The Heart of Mathematics: An Invitation to Effective Thinking
4th Edition
ISBN: 9781118156599
Author: Edward B. Burger, Michael Starbird
Publisher: Wiley, John & Sons, Incorporated
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 6.3, Problem 11MS
Yet one more vertex (H). The graph shown is drawn to show that it’s planar (there are no edge crossings). Can you add a new vertex v to the graph and draw an edge from v to each of the original vertices without creating any edge crossings? Do it or explain why you can’t.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
A cable television company estimates that with x thousand subscribers, its monthly revenue and cost (in thousands of dollars) are given by the following equations.
R(x) = 45x - 0.24x2 C(x) = 257 + 13x
Compare the interest earned from #1 (where simple interest was used) to #5 (where compound interest was used). The principal, annual interest rate, and time were all the same; the only difference was that for #5, interest was compounded quarterly. Does the difference in interest earned make sense? Select one of the following statements. a. No, because more money should have been earned through simple interest than compound interest. b. Yes, because more money was earned through simple interest. For simple interest you earn interest on interest, not just on the amount of principal. c. No, because more money was earned through simple interest. For simple interest you earn interest on interest, not just on the amount of principal. d. Yes, because more money was earned when compounded quarterly. For compound interest you earn interest on interest, not just on the amount of principal.
Reduce the matrix
to reduced row-echelon form.
[3 2
-2-191
A = 3 -2 0 5
+
2 1 -2 -14
17
1
0
0
3
0
1
0
0
0
4
Chapter 6 Solutions
The Heart of Mathematics: An Invitation to Effective Thinking
Ch. 6.1 - Map maker, map maker make me a graph. Represent...Ch. 6.1 - Unabridged list. Represent cach landmass from...Ch. 6.1 - Will the walk work? Does your graph from...Ch. 6.1 - Walk around the house. Is it possibel to traverse...Ch. 6.1 - Walk the line. Does this graph above have an Euler...Ch. 6.1 - Walkabout. Does this graph have an Euler circuit?...Ch. 6.1 - Linking the loops. In this map, the following...Ch. 6.1 - Scenic drive. (S) Here is a map of Rockystone...Ch. 6.1 - Under-edged. (H) Does this graph have an Euler...Ch. 6.1 - No man is an island. The country of Pelago...
Ch. 6.1 - Path-o-rama. For each graph below, determine if...Ch. 6.1 - Walk around the block. Create a graph of the...Ch. 6.1 - Walking the dogs. Your dogs, Abbey and Bear, love...Ch. 6.1 - Delivery query. The next time you see a postal...Ch. 6.1 - Snow job. (ExH) Shown here is a map of the tiny...Ch. 6.1 - Special delivery. (ExH) Julia is the letter...Ch. 6.1 - Draw this old house. Suppose you wanted to trace...Ch. 6.1 - Path of no return. Consider this map showing a...Ch. 6.1 - Without a trace. Is it possibel to trace out...Ch. 6.1 - New Euler. In the three previous Mindscapes, you...Ch. 6.1 - New edge—new circuit. Look at the graph for...Ch. 6.1 - New edge—new path. Review your work for...Ch. 6.1 - Path to proof. Suppose you have a connected graph...Ch. 6.1 - No Euler no how. Look at graph (a) for Mindscape...Ch. 6.1 - Degree day. (S) For cach graph below, determine...Ch. 6.1 - degrees of proof. Review your work for Mindscape...Ch. 6.1 - Degrees in sequence. Can you draw a graph that has...Ch. 6.1 - Even Steven. Review your work in Mindscape 28 to...Ch. 6.1 - Little League lesson. (H) You are in charge of...Ch. 6.1 - With a group of folks. In a small group, discuss...Ch. 6.1 - Power beyond the mathematics. Provide several...Ch. 6.1 - Here we celebrate the power of algebra as a...Ch. 6.1 - Here we celebrate the power of algebra as a...Ch. 6.1 - Here we celebrate the power of algebra as a...Ch. 6.1 - Here we celebrate the power of algebra as a...Ch. 6.1 - Here we celebrate the power of algebra as a...Ch. 6.2 - What a character! What expression gives the Euler...Ch. 6.2 - Count, then verify. What are the values of V, E,...Ch. 6.2 - Sneeze, then verify. Look at an unopened tissue...Ch. 