Concept explainers
Tofind :How wide is the archway at ground level?
Answer to Problem 69E
Explanation of Solution
Given information: A parabolic archway is 12 meters high at the vertex. At a height of 10 meters, the width of the archway is 8 meters(see figure).
Calculation:
The standard equation of parabola is of form
where ( h,k ) is the position of vertex of parabola and a is distance of focus from vertex.
The x- axis is along ground level and y- axis is line perpendicular to x -axis and passing through vertex of parabolic arch.
The vertex is 12 feet above from x -axis and lie on the line y=0, therefore position of vertex of the parabola is (0,12),so
h =0 and k =12
Therefore, equation of parabola is
Also, at a height of 10 meters, the width of the archway is 8 meters
Therefore, the point (4,10) lie on the parabola, so we have
Therefore, equation of parabola is
At ground level, y =0, so we have
Therefore, width of arch at ground level is
Chapter 10 Solutions
EBK PRECALCULUS W/LIMITS
- 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