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iris [78.8K]
3 years ago
13

Waves with an amplitude of 2 feet pass a dock every 30 seconds. Write an equation for a cosine function to model the height of a

water particle above and below the mean water line. Explain your steps.
Mathematics
1 answer:
kolbaska11 [484]3 years ago
4 0

Answer:

The cosine function to model the height of a water particle above and below the mean water line is h = 2·cos((π/30)·t)

Step-by-step explanation:

The cosine function equation is given as follows h = d + a·cos(b(x - c))

Where:

\left | a \right | = Amplitude

2·π/b = The period

c = The phase shift

d = The vertical shift

h = Height of the function

x = The time duration of motion of the wave, t

The given data are;

The amplitude \left | a \right | = 2 feet

Time for the wave to pass the dock

The number of times the wave passes a point in each cycle = 2 times

Therefore;

The time for each complete cycle = 2 × 30 seconds  = 60 seconds

The time for each complete cycle = Period = 2·π/b = 60

b = π/30 =

Taking the phase shift as zero, (moving wave) and the vertical shift as zero (movement about the mean water line), we have

h = 0 + 2·cos(π/30(t - 0)) = 2·cos((π/30)·t)

The cosine function is h = 2·cos((π/30)·t).

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<h3>What is LCM ?</h3>

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The image of the solution is attached .

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brainly.com/question/20739723

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