# Rational Expressions Algebra

Electronics

The electrical resistance (r) of a cable varies directly (y=kx) as its length (l) and inversely (y= k/x) as the square of its diaeter (d). If a cable 16,000 ft long and 1/4 in. in diameter has a resistance of 3.2 ohms, what is the resistance of a cable that is 8000ft long and 1/2 in. in diameter?

Since R = K L/d^2,
where K is a constant, reducing the length L by 1/2 and doubling the diameter d will cause R to decrease by a factor 1/2 x (1/2^2) = 1/8.

What is 1/8 of 3.2 ohms?

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