Discrete Mathematics
5th Edition
ISBN: 9780134689562
Author: Dossey, John A.
Publisher: Pearson,
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Chapter 4.5, Problem 15E
To determine
To list: The vertices which have directed edges from vertex A and directed to the vertex A, the in and out degree of A.
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Please provide the solution for the attached image in detailed.
5
Obtain by multiplying matrices the composite coordinate transformation of two transformations, first
x' = (x + y√2+ z)/2
followed by
y' =
(x√√2-2√2)/2
z' = (-x+y√2-2)/2
x"
=
y"
2"
=
(x'√√2+2'√√2)/2
(-x'y'√√2+)/2
(x'y' √√2-z)/2.
20 km, because
GISS
Worksheet 10
Jesse runs a small business selling and delivering mealie meal to the spaza shops.
He charges a fixed rate of R80, 00 for delivery and then R15, 50 for each packet of
mealle meal he delivers. The table below helps him to calculate what to charge
his customers.
10
20
30
40
50
Packets of mealie
meal (m)
Total costs in Rands
80
235
390
545
700
855
(c)
10.1.
Define the following terms:
10.1.1. Independent Variables
10.1.2. Dependent Variables
10.2.
10.3.
10.4.
10.5.
Determine the independent and dependent variables.
Are the variables in this scenario discrete or continuous values? Explain
What shape do you expect the graph to be? Why?
Draw a graph on the graph provided to represent the information in the
table above.
TOTAL COST OF PACKETS OF MEALIE MEAL
900
800
700
600
COST (R)
500
400
300
200
100
0
10
20
30
40
60
NUMBER OF PACKETS OF MEALIE MEAL
Chapter 4 Solutions
Discrete Mathematics
Ch. 4.1 - In Exercises 1–4, list the set of edges and set of...Ch. 4.1 - Prob. 2ECh. 4.1 - Prob. 3ECh. 4.1 - Prob. 4ECh. 4.1 - Prob. 5ECh. 4.1 - In Exercises 5–8, draw a diagram representing the...Ch. 4.1 - Prob. 7ECh. 4.1 - In Exercises 5–8, draw a diagram representing the...Ch. 4.1 - Prob. 9ECh. 4.1 - In Exercises 9–14, determine whether a graph is...
Ch. 4.1 - Prob. 11ECh. 4.1 - Prob. 12ECh. 4.1 - Prob. 13ECh. 4.1 - Prob. 14ECh. 4.1 - Prob. 15ECh. 4.1 - Prob. 16ECh. 4.1 - Prob. 17ECh. 4.1 - Draw the graph with ν = {1, 2, … , 10} as its set...Ch. 4.1 - Prob. 19ECh. 4.1 - Prob. 20ECh. 4.1 - Prob. 21ECh. 4.1 - Show that there are an even number of vertices...Ch. 4.1 - Prob. 23ECh. 4.1 - Prob. 24ECh. 4.1 - Prob. 25ECh. 4.1 - Prob. 26ECh. 4.1 - Prob. 27ECh. 4.1 - In Exercises 26–29, find the adjacency matrix and...Ch. 4.1 - Prob. 29ECh. 4.1 - In Exercises 30 and 31, construct the graph for...Ch. 4.1 - Prob. 31ECh. 4.1 - In Exercises 32 and 33, construct the graph for...Ch. 4.1 - Prob. 33ECh. 4.1 - Prob. 34ECh. 4.1 - Prob. 35ECh. 4.1 - In Exercises 35-37, can each matrix be an...Ch. 4.1 - Prob. 37ECh. 4.1 - Prob. 38ECh. 4.1 - Prob. 39ECh. 4.1 - Prob. 40ECh. 4.1 - Prob. 41ECh. 4.1 - Are the pairs of graphs in (a), (b), and (c)...Ch. 4.1 - Are the pairs of graphs in (a), (b), and (c)...Ch. 4.1 - Draw all the non isomorphic graphs with three...Ch. 4.1 - Prob. 45ECh. 4.1 - Draw all the nonisomorphic graphs with five...Ch. 4.1 - Prob. 47ECh. 4.1 - Prob. 48ECh. 4.1 - Prob. 49ECh. 4.1 - Suppose a graph has n vertices, each with degree...Ch. 4.1 - Prob. 51ECh. 4.1 - Prob. 52ECh. 4.1 - Suppose Mr. and Mrs. Lewis attended a bridge party...Ch. 4.1 - Prove that if a graph has at least two vertices,...Ch. 4.2 - In Exercises 1–4, determine whether the multigraph...Ch. 