Explanation Given information: Some of the highest tides in the world occur in the Bay of Fundy on the Atlantic Coast of Canada. At Hopewell Cape the water depth at low tide is about 2.0m and at high tide it is about 12.0 m. the natural period of oscillation is about 12 hours and on June 30, 2009, high tide occurred at 6:45 AM. Calculation: Given that high tide occurred at 6:45 AM means 6 hours 45 minutes = 6 hrs 45 min 60 min = 6.75 hr . For standard cosine function, the following equation is Y = A ↓ cos [ B ( x − c ) ] + D ↑ Amplitude midline Taking an average of high and low tides 12 + 2 2 = 14 2 = 7 So the value of midline is, D =7 Next we will find amplitude. Now the amplitude is simply measure from the midline to either the highest value or the lowest value like 12 − 7 = 5 or 7 − 2 = 5 So, A = 5 M=next we find the value of c c is simply the x-coordinate of where our curve begins its cycle

15th Edition

ISBN: 9781133109631

Author: Stewart, JAMES, Day, Troy

Publisher: Cengage Learning,

See similar textbooks

Videos

Question

Chapter 1.3, Problem 23E

To determine

To find: a function involving the cosine function that models the water depth D(t) (in meters) as a function of time t (in hours after midnight) on that day.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 1.3, Problem 22E

Chapter 1.3, Problem 24E

Chapter 1 Solutions

Biocalculus

Ch. 1.1 - Prob. 1E Ch. 1.1 - Prob. 2E Ch. 1.1 - Prob. 3E Ch. 1.1 - Prob. 4E Ch. 1.1 - Prob. 5E Ch. 1.1 - Prob. 6E Ch. 1.1 - Prob. 7E Ch. 1.1 - Prob. 8E Ch. 1.1 - Prob. 9E Ch. 1.1 - Prob. 10E

