What is kinematics =_=? ⛄

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

Use 4 to 5 complete sentences, explain the concepts of beats and how beats are produces.

Ihave this 50 question test the layer of earth's atmosphere where atoms and molecules escape into space is referred to as the a) exosphere b) ionosphere. c) mesosphere d) thermosphere