Mathematical Ideas (13th Edition) - Standalone book
13th Edition
ISBN: 9780321977076
Author: Charles D. Miller, Vern E. Heeren, John Hornsby, Christopher Heeren
Publisher: PEARSON
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Chapter 14.1, Problem 17E
To determine
Whether the graphs are connected or not and how many components does the graph have. The graph is shown below.
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2. A tank with a capacity of 650 gal. originally contains 200 gal of water with 100 lb. of salt in
solution. Water containing 1 lb. of salt per gallon is entering at a rate of 4 gal/min, and the
mixture is allowed to flow out of the tank at a rate of 3 gal/min.
a. Find the amount of salt in the tank at any time prior to the instant when the tank
begins to overflow (650 gallons).
b. Find the concentration (in pounds per gallon) of salt in the tank when the tank hits
400 gallons.
D.E. for mixture problems:
dv
dt=11-12
dA
A(t)
dt
- Suppose that you have the differential equation:
dy
= (y - 2) (y+3)
dx
a. What are the equilibrium solutions for the differential equation?
b. Where is the differential equation increasing or decreasing? Show how you know.
Showing them on the drawing is not enough.
c. Where are the changes in concavity for the differential equation? Show how you
know. Showing them on the drawing is not enough.
d. Consider the slope field for the differential equation. Draw solution curves given the
following initial conditions:
i. y(0) = -5
ii. y(0) = -1
iii. y(0) = 2
5. Suppose that a mass of 5 stretches a spring 10. The mass is acted on by an external force
of F(t)=10 sin () and moves in a medium that gives a damping coefficient of ½. If the mass
is set in motion with an initial velocity of 3 and is stretched initially to a length of 5. (I
purposefully removed the units- don't worry about them. Assume no conversions are
needed.)
a) Find the equation for the displacement of the spring mass at time t.
b) Write the equation for the displacement of the spring mass in phase-mode form.
c) Characterize the damping of the spring mass system as overdamped, underdamped or
critically damped. Explain how you know.
D.E. for Spring Mass Systems
k
m* g = kLo
y" +—y' + — —±y = —±F(t), y(0) = yo, y'(0) = vo
m
2
A₁ = √c₁² + C₂²
Q = tan-1
Chapter 14 Solutions
Mathematical Ideas (13th Edition) - Standalone book
Ch. 14.1 - Vertices and Edges In Exercises 1-6, determine how...Ch. 14.1 - Vertices and Edges In Exercises 1-6, determine how...Ch. 14.1 - Vertices and Edges In Exercises 1-6, determine how...Ch. 14.1 - Prob. 4ECh. 14.1 - Prob. 5ECh. 14.1 - Prob. 6ECh. 14.1 - Prob. 7ECh. 14.1 - Prob. 8ECh. 14.1 - Prob. 9ECh. 14.1 - Prob. 10E