Ch. 1.1 - Prob. 11E Ch. 1.1 - Prob. 12E Ch. 1.1 - Prob. 13E Ch. 1.1 - Prob. 14E Ch. 1.1 - Prob. 15E Ch. 1.1 - Prob. 16E Ch. 1.1 - Prob. 17E Ch. 1.1 - Prob. 18E Ch. 1.1 - Prob. 19E Ch. 1.1 - Prob. 20E Ch. 1.1 - Prob. 21E Ch. 1.1 - Prob. 22E Ch. 1.1 - Prob. 23E Ch. 1.1 - Prob. 24E Ch. 1.1 - Prob. 25E Ch. 1.1 - Prob. 26E Ch. 1.1 - Prob. 27E Ch. 1.1 - Prob. 28E Ch. 1.1 - Prob. 29E Ch. 1.1 - Prob. 30E Ch. 1.1 - Prob. 31E Ch. 1.1 - Prob. 32E Ch. 1.1 - Prob. 33E Ch. 1.1 - Prob. 34E Ch. 1.1 - Prob. 35E Ch. 1.1 - Prob. 36E Ch. 1.1 - Prob. 37E Ch. 1.1 - Prob. 38E Ch. 1.1 - Prob. 39E Ch. 1.1 - Prob. 40E Ch. 1.1 - Prob. 41E Ch. 1.1 - Prob. 42E Ch. 1.1 - Prob. 43E Ch. 1.1 - Prob. 44E Ch. 1.1 - Prob. 45E Ch. 1.1 - Prob. 46E Ch. 1.1 - Prob. 47E Ch. 1.1 - Prob. 48E Ch. 1.1 - Prob. 49E Ch. 1.1 - Prob. 50E Ch. 1.1 - Prob. 51E Ch. 1.1 - Prob. 52E Ch. 1.1 - Prob. 53E Ch. 1.1 - Prob. 54E Ch. 1.1 - Prob. 55E Ch. 1.1 - Prob. 56E Ch. 1.1 - Prob. 57E Ch. 1.1 - Prob. 58E Ch. 1.1 - Prob. 59E Ch. 1.1 - Prob. 60E Ch. 1.1 - Prob. 61E Ch. 1.1 - Prob. 62E Ch. 1.1 - Prob. 63E Ch. 1.1 - Prob. 64E Ch. 1.1 - Prob. 65E Ch. 1.1 - Prob. 66E Ch. 1.1 - Prob. 67E Ch. 1.1 - Prob. 68E Ch. 1.1 - Prob. 69E Ch. 1.1 - Prob. 70E Ch. 1.1 - Prob. 71E Ch. 1.1 - Prob. 72E Ch. 1.1 - Prob. 73E Ch. 1.1 - Prob. 74E Ch. 1.2 - Prob. 1E Ch. 1.2 - Prob. 2E Ch. 1.2 - Prob. 3E Ch. 1.2 - Prob. 4E Ch. 1.2 - Prob. 5E Ch. 1.2 - Prob. 6E Ch. 1.2 - Prob. 7E Ch. 1.2 - Prob. 8E Ch. 1.2 - Prob. 9E Ch. 1.2 - Prob. 10E Ch. 1.2 - Prob. 11E Ch. 1.2 - Prob. 12E Ch. 1.2 - Prob. 13E Ch. 1.2 - Prob. 14E Ch. 1.2 - Prob. 15E Ch. 1.2 - Prob. 16E Ch. 1.2 - Prob. 17E Ch. 1.2 - Prob. 18E Ch. 1.2 - Prob. 19E Ch. 1.2 - Prob. 20E Ch. 1.2 - Prob. 21E Ch. 1.2 - Prob. 22E Ch. 1.2 - Prob. 23E Ch. 1.2 - Prob. 24E Ch. 1.2 - Prob. 25E Ch. 1.2 - Prob. 26E Ch. 1.2 - Prob. 27E Ch. 1.3 - Prob. 1E Ch. 1.3 - Prob. 2E Ch. 1.3 - Prob. 3E Ch. 1.3 - Prob. 4E Ch. 1.3 - Prob. 5E Ch. 1.3 - Prob. 6E Ch. 1.3 - Prob. 7E Ch. 1.3 - Prob. 8E Ch. 1.3 - Prob. 9E Ch. 1.3 - Prob. 10E Ch. 1.3 - Prob. 11E Ch. 1.3 - Prob. 12E Ch. 1.3 - Prob. 13E Ch. 1.3 - Prob. 14E Ch. 1.3 - Prob. 15E Ch. 1.3 - Prob. 16E Ch. 1.3 - Prob. 17E Ch. 1.3 - Prob. 18E Ch. 1.3 - Prob. 19E Ch. 1.3 - Prob. 20E Ch. 1.3 - Prob. 21E Ch. 1.3 - Prob. 22E Ch. 1.3 - Prob. 23E Ch. 1.3 - Prob. 24E Ch. 1.3 - Prob. 25E Ch. 1.3 - Prob. 26E Ch. 1.3 - Prob. 27E Ch. 1.3 - Prob. 28E Ch. 1.3 - Prob. 29E Ch. 1.3 - Prob. 30E Ch. 1.3 - Prob. 31E Ch. 1.3 - Prob. 32E Ch. 1.3 - Prob. 33E Ch. 1.3 - Prob. 34E Ch. 1.3 - Prob. 35E Ch. 1.3 - Prob. 36E Ch. 1.3 - Prob. 37E Ch. 1.3 - Prob. 38E Ch. 1.3 - Prob. 39E Ch. 1.3 - Prob. 40E Ch. 1.3 - Prob. 41E Ch. 1.3 - Prob. 42E Ch. 1.3 - Prob. 43E Ch. 1.3 - Prob. 44E Ch. 1.3 - Prob. 45E Ch. 1.3 - Prob. 46E Ch. 1.3 - Prob. 47E Ch. 1.3 - Prob. 48E Ch. 1.3 - Prob. 49E Ch. 1.3 - Prob. 50E Ch. 1.3 - Prob. 51E Ch. 1.3 - Prob. 52E Ch. 1.3 - Prob. 53E Ch. 1.3 - Prob. 54E Ch. 1.3 - Prob. 55E Ch. 1.3 - Prob. 56E Ch. 1.3 - Prob. 57E Ch. 1.3 - Prob. 58E Ch. 1.3 - Prob. 59E Ch. 1.3 - Prob. 1P Ch. 1.3 - Prob. 2P Ch. 1.3 - Prob. 3P Ch. 1.4 - Prob. 1E Ch. 1.4 - Prob. 2E Ch. 1.4 - Prob. 3E Ch. 1.4 - Prob. 4E Ch. 1.4 - Prob. 5E Ch. 1.4 - Prob. 6E Ch. 1.4 - Prob. 7E Ch. 1.4 - Prob. 8E Ch. 1.4 - Prob. 9E Ch. 1.4 - Prob. 10E Ch. 1.4 - Prob. 11E Ch. 1.4 - Prob. 12E Ch. 1.4 - Prob. 13E Ch. 1.4 - Prob. 14E Ch. 1.4 - Prob. 15E Ch. 1.4 - Prob. 16E Ch. 1.4 - Prob. 17E Ch. 1.4 - Prob. 18E Ch. 1.4 - Prob. 19E Ch. 1.4 - Prob. 20E Ch. 1.4 - Prob. 21E Ch. 1.4 - Prob. 22E Ch. 1.4 - Prob. 23E Ch. 1.4 - Prob. 24E Ch. 1.4 - Prob. 25E Ch. 1.4 - Prob. 26E Ch. 1.4 - Prob. 27E Ch. 1.4 - Prob. 28E Ch. 1.4 - Prob. 29E Ch. 1.4 - Prob. 30E Ch. 1.4 - Prob. 31E Ch. 1.4 - Prob. 32E Ch. 1.4 - Prob. 33E Ch. 1.4 - Prob. 34E Ch. 1.4 - Prob. 35E Ch. 1.4 - Prob. 36E Ch. 1.4 - Prob. 37E Ch. 1.4 - Prob. 38E Ch. 1.5 - Prob. 1E Ch. 1.5 - Prob. 2E Ch. 1.5 - Prob. 3E Ch. 1.5 - Prob. 4E Ch. 1.5 - Prob. 5E Ch. 1.5 - Prob. 6E Ch. 1.5 - Prob. 7E Ch. 1.5 - Prob. 8E Ch. 1.5 - Prob. 9E Ch. 1.5 - Prob. 10E Ch. 1.5 - Prob. 11E Ch. 1.5 - Prob. 12E Ch. 1.5 - Prob. 13E Ch. 1.5 - Prob. 14E Ch. 1.5 - Prob. 15E Ch. 1.5 - Prob. 16E Ch. 1.5 - Prob. 17E Ch. 1.5 - Prob. 18E Ch. 1.5 - Prob. 19E Ch. 1.5 - Prob. 20E Ch. 1.5 - Prob. 21E Ch. 1.5 - Prob. 22E Ch. 1.5 - Prob. 23E Ch. 1.5 - Prob. 24E Ch. 1.5 - Prob. 25E Ch. 1.5 - Prob. 26E Ch. 1.5 - Prob. 27E Ch. 1.5 - Prob. 28E Ch. 1.5 - Prob. 29E Ch. 1.5 - Prob. 30E Ch. 1.5 - Prob. 31E Ch. 1.5 - Prob. 32E