MYLAB W/ETEXT FOR MATHEMATICS ALL AROUN
6th Edition
ISBN: 9780135902783
Author: Pirnot
Publisher: PEARSON
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Chapter 4.2, Problem 40E
To determine
To devise:
The Hamilton circuit using the brut force algorithm and state the weight of the path.
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7.
Let F(x1, x2) (F₁(x1, x2), F2(x1, x2)), where
=
X2
F1(x1, x2)
X1
F2(x1, x2)
x+x
(i) Using the definition, calculate the integral
LF.dy,
where (t) = (cos(t), sin(t)) and t = [0,2].
[5 Marks]
(ii) Explain why Green's Theorem cannot be used to find the
integral in part (i).
[5 Marks]
6.
Sketch the trace of the following curve on R²,
п 3п
(t) = (t2 sin(t), t2 cos(t)),
tЄ
22
[3 Marks]
Find the length of this curve.
[7 Marks]
Total marks 10
Total marks
on
naner: 80
7.
Let DCR2 be a bounded domain with the boundary OD which can be
represented as a smooth closed curve : [a, b] R2, oriented in the anticlock-
wise direction.
Use Green's Theorem to justify that the area of the domain D
can be computed by the formula
1
Area(D)
=
½ (−y, x) · dy.
[5 Marks]
(ii) Use the area formula in (i) to find the area of the domain D
enclosed by the ellipse
y(t) = (10 cos(t), 5 sin(t)),
t = [0,2π].
[5 Marks]
Chapter 4 Solutions
MYLAB W/ETEXT FOR MATHEMATICS ALL AROUN
Ch. 4.1 - In Exercise 1-6, determine whether the graph is...Ch. 4.1 - In Exercise 1-6, determine whether the graph is...Ch. 4.1 - In Exercise 1-6, determine whether the graph is...Ch. 4.1 - In Exercise 1-6, determine whether the graph is...Ch. 4.1 - In Exercise 1-6, determine whether the graph is...Ch. 4.1 - In Exercise 1-6, determine whether the graph is...Ch. 4.1 - In Exercises 7-12, use Eulers theorem to decide...Ch. 4.1 - In Exercises 7-12, use Eulers theorem to decide...Ch. 4.1 - In Exercises 7-12, use Eulers theorem to decide...Ch. 4.1 - In Exercises 7-12, use Eulers theorem to decide...
Ch. 4.1 - In Exercises 7-12, use Eulers theorem to decide...Ch. 4.1 - In Exercises 7-12, use Eulers theorem to decide...Ch. 4.1 - In Exercise 13-16, if the given graph is Eulerian,...Ch. 4.1 - In Exercise 13-16, if the given graph is Eulerian,...Ch. 4.1 - In Exercise 13-16, if the given graph is Eulerian,...Ch. 4.1 - In Exercise 13-16, if the given graph is Eulerian,...Ch. 4.1 - In Exercises 17-24, try to give an example of each...Ch. 4.1 - Prob. 18ECh. 4.1 - In Exercises 17-24, try to give an example of each...Ch. 4.1 - In Exercises 17-24, try to give an example of each...Ch. 4.1 - In Exercises 17-24, try to give an example of each...Ch. 4.1 - Prob. 22ECh. 4.1 - Prob. 23ECh. 4.1 - Prob. 24ECh. 4.1 - In Exercise 25-28, remove one edge to make the...Ch. 4.1 - Prob. 26ECh. 4.1 - Prob. 27ECh. 4.1 - In Exercise 25-28, remove one edge to make the...Ch. 4.1 - In Exercise 29-32, try to redraw the given graph...Ch. 4.1 - In Exercise 29-32, try to redraw the given graph...Ch. 4.1 - In Exercise 29-32, try to redraw the given graph...Ch. 4.1 - In Exercise 29-32, try to redraw the given graph...Ch. 4.1 - Finding an efficient route. A taxi driver wants to...Ch. 4.1 - Finding an efficient route. Repeat Exercises 33...Ch. 4.1 - Exercise 35 and 36 are similar to DUCK tour...Ch. 4.1 - Exercise 35 and 36 are similar to DUCK tour...Ch. 4.1 - Represent the maps given in Exercises 37-40 by...Ch. 4.1 - Represent the maps given in Exercises 37-40 by...Ch. 4.1 - Represent the maps given in Exercises 37-40 by...Ch. 4.1 - Represent the maps given in Exercises 37-40 by...Ch. 4.1 - Prob. 41ECh. 4.1 - Prob. 42ECh. 4.1 - Prob. 43ECh. 4.1 - Prob. 44ECh. 4.1 - Prob. 45ECh. 4.1 - Prob. 46ECh. 4.1 - Prob. 47ECh. 4.1 - In Exercises 4548, we give you a group of states....Ch. 4.1 - Finding an efficient route. Because of Michaels...Ch. 4.1 - Prob. 50ECh. 4.1 - Use the technique that we used in Example 7 to do...Ch. 4.1 - Use the technique that we used in Example 7 to do...Ch. 4.1 - Use the technique that we used in Example 7 to do...Ch. 4.1 - Use the technique that we used in Example 7 to do...Ch. 4.1 - If, in tracing a graph, we neither begin nor end...Ch. 4.1 - Examine a number of the graphs that we have drawn...Ch. 4.1 - Can an Eulerian graph have a bridge? In order to...Ch. 4.1 - Consider any graph that has some odd and also some...Ch. 4.1 - Discuss specific examples of ways that...Ch. 4.1 - Prob. 60ECh. 4.1 - Draw a graph that can be colored with only two...Ch. 4.1 - Draw a graph that cannot be colored with two...Ch. 4.1 - Draw a graph that cannot be colored with three...Ch. 4.1 - Can you state what configuration of vertices will...Ch. 4.1 - Different notes on a trumpet are obtained by...Ch. 4.1 - If an instrument has four valves, there are 16...Ch. 4.1 - Assume that the registrar at your school is...Ch. 4.1 - Make up a scheduling problem that would be of some...Ch. 4.2 - Prob. 1ECh. 4.2 - Prob. 2ECh. 4.2 - Prob. 3ECh. 4.2 - Prob. 4ECh. 4.2 - Prob. 5ECh. 4.2 - Prob. 6ECh. 4.2 - Prob. 7ECh. 4.2 - Prob. 8ECh. 4.2 - How many Hamilton circuits are in K7?Ch. 4.2 - How many Hamilton circuits are in K8?Ch. 4.2 - Prob. 11ECh. 4.2 - Prob. 12ECh. 4.2 - Prob. 13ECh. 4.2 - Prob. 14ECh. 4.2 - Prob. 15ECh. 4.2 - Prob. 16ECh. 4.2 - Prob. 17ECh. 4.2 - Prob. 18ECh. 4.2 - Prob. 19ECh. 4.2 - Prob. 20ECh. 4.2 - Prob. 21ECh. 4.2 - Prob. 22ECh. 4.2 - Prob. 23ECh. 4.2 - Prob. 24ECh. 4.2 - In Exercises 23 -28, use the best edge algorithm...Ch. 4.2 - Prob. 26ECh. 4.2 - In Exercise 23 -28, use the best edge algorithm to...Ch. 4.2 - In Exercise 23 -28, use the best edge algorithm to...Ch. 4.2 - Simon Cowell plans a series of live shows from...Ch. 4.2 - ESPN is planning to do a special series called...Ch. 4.2 - Foodandwine.com states that the best ice cream...Ch. 4.2 - In order to try to solve a European financial...Ch. 4.2 - Prob. 33ECh. 4.2 - Prob. 34ECh. 4.2 - Prob. 35ECh. 4.2 - Prob. 36ECh. 4.2 - Prob. 37ECh. 4.2 - Prob. 38ECh. 4.2 - Prob. 39ECh. 4.2 - Prob. 40ECh. 4.2 - Prob. 41ECh. 4.2 - Prob. 42ECh. 4.2 - Prob. 43ECh. 4.2 - Prob. 44.1ECh. 4.2 - Prob. 44.2ECh. 4.2 - Prob. 45.1ECh. 4.2 - Prob. 45.2ECh. 4.2 - Prob. 45.3ECh. 4.2 - Prob. 49ECh. 4.2 - Prob. 51ECh. 4.2 - Prob. 52ECh. 4.3 - In Exercises 1-4, use each graph to find the...Ch. 4.3 - In Exercises 1-4, use each graph to find the...Ch. 4.3 - In Exercises 1-4, use each graph to find the...Ch. 4.3 - In Exercises 1-4, use each graph to find the...Ch. 4.3 - Prob. 5ECh. 4.3 - Prob. 6ECh. 4.3 - Prob. 7ECh. 4.3 - Prob. 8ECh. 4.3 - Modeling the spread of rumours. Ryan, Dwight, Pam,...Ch. 4.3 - Modeling the spread of classified information....Ch. 4.3 - Modeling the flow of paperwork through a...Ch. 4.3 - Modeling the spread of disease. The