6.2 - Blow, then verify. Inflate a ballon and use a...Ch. 6.2 - Add one. Find the values V, E, and F for the graph...Ch. 6.2 - Bowling. What is the Euler Characteristic of the...Ch. 6.2 - Making change. We begin with the graph pictured at...Ch. 6.2 - Making a point. Take a connected graph and add a...Ch. 6.2 - On the edge (H). Is it possible to add an edge to...Ch. 6.2 - Soap films. Consider the following sequence of...Ch. 6.2 - Dualing. What is the relationship between the...Ch. 6.2 - Prob. 12MSCh. 6.2 - Lots of separation. Suppose we are told that a...Ch. 6.2 - Prob. 14MSCh. 6.2 - Psychic readings. Someone is thinking of a...Ch. 6.2 - Prob. 16MSCh. 6.2 - Prob. 17MSCh. 6.2 - Circular reasoning. Create a connected graph as...Ch. 6.2 - Prob. 19MSCh. 6.2 - More circles. Consider the sphere described in...Ch. 6.2 - In the rough (S). Count the number of facets,...Ch. 6.2 - Cutting corners (H). The following collection of...Ch. 6.2 - Stellar. The following collection of pictures...Ch. 6.2 - A torus graph (ExH). The Euler Characteristic...Ch. 6.2 - Regular unfolding. Each graph below represents...Ch. 6.2 - A tale of two graphs. Suppose we draw a graph that...Ch. 6.2 - Two graph conjectures (S). Can you conjecture a...Ch. 6.2 - Lots of graphs conjecture. Can you conjecture a...Ch. 6.2 - Torus count. Three hollowed, triangular prisms...Ch. 6.2 - Torus two count (H). Carefully count the number of...Ch. 6.2 - Torus many count. Using the preceding calculations...Ch. 6.2 - Prob. 32MSCh. 6.2 - Tell the truth. Someone said that she made a...Ch. 6.2 - No sphere. Suppose we have a sphere built out of...Ch. 6.2 - Soccer ball. A soccer ball is made of pentagons...Ch. 6.2 - Klein bottle. Using the diagram here for building...Ch. 6.2 - Not many neighbors. Show that every map has at...Ch. 6.2 - Infinite edges. Suppose we consider a conn ected...Ch. 6.2 - Here we celebrate the power of algebra as a...Ch. 6.2 - Prob. 44MSCh. 6.2 - Prob. 45MSCh. 6.2 - Here we celebrate the power of algebra as a...Ch. 6.2 - Here we celebrate the power of algebra as a...Ch. 6.3 - Dont be cross. Here is a drawing of a graph with...Ch. 6.3 - De Plane! De Plane! (S) Is the graph given in...Ch. 6.3 - Countdown (H). For the graph drawing shown, count...Ch. 6.3 - Prob. 4MSCh. 6.3 - Criss-Cross. Is it possible to redraw the graph...Ch. 6.3 - Dont cross in the edge. Each of the graphs drawn...Ch. 6.3 - Hot crossed buns. Each of the graphs drawn below...Ch. 6.3 - Prob. 8MSCh. 6.3 - Spider on a mirror. Is it possible to redraw the...Ch. 6.3 - One more vertex. The graph here is drawn to show...Ch. 6.3 - Yet one more vertex (H). The graph shown is drawn...Ch. 6.3 - Familiar freckles. Is it possible to redraw the...Ch. 6.3 - Remind you of anyone you know? Is it possible to...Ch. 6.3 - Final countdown. For this graph drawing, count the...Ch. 6.3 - Euler check-up. Use your answer to the previous...Ch. 6.3 - Euler second opinion. For the graph drawing shown...Ch. 6.3 - Prob. 17MSCh. 6.3 - Prob. 18MSCh. 6.3 - A colorful museum. This figure shows the floor...Ch. 6.3 - Limit of 5. Start drawing a planar graph. Keep...Ch. 6.3 - Starring the hexagon. Is it possible to redraw...Ch. 6.3 - Prob. 22MSCh. 6.3 - Prob. 23MSCh. 6.3 - Getting greedy. (H) Suppose you are asked to color...Ch. 6.3 - Stingy rather than greedy. By coloring the...Ch. 6.3 - Getting more colorful. Graphs dont have to be...Ch. 6.3 - Prob. 27MSCh. 6.3 - Prob. 28MSCh. 6.3 - Chromatically applied. There are eight radio...Ch. 6.3 - Prob. 30MSCh. 6.3 - Personal perspectives. Write a short essay...Ch. 6.3 - Here we celebrate the power of algebra as a...Ch. 6.3 - Here we celebrate the power of algebra as a...Ch. 6.3 - Prob. 37MSCh. 6.3 - Here we celebrate the power of algebra as a...Ch. 6.3 - Here we celebrate the power of algebra as a...Ch. 6.4 - Up close and personal. Create a graph to model...Ch. 6.4 - Network lookout. Find an examle of a network...Ch. 6.4 - Prob. 3MSCh. 6.4 - Hamiltonian holiday (S). You are interning for a...Ch. 6.4 - Home style. Create a graph to model the rooms in...Ch. 6.4 - Six degrees or less. Suppose this graph is a model...Ch. 6.4 - Degrees of you. Find ten