Excursions in Modern Mathematics (9th Edition)
9th Edition
ISBN: 9780134468372
Author: Peter Tannenbaum
Publisher: PEARSON
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Chapter 3, Problem 18E
Suppose that they flip a coin and Nick ends up being the divider.
a. Describe how Nick would cut the sandwich into two shares
b. After Nick cuts, Martha gets to choose. Specify which of the two shares Martha should choose and give the value of the share to Martha.
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Refer to page 311 for a sequence of functions defined on a given interval.
Instructions:
•
Analyze whether the sequence converges pointwise and/or uniformly on the given interval.
• Discuss the implications of uniform convergence for integration and differentiation of the
sequence.
•
Provide counterexamples if any condition fails.
Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qo Hazb9tC440 AZF/view?usp=sharing]
Chapter 3 Solutions
Excursions in Modern Mathematics (9th Edition)
Ch. 3 - Henry, Tom, and Fred are breaking up their...Ch. 3 - Alice, Bob, and Carlos are dividing among...Ch. 3 - Angie, Bev, Ceci, and Dina are dividing among...Ch. 3 - Mark, Tim, Maia, and Kelly are dividing among...Ch. 3 - Allen, Brady, Cody, and Diane are sharing a cake....Ch. 3 - Carlos, Sonya, Tanner, and Wen are sharing a cake....Ch. 3 - Four partners Adams, Benson, Cagle, and Duncan...Ch. 3 - Prob. 8ECh. 3 - Suppose that Angelina values strawberry cake twice...Ch. 3 - Suppose that Brad values chocolate cake thrice as...
Ch. 3 - Suppose that Brad values chocolate cake four as...Ch. 3 - Suppose that Angelina values strawberry cake five...Ch. 3 - Karla and five other friends jointly buy the...Ch. 3 - Marla and five other friends jointly buy the...Ch. 3 - Suppose that they flip a coin and Jackie ends up...Ch. 3 - Suppose they flip a coin and Karla ends up being...Ch. 3 - Suppose that they flip a coin and Martha ends up...Ch. 3 - Suppose that they flip a coin and Nick ends up...Ch. 3 - Suppose that David is the divider and Paula is the...Ch. 3 - Suppose that Paula is the divider and David is the...Ch. 3 - Three partners are dividing a plot of land among...Ch. 3 - Three partners are dividing a plot of land among...Ch. 3 - Four partners are dividing a plot of land among...Ch. 3 - Four partners are dividing a plot of land among...Ch. 3 - Mark, Tim, Maia, and Kelly are dividing a cake...Ch. 3 - Allen, Brady, Cody; and Diane are sharing a cake...Ch. 3 - Prob. 27ECh. 3 - Four partners are dividing a plot of land among...Ch. 3 - Prob. 29ECh. 3 - Five players are dividing a cake among themselves...Ch. 3 - Four partners Egan, Fine, Gong, and Hart jointly...Ch. 3 - Four players Abe, Betty, Cory, and Dana are...Ch. 3 - Exercises 33 and 34 refer to the following...Ch. 3 - Exercises 33 and 34 refer to the following...Ch. 3 - Exercise 35 through 38 refer to the following...Ch. 3 - Exercise 35 through 38 refer to the following...Ch. 3 - Prob. 37ECh. 3 - Prob. 38ECh. 3 - Exercises 39 and 40 refer to the following:...Ch. 3 - Exercises 39 and 40 refer to the following:...Ch. 3 - Jackie, Karla, and Lori are dividing the foot-long...Ch. 3 - Jackie, Karla, and Lori are dividing the foot-long...Ch. 3 - Ana, Belle, and Chloe are dividing four pieces of...Ch. 3 - Andre, Bea, and Chad are dividing an estate...Ch. 3 - Five heirs A,B,C,D, and E are dividing an estate...Ch. 3 - Oscar, Bert, and Ernie are using the method of...Ch. 3 - Anne, Bette, and Chia jointly own a flower shop....Ch. 3 - Al, Ben and Cal jointly own a fruit stand. They...Ch. 3 - Ali, Briana, and Caren are roommates planning to...Ch. 3 - Anne, Bess and Cindy are the roommates planning to...Ch. 3 - Prob. 51ECh. 3 - Three players (A,B and C) are dividing the array...Ch. 3 - Three players (A,B,andC) are dividing the array of...Ch. 3 - Three players (A,B,andC) are dividing the array of...Ch. 3 - Five players (A,B,C,D,andE) are dividing the array...Ch. 3 - Four players (A,B,C,andD) are dividing the array...Ch. 3 - Prob. 57ECh. 3 - Queenie, Roxy, and Sophie are dividing a set of 15...Ch. 3 - Ana, Belle, and Chloe are dividing 3 Choko bars, 3...Ch. 3 - Prob. 60ECh. 3 - Prob. 61ECh. 3 - Prob. 62ECh. 3 - Prob. 63ECh. 3 - Prob. 64ECh. 3 - Three players A, B, and C are sharing the...Ch. 3 - Angeline and Brad are planning to divide the...Ch. 3 - Prob. 67ECh. 3 - Efficient and envy-free fair divisions. A fair...Ch. 3 - Suppose that N players bid on M items using the...Ch. 3 - Asymmetric method of sealed bids. Suppose that an...Ch. 3 - Prob. 73E
