The maximum height of any bubble tower with n chambers using mathematical induction.
Explanation of Solution
Given information:
A hemispherical bubble is placed on a spherical bubble of radius 1.A small hemispherical bubble is placed on the first one. This process is continued until n chambers including the sphere is formed
Calculations:
Suppose that the maximum height of a bubble tower of
If we now consider a tower of
Thus the height of the part of the tower from the centre of the bottom bubble (of the sub tower) to the top will be
so we need to choose
Since
We see that
Thus we deduce, by induction, that the maximum height of a tower of
Chapter 4 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced 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