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 - Prob. 9ECh. 4.2 - In Exercises 9 and 10, perform the following...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 - In Exercises 18–23, determine whether the...Ch. 4.2 - Prob. 19ECh. 4.2 - In Exercises 18–23, determine whether the...Ch. 4.2 - Prob. 21ECh. 4.2 - In Exercises 18–23, determine whether the...Ch. 4.2 - Prob. 23ECh. 4.2 - In Exercises 24–29, determine whether the...Ch. 4.2 - Prob. 25ECh. 4.2 - Prob. 26ECh. 4.2 - Prob. 27ECh. 4.2 - Prob. 28ECh. 4.2 - Prob. 29ECh. 4.2 - Prob. 30ECh. 4.2 - Prob. 31ECh. 4.2 - Prob. 32ECh. 4.2 - Prob. 33ECh. 4.2 - Prob. 34ECh. 4.2 - Prob. 35ECh. 4.2 - Prob. 36ECh. 4.2 - Prob. 37ECh. 4.2 - An old childhood game asks children to trace a...Ch. 4.2 - Prob. 39ECh. 4.2 - In 1859, Sir William Rowan Hamilton, a famous...Ch. 4.2 - Give examples of connected graphs satisfying each...Ch. 4.2 - Prob. 42ECh. 4.2 - Prob. 43ECh. 4.2 - Prob. 44ECh. 4.2 - Prob. 45ECh. 4.2 - Prob. 46ECh. 4.2 - Prob. 47ECh. 4.2 - Prob. 48ECh. 4.2 - Prob. 49ECh. 4.2 - Are the following two graphs isomorphic? Justify...Ch. 4.2 - Prob. 51ECh. 4.2 - A bipartite graph is a graph in which the vertices...Ch. 4.2 - Prob. 53ECh. 4.2 - Prob. 54ECh. 4.2 - Prob. 55ECh. 4.2 - Prob. 56ECh. 4.2 - Prob. 57ECh. 4.2 - Prob. 58ECh. 4.2 - Prob. 59ECh. 4.2 - Prob. 60ECh. 4.2 - Prob. 61ECh. 4.2 - Prob. 62ECh. 4.2 - Prob. 64ECh. 4.2 - Prob. 65ECh. 4.3 - In Exercises 1–4, use the breadth-first search...Ch. 4.3 - In Exercises 1–4, use the breadth-first search...Ch. 4.3 - Prob. 3ECh. 4.3 - In Exercises 1–4, use the breadth-first search...Ch. 4.3 - In Exercises 5–8, determine the distance from S to...Ch. 4.3 - In Exercises 5–8, determine the distance from S to...Ch. 4.3 - Prob. 7ECh. 4.3 - Prob. 8ECh. 4.3 - Prob. 9ECh. 4.3 - Prob. 10ECh. 4.3 - Prob. 11ECh. 4.3 - Prob. 12ECh. 4.3 - Prob. 13ECh. 4.3 - Prob. 14ECh. 4.3 - For the following graph, determine the number of...Ch. 4.3 - Prob. 16ECh. 4.3 - Prob. 17ECh. 4.3 - Prob. 18ECh. 4.3 - Prob. 19ECh. 4.3 - Prob. 20ECh. 4.3 - Prob. 21ECh. 4.3 - Prob. 22ECh. 4.3 - Prob. 23ECh. 4.4 - In Exercises 1–8, find the chromatic number of the...Ch. 4.4 - Prob. 2ECh. 4.4 - Prob. 3ECh. 4.4 - Prob. 4ECh. 4.4 - Prob. 5ECh. 4.4 - Prob. 6ECh. 4.4 - Prob. 7ECh. 4.4 - Prob. 8ECh. 4.4 - Prob. 9ECh. 4.4 - Prob. 10ECh. 4.4 - Prob. 11ECh. 4.4 - It might be supposed that if a graph has a large...Ch. 4.4 - Prob. 13ECh. 4.4 - Prob. 15ECh. 4.4 - Prob. 16ECh. 4.4 - Prob. 17ECh. 4.4 - Prob. 18ECh. 4.4 - Prob. 19ECh. 4.4 - Suppose is a graph with three vertices. How many...Ch. 4.4 - Prob. 21ECh. 4.4 - Prob. 22ECh. 4.4 - Prob. 