Ways that charges can be transferred

Asmall blob of putty of mass m falls from the ceiling and lands on the outer rim of a turntable of radius r and moment of inertia i0 that is rotating freely with angular speed ω0 about its vertical fixed-symmetry axis. (use any variable or symbol stated above as necessary.)

Aforce of 200 n is applied to an input piston of cross-sectional area 2 sq. cm pushing it downward 2.8 cm. how far does the output piston of cross-sectional area 12 sq. cm move upward? show all work.

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