![Precalculus Enhanced with Graphing Utilities](https://www.bartleby.com/isbn_cover_images/9780321795465/9780321795465_largeCoverImage.gif)
Tides The length of time between consecutive high tides is 12 hours and 25 minutes. According to the National Oceanic and Atmospheric Administration, on Saturday, March 28. 2015, in Sitka, Alaska, high tide occurred at AM ( hours) and low tide occurred at PM ( hours). Water heights arc measured as the amounts above or below' the mean lower low water. The height of the water at high tide was feet, and the height of the water at low tide was feet.
(a) Approximately when will the next high tide occur?
(b) Find a sinusoidal function of the form that models the data.
(c) Use the function found in part to predict the height of the water at 6 PM on March 28, 2015.
![Check Mark](/static/check-mark.png)
To find:
a. Approximately when will the next high tide occur?
Answer to Problem 34AYU
Solution:
a. 8:31 PM
Explanation of Solution
Given:
The length of time between consecutive high tides is 12 hours and 25 minutes. According to the National Oceanic and Atmospheric Administration, on Saturday, March 28, 2015, in Sitka, Alaska, high tide occurred at 8:06 am (8.10 hours) and low tide occurred at 2:48 pm (14.8 hours). Water heights are measured as the amounts above or below the mean lower low water. The height of the water at high tide was 8.13 feet, and the height of the water at low tide was 1.95 feet.
Calculation:
a. Approximately when will the next high tide occur?
Charleston, South Carolina, high tide occurred at 8:06 am, since the length of time between consecutive high tides is 12 hours and 25 minutes. Therefore the next high tide occur .
![Check Mark](/static/check-mark.png)
To find:
b. Find a sinusoidal function of the form that models the data.
Answer to Problem 34AYU
Solution:
b.
Explanation of Solution
Given:
The length of time between consecutive high tides is 12 hours and 25 minutes. According to the National Oceanic and Atmospheric Administration, on Saturday, March 28, 2015, in Sitka, Alaska, high tide occurred at 8:06 am (8.10 hours) and low tide occurred at 2:48 pm (14.8 hours). Water heights are measured as the amounts above or below the mean lower low water. The height of the water at high tide was 8.13 feet, and the height of the water at low tide was 1.95 feet.
Calculation:
b. Find a sinusoidal function of the form that models the data.
Determine A, the amplitude of the function.
Determine B, the vertical shift of the function.
Determine , It is easier to find the horizontal stretch factor first. Since the period of the function is . Therefore .
Now superimpose the graph of
Determine the horizontal shift of the function by using the period of the data.
units to the right by replacing by
![Check Mark](/static/check-mark.png)
To find:
c. Use the function found in part (b) to predict the height of the water at 6 pm on March 28, 2015.
Answer to Problem 34AYU
Solution:
c.
Explanation of Solution
Given:
The length of time between consecutive high tides is 12 hours and 25 minutes. According to the National Oceanic and Atmospheric Administration, on Saturday, March 28, 2015, in Sitka, Alaska, high tide occurred at 8:06 am (8.10 hours) and low tide occurred at 2:48 pm (14.8 hours). Water heights are measured as the amounts above or below the mean lower low water. The height of the water at high tide was 8.13 feet, and the height of the water at low tide was 1.95 feet.
Calculation:
c. Use the function found in part (b) to predict the height of the water at 6 pm on March 28, 2015.
.
Chapter 6 Solutions
Precalculus Enhanced with Graphing Utilities
Additional Math Textbook Solutions
Calculus, Single Variable: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (2nd Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Calculus: Early Transcendentals (3rd Edition)
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning
![Text book image](https://www.bartleby.com/isbn_cover_images/9781285741550/9781285741550_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9780134438986/9780134438986_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9780134763644/9780134763644_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781319050740/9781319050740_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9780135189405/9780135189405_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781337552516/9781337552516_smallCoverImage.gif)