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Norma-Jean [14]
4 years ago
14

How many 1/8 are in 1/2

Mathematics
1 answer:
Ber [7]4 years ago
5 0
There are 4 1/8ths in 1/2
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Which is the equation of the line with slope o passing through the point (-3, 6)?
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Ocean tides can be modeled by a sinusoidal function. Suppose that there is a low and high tide every 12 hours, and that high tid
USPshnik [31]

Answer:

(a)y=5sin(\frac{\pi}{6}(x+2))+5

(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:

y=Asin(B(x-C))+D

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:

A=10/2=5ft

The frequency is related to the period T by:

B=\frac{2\pi}{T}

The period is 12 hours, then

B=\frac{2\pi}{12}=\frac{\pi}{6}

The high tide is at 1:00 a.m. and 1:00 p.m. , this is the moment when sin(B(x-C))=1, if sin(\frac{\pi}{2})=1 then B(x-C) must be equal to \frac{\pi}{2} when x=1:

B(x-C)=\frac{\pi}{2}\\\frac{\pi}{6}(1-C)=\frac{\pi}{2}\\\frac{1}{6}(1-C)=\frac{1}{2}\\(1-C)=\frac{6}{2}\\-C=3-1\\C=-2

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

D=5+lt

The function is:

y=5sin(\frac{\pi}{6} (x+2))+5+lt

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

y=5sin(\frac{\pi}{6} (x+2))+5+lt-lt

y=5sin(\frac{\pi}{6} (x+2))+5

(b) Use x=11 in the function

y=5sin(\frac{\pi}{6} (11+2))+5=2.5+5=7.5ft above the low tide.

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4 years ago
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