Ch. 1.5 - Prob. 33E Ch. 1.5 - Prob. 34E Ch. 1.5 - Prob. 35E Ch. 1.5 - Prob. 36E Ch. 1.5 - Prob. 37E Ch. 1.5 - Prob. 38E Ch. 1.5 - Prob. 39E Ch. 1.5 - Prob. 40E Ch. 1.5 - Prob. 41E Ch. 1.5 - Prob. 42E Ch. 1.5 - Prob. 43E Ch. 1.5 - Prob. 44E Ch. 1.5 - Prob. 45E Ch. 1.5 - Prob. 46E Ch. 1.5 - Prob. 47E Ch. 1.5 - Prob. 48E Ch. 1.5 - Prob. 49E Ch. 1.5 - Prob. 50E Ch. 1.5 - Prob. 51E Ch. 1.5 - Prob. 52E Ch. 1.5 - Prob. 53E Ch. 1.5 - Prob. 54E Ch. 1.5 - Prob. 55E Ch. 1.5 - Prob. 56E Ch. 1.5 - Prob. 57E Ch. 1.5 - Prob. 58E Ch. 1.5 - Prob. 59E Ch. 1.5 - Prob. 60E Ch. 1.5 - Prob. 61E Ch. 1.5 - Prob. 62E Ch. 1.5 - Prob. 63E Ch. 1.5 - Prob. 64E Ch. 1.5 - Prob. 65E Ch. 1.5 - Prob. 66E Ch. 1.5 - Prob. 67E Ch. 1.5 - Prob. 68E Ch. 1.5 - Prob. 69E Ch. 1.5 - Prob. 70E Ch. 1.5 - Prob. 1P Ch. 1.5 - Prob. 2P Ch. 1.5 - Prob. 3P Ch. 1.5 - Prob. 4P Ch. 1.5 - Prob. 5P Ch. 1.6 - Prob. 1E Ch. 1.6 - Prob. 2E Ch. 1.6 - Prob. 3E Ch. 1.6 - Prob. 4E Ch. 1.6 - Prob. 5E Ch. 1.6 - Prob. 6E Ch. 1.6 - Prob. 7E Ch. 1.6 - Prob. 8E Ch. 1.6 - Prob. 9E Ch. 1.6 - Prob. 10E Ch. 1.6 - Prob. 11E Ch. 1.6 - Prob. 12E Ch. 1.6 - Prob. 13E Ch. 1.6 - Prob. 14E Ch. 1.6 - Prob. 15E Ch. 1.6 - Prob. 16E Ch. 1.6 - Prob. 17E Ch. 1.6 - Prob. 18E Ch. 1.6 - Prob. 19E Ch. 1.6 - Prob. 20E Ch. 1.6 - Prob. 21E Ch. 1.6 - Prob. 22E Ch. 1.6 - Prob. 23E Ch. 1.6 - Prob. 24E Ch. 1.6 - Prob. 25E Ch. 1.6 - Prob. 26E Ch. 1.6 - Prob. 27E Ch. 1.6 - Prob. 28E Ch. 1.6 - Prob. 29E Ch. 1.6 - Prob. 30E Ch. 1.6 - Prob. 31E Ch. 1.6 - Prob. 32E Ch. 1.6 - Prob. 33E Ch. 1.6 - Prob. 34E Ch. 1.6 - Prob. 35E Ch. 1.6 - Prob. 36E Ch. 1.6 - Prob. 37E Ch. 1.6 - Prob. 38E Ch. 1.6 - Prob. 39E Ch. 1.6 - Prob. 40E Ch. 1.6 - Prob. 1P Ch. 1.6 - Prob. 2P Ch. 1.6 - Prob. 3P Ch. 1.6 - Prob. 4P Ch. 1 - Prob. 1CC Ch. 1 - Prob. 2CC Ch. 1 - Prob. 3CC Ch. 1 - Prob. 4CC Ch. 1 - Prob. 5CC Ch. 1 - Prob. 6CC Ch. 1 - Prob. 7CC Ch. 1 - Prob. 8CC Ch. 1 - Prob. 9CC Ch. 1 - Prob. 10CC Ch. 1 - Prob. 11CC Ch. 1 - Prob. 12CC Ch. 1 - Prob. 13CC Ch. 1 - Prob. 14CC Ch. 1 - Prob. 15CC Ch. 1 - Prob. 16CC Ch. 1 - Prob. 1TFQ Ch. 1 - Prob. 2TFQ Ch. 1 - Prob. 3TFQ Ch. 1 - Prob. 4TFQ Ch. 1 - Prob. 5TFQ Ch. 1 - Prob. 6TFQ Ch. 1 - Prob. 7TFQ Ch. 1 - Prob. 8TFQ Ch. 1 - Prob. 9TFQ Ch. 1 - Prob. 10TFQ Ch. 