Concept explainers
(a)
To find: Where should the thumbtacks be placed
(a)
Answer to Problem 52E
The thumbtacks should be 3.71 feet from center
Explanation of Solution
Given information: Construction: The arch of a fireplace is to be constructed in the shape of a semi-ellipse. The opening is to have a height of 3 feet at the center and a width of 8 feet along the base. To sketch the outline of the fireplace, the contractor uses an
8-foot string tied to two thumbtacks.
Calculation:
Creating the equation with
You can find the location of the foci by:
This means the thumbtacks should be 3.71 feet from the center.
(b)
To explain: Why this technique works.
(b)
Explanation of Solution
Given information: Construction: The arch of a fireplace is to be constructed in the shape of a semi-ellipse. The opening is to have a height of 3 feet at the center and a width of 8 feet along the base. To sketch the outline of the fireplace, the contractor uses an
8-foot string tied to two thumbtacks.
Calculation:
This works on the principal of the ellipse.
By placing the thumbtacks 3.71 feet from center using and 8 foot string, will allow to create the elliptical shape desired.
Chapter 10 Solutions
Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
Additional Math Textbook Solutions
Precalculus (10th Edition)
University Calculus: Early Transcendentals (4th Edition)
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
Calculus: Early Transcendentals (3rd Edition)
Calculus and Its Applications (11th 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