following...Ch. 4.3 - Prob. 13ECh. 4.3 - Modeling a communication network. An AMBER alert...Ch. 4.3 - Ranking football teams. The given graph shows the...Ch. 4.3 - Ranking American Gladiators. The graph below shows...Ch. 4.3 - Modeling influence. A designer who wishes to...Ch. 4.3 - Prob. 18ECh. 4.3 - Prob. 19ECh. 4.3 - Ranking CrossFit competitors. CrossFit is a...Ch. 4.3 - Prob. 21ECh. 4.3 - Prob. 22ECh. 4.3 - Prob. 23ECh. 4.3 - Prob. 24ECh. 4.3 - Prob. 25ECh. 4.3 - Prob. 26ECh. 4.3 - Prob. 27ECh. 4.3 - Prob. 28ECh. 4.3 - Prob. 29ECh. 4.3 - Communicating Mathematics In the incidence...Ch. 4.3 - Math in Your Life: Between the Numbers The history...Ch. 4.3 - Prob. 32ECh. 4.3 - Prob. 33ECh. 4.3 - Prob. 34ECh. 4.4 - Sharpening Your Skills. In Exercises 1 4, assume...Ch. 4.4 - Sharpening Your Skills. In Exercises 1 4, assume...Ch. 4.4 - Sharpening Your Skills. In Exercises 1 4, assume...Ch. 4.4 - Sharpening Your Skills. In Exercises 1 4, assume...Ch. 4.4 - Sharpening Your Skills. In Exercises 5 8, use the...Ch. 4.4 - Sharpening Your Skills. In Exercises 5 8, use the...Ch. 4.4 - Sharpening Your Skills. In Exercises 5 8, use the...Ch. 4.4 - Sharpening Your Skills. In Exercises 5 8, use the...Ch. 4.4 - Applying What Youve Learned. Planning a festival....Ch. 4.4 - Applying What Youve Learned. Organizing a project....Ch. 4.4 - Applying What Youve Learned. Building a student...Ch. 4.4 - Applying What Youve Learned. Organizing a health...Ch. 4.4 - Applying What Youve Learned. Organizing an...Ch. 4.4 - Communicating Mathematics. Study Figure 4.35 with...Ch. 4.4 - Communicating Mathematics. Write a brief report on...Ch. 4.4 - Challenge yourself. Planning an innovative house....Ch. 4.CR - Section 4.1 Use the preceding graph to answer the...Ch. 4.CR - Section 4.1 Explain how graphs are used to model a...Ch. 4.CR - Section 4.1 Which of the following graphs can be...Ch. 4.CR - Section 4.1 Use Fleurys algorithm to find an Euler...Ch. 4.CR - Section 4.1 Model the following street map with a...Ch. 4.CR - Prob. 6CRCh. 4.CR - Section 4.1 Allison, Branden, Colin, Donny, Erica,...Ch. 4.CR - Section 4.2 Find all Hamilton circuits that begin...Ch. 4.CR - Section 4.2 Use the following weighted graph to...Ch. 4.CR - Section 4.2 Use the following weighted graph to...Ch. 4.CR - Prob. 11CRCh. 4.CR - Prob. 12CRCh. 4.CR - Section 4.3 When are directed graphs rather than...Ch. 4.CR - Section 4.3 A student action committee has been...Ch. 4.CR - Section 4.4 Use the following PERT diagram to...Ch. 4.CR - Section 4.4 Congratulations You are planning your...Ch. 4.CT - Use the preceding graph to answer the following...Ch. 4.CT - Which of the following graphs can be traced? If a...Ch. 4.CT - Use Fleurys algorithm to find an Euler circuit in...Ch. 4.CT - Find all Hamilton circuits that begin at vertex A...Ch. 4.CT - Model the following street map with a graph and...Ch. 4.CT - Prob. 6CTCh. 4.CT - Use the following weighted graph to answer...Ch. 4.CT - Use the following weighted graph to answer...Ch. 4.CT - Use the following weighted graph to answer...Ch. 4.CT - Use the given directed graph to find the following...Ch. 4.CT - Use the given PERT diagram to answer the following...Ch. 4.CT - The following graph models one- and two-stage...
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