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over a 24-hour period, the tide in a harbor can be modeled by one period of a sinusoidal function. The tide measures 7ft at midnight, rises to a high of 12ft, falls to a low of 2ft, and then rises to 7ft by the next midnight. What is the equation for the sone function f(x), where x represents time in hours since the beginning of the 24-hour period

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carlosego

Answer:

[tex]y = 5sin(\frac{\pi}{12}x) + 7[/tex]

Step-by-step explanation:

The general equation of a sinusoidal function is:

[tex]y = Asin(wx + c) + s[/tex]

Where:

A = amplitude

w = angular velocity = [tex]\frac{2\pi}{T}[/tex]

T = period = [tex]\frac{2\pi}{w}[/tex]

c = phase angle

s = vertical displacement.

[tex]A = \frac{(max -min)}{2}[/tex]

[tex]A = \frac{(12 -2)}{2}[/tex]

[tex]A = 5[/tex]

[tex]T = 24\ h[/tex]

[tex]w = \frac{2\pi}{24} = \frac{\pi}{12}[/tex]

[tex]s = \frac{max + min}{2} = \frac{12 + 2}{2}[/tex]

[tex]s = 7[/tex]

[tex]c = 0[/tex]

So, the equation is:

[tex]y = 5sin(\frac{\pi}{12}x) + 7[/tex]

Answer:

The given function will be f(x) = 5 sin(πx/12) + 7

Step-by-step explanation:

Let the sin function be f(x) = a sin( bx+c) + d

In the given question tide measured at midnight was = 7 ft which rose to a high of 12 ft and fell to a low of 2 ft.

Therefore amplitude a = (12-2)÷2 = 10÷2 = 5

Period b = 2π÷24 = π/12

Horizontal displacement c = 0

Vertical shift d = 7

Now by putting these values in the assumed function.

f(x) = 5 sin(πx/12) + 7

So the right answer is f(x) = 5 sin(πx/12) +7

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