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 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,