5. a pendulum consisting of a mass m = 0.2 kg attached to a massless rod of length l = 0.3 m is pulled to an angle θ = 15° and released. the speed of the mass at the bottom of the swing is

a) 0.742 m/s

b) 1.03 m/s

c) 0.254 m/s

d) 0.448 m/s

e) 0.595 m/s

Choose all the answers that apply. our solar system: is in a spiral galaxy no longer includes pluto is made mostly of empty space is in the andromeda galaxy is the only known system that supports life

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

In a game of pool, ball a is moving with a velocity v0 of magnitude v0 = 15 ft/s when it strikes balls b and c, which are at rest and aligned as shown. knowing that after the collision the three balls move in the directions indicated and assuming frictionless surfaces and perfectly elastic impact (that is, conservation of energy), determine the magnitudes of the velocities va, vb, and vc.