Mathematics For Machine Technology
8th Edition
ISBN: 9781337798310
Author: Peterson, John.
Publisher: Cengage Learning,
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Chapter 87, Problem 5A
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Chapter 87 Solutions
Mathematics For Machine Technology
Ch. 87 - Prob. 1ACh. 87 - Express the binary number 1101.0012as a decimal...Ch. 87 - Prob. 3ACh. 87 - Prob. 4ACh. 87 - Prob. 5ACh. 87 - Prob. 6ACh. 87 - Prob. 7ACh. 87 - What does a G01 tell a machine to perform?Ch. 87 - Prob. 9ACh. 87 - Prob. 10A
Ch. 87 - Prob. 11ACh. 87 - Prob. 12ACh. 87 - Prob. 13ACh. 87 - Prob. 14ACh. 87 - Prob. 15ACh. 87 - Prob. 16ACh. 87 - Prob. 17ACh. 87 - Prob. 18ACh. 87 - Prob. 19ACh. 87 - Prob. 20ACh. 87 - Prob. 21ACh. 87 - Prob. 22ACh. 87 - Write a G-code program for the counterclockwise...Ch. 87 - Prob. 24ACh. 87 - Prob. 25ACh. 87 - Prob. 26ACh. 87 - Write a CNC G-code program to machine the part in...Ch. 87 - Prob. 28A
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- 7. [10 marks] Let G = (V,E) be a 3-connected graph with at least 6 vertices. Let C be a cycle in G of length 5. We show how to find a longer cycle in G. (a) Let x be a vertex of G that is not on C. Show that there are three C-paths Po, P1, P2 that are disjoint except at the shared initial vertex and only intersect C at their final vertices. (b) Show that at least two of P0, P1, P2 have final vertices that are adjacent along C. (c) Combine two of Po, P1, P2 with C to produce a cycle in G that is longer than C.arrow_forwardLet G be a connected graph with n ≥ 2 vertices. Let A be the adjacency matrix of G. Prove that the diameter of G is the least number d such that all the non-diagonal entries of the matrix A are positive.arrow_forward8. [10 marks] Suppose that 15 people are at a dinner and that each person knows at least 9 of the others. Can the diners be seated around a circular table so that each person knows both of their immediate neighbors? Explain why your answer is correct.arrow_forward
- 9. [10 marks] Consider the following graph G. (a) Find the Hamilton closure of G. Explain why your answer is correct. (b) Is G Hamiltonian? Explain why your answer is correct.arrow_forward7. [10 marks] Let G = (V,E) be a 3-connected graph with at least 6 vertices. Let C be a cycle in G of length 5. We show how to find a longer cycle in G. Ꮖ (a) Let x be a vertex of G that is not on C. Show that there are three C-paths Po, P1, P2 that are disjoint except at the shared initial vertex x and only intersect C at their final vertices. (b) Show that at least two of Po, P1, P2 have final vertices that are adjacent along C.arrow_forwardNo chatgpt pls will upvotearrow_forward
- 4. [10 marks] Let T be the following tree: Find a graph G whose block graph BL(G) is isomorphic to T. Explain why your answer is correct.arrow_forward5. [10 marks] Determine whether the graph below has a perfect matching. Explain why your answer is correct. ข พarrow_forwardLet k ≥ 1, and let G be a k-regular bipartite graph with bipartition X, Y . Prove that |X| is the minimum size of a vertex cover in G.arrow_forward
- 3. [10 marks] Let Go = (V,E) and G₁ = (V,E₁) be two graphs on the same set of vertices. Let (V, EU E1), so that (u, v) is an edge of H if and only if (u, v) is an edge of Go or of G1 (or of both). H = (a) Show that if Go and G₁ are both Eulerian and En E₁ = Ø (i.e., Go and G₁ have no edges in common), then H is also Eulerian. (b) Give an example where Go and G₁ are both Eulerian, but H is not Eulerian.arrow_forwardLet T be a tree with n vertices. Let k be the maximum degree of a vertex of T. Let l be the length of the longest path in T. Prove that l ≤ n − k +1.arrow_forwardNo chatgpt pls will upvotearrow_forward
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