The electrical resistance of copper wire varies directly with its length and inversely with the square of the diameter of the wire. if a wire 30m long with a diameter of 3 mm has a resistance of 25 ohms, find the resistance of a wire 40m long with a diameter of 3.5 mm

Arunner is training for an upcoming marathon by running around a 100-m-diameter circular track at constant speed. let a coordinate system have its origin at the center of the circle with the x-axis pointing east and the y-axis north. the runner starts at (x, y) = (50 m, 0 m) and runs 2.5 times around the track in a clockwise direction.

An electromagnet is a device in which moving electric chargers in a coil of wire create a magnet.whats one advantage of using electromagnetic in devices

Suppose that f : rn → rm and that a ∈ k, where k is a connected subset of rn . suppose further that for each x ∈ k there exists a δx > 0 such that f(x) = f(y) for all y ∈ bδx (x). prove that f is constant on k; that is, f(x) = f(a) for all x ∈ k