Pls help :( this is really hard and I need to pass this grade lol

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

The items in the following list are all units of matter. which is the smallest unit that retains the properties of the matter? a.) atom b.) compound c.) electron d.) element

1which body contains the majority of the mass in the solar system earth jupiter the moon the sun 2 what keeps the objects in the solar system such as planets orbiting around the sun the force of gravity the galaxy exerts on all objects within it including the solar system the great distance between the sun and the planets the sun's nuclear fusion which acts on each object the gravitational force between the sun and each object in the solar system