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1. Might the graph in Figure 11.15 be planar?
2. The goal of this problem is to use Euler's formula to list all possible regular polyhedra. (In this case, regular means that every face has the same number of edges and every vertex has the same degree.)
(a) Convert the idea of a regular polyhedron into a graph in some way.
(b) Find an upper bound on the possible degrees of the vertices.
(c) Find a lower bound on the possible degrees of the vertices.
(d) Find a relationship between the number of vertices and the number of edges.
(e) Find a relationship between the number of faces and the number of edges.
(f) Now use Euler's formula and solve some equations. (g) Find graphs, and polyhedra, that correspond to your solutions.
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budget rental cars charges 35 a day plus 0.40 per mile. enterprise charges 20 a day plus 0.55 per mile. wirte and solve
A large commercial farm needs 43,500 pounds of potash, 83,500 pounds of nitrogen, and 31,000 pounds of phosphoric acid. Three brands of fertilizer, Growrite, MiricalMix and GreatGreen, are available and contain the amounts of potash, nitrogen and ..
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a 5 year projection of population trends suggest that t years from now, the population of a certain community will be P(t)=-t3+9t2+48t+200.
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