Excursions In Modern Mathematics, 9th Edition
9th Edition
ISBN: 9780134494142
Author: Tannenbaum
Publisher: PEARSON
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Chapter 5, Problem 69E
This exercise comes to you courtesy of Euler himself. Here is the question in Euler's own words,
accompanied by the diagram shown in Fig. 5-63.
Let us take an example of two islands with four rivers forming the surrounding water. There are fifteen bridges marked a, b, c, d, etc., across the water around the islands and the adjoining rivers. The question is whether a journey can be arranged that will pass over all the bridges but not over any of them more than once.
Figure 5-63
What is the answer to Euler's question? If the “journey” is possible, describe it. If it isn't, explain why not.
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stacie is a resident at a medical facility you work at. You are asked to chart the amount of solid food that she consumes.For the noon meal today, she ate 1/2 of a 3 ounce serving of meatloaf, 3/4 of her 3 ounce serving of mashed potatoes, and 1/3 of her 2 ounce serving of green beans. Show in decimal form how many ounces of solid food that Stacie consumed
Find the area of the shaded region.
(a)
5-
y
3
2-
(1,4)
(5,0)
1
3
4
5
6
(b)
3 y
2
Decide whether the problem can be solved using precalculus, or whether calculus is required. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, use a graphical or numerical approach to
estimate the solution.
STEP 1: Consider the figure in part (a). Since this region is simply a triangle, you may use precalculus methods to solve this part of the problem. First determine the height of the triangle and the length of the triangle's base.
height 4
units
units
base
5
STEP 2: Compute the area of the triangle by employing a formula from precalculus, thus finding the area of the shaded region in part (a).
10
square units
STEP 3: Consider the figure in part (b). Since this region is defined by a complicated curve, the problem seems to require calculus. Find an approximation of the shaded region by using a graphical approach. (Hint: Treat the shaded regi
as…
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Chapter 5 Solutions
Excursions In Modern Mathematics, 9th Edition
Ch. 5 - For the graph shown in Fig 5-29, a.give the vertex...Ch. 5 - For the graph shown in Fig. 5-30, a.give the...Ch. 5 - For the graph shown in Fig. 5-31, 1.give the...Ch. 5 - For the graph shown in Fig. 5-32, a.give the...Ch. 5 - Consider the graph with vertex set {K,R,S,T,W} and...Ch. 5 - Consider the graph with vertex set {A,B,C,D,E} and...Ch. 5 - Consider the graph with vertex set {A,B,C,D,E} and...Ch. 5 - Consider the graph with vertex set {A,B,C,X,Y,Z}...Ch. 5 - a.Give an example of a connected graph with eight...Ch. 5 - a.Give an example of a connected graph with eight...
Ch. 5 - Consider the graph in Fig. 5-33. a. Find a path...Ch. 5 - Consider the graph in Fig. 5-33. a. Find a path...Ch. 5 - Consider the graph in Fig. 5-33. a. Find all...Ch. 5 - Consider the graph in Fig 5-34 a.Find all circuits...Ch. 5 - List all the bridges in each of the following...Ch. 5 - List all the bridges in each of the following...Ch. 5 - Consider the graph in Fig 5-35. a. List all the...Ch. 5 - Consider the graph in Fig 5-36. a. List all the...Ch. 5 - Figure 5-37 shows a map of the downtown area of...Ch. 5 - Figure 5-38 is a map of downtown Royalton, showing...Ch. 5 - A night watchman must walk the streets of the...Ch. 5 - A mail carrier must deliver mail on foot along the...Ch. 5 - Six teams (A,B,C,D,E,andF) are entered in a...Ch. 5 - The Kangaroo Lodge of Madison Country has 10...Ch. 5 - Table 5-3 summarizes the Facebook friendships...Ch. 5 - The Dean of students office wants to know how the...Ch. 5 - Figure 5-40 shows the downtown area of the small...Ch. 5 - Prob. 28ECh. 5 - In Exercise 29 through 34 choose from the...Ch. 5 - In Exercise 29 through 34 choose from the...Ch. 5 - In Exercise 29 through 34 choose from the...Ch. 5 - In Exercises 29 through 34 choose from the...Ch. 5 - In Exercise 29 through 34 choose from the...Ch. 5 - In Exercise 29 through 34 choose from the...Ch. 5 - Find the Euler circuit for the graph in Fig.5-47....Ch. 5 - Find the Euler circuit for the graph in Fig.5.48_....Ch. 5 - Find the Euler path for the graph in Fig.5-49_....Ch. 5 - Find the Euler path for the graph in Fig.5-50....Ch. 5 - Find an Euler circuit for the graph in Fig 5-51....Ch. 5 - Find the Euler circuit for the graph in Fig 5-52....Ch. 5 - Suppose you are using Fleurys algorithm to find an...Ch. 5 - Suppose you are using Fleurys algorithm to find an...Ch. 5 - Find an optimal eulerization for the graph in Fig...Ch. 5 - Find an optimal eulerization for the graph in Fig....Ch. 5 - Find an optimal eulerization for the graph in Fig....Ch. 5 - Find an optimal eulerization for the graph in Fig...Ch. 5 - Find an optimal semi-eulerization for the graph in...Ch. 5 - Find an optimal semi-eulerization for the graph in...Ch. 5 - Prob. 49ECh. 5 - Prob. 50ECh. 5 - Prob. 51ECh. 5 - Prob. 52ECh. 5 - A security guard must patrol on foot the streets...Ch. 5 - A mail carrier must deliver mail on foot along the...Ch. 5 - This exercise refers to the Fourth of July parade...Ch. 5 - This exercise refers to the Fourth of July parade...Ch. 5 - Consider the following puzzle: You must trace Fig...Ch. 5 - a.Explain why in every graph the sum of the...Ch. 5 - Prob. 59ECh. 5 - Regular graphs. A graph is called regular if every...Ch. 5 - Suppose G is a disconnected graph with exactly two...Ch. 5 - Consider the following game. You are given N...Ch. 5 - Figure 5-59 shows a map of the downtown area of...Ch. 5 - Kissing circuits. When two circuits in a graph...Ch. 5 - Prob. 65ECh. 5 - Exercises 66 through 68 refer to Example 5.23 . In...Ch. 5 - Exercises 66 through 68 refer to Example 5.23 . In...Ch. 5 - Exercises 66 through 68 refer to Example 5.23 . In...Ch. 5 - This exercise comes to you courtesy of Euler...Ch. 5 - Running Suppose G is a connected graph with N...Ch. 5 - Running Suppose G is a connected graph with N2...Ch. 5 - Running Complete bipartite graphs. A complete...Ch. 5 - Running Suppose G is a simple graph with N...
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