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1. Prove that for a planar graph with k components, |V(G)|-|E(G)|+|F(G)| = 1+k.
2. Prove that the Petersen graph (shown in Figure 11.6) is not planar.
3. Show that if every face of a planar graph has four edges, then |E(G)| = 2|V(G)| -4.
4. For which n is Kn planar and for which n is Kn non planar? Make and prove a conjecture.
Prove that if a real number y satisfies 0
A deep low with pressure 972 mb is moving over northeast Iowa. Estimate the value of the directional derivative of the pressure function at Kearney in the direction of Sioux City.
The width is increased by 4 while the length is unchanged. Using a as the variable, express the change in area in terms of a.
Probabilities of Selecting Multiples of Fixed Numbers. Let N = 1000 and let S = {1, 2, ... , N}. Let D_i = {m belongs to S: i|m} for integers i between 1 and N.
Automorphism of a Group, Let G be a group, T an automorphism of G, N a normal subgroup of G. Prove that (N)T is a normal subgroup of G.
factor the polynomial and state the multiplicity of each zero.1given x 2 and x 3i are two zeroes of a real polynomial
Find the point of equilibrium for a system that has a demand equation p = 45 - 0.0003x and a supply equation p = 29 + 0.00002x
Examples of Probability and Statistics in Real Life, Can you think of situations in the business world or other real life situations where you would need to calculate or estimate probabilities?
Find an equation of the line tangent to the following curves at the given value of x. Use a graphing utility to plot the curve and the tangent line.
Independent measures research study.
Weight them half as much as the three interior points.
Briefly describe the four basic categories of innovations. Briefly distinguish between product R&D and process R&D.
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