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- Refer to page 310 for a matrix and its associated system of differential equations. Instructions: • Find the eigenvalues of the given matrix and classify the stability of the system (e.g., stable, • unstable, saddle point). Discuss the geometric interpretation of eigenvalues in the context of system behavior. • Provide conditions under which the system exhibits periodic solutions. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440 AZF/view?usp=sharing]arrow_forwardRefer to page 313 for a nonlinear differential equation and its linear approximation. Instructions: • Linearize the given nonlinear system around the equilibrium points. • Analyze the stability of each equilibrium using the Jacobian matrix and its eigenvalues. • Discuss the limitations of linearization for determining global behavior. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440 AZF/view?usp=sharing]arrow_forwardRefer to page 314 for a matrix and its decomposed form. Instructions: • Verify the given singular value decomposition of the matrix. • • Discuss the geometric interpretation of the left and right singular vectors. Use the SVD to analyze the matrix's rank and nullity. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440 AZ F/view?usp=sharing]arrow_forward
- Refer to page 312 for a set of mappings between two groups G and H. Instructions: • • Verify which of the provided mappings are homomorphisms. Determine the kernel and image of valid homomorphisms and discuss their properties. • State whether the groups are isomorphic, justifying your conclusion. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qo Hazb9tC440 AZF/view?usp=sharing]arrow_forward12:25 AM Sun Dec 22 uestion 6- Week 8: QuX Assume that a company X + → C ezto.mheducation.com Week 8: Quiz i Saved 6 4 points Help Save & Exit Submit Assume that a company is considering purchasing a machine for $50,000 that will have a five-year useful life and a $5,000 salvage value. The machine will lower operating costs by $17,000 per year. The company's required rate of return is 15%. The net present value of this investment is closest to: Click here to view Exhibit 12B-1 and Exhibit 12B-2, to determine the appropriate discount factor(s) using the tables provided. 00:33:45 Multiple Choice О $6,984. $11,859. $22,919. ○ $9,469, Mc Graw Hill 2 100-arrow_forwardNo chatgpt pls will upvotearrow_forward
- 7. [10 marks] Let G = (V,E) be a 3-connected graph. We prove that for every x, y, z Є V, there is a cycle in G on which x, y, and z all lie. (a) First prove that there are two internally disjoint xy-paths Po and P₁. (b) If z is on either Po or P₁, then combining Po and P₁ produces a cycle on which x, y, and z all lie. So assume that z is not on Po and not on P₁. Now prove that there are three paths Qo, Q1, and Q2 such that: ⚫each Qi starts at z; • each Qi ends at a vertex w; that is on Po or on P₁, where wo, w₁, and w₂ are distinct; the paths Qo, Q1, Q2 are disjoint from each other (except at the start vertex 2) and are disjoint from the paths Po and P₁ (except at the end vertices wo, W1, and w₂). (c) Use paths Po, P₁, Qo, Q1, and Q2 to prove that there is a cycle on which x, y, and z all lie. (To do this, notice that two of the w; must be on the same Pj.)arrow_forward6. [10 marks] Let T be a tree with n ≥ 2 vertices and leaves. Let BL(T) denote the block graph of T. (a) How many vertices does BL(T) have? (b) How many edges does BL(T) have? Prove that your answers are correct.arrow_forward4. [10 marks] Find both a matching of maximum size and a vertex cover of minimum size in the following bipartite graph. Prove that your answer is correct. ย ພarrow_forward
- 5. [10 marks] Let G = (V,E) be a graph, and let X C V be a set of vertices. Prove that if |S||N(S)\X for every SCX, then G contains a matching M that matches every vertex of X (i.e., such that every x X is an end of an edge in M).arrow_forwardQ/show that 2" +4 has a removable discontinuity at Z=2i Z(≥2-21)arrow_forwardRefer to page 100 for problems on graph theory and linear algebra. Instructions: • Analyze the adjacency matrix of a given graph to find its eigenvalues and eigenvectors. • Interpret the eigenvalues in the context of graph properties like connectivity or clustering. Discuss applications of spectral graph theory in network analysis. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440 AZF/view?usp=sharing]arrow_forward
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