Ch. 14.1 - Prob. 11ECh. 14.1 - Prob. 12ECh. 14.1 - Prob. 13ECh. 14.1 - Prob. 14ECh. 14.1 - Prob. 15ECh. 14.1 - Prob. 16ECh. 14.1 - Prob. 17ECh. 14.1 - Prob. 18ECh. 14.1 - Prob. 19ECh. 14.1 - Prob. 20ECh. 14.1 - Prob. 21ECh. 14.1 - Prob. 22ECh. 14.1 - Prob. 23ECh. 14.1 - Prob. 24ECh. 14.1 - Prob. 25ECh. 14.1 - Number of Edges In Exercises 23-26, use the...Ch. 14.1 - Prob. 27ECh. 14.1 - Prob. 28ECh. 14.1 - Prob. 29ECh. 14.1 - Prob. 30ECh. 14.1 - Prob. 31ECh. 14.1 - Prob. 32ECh. 14.1 - Prob. 33ECh. 14.1 - Prob. 34ECh. 14.1 - Prob. 35ECh. 14.1 - Prob. 36ECh. 14.1 - Prob. 37ECh. 14.1 - Prob. 38ECh. 14.1 - Prob. 39ECh. 14.1 - Prob. 40ECh. 14.1 - Prob. 41ECh. 14.1 - Prob. 42ECh. 14.1 - Prob. 43ECh. 14.1 - 44. Chess Competition Students from two schools...Ch. 14.1 - Prob. 45ECh. 14.1 - Prob. 46ECh. 14.1 - Prob. 47ECh. 14.1 - Number of Handshakes There are seven people at a...Ch. 14.1 - Prob. 49ECh. 14.1 - Prob. 50ECh. 14.1 - Prob. 51ECh. 14.1 - 52. Students in the Same Class Mary, Erin, Sue,...Ch. 14.1 - Here is another theorem about graphs: In any...Ch. 14.1 - Draw two nonisomorphic (simple) graphs with 6...Ch. 14.1 - Explain why the two graphs drawn in Exercise 54...Ch. 14.1 - Analyzing a Cube with a Graph Draw a graph whose...Ch. 14.1 - Prob. 57ECh. 14.1 - Prob. 58ECh. 14.1 - Prob. 59ECh. 14.1 - Prob. 60ECh. 14.1 - Prob. 61ECh. 14.1 - Prob. 62ECh. 14.1 - Prob. 63ECh. 14.1 - Prob. 64ECh. 14.1 - Prob. 65ECh. 14.1 - Prob. 66ECh. 14.1 - Prob. 67ECh. 14.1 - Prob. 68ECh. 14.1 - Prob. 69ECh. 14.1 - Prob. 70ECh. 14.1 - 71. Inviting Colleagues to a Gathering Several of...Ch. 14.1 - Prob. 72ECh. 14.1 - Prob. 73ECh. 14.1 - Prob. 74ECh. 14.1 - Prob. 75ECh. 14.1 - Graph Coloring In Exercises 75 and 76, draw a...Ch. 14.1 - Prob. 77ECh. 14.1 - Prob. 78ECh. 14.1 - Prob. 79ECh. 14.1 - Prob. 80ECh. 14.1 - Prob. 81ECh. 14.1 - Prob. 82ECh. 14.1 - The Six Degrees of Kevin Bacon Use the Web site...Ch. 14.1 - The Six Degrees of Kevin BaconUse the Web site...Ch. 14.1 - The Six Degrees of Kevin BaconUse the Web site...Ch. 14.1 - The Six Degrees of Kevin Bacon Use the Web...Ch. 14.1 - The Six Degrees of Kevin Bacon Use the Web...Ch. 14.1 - The Six Degrees of Kevin Bacon Use the Web site...Ch. 14.1 - The Six Degrees of Kevin BaconUse the Web site...Ch. 14.1 - The Six Degrees of Kevin BaconUse the Web site...Ch. 14.1 - The Six Degrees of Kevin BaconUse the Web site...Ch. 14.1 - The Six Degrees of Kevin BaconUse the Web site...Ch. 14.1 - 93. Lines from She Walks in Beauty, by Lord...Ch. 14.1 - 94. Lines from Annabel Lee, by Edgar Allan Poe
It...Ch. 14.1 - Poetry Analysis Graphs may be used to clarify the...Ch. 14.1 - 96. Lines from Sailing to Byzantium, by William...Ch. 14.2 - Euler Circuits. In Exercises 1-3, a graph is shown...Ch. 14.2 - Prob. 2ECh. 14.2 - Euler Circuits In Exercises 1-3, a graph is shown...Ch. 14.2 - Prob. 4ECh. 14.2 - Euler's Theorem In Exercises 4-8, use Eulers...Ch. 14.2 - Prob. 6ECh. 14.2 - Euler's Theorem.In Exercises 4-8, use Eider's...Ch. 14.2 - Prob. 8ECh. 14.2 - Euler's Theorem In Exercises 9 and 10, use Eider's...Ch. 14.2 - Prob. 10ECh. 14.2 - Euler's Theorem In Exercises 11-14, use Eider's...Ch. 14.2 - Prob. 12ECh. 14.2 - Euler's Theorem In Exercises 11-14, use Euler's...Ch. 14.2 - Prob. 14ECh. 14.2 - Floor Tilings In