Question

. The depth of the Atlantic Ocean at a channel buoy off the coast of
Maine can be modeled by y = 5 - 3cos (pi/6t) where y is the water depth
in feet and t is the time in hours. Consider a day in which t=0
represents 12:00 midnight.
a. For that day (in 24 hours), when do the high and low tides occur?
b. What are the respective depths of the ocean at high tides and low
tides?

Answer 1

a)The high and low tides occur at when the value of cos function is an odd and even multiple of the π respectively.

b)The respective depths of the ocean at high tides and low tides will be 8 ft and 2 ft.

What exactly is a function?

A function is a statement, rule, or law that specifies the connection between two variables. Functions are common in mathematics and are required for the formulation of physical connections.

Modeling the depth of the Atlantic Ocean at a channel buoy off the coast of Maine is;

$\rm y = 5-3 cos (\frac{\pi}{6} t)$

a) High tide's value of 'y' when the value of y is maximum. value of cosine is minimum.

The minimum value of cosθ  = 1.

The standard form to write the cos function is as;

θ=(2n+1)π

Whenever. high tides occur when it equals odd multiples of π. Similarly, at a Value of even multiples of even function, low tides are at their peak.

Hence,the high and low tides occur at when the value of cos function is an odd and even multiple of the π respectively.

At high tide;

соsӨ = - 1 (min value)

y= 5-3(-1)

y = 5+3

y=8 ft

At low tide,соsӨ = + 1 (max value)

y =5-3(1)

y= 5-3

y= 2

Hence,the respective depths of the ocean at high tides and low tides will be 8 ft and 2 ft.

To learn more about the function refer:

https://brainly.com/question/5245372

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