The water depth in a narrow channel varies with the tides. The depth of the channel is deepest at the high tide that occurs at 2 AM in the morning when it is 12 ft. The channel is lowest at low tide, which occurs at 2 PM, when the depth is 5.4 ft. If t represents the hours after midnight, find a cosine model for the depth, D(t), of the channel (in feet) as a function of time. D(t) -

The water depth in a narrow channel varies with the tides. The depth of the channel is deepest at the high tide that occurs at 2 AM in the morning when it is 12 ft. The channel is lowest at low tide, which occurs at 2 PM, when the depth is 5.4 ft. If t represents the hours after midnight, find a cosine model for the depth, D(t), of the channel (in feet) as a function of time. D(t) -

Trigonometry (11th Edition)

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

See similar textbooks

Related questions

Q: Given y=-3sin[2(x-60)]+1, what is the period of the function?

A: indin

Q: he voltage for alternating current is modeled by the function (t) inimum voltage for this model? 231…

A: Given query is to find the minimum voltage.

Q: The temperature, A, of a chemical reaction oscillates between a low of 30oC and high of 110oC. The…

Q: Find the period, midline (ie vertical shift), and sketch the graph for y= 2tan(x/2 )−1 Draw at…

A: Given: y= 2tanx2−1 To find: Period, midline (vertical shift) and sketch the graph for given…

Q: = 15 cos (t) + 65, where h is the 1. The path of a swing could be modeled by the function h(t)…

A: Step 1: Step 2: Step 3: Step 4:

Q: The phase shift of the function y= -2sin 4x- is: Select one: a. 4 T units down b. units to the right…

A: The Phase Shift is how far the function is shifted horizontally from the usual position. The…

Q: A ferris wheel is 45 meters in diameter and boarded from a platform that is 3 meters above the…

Q: Each time your heart beats, your blood pressure first increases and then decreases as the heart…

Q: is I meter above the ground. The six o'clock position on the Ferris wheel is level with the loading…

Q: Each person's blood pressure is different, but there is a range of blood pressure values that is…

A: A function Pt=-20cos5π3t+100 models the blood pressure P in millimeters in mercury. To Find: What…

Q: A ferris wheel is 25 meters in diameter and boarded from a platform that is 1 meters above the…

Q: xt The function h(t)= -120 cos + 125 represents the height h, in feet, of a seat on a Ferris wheel…

A: Note: As per the honor code, only one question can be answered and up to 3 sub-parts only. Please…

Q: On a wintry day in Bismarck, North Dakota, temperature t hours after 2p.m. is given by…

Q: 2) A 50 foot diameter Ferris wheel is constantly turning at four revolutions per hour. The bottom of…

A: Amplitude, A:The diameter of the wheel,d = 50 ftThe radius of the wheel is,r = d2 = 25 ftAmplitude…

Q: what is the period of this function? y=-1cos(kx)+5.4

Question

The water depth in a narrow channel varies with the tides. The depth of the channel is deepest at the high
tide that occurs at 2 AM in the morning when it is 12 ft. The channel is lowest at low tide, which occurs at
2 PM, when the depth is 5.4 ft. If t represents the hours after midnight, find a cosine model for the depth,
D(t), of the channel (in feet) as a function of time.
D(t) =

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

The population of arctic foxes in Yukon can be modelled by the following equation: P = 400 cos(30t - 180) + 1100 Where 't' represents the number of years since 1992. a. b. C. d. c. What was the population of arctic foxes in Yukon in 1992? What are the maximum and minimum number of arctic foxes? Sketch a graph that represents how the population of artic foxes changes over time (since 1992). What will be the population of arctic foxes in 2030? When was the first time the population of arctic foxes reached 1300 (since 1992)?
At noon, the tide is at mid tide of 11 feet. At 6:00 pm, the tide is at low tide of 3 feet. At 6:00 am, the tide is at its high tide of 19 feet. It takes 24 hours for the tide to complete a full cycle. Determine a sinusoidal function that models the tide height h as a function of time t(in hours). Let t = 0 correspond to noon. - High tide Mid tide Low tide d
The electric power P (in W) as a function of the current i (in A) in a certain circuit is given by P = 12i2 + 60i. Find the instantaneous rate of change of P with respect to i for i = 0.75 A. The instantaneous rate of change of P is WIA for i = 0.75. (Simplify your answer.)
The San Francisco Bay tides vary between 1 foot and 7 feet. The tide is at its lowest point when time (t) is 0 and completes a full cycle in 8 hours. What is the amplitude, period, and midline of a function that would model this periodic phenomenon? A. Amplitude = 6 feet; period = 8 hours; midline: y = 4 B. Amplitude = 6 feet; period = 4 hours; midline: y = 3 C. Amplitude = 3 feet; period = 8 hours; midline: y = 4 D. Amplitude = 3 feet; period = 4 hours; midline: y = 3