Exercises 15-18, different floor...Ch. 14.2 - Prob. 16ECh. 14.2 - Floor Tilings In Exercises 15-18, different floor...Ch. 14.2 - Prob. 18ECh. 14.2 - Prob. 19ECh. 14.2 - Prob. 20ECh. 14.2 - Prob. 21ECh. 14.2 - Prob. 22ECh. 14.2 - Fleury's Algorithm In Exercises 23-25, a graph is...Ch. 14.2 - Prob. 24ECh. 14.2 - Prob. 25ECh. 14.2 - Prob. 26ECh. 14.2 - Fleury's Algorithm In Exercises 26-28\ use...Ch. 14.2 - Prob. 28ECh. 14.2 - Euler's Theorem and Fleury's Algorithm In...Ch. 14.2 - Euler's Theorem and Fleury's Algorithm In...Ch. 14.2 - Euler's Theorem and Fleury's Algorithm In...Ch. 14.2 - Prob. 32ECh. 14.2 - 33. Parking Pattern The map shows the roads on...Ch. 14.2 - Prob. 34ECh. 14.2 - Floor Plans In Exercises 34-36, the floor plan of...Ch. 14.2 - Prob. 36ECh. 14.2 - Exercises 37-44 are based on the following...Ch. 14.2 - Prob. 38ECh. 14.2 - Exercises 37-44 are based on the following...Ch. 14.2 - Prob. 40ECh. 14.2 - Exercises 37-44 are based on the following...Ch. 14.2 - Floor PlansIn Exercises 41-43, refer to the floor...Ch. 14.2 - Prob. 43ECh. 14.2 - Prob. 44ECh. 14.2 - Prob. 45ECh. 14.2 - Prob. 46ECh. 14.2 - Prob. 47ECh. 14.2 - Prob. 48ECh. 14.2 - Prob. 49ECh. 14.2 - Route Planning For each street grid in Exercise...Ch. 14.2 - Route Planning For each street grid in Exercise...Ch. 14.2 - Route Planning For each street grid in Exercise...Ch. 14.3 - Prob. 1ECh. 14.3 - Prob. 2ECh. 14.3 - Euler and Hamilton Circuits In Exercises 3 and 4,...Ch. 14.3 - Euler and Hamilton Circuits In Exercises 3 and 4,...Ch. 14.3 - Hamilton Circuits In Exercises 5-10, determine...Ch. 14.3 - Hamilton Circuits In Exercises 5-10, determine...Ch. 14.3 - Hamilton Circuits In Exercises 5-10, determine...Ch. 14.3 - Hamilton Circuits In Exercises 5-10, determine...Ch. 14.3 - Hamilton Circuits In Exercises 5-10, determine...Ch. 14.3 - Hamilton Circuits In Exercises 5-10, determine...Ch. 14.3 - Prob. 11ECh. 14.3 - Prob. 12ECh. 14.3 - Prob. 13ECh. 14.3 - Decide whether each statement is true or false. If...Ch. 14.3 - Hamilton and Euler Circuits In Exercises 15-20,...Ch. 14.3 - Hamilton and Euler Circuits In Exercises 15-20,...Ch. 14.3 - Hamilton and Euler Circuits In Exercises 15-20,...Ch. 14.3 - Hamilton and Euler Circuits In Exercises 15-20,...Ch. 14.3 - Hamilton and Euler Circuits In Exercises 15-20,...Ch. 14.3 - Hamilton and Euler Circuits In Exercises 15-20,...Ch. 14.3 - FactorialsIn Exercises 21-24, use a calculator, if...Ch. 14.3 - Factorials In Exercises 21-24, use a calculator,...Ch. 14.3 - Factorials In Exercises 21-24, use a calculator,...Ch. 14.3 - Prob. 24ECh. 14.3 - Hamilton Circuit In Exercises 25-28, determine how...Ch. 14.3 - Prob. 26ECh. 14.3 - Prob. 27ECh. 14.3 - Prob. 28ECh. 14.3 - List all Hamilton circuits in the graph that start...Ch. 14.3 - Prob. 30ECh. 14.3 - Prob. 31ECh. 14.3 - Prob. 32ECh. 14.3 - Prob. 33ECh. 14.3 - Prob. 34ECh. 14.3 - Prob. 35ECh. 14.3 - Prob. 36ECh. 14.3 - Prob. 37ECh. 14.3 - Brute Force Algorithm In Exercises 38-41, use the...Ch. 