willing friends or...Ch. 6.4 - Campus shortcut. Find a map of your campus and...Ch. 6.4 - Arborist lesson. Which of the graphs below are...Ch. 6.4 - Prob. 10MSCh. 6.4 - Prob. 11MSCh. 6.4 - Prob. 12MSCh. 6.4 - Prob. 13MSCh. 6.4 - Prob. 14MSCh. 6.4 - Prob. 15MSCh. 6.4 - Hamilton Study. Look at the graph you drew to...Ch. 6.4 - Business trip redux. Look back in the section and...Ch. 6.4 - Handling Hamiltons. For each graph below, find a...Ch. 6.4 - Road trip. You are checking out gradua te programs...Ch. 6.4 - Back to Hatties trip. Look back in this section...Ch. 6.4 - Solve the Icosian Game. Find a Hamiltonian circuit...Ch. 6.4 - Hunt for Hamilton (S). A large island country has...Ch. 6.4 - Has no Hamilton. Give some characteristics that...Ch. 6.4 - Cubing Hamilton (ExH). Can you find a Hamihonian...Ch. 6.4 - Hamiltonian path. A Hamiltonian path is a path in...Ch. 6.4 - Sorry, no path. Give some characteristics that...Ch. 6.4 - Prob. 27MSCh. 6.4 - Prob. 28MSCh. 6.4 - Prob. 29MSCh. 6.4 - Prob. 30MSCh. 6.4 - Edge count. Look at all the trees you drew in the...Ch. 6.4 - Personal perspecthes. Write a short essay...Ch. 6.4 - Prob. 33MSCh. 6.4 - Prob. 34MSCh. 6.4 - Dollars and cents. Your spanning tree has three...Ch. 6.4 - Adding up. Your spanning tree has four edges with...Ch. 6.4 - Prob. 38MSCh. 6.4 - Vertex search (H). Your graph has a Hamiltonian...Ch. 6.4 - Binary gossip tree. You told a secret to two of...
Additional Math Textbook Solutions
Find more solutions based on key concepts
In hypothesis testing, the common level of significance is =0.05. Some might argue for a level of significance ...
Basic Business Statistics, Student Value Edition
CHECK POINT 1 In a survey on musical tastes, respondents were asked: Do you listed to classical music? Do you l...
Thinking Mathematically (6th Edition)
Assessment 71A Write each of the following as a sum in expanded place value form. a. 0.023 b. 206.06 c. 312.010...
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
43-44. Energy Savings. For these questions, assume 365 days in a year.
44. Suppose you have a clothes dryer t...
Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
Show that the mean, variance, and mgf of the uniform distribution are as given in this section. Also verify tha...
Probability And Statistical Inference (10th Edition)
Fill in each blank so that the resulting statement is true. If n is a counting number, bn, read ______, indicat...
College Algebra (7th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- Compare and contrast the simple and compound interest formulas. Which one of the following statements is correct? a. Simple interest and compound interest formulas both yield principal plus interest, so you must subtract the principal to get the amount of interest. b. Simple interest formula yields principal plus interest, so you must subtract the principal to get the amount of interest; Compound interest formula yields only interest, which you must add to the principal to get the final amount. c. Simple interest formula yields only interest, which you must add to the principal to get the final amount; Compound interest formula yields principal plus interest, so you must subtract the principal to get the amount of interest. d. Simple interest and compound interest formulas both yield only interest, which you must add to the principal to get the final amount.arrow_forwardSara would like to go on a vacation in 5 years and she expects her total costs to be $3000. If she invests $2500 into a savings account for those 5 years at 8% interest, compounding semi-annually, how much money will she have? Round your answer to the nearest cent. Show you work. Will she be able to go on vacation? Why or why not?arrow_forwardIf $8000 is deposited into an account earning simple interest at an annual interest rate of 4% for 10 years, howmuch interest was earned? Show you work.arrow_forward
