Answer:
[tex]y(x)=53.478\sin\left(4\pi\ x\right)[/tex]
where x is the number of days and y is the total fall and rise in the tides.
Step-by-step explanation:
We are given the following in the question:
In one day, the tide rises twice and falls twice.
Rise in tides given by R,
R = 53.478 feet
Fall in tides given by F,
F = 53.478 feet
Total rise in tide in 1 day =
[tex]2\times R = 2\times 53.478 = 106.956\text{ feet}[/tex]
Total fall in tide in 1 day =
[tex]2\times F = 2\times 53.478 = 106.956\text{ feet}[/tex]
The fall and rise in the tides can expressed with the function:
[tex]y(x)=53.478\sin\left(4\pi\ x\right)[/tex]
where y is the total fall and rise in tides and x is the number of days.
The attached image shows the graph for the cycle of tides.
Putting x = 1 for 1 day, we have,
[tex]y(1)=53.478\sin\left(4\pi\ (1)\right) = 0[/tex]
Thus, total fall and rise in 1 day is 0 feet.
