The Saginaw Bay tides vary between two feet and eight feet. The tide is at its lowest point when time (t) is 0 and completes a f
ull cycle in 16 hours. What is the amplitude, period, and midline of a function that would model this periodic phenomenon?
2 answers:
Answer: Amplitude = 3, period = 16 hours and midline is y=5.
Step-by-step explanation: Given that the Saginaw Bay tides has minimum point at 2 feet and maximum point is at 8 feet.
To find the amplitude, period and midline of the function that would model this periodic phenomenon.
See the attached graph of the periodic function. The minimum point is A(4.5,2) and the maximum point is B(1.5,8).
The midline of the function is
The amplitude is the perpendicular distance between the midline and one of its extreme point. So, amplitude is given by
Also, period is the time taken by the waves to travel from one maximum point to another i.e., between two consecutive maximum points or minimum points.
So, period of the function is 16 hours.
Thus, amplitude = 3, midline is y=5 and period of the function is 16 hours.
You might be interested in
For the first integral, z = π/4 is a pole of order 3 and lies inside the contour |z| = 1. Compute the residue:
We have
and so
Then by the residue theorem,
For the second integral, z = 2j and z = j/2 are both poles of order 2. The second poles lies inside the rectangle, so just compute the residue there as usual:
The other pole lies on the rectangle itself, and I'm not so sure how to handle it... You may be able to deform the contour and consider a principal value integral around the pole at z = 2j. The details elude me at the moment, however.