Mathematical Applications for the Management, Life, and Social Sciences
12th Edition
ISBN: 9781337625340
Author: Ronald J. Harshbarger, James J. Reynolds
Publisher: Cengage Learning
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Chapter 2.5, Problem 3E
In Problems 1-8, determine whether the
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7. [10 marks]
Let G
=
(V,E) be a 3-connected graph. We prove that for every x, y, z Є V, there is a
cycle in G on which x, y, and z all lie.
(a) First prove that there are two internally disjoint xy-paths Po and P₁.
(b) If z is on either Po or P₁, then combining Po and P₁ produces a cycle on which
x, y, and z all lie. So assume that z is not on Po and not on P₁. Now prove that
there are three paths Qo, Q1, and Q2 such that:
⚫each Qi starts at z;
• each Qi ends at a vertex w; that is on Po or on P₁, where wo, w₁, and w₂ are
distinct;
the paths Qo, Q1, Q2 are disjoint from each other (except at the start vertex
2) and are disjoint from the paths Po and P₁ (except at the end vertices wo,
W1, and w₂).
(c) Use paths Po, P₁, Qo, Q1, and Q2 to prove that there is a cycle on which x, y, and
z all lie. (To do this, notice that two of the w; must be on the same Pj.)
Chapter 2 Solutions
Mathematical Applications for the Management, Life, and Social Sciences
Ch. 2.1 - The factoring method for solving a quadratic...Ch. 2.1 - Solve the following equations by factoring.
Ch. 2.1 - Prob. 3CPCh. 2.1 - Prob. 4CPCh. 2.1 - Prob. 1ECh. 2.1 - Prob. 2ECh. 2.1 - Prob. 3ECh. 2.1 - Prob. 4ECh. 2.1 - In Problems 5-14, solve each question by...Ch. 2.1 - Prob. 6E
Ch. 2.1 - In Problems 5-14, solve each question by...Ch. 2.1 - Prob. 8ECh. 2.1 - In Problems 5-14, solve each question by...Ch. 2.1 - Prob. 10ECh. 2.1 - In Problems 5-14, solve each question by...Ch. 2.1 - Prob. 12ECh. 2.1 - In Problems 5-14, solve each question by...Ch. 2.1 - Prob. 14ECh. 2.1 - In Problems 15-20, solve each equation using the...Ch. 2.1 - In Problems 15-20, solve each equation using the...Ch. 2.1 - In Problems 15-20, solve each equation using the...Ch. 2.1 - Prob. 18ECh. 2.1 - In Problems 15-20, solve each equation using the...Ch. 2.1 - Prob. 20ECh. 2.1 - In Problems 21-26, find the exact real solutions...Ch. 2.1 - Prob. 22ECh. 2.1 - Prob. 23ECh. 2.1 - Prob. 24ECh. 2.1 - In Problems 21-26, find the exact real solutions...Ch. 2.1 - In Problems 21-26, find the exact real solutions...Ch. 2.1 - In Problems 27-36, use any method to find the...Ch. 2.1 - In Problems 27-36, use any method to find the...Ch. 2.1 - In Problems 27-36, use any method to find the...Ch. 2.1 - Prob. 30ECh. 2.1 - Prob. 31ECh. 2.1 - Prob. 32ECh. 2.1 - In Problems 27-36, use any method to find the...Ch. 2.1 - Prob. 34ECh. 2.1 - Prob. 35ECh. 2.1 - Prob. 36ECh. 2.1 - Prob. 37ECh. 2.1 - Prob. 38ECh. 2.1 - In problems 37-42, solve each equation using a...Ch. 2.1 - Prob. 40ECh. 2.1 - In problems 37-42, solve each equation using a...Ch. 2.1 - Prob. 42ECh. 2.1 - Prob. 43ECh. 2.1 - Prob. 44ECh. 2.1 - In Problems 43-46, multiply both sides of the...Ch. 2.1 - Prob. 46ECh. 2.1 - Prob. 47ECh. 2.1 - Prob. 48ECh. 2.1 - Applications Profit If the profit from the sale of...Ch. 2.1 - Profit If the profit from the sale of x units of a...Ch. 2.1 - Profit Suppose the profit from the sale of x units...Ch. 2.1 - Profit Suppose the profit from the sale of x units...Ch. 2.1 - Flight