he resistance. R. of a wire varies directly as its length and inversely as the square of its diameter. If the resistance of a wire 1700 ft long with a diameter of 0.13 inches 5 1414 ohms, what is the resistance of 2900 ft of the same type of wire with a diameter of 0.32 inches? (Leave k in fraction form or round to at least 3 decimal places.
Round off your final answer to the nearest hundredth.)
Let's denote the resistance of the wire as R, the length as L, and the diameter as D. We are given that the resistance varies directly with the length and inversely with the square of the diameter. This can be expressed by the equation:
R = k * (L/D^2)
where k is the constant of variation.
We are given that the resistance of a wire 1700 ft long with a diameter of 0.13 inches is 1414 ohms. Plugging these values into the equation, we can solve for k:
1414 = k * (1700/0.13^2)
1414 = k * (1700/0.0169)
1414 = k * 100592.96
k ≈ 1414/100592.96
k ≈ 0.01405
Now that we have the value of k, we can use it to find the resistance of 2900 ft of wire with a diameter of 0.32 inches:
R = 0.01405 * (2900/0.32^2)
R = 0.01405 * (2900/0.1024)
R = 0.01405 * 28320.3125
R ≈ 398.05 ohms
Therefore, the resistance of 2900 ft of wire with a diameter of 0.32 inches is approximately 398.05 ohms.