Question 209297
First, write the equation of variation for the resistance, R:
{{{R = L*k/d^2}}} where L = length of the wire, d = the diameter of the wire, and k = the constant of variation.
Now substitute the given values of L (100 ft.), R (80 ohms) and d (0.01 inch) in order to find the value of k.
{{{80 = 100*k/(0.01)^2}}} 
{{{k = 80(0.01)^2/100}}}
{{{k = 0.00008}}}
Now you can solve on the problem given:
{{{R = L*k/d^2}}} Substitute: k = 0.00008, L = 90, and d = 0.04
{{{R = (90)(0.00008)/(0.04)^2}}}
{{{R = 0.0072/0.0016}}}
{{{highlight(R = 4.5)}}}ohms.