of a ball If a ball is thrown upward at 96...Ch. 2.1 - Flight of a ball A tennis ball is thrown into the...Ch. 2.1 - Wind and pollution The amount of airborne...Ch. 2.1 - Drug sensitivity The sensitivity S to a drug is...Ch. 2.1 - 57. Corvette acceleration The time t, in seconds ,...Ch. 2.1 - 58.Consumer Price Index Using Social Security...Ch. 2.1 - 59. Marijuana use For the years since 2001 , the...Ch. 2.1 - Prob. 60ECh. 2.1 - 61. Percent profit Ace Jewelry Store sold a...Ch. 2.1 - Prob. 62ECh. 2.1 - 63. National health care Using data from 2002 and...Ch. 2.1 - 64. Velocity of blood Because of friction from the...Ch. 2.1 - 65. Body-heat loss The model for body-heat loss...Ch. 2.1 - 66. Depth of Fissure A fissure in the earth...Ch. 2.2 - Name the graph of a quadratic function.
Ch. 2.2 - (a) What is the coordinate of the vertex of ?
(b)...Ch. 2.2 - Prob. 3CPCh. 2.2 - Prob. 4CPCh. 2.2 - Prob. 5CPCh. 2.2 - In Problems 1-6,(a)find the vertex of the graph of...Ch. 2.2 - Prob. 2ECh. 2.2 - In Problems 1-6,(a) find the vertex of the graph...Ch. 2.2 - In Problem 1-6,(a)find the vertex of the graph of...Ch. 2.2 - In Problems 1-6,(a) find the vertex of the graph...Ch. 2.2 - In Problems 1-6,(a) find the vertex of the graph...Ch. 2.2 - In Problems 7-12,determine whether each...Ch. 2.2 - In Problems7-12,determine whether each functions...Ch. 2.2 - In Problems 7-12,determine whether each function’s...Ch. 2.2 - In Problem 7-12, determine whether each function’s...Ch. 2.2 - Prob. 11ECh. 2.2 - Prob. 12ECh. 2.2 - Prob. 13ECh. 2.2 - Prob. 14ECh. 2.2 - Prob. 15ECh. 2.2 - Prob. 16ECh. 2.2 - Prob. 17ECh. 2.2 - Prob. 18ECh. 2.2 - Prob. 19ECh. 2.2 - In Problems , graph each function with a graphing...Ch. 2.2 - Prob. 21ECh. 2.2 - In Problem 21 and 22, find the average rate of...Ch. 2.2 - In Problems , find the vertex and zeros and use...Ch. 2.2 - Prob. 24ECh. 2.2 - Prob. 25ECh. 2.2 - Prob. 26ECh. 2.2 - Prob. 27ECh. 2.2 - Prob. 28ECh. 2.2 - Prob. 29ECh. 2.2 - Prob. 30ECh. 2.2 - 31. Profit The monthly profit from the sale of x...Ch. 2.2 - 32. Profit The monthly profit from the sale of x...Ch. 2.2 - 33. Crop Yield The yield in bushels from a grove...Ch. 2.2 - 34. Stimulus-response One of the early results in...Ch. 2.2 - Drug Sensitivity The sensitivity S to a drug is...Ch. 2.2 - 36. Maximizing an enclosed area Iffeet of fence
...Ch. 2.2 - Photosynthesis The rate of photosynthesis R for a...Ch. 2.2 - 38. Projectiles A ball thrown vertically into the...Ch. 2.2 - Projectiles Two projectiles are shot into the air...Ch. 2.2 - Flow rates of water The speed at which water...Ch. 2.2 - Prob. 41ECh. 2.2 - Prob. 42ECh. 2.2 - Apartment rental The owner of an apartment...Ch. 2.2 - Revenue The owner of a skating rink rents the...Ch. 2.2 - Pension resources The Pension Benefit Guaranty...Ch. 2.2 - Prob. 46ECh. 2.2 - Health care costs per capita Rising health care...Ch. 2.2 - Women in the workforce Using U.S. Census Bureau...Ch. 2.2 - Prob. 49ECh. 2.2 - E-commerce Online sales in the United States are...Ch. 2.3 - The point of intersection of the revenue function...Ch. 2.3 - If and , finding the break-even points requires...Ch. 2.3 - Prob. 3CPCh. 2.3 - Prob. 4CPCh. 2.3 - BREAK-EVEN POINTS AND MAXIMIZATION
1.The total...Ch. 2.3 - 2. If a firm has the following cost and revenue...Ch. 2.3 - 3.If a company has total costs
And total revenues...Ch. 2.3 - 4. If total costs are and total revenues
