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Question 1083857: At a fixed temperature, the resistance R of a wire varies directly as the length 1 and inversely as the square of its diameter d. If the resistance is 1.2 ohm when the diameter is 1 mm and the length is 240 cm, what is the resistance when the diameter is 3 mm and the length is 610 cm?
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the direct variation formula is y = k * x
the indirect variation formula is y = k / x
the combined direct and indirect variation formula is z = k * x / y
replace z with R and replace x with L and replace Y with D^2 and the formula becomes:
R = k * L / D^2
R is equal to 1.2 when L is 240 and d is 1.
formula becomes 1.2 = k * 240 / 1^2
solve for k to get k = 1.2 * 1^2 / 240 = 1.2 / 240 = .005
that's the value of k which is the constant of variation.
it remains the same regardless of the values of R or D or L.
when d = 3 and L = 610, and k = .005, the formula becomes R = .005 * 610 / 3^2.
this results in R = .3389 ohms.
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website!
At a fixed temperature, the resistance R of a wire varies directly as the length 1 and inversely as the square of its diameter d. If the resistance is 1.2 ohm when the diameter is 1 mm and the length is 240 cm, what is the resistance when the diameter is 3 mm and the length is 610 cm?
With R being resistance, L being length, D being diameter, and k, the CONSTANT of PROPORTIONALITY, you need to use the formula: 
Before you do so though, you need to convert the units from cm to mm, or vice-versa.
After finding k, substitute the cm or mm values for diameter and length to find R, the resistance.
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