Applications and ExamplesA round underwater transmission

Thomas' Calculus: Early Transcendentals | 13th Edition | ISBN: 9780321884077 | Authors: George B. Thomas Jr., Maurice D. Weir, Joel R. Hass

Problem 136PE Chapter 4

Thomas' Calculus: Early Transcendentals | 13th Edition

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Thomas' Calculus: Early Transcendentals | 13th Edition | ISBN: 9780321884077 | Authors: George B. Thomas Jr., Maurice D. Weir, Joel R. Hass

Thomas' Calculus: Early Transcendentals | 13th Edition

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Problem 136PE

Applications and Examples

A round underwater transmission cable consists of a core of copper wires surrounded by nonconducting insulation. If x denotes the ratio of the radius of the core to the thickness of the insulation, it is known that the speed of the transmission signal is given by the equation If the radius of the core is 1 cm, what insulation thickness h will allow the greatest transmission speed?

Step-by-Step Solution:

Step 1 of 3:

In this problem, we need to find insulation thickness h.

Step 2 of 3:

Given:………(1)

Radius of the core is 1 cm.

That is,

From (1) we get

 

       

Hence,

Step 3 of 3

Chapter 4, Problem 136PE is Solved
Textbook: Thomas' Calculus: Early Transcendentals
Edition: 13th
Author: George B. Thomas Jr., Maurice D. Weir, Joel R. Hass
ISBN: 9780321884077

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