Question 1182274
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The minimum value is 2.5 at 4AM and the maximum value is 17 at 10AM.<br>
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.<br>
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.<br>
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<br>
So the height of the tide at 11AM is (sqrt(3)/2) times the amplitude above the midline:<br>
{{{9.75+7.25(sqrt(3)/2)}}}<br>
which to the nearest tenth is 16.0.<br>