Concept explainers
The Arch of a Bridge The opening of a railway bridge over a roadway is in the shape of a parabola. A surveyor measures the heights of three points on the bridge, as shown in the figure. He wishes to find an equation of the form
to model the shape of the arch.
- (a) Use the surveyed points to set up a system of linear equations for the unknown coefficients a, b, and c.
- (b) Solve the system using Cramer’s Rule.
(a)
The system for linear equations from given measures.
Answer to Problem 61E
The linear equations for the system are
Explanation of Solution
Given:
The shape of the railway bridge over a roadway is in shape of parabola,
The coordinates of railway bridge from the Figure (1) are,
Compare the above coordinates with
Substitute 10 as
The first equation is,
Substitute 15 for
Thus, the second equation is
Substitute 40 for
Thus, the third equation is
Thus the linear equations for the system are
(b)
To find: The solution of the linear system using Cramer’s rule.
Answer to Problem 61E
The value of x is
Explanation of Solution
Given:
From part (a) the linear system is
Evaluate the left hand side of equation for determinant.
Apply
Expand along
Now replace the terms of first column of
Apply
Expand along
Similarly,
Similarly,
Now, from Cramer’s rule for solution,
Similarly,
Similarly,
Thus, the value of a is
Chapter 10 Solutions
Precalculus: Mathematics for Calculus - 6th 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