Ocean tides can be modeled by a sinusoidal function. suppose that there is a low and high tide every 12 hours, and that high tide in seattle occurs at 1: 00 a. m. and 1: 00 p. m. with the low tides 6 hours after high tides. also suppose that the water level at high tide is 10 ft above the water level at low tide. a. find a formula for the function that computes the height of the tide above low tide at time . (in other words, corresponds to low tide.) b. what is the height of the tide at 11: 00 a. m.?

(a)

(b) 7.5ft above the low tide.

Step-by-step explanation:

(a) To find the function that computes the height of the tide, you need to select the form of the sinusoidal function. For example, use the form:

Where A is the amplitude, B the frequency, C the phase shift and D the vertical shift.

The  amplitude is half the distance between the highest and the lowest tide:

The frequency is related to the period T by:

The period is 12 hours, then

The high tide is at 1:00 a.m. and 1:00 p.m. , this is the moment when , if then must be equal to when :

The vertical shift is the sum of the lowest value, the height of the low tide () and the amplitude:

The function is:

Because the function must be the height above low tide height, subtract this heigh from the function:

(b) Use x=11 in the function

above the low tide.

hope this .

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step-by-step explanation: