a.
To find:The equation that models the curve sides of the sculpture.
a.
Answer to Problem 47E
The equation of the curved sides of the sculpture is
Explanation of Solution
Given information:
The given sculpture of hyperbolic cross section is shown in figure (1).
Figure (1)
Calculation:
The curved part of sculpture is having the shape of a hyperbola.
From the figure (1), the vertices of the hyperbola are
And the transverse axis is horizontal, and the hyperbola passes through
The equation of the hyperbola in the given as.
The center of the hyperbola is given by the midpoint of the line segment joining the vertices.
Calculate the midpoint between the
The center is at
Calculate the value of
The hyperbola passes through the point
Substitute value of
Calculate the standard form of the hyperbola.
Therefore, the equation of the curved sides of the sculptureis
b.
To find: The width of the sculpture at height of the
b.
Answer to Problem 47E
The width of the sculpture at height of the
Explanation of Solution
Given information:
Each unit is equal to
The given sculpture of hyperbolic cross section is shown in figure (1).
Figure (1)
Calculation:
Let
Calculate the
The sculpture is symmetric about
Therefore, the width of the sculpture at height of the
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