Are ,find...Ch. 2.3 - Given that profit is P(x)=11.5x-0.1x2-150 And that...Ch. 2.3 - 6.If the profit function for a firm is given by...Ch. 2.3 - 7.Find the maximum revenue for the revenue...Ch. 2.3 - 8.Find the maximum revenue for the revenue...Ch. 2.3 - 9.If in a monopoly market the demand for a...Ch. 2.3 - 10.If in a monopoly market the demand for a...Ch. 2.3 - The profit function for a certain commodity is...Ch. 2.3 - The profit function for a firm making widgets is ...Ch. 2.3 - (a) Graph the profit function .
(b) Find the...Ch. 2.3 - Prob. 14ECh. 2.3 - (a) Form the profit function for the cost and...Ch. 2.3 - Prob. 16ECh. 2.3 - 17. Suppose a company has fixed costs of and...Ch. 2.3 - 18. Suppose a company has fixed costs of and...Ch. 2.3 - The following table gives the total revenues of ...Ch. 2.3 - The data in the table give sales revenue and costs...Ch. 2.3 - Prob. 21ECh. 2.3 - In Problems 22-24, a supply function and a demand...Ch. 2.3 - In Problems 22-24, a supply function and a demand...Ch. 2.3 - In Problems 22-24, a supply function and a demand...Ch. 2.3 - 25. If the supply function for a commodity is and...Ch. 2.3 - If the supply function for a commodity is and the...Ch. 2.3 - If the demand function for a commodity is given by...Ch. 2.3 - If the supply and demand functions for a commodity...Ch. 2.3 - If the supply and demand functions for a commodity...Ch. 2.3 - If the supply and demand functions for a certain...Ch. 2.3 - The supply function for a product is , while the...Ch. 2.3 - The supply and demand for a product are given by ...Ch. 2.3 - For the product in problem 31, if a $22 tax is...Ch. 2.3 - Prob. 34ECh. 2.4 - All constant functions [such as ] have graphs that...Ch. 2.4 - Which of the following are polynomial...Ch. 2.4 - A third-degree polynomial can have at most _____...Ch. 2.4 - Prob. 4CPCh. 2.4 - Prob. 5CPCh. 2.4 - In problems 1-12, match each of the function with...Ch. 2.4 - In problems 1-12, match each of the function with...Ch. 2.4 - In problems 1-12, match each of the function with...Ch. 2.4 - In problems 1-12, match each of the function with...Ch. 2.4 - In problems 1-12, match each of the function with...Ch. 2.4 - In problems 1-12, match each of the function with...Ch. 2.4 - In problems 1-12, match each of the function with...Ch. 2.4 - In problems 1-12, match each of the function with...Ch. 2.4 - In problems 1-12, match each of the function with...Ch. 2.4 - In problems 1-12, match each of the function with...Ch. 2.4 - In problems 1-12, match each of the function with...Ch. 2.4 - In problems 1-12, match each of the function with...Ch. 2.4 - In problem 13, decide whether each function whose...Ch. 2.4 - In problem 14, decide whether each function whose...Ch. 2.4 - In Problems 15-22, match each equation with the...Ch. 2.4 - In Problems 15-22, match each equation with the...Ch. 2.4 - In Problems 15-22, match each equation with the...Ch. 2.4 - In Problems 15-22, match each equation with the...Ch. 2.4 - In Problems 15-22, match each equation with the...Ch. 2.4 - In Problems 15-22, match each equation with the...Ch. 2.4 - In Problems 15-22, match each equation with the...Ch. 2.4 - In Problems 15-22, match each equation with the...Ch. 2.4 -
Ch. 2.4 - Prob. 24ECh. 2.4 - Prob. 25ECh. 2.4 - Prob. 26ECh. 2.4 - Prob. 27ECh. 2.4 - In Problems 23-28, graph the function.
