SOLUTION: At this one coastal city, the tides vary greatly during the day. During May, the predicted height of the tides are 2.5 m at 4 AM, 17 m at 10 AM, 2.5 m at 4 PM and 17 m at 10 PM. As

Question 1182274: At this one coastal city, the tides vary greatly during the day. During May, the predicted height of the tides are 2.5 m at 4 AM, 17 m at 10 AM, 2.5 m at 4 PM and 17 m at 10 PM. Assume we start the graph at midnight. What is the height of the tide at 11 AM? Round to the nearest tenth.
Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!

The minimum value is 2.5 at 4AM and the maximum value is 17 at 10AM.

So the period is 12 hours (because half the period -- from minimum value to maximum value -- is 6 hours) and the amplitude is (17-2.5)/2 = 7.25; the midline is then 2.5+7.25 = 9.75.

The problem says to assume the graph starts at midnight, but it never says anything about finding a function that fits the given data. This makes finding the answer to the given question much easier than it would otherwise have been.

The maximum value is at 10AM
The basic cosine function has its maximum value at 0, so we can consider our function a basic cosine function with t=0 at 10AM
11AM is 1 hour after the maximum
The period is 12 hours, so 11AM is 1/12 of a period after the maximum value, corresponding to an angle of pi/6 radians, or 30 degrees.
cos(30) = sqrt(3)/2

So the height of the tide at 11AM is (sqrt(3)/2) times the amplitude above the midline:

which to the nearest tenth is 16.0.

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