23ECh. 4.4 - Prob. 24ECh. 4.4 - Prob. 25ECh. 4.4 - Prob. 26ECh. 4.4 - Prob. 27ECh. 4.4 - Prob. 28ECh. 4.4 - Prob. 29ECh. 4.4 - Prob. 30ECh. 4.4 - Prob. 31ECh. 4.4 - Prob. 32ECh. 4.4 - Prob. 33ECh. 4.4 - Show that it is possible to assign one of the...Ch. 4.4 - Prob. 35ECh. 4.4 - Prove Theorem 4.9 by mathematical induction on the...Ch. 4.4 - Suppose that each vertex of a graph is such that...Ch. 4.5 - In Exercises 1–4, list the vertices and directed...Ch. 4.5 - Prob. 2ECh. 4.5 - Prob. 3ECh. 4.5 - Prob. 4ECh. 4.5 - Prob. 5ECh. 4.5 - Prob. 6ECh. 4.5 - Prob. 7ECh. 4.5 - Prob. 8ECh. 4.5 - Prob. 9ECh. 4.5 - Prob. 10ECh. 4.5 - Prob. 11ECh. 4.5 - Prob. 12ECh. 4.5 - Prob. 13ECh. 4.5 - Prob. 14ECh. 4.5 - Prob. 15ECh. 4.5 - Prob. 16ECh. 4.5 - Prob. 17ECh. 4.5 - Prob. 18ECh. 4.5 - Prob. 19ECh. 4.5 - Prob. 20ECh. 4.5 - Prob. 21ECh. 4.5 - Prob. 22ECh. 4.5 - Prob. 23ECh. 4.5 - Prob. 24ECh. 4.5 - Prob. 25ECh. 4.5 - Prob. 26ECh. 4.5 - Prob. 27ECh. 4.5 - Prob. 28ECh. 4.5 - Prob. 29ECh. 4.5 - Prob. 30ECh. 4.5 - Prob. 31ECh. 4.5 - Prob. 32ECh. 4.5 - Prob. 33ECh. 4.5 - Prob. 34ECh. 4.5 - Prob. 35ECh. 4.5 - Prob. 36ECh. 4.5 - Prob. 37ECh. 4.5 - Prob. 39ECh. 4.5 - Prob. 40ECh. 4.5 - Prob. 41ECh. 4.5 - Prob. 42ECh. 4.5 - Prob. 43ECh. 4.5 - Prob. 44ECh. 4.5 - Prob. 45ECh. 4.5 - Prob. 46ECh. 4.5 - Prob. 47ECh. 4.5 - Prob. 48ECh. 4.5 - Prob. 49ECh. 4.5 - Prob. 51ECh. 4.5 - Prob. 52ECh. 4.5 - Prob. 53ECh. 4.5 - Prob. 54ECh. 4.5 - Prob. 55ECh. 4.5 - Prob. 56ECh. 4.5 - Prob. 57ECh. 4.5 - Prob. 58ECh. 4.5 - Prob. 59ECh. 4.5 - Prob. 60ECh. 4.5 - Write a breadth-first search algorithm for...Ch. 4.5 - Prob. 62ECh. 4.5 - Prob. 63ECh. 4.5 - Prob. 64ECh. 4.5 - Prob. 65ECh. 4.5 - Prob. 66ECh. 4.5 - Prob. 67ECh. 4.5 - In Exercises 67–70, determine the distance from S...Ch. 4.5 - In Exercises 67–70, determine the distance from S...Ch. 4.5 - Prob. 70ECh. 4.5 - Prob. 71ECh. 4.5 - Prob. 72ECh. 4.5 - Prob. 73ECh. 4.5 - Prob. 74ECh. 4.5 - Prob. 75ECh. 4.5 - Determine whether the following pairs of directed...Ch. 4.5 - Determine whether the following pairs of directed...Ch. 4.5 - Prob. 78ECh. 4.5 - Prob. 79ECh. 4.5 - Prob. 80ECh. 4.5 - Prob. 82ECh. 4.5 - Prob. 83ECh. 4.5 - Prob. 84ECh. 4 - Prob. 1SECh. 4 - Prob. 2SECh. 4 - Prob. 3SECh. 4 - Prob. 4SECh. 4 - Prob. 5SECh. 4 - Prob. 6SECh. 4 - Prob. 7SECh. 4 - Prob. 8SECh. 4 - Prob. 9SECh. 4 - Prob. 10SECh. 4 - Prob. 11SECh. 4 - Prob. 12SECh. 4 - Prob. 13SECh. 4 - Prob. 14SECh. 4 - Is the property “is connected” a graph isomorphism...Ch. 4 - Prob. 16SECh. 4 - Prob. 17SECh. 4 - Prob. 18SECh. 4 - Prob. 19SECh. 4 - Prob. 20SECh. 4 - Prob. 21SECh. 4 - Prob. 22SECh. 4 - Prob. 23SECh. 4 - Prob. 24SECh. 4 - Prob. 25SECh. 4 - Prob. 26SECh. 4 - Prob. 28SECh. 4 - Prob. 29SECh. 4 - Prob. 30SECh. 4 - Prob. 31SECh. 4 - Prob. 32SECh. 4 - Prob. 34SECh. 4 - Prob. 35SECh. 4 - Prob. 36SECh. 4 - Prob. 37SECh. 4 - Prob. 38SECh. 4 - Prob. 39SECh. 4 - Prob. 40SECh. 4 - Prob. 6CPCh. 4 - Prob. 9CPCh. 4 - Prob. 14CP
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