- Why is this proof incorrect? State what statement and/or reason is incorrect and why. Given: Overline OR is congruent to overline OQ, angle N is congruent to angle PProve: Angle 3 is congruent to angle 5 Why is this proof incorrect? Statements Reasons 1. Overline OR is congruent to overline OQ, angle N is congruent to angle P 1. Given 2. Overline ON is congruent to overline OP 2. Converse of the Isosceles Triangle Theorem 3. Triangle ONR is congruent to triangle OPQ 3. SAS 4. Angle 3 is congruent to angle 5 4. CPCTCarrow_forwardx³-343 If k(x) = x-7 complete the table and use the results to find lim k(x). X-7 x 6.9 6.99 6.999 7.001 7.01 7.1 k(x) Complete the table. X 6.9 6.99 6.999 7.001 7.01 7.1 k(x) (Round to three decimal places as needed.)arrow_forward(3) (4 points) Given three vectors a, b, and c, suppose: |bx c = 2 |a|=√√8 • The angle between a and b xc is 0 = 135º. . Calculate the volume a (bxc) of the parallelepiped spanned by the three vectors.arrow_forward
- Calculate these limits. If the limit is ∞ or -∞, write infinity or-infinity. If the limit does not exist, write DNE: Hint: Remember the first thing you check when you are looking at a limit of a quotient is the limit value of the denominator. 1. If the denominator does not go to 0, you should be able to right down the answer immediately. 2. If the denominator goes to 0, but the numerator does not, you will have to check the sign (±) of the quotient, from both sides if the limit is not one-sided. 3. If both the numerator and the denominator go to 0, you have to do the algebraic trick of rationalizing. So, group your limits into these three forms and work with them one group at a time. (a) lim t-pi/2 sint-√ sin 2t+14cos ² t 7 2 2 2cos t (b) lim sint + sin 2t+14cos = ∞ t-pi/2 2 2cos t (c) lim cost-√sin 2t+14cos² t = t-pi/2 2cos t (d) lim t→pi/2 cost+√ sin t + 14cos 2cos ² t = ∞ (e) lim sint-v sin 2 t + 14cos = 0 t-pi/2 (f) lim t-pi/2 sin t +√ sin 2sin 2 t 2 t + 14cos t 2sin t cost- (g)…arrow_forwardThink of this sheet of paper as the plane containing the vectors a = (1,1,0) and b = (2,0,0). Sketch the parallelogram P spanned by a and b. Which diagonal of P represents the vector a--b geometrically?arrow_forwardGiven: AABE ~ ACDE. Prove: AC bisects BD. Note: quadrilateral properties are not permitted in this proof. Step Statement Reason AABE ACDE Given 2 ZDEC ZAEB Vertical angles are congruent try Type of Statement A E B D Carrow_forward
- 10-2 Let A = 02-4 and b = 4 Denote the columns of A by a₁, a2, a3, and let W = Span {a1, a2, a̸3}. -4 6 5 - 35 a. Is b in {a1, a2, a3}? How many vectors are in {a₁, a₂, a3}? b. Is b in W? How many vectors are in W? c. Show that a2 is in W. [Hint: Row operations are unnecessary.] a. Is b in {a₁, a2, a3}? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. ○ A. No, b is not in {a₁, a2, 3} since it cannot be generated by a linear combination of a₁, a2, and a3. B. No, b is not in (a1, a2, a3} since b is not equal to a₁, a2, or a3. C. Yes, b is in (a1, a2, a3} since b = a (Type a whole number.) D. Yes, b is in (a1, a2, 3} since, although b is not equal to a₁, a2, or a3, it can be expressed as a linear combination of them. In particular, b = + + ☐ az. (Simplify your answers.)arrow_forward(1) (14 points) Let a = (-2, 10, -4) and b = (3, 1, 1). (a) (4 points) Using the dot product determine the angle between a and b. (b) (2 points) Determine the cross product vector axb. (c) (4 points) Calculate the area of the parallelogram spanned by a and b. Justify your answer. 1arrow_forward(d) (4 points) Think of this sheet of paper as the plane containing the vectors a = (1,1,0) and b = (2,0,0). Sketch the parallelogram P spanned by a and b. Which diagonal of P represents the vector ab geometrically? d be .dx adjarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Trigonometry (MindTap Course List)
Trigonometry
ISBN:9781337278461
Author:Ron Larson
Publisher:Cengage Learning
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Elementary Geometry For College Students, 7e
Geometry
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Cengage,
Graph Theory: Euler Paths and Euler Circuits; Author: Mathispower4u;https://www.youtube.com/watch?v=5M-m62qTR-s;License: Standard YouTube License, CC-BY
WALK,TRIAL,CIRCUIT,PATH,CYCLE IN GRAPH THEORY; Author: DIVVELA SRINIVASA RAO;https://www.youtube.com/watch?v=iYVltZtnAik;License: Standard YouTube License, CC-BY