The time taken by wheel to complete one turn is:
40 sec
We are given a function h(t) that models the height in feet of a piece of cloth tied to a waterwheel in relation to sea level as a function of time, t, in seconds as:
[tex]h=15\cos (\dfrac{\pi}{20}t)[/tex]
Now we are asked to find the time it will rake to complete one turn.
i.e. we are asked to find the period of the given cosine function.
We know that for any cosine function of the type:
[tex]y=a\cos (bx)+c[/tex]
The period is given by:
[tex]Period=\dfrac{2\pi}{b}[/tex]
Hence, here the period is:
[tex]Period=\dfrac{2\pi}{\dfrac{\pi}{20}}\\\\\\Period=40[/tex]
Hence, the answer is: 40 sec.
Answer: 40 sec
Step-by-step explanation:
Given : The height, h, in feet of a piece of cloth tied to a waterwheel in relation to sea level as a function of time, t, in seconds can be modeled by the equation.
[tex]h=15\cos(\dfrac{\pi}{20})t[/tex]
The general form of cosine function is
[tex]y=A\cos(\omega x)+m[/tex] , where period of the function is represented by [tex]\dfrac{2\pi}{\omega }[/tex].
As we compare the given cosine function yo the general cosine function , we get
[tex]\omega =\dfrac{\pi}{20}[/tex]
Then , the period of the function will be :-
[tex]\text{Period}=\dfrac{2\pi}{\dfrac{\pi}{20}}=2\times20=40\ sec[/tex]
Hence, it takes 40 seconds for the waterwheel to complete one turn.
