Let g = (v; e; w) be an edge-weighted digraph. a branching of g is a subset b of e such that b contains no undirected circuit and such that for each vertex v there is at most one edge in b entering v. show that a branching of g with maximum total weight can be computed in polynomial time.

Scientists have changed the model of the atom as they have gathered new evidence. one of the atomic models is shown below. what experimental evidence led to the development of this atomic model from the one before it? a few of the positive particles aimed at a gold foil seemed to bounce back. the colors of light emitted from heated atoms had very specific energies. experiments with water vapor showed that elements combine in specific proportions. cathode rays were bent in the same way whenever a magnet was brought near them.