14.3 - Brute Force Algorithm In Exercises 38-41, use the...Ch. 14.3 - Brute Force Algorithm In Exercises 38-41, use the...Ch. 14.3 - Brute Force Algorithm In Exercises 38-41, use the...Ch. 14.3 - Prob. 42ECh. 14.3 - Prob. 43ECh. 14.3 - Nearest Neighbor Algorithm In Exercises 42-44, use...Ch. 14.3 - 45. Nearest Neighbor Algorithm Refer to the...Ch. 14.3 - Prob. 46ECh. 14.3 - Prob. 47ECh. 14.3 - Prob. 48ECh. 14.3 - Prob. 49ECh. 14.3 - Hamilton Circuits In Exercises 47-50, find all...Ch. 14.3 - Traveling Salesman Problem The diagram represents...Ch. 14.3 - Prob. 52ECh. 14.3 - The Icosian Game The graph below shows the Icosian...Ch. 14.3 - Prob. 54ECh. 14.3 - Dirac's Theorem Paul A. M. Dirac proved the...Ch. 14.4 - Prob. 1ECh. 14.4 - Prob. 2ECh. 14.4 - Prob. 3ECh. 14.4 - Prob. 4ECh. 14.4 - Prob. 5ECh. 14.4 - Prob. 6ECh. 14.4 - Prob. 7ECh. 14.4 - Prob. 8ECh. 14.4 - Prob. 9ECh. 14.4 - Prob. 10ECh. 14.4 - Prob. 11ECh. 14.4 - Tree or Not a Tree? In Exercises 11-13, determine...Ch. 14.4 - Prob. 13ECh. 14.4 - Prob. 14ECh. 14.4 - Trees and Cut Edges In Exercises 14-17, determine...Ch. 14.4 - Trees and Cut Edges In Exercises 14-17, determine...Ch. 14.4 - Prob. 17ECh. 14.4 - Prob. 18ECh. 14.4 - Prob. 19ECh. 14.4 - Prob. 20ECh. 14.4 - Prob. 21ECh. 14.4 - Prob. 22ECh. 14.4 - Prob. 23ECh. 14.4 - Prob. 24ECh. 14.4 - Prob. 25ECh. 14.4 - Prob. 26ECh. 14.4 - Prob. 27ECh. 14.4 - Prob. 28ECh. 14.4 - Prob. 29ECh. 14.4 - Prob. 30ECh. 14.4 - Prob. 31ECh. 14.4 - Prob. 32ECh. 14.4 - Prob. 33ECh. 14.4 - Town Water Distribution A town council is planning...Ch. 14.4 - Prob. 35ECh. 14.4 - Prob. 36ECh. 14.4 - Prob. 37ECh. 14.4 - Prob. 38ECh. 14.4 - Prob. 39ECh. 14.4 - For Exercise 34
Trees, Edges, and Vertices Work...Ch. 14.4 - 41. Suppose we have a tree with 10 vertices.
(a)...Ch. 14.4 - Prob. 42ECh. 14.4 - Prob. 43ECh. 14.4 - 44. Design of a Garden Maria has 12 vegetable and...Ch. 14.4 - Prob. 45ECh. 14.4 - Prob. 46ECh. 14.4 - Prob. 47ECh. 14.4 - Prob. 48ECh. 14.4 - Prob. 49ECh. 14.4 - Prob. 50ECh. 14.4 - Prob. 51ECh. 14.4 - Prob. 52ECh. 14.4 - Prob. 53ECh. 14.4 - Prob. 54ECh. 14.4 - Prob. 55ECh. 14.4 - Vertex/Edge Relationship In this exercise, we...Ch. 14 - Basic Concepts In Exercises 1-5, refer to the...Ch. 14 - Basic Concepts In Exercises 1-5, refer to the...Ch. 14 - Prob. 3TCh. 14 - Prob. 4TCh. 14 - Prob. 5TCh. 14 - Prob. 6TCh. 14 - Prob. 7TCh. 14 - Prob. 8TCh. 14 - Planning for Dinner Julia is planning to invite...Ch. 14 - Prob. 10TCh. 14 - Prob. 11TCh. 14 - Prob. 12TCh. 14 - Prob. 13TCh. 14 - Scheduling Exams A teacher at a high school must...Ch. 14 - Prob. 15TCh. 14 - Prob. 16TCh. 14 - Prob. 17TCh. 14 - Prob. 18TCh. 14 - Prob. 19TCh. 14 - Prob. 20TCh. 14 - Prob. 21TCh. 14 - Prob. 22TCh. 14 - Prob. 23TCh. 14 - Prob. 24TCh. 14 - Prob. 25TCh. 14 - 26. Nonisomorphic Trees Draw three nonisomorphic...Ch. 14 - Prob. 27TCh. 14 - Prob. 28TCh. 14 - Prob. 29TCh. 14 - Prob. 30TCh. 14 - Prob. 31TCh. 14 - Prob. 32T
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