The resistance R of a wire varies directly as its length L and inversely as the square of its diameter d. (a) Write an equation that expresses this joint variation. (Use k for the constant of proportionality.) (b) Find the constant of proportionality if a wire 1.4 m long and 0.005 m in diameter has a resistance of 100 ohms. (Round your answer to six decimal places.) k= (c) Find the resistance (in ohms) of a wire made of the same material that is 4 m long and has a diameter of 0.009 m. (Round your answer to the nearest whole number.) R = ohms (d) If the diameter is doubled and the length is tripled, by what factor is the resistance changed?
The resistance R of a wire varies directly as its length L and inversely as the square of its diameter d. (a) Write an equation that expresses this joint variation. (Use k for the constant of proportionality.) (b) Find the constant of proportionality if a wire 1.4 m long and 0.005 m in diameter has a resistance of 100 ohms. (Round your answer to six decimal places.) k= (c) Find the resistance (in ohms) of a wire made of the same material that is 4 m long and has a diameter of 0.009 m. (Round your answer to the nearest whole number.) R = ohms (d) If the diameter is doubled and the length is tripled, by what factor is the resistance changed?
Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
Problem 6ECP: The resistance of a copper wire carrying an electrical current is directly proportional to its...
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Transcribed Image Text:The resistance R of a wire varies directly as its length L and inversely as the square of its diameter d.
(a) Write an equation that expresses this joint variation. (Use k for the constant of proportionality.)
(b) Find the constant of proportionality if a wire 1.4 m long and 0.005 m in diameter has a resistance of 100 ohms. (Round your
answer to six decimal places.)
k =
(c) Find the resistance (in ohms) of a wire made of the same material that is 4 m long and has a diameter of 0.009 m. (Round
your answer to the nearest whole number.)
R =
ohms.
(d) If the diameter is doubled and the length is tripled, by what factor is the resistance changed?
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