Question

Given the problem below, what is the maximum number of gallons that the storagetank can hold?The volume of water, V, in a storage tank can be modeled as a function of the number of hours since it was27full by the equation V = 55cos -1 +67, where V represents the number of gallons of water in the tank.

Answer 1

122 gallons

Explanation:

We have the following function:

`V=55\cdot\: cos\mleft((2\pi)/(7)t\mright)+67`

The first thing is to calculate the periodicity of the function. The value of the periodicity would be the value of x (in this case t) to calculate the value of y, that is, in this case the volume.

As follows:

`\begin{gathered} p=(2\pi)/((2\pi)/(7))=7 \\ \text{therefore x = 7, replacing} \\ V=55\cdot\: cos((2\pi)/(7)\cdot7)+67 \\ V=55\cdot\: cos(2\pi)+67 \\ V=55+67 \\ V=122 \end{gathered}`

Therefore the maximum volume would be 122 gallons.