1 - Prob. 11TFQ Ch. 1 - Prob. 12TFQ Ch. 1 - Prob. 1E Ch. 1 - Prob. 2E Ch. 1 - Prob. 3E Ch. 1 - Prob. 4E Ch. 1 - Prob. 5E Ch. 1 - Prob. 6E Ch. 1 - Prob. 7E Ch. 1 - Prob. 8E Ch. 1 - Prob. 9E Ch. 1 - Prob. 10E Ch. 1 - Prob. 11E Ch. 1 - Prob. 12E Ch. 1 - Prob. 13E Ch. 1 - Prob. 14E Ch. 1 - Prob. 15E Ch. 1 - Prob. 16E Ch. 1 - Prob. 17E Ch. 1 - Prob. 18E Ch. 1 - Prob. 19E Ch. 1 - Prob. 20E Ch. 1 - Prob. 21E Ch. 1 - Prob. 22E Ch. 1 - Prob. 23E Ch. 1 - Prob. 24E Ch. 1 - Prob. 25E Ch. 1 - Prob. 26E Ch. 1 - Prob. 27E Ch. 1 - Prob. 28E Ch. 1 - Prob. 29E Ch. 1 - Prob. 30E Ch. 1 - Prob. 31E Ch. 1 - Prob. 32E Ch. 1 - Prob. 33E Ch. 1 - Prob. 34E Ch. 1 - Prob. 35E Ch. 1 - Prob. 36E Ch. 1 - Prob. 37E Ch. 1 - Prob. 38E Ch. 1 - Prob. 39E Ch. 1 - Prob. 40E Ch. 1 - Prob. 1CS Ch. 1 - Prob. 2CS Ch. 1 - Prob. 3CS Ch. 1 - Prob. 4CS Ch. 1 - Prob. 5CS Ch. 1 - Prob. 6CS Ch. 1 - Prob. 7CS Ch. 1 - Prob. 8CS Ch. 1 - Prob. 9CS

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Recommended textbooks for you

Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Intermediate Algebra
Algebra
ISBN:9780998625720
Author:Lynn Marecek
Publisher:OpenStax College

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:9781133382119

Author:Swokowski

Publisher:Cengage

Intermediate Algebra

Algebra

ISBN:9780998625720

Author:Lynn Marecek

Publisher:OpenStax College

SEE MORE TEXTBOOKS

Trigonometry - Harmonic Motion - Equation Setup; Author: David Hays;https://www.youtube.com/watch?v=BPrZnn3DJ6Q;License: Standard YouTube License, CC-BY

Simple Harmonic Motion - An introduction : ExamSolutions Maths Revision; Author: ExamSolutions;https://www.youtube.com/watch?v=tH2vldyP5OE;License: Standard YouTube License, CC-BY

a function involving the cosine function that models the water depth D ( t ) (in meters) as a function of time t (in hours after midnight) on that day.

Solution Summary: The author explains the cosine function that models the water depth as a function of time t (in hours after midnight).

Videos

To find: a function involving the cosine function that models the water depth D(t) (in meters) as a function of time t (in hours after midnight) on that day.

Want to see the full answer?

Chapter 1 Solutions