Concept explainers
Sawing a Wooden Beam A rectangular beam is to be cut from a cylindrical log of diameter 20 in.
- (a) Show that the cross-sectional area of the beam is modeled by the function
- (b) Show that the maximum cross-sectional area of such a beam is 200 in2. [Hint: Use the fact that sin u achieves its maximum value at u = π/2.]
(a)
To show: The cross sectional area of the beam of diameter 20in is
Explanation of Solution
Formula used:
Double-Angle Formulae:
Double-Angle Formulae:
Formula for sine:
Proof:
Suppose the rectangle be named as ABCD.
Denote the diagonal of the rectangle as AC.
Consider the right angled triangle ABC, so by Pythagoras theorem, find the length l.
Use Pythagoras theorem to find the breadth b.
Compute the cross-sectional area of the beam of diameter 20in.
Hence, it is verified that the cross sectional area of the beam of diameter 20in is
(b)
To show: The maximum cross-sectional area of such a beam is 200
Explanation of Solution
Proof:
The cross sectional area of the beam of diameter 20in is
Notice that
Therefore, the maximum cross-sectional area of such a beam is
Chapter 7 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