To calculate: The equation that represent the curved sides of the sculpture,
Answer to Problem 49E
The equation that represent the curved sides of the sculpture is
Explanation of Solution
Given information:
The cross section of a sculpture is provided below,
Formula used:
The equation of horizontal hyperbola is
Calculation:
Consider cross section of a sculpture that is provided below,
Observe that it is in shape of hyperbola whose transverse axis is horizontal.
Recall that the equation of horizontal hyperbola is
Here center is origin so
Also, the hyperbola passes through the point
Substitute x as 2, y as 13, a as 1, h as 0 and k as 0 in the equation
Now, substitute
Thus, the equation that represent the curved sides of the sculpture is
To calculate: The width of the sculpture at a height of 18 feet,
Answer to Problem 49E
The width of the sculpture at a height of 18 feet is
Explanation of Solution
Given information:
The cross section of a sculpture is provided below,
Formula used:
The equation of horizontal hyperbola is
Calculation:
Consider cross section of a sculpture that is provided below,
Observe that it is in shape of hyperbola whose transverse axis is horizontal.
Recall that the equation of horizontal hyperbola is
Here center is origin so
Also, the hyperbola passes through the point
Substitute x as 2, y as 13, a as 1, h as 0 and k as 0 in the equation
Now, substitute
Therefore, the equation that represent the curved sides of the sculpture is
Now, it is provided that each unit in coordinate plane represents 1 foot. So width of sculpture at height of 18 feet is evaluated below
Substitute
Therefore, width is twice of x that is,
Thus, the width of the sculpture at a height of 18 feet 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