At the gym, a man pulls a bar on a machine that works the muscles of the upper back. It takes him 0.5 seconds to raise 30 kilograms of weight a vertical distance of 0.5 meters. Which of these exerts the same power output? (Estimate g as 10m/s2.)

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