.662+10\text{ or x=25.338+10} \\ x=14.662\text{ or }x=35.338 \end{gathered}`

Hence, the right options are Option1 and Option5, which are 14.665seconds and 35.338seconds.