28.
Ch. 2.4 - Prob. 29ECh. 2.4 - Prob. 30ECh. 2.4 - Prob. 31ECh. 2.4 - Prob. 32ECh. 2.4 - Prob. 33ECh. 2.4 - 34. If
find the following.
(b) (c) (d)...Ch. 2.4 - In Problems 35-40, (a) graph each function with a...Ch. 2.4 - In Problems 35-40, (a) graph each function with a...Ch. 2.4 - [Type here]
In Problems 35-40, (a) graph each...Ch. 2.4 - [Type here]
In Problems 35-40, (a) graph each...Ch. 2.4 - Prob. 39ECh. 2.4 - Prob. 40ECh. 2.4 - 41. Postal restrictions If a box with a square...Ch. 2.4 - Prob. 42ECh. 2.4 - Latin American Internet use Using data from and...Ch. 2.4 - Prob. 44ECh. 2.4 - 45. Pollution Suppose that the cost (in dollars)...Ch. 2.4 - Average cost If the weekly total cost of producing...Ch. 2.4 - Area If 100 feet of fence is to be used to enclose...Ch. 2.4 - Water usage The monthly charge for water in a...Ch. 2.4 - Prob. 49ECh. 2.4 - Commercial electrical usage The monthly charge (in...Ch. 2.4 - First-class postage The postage charged for...Ch. 2.4 - Income tax In a given year, the U.S. federal...Ch. 2.4 - Prob. 53ECh. 2.4 - Prob. 54ECh. 2.4 - Prob. 55ECh. 2.5 - The following table gives the Social Security...Ch. 2.5 - Prob. 2CPCh. 2.5 - Prob. 1ECh. 2.5 - Prob. 2ECh. 2.5 - In Problems 1-8, determine whether the scatter...Ch. 2.5 - In Problems 1-8, determine whether the scatter...Ch. 2.5 - Prob. 5ECh. 2.5 - In Problems 1-8, determine whether the scatter...Ch. 2.5 - Prob. 7ECh. 2.5 - Prob. 8ECh. 2.5 - Prob. 9ECh. 2.5 - Prob. 10ECh. 2.5 - In Problems 9- 16, find the equation of the...Ch. 2.5 - Prob. 12ECh. 2.5 - Prob. 13ECh. 2.5 - In Problems 9- 16, find the equation of the...Ch. 2.5 - Prob. 15ECh. 2.5 - In Problems 9- 16, find the equation of the...Ch. 2.5 - Prob. 17ECh. 2.5 - Prob. 18ECh. 2.5 - Prob. 19ECh. 2.5 - Prob. 20ECh. 2.5 - In Problems 17-24, (a) plot the given points, (b)...Ch. 2.5 - In Problems 17-24, (a) plot the given points, (b)...Ch. 2.5 - In Problems 17-24, (a) plot the given points, (b)...Ch. 2.5 - Prob. 24ECh. 2.5 - Prob. 25ECh. 2.5 - emission The following table gives the millions...Ch. 2.5 - Disposable income Disposable income is the amount...Ch. 2.5 - Diabetes As the following table shows ,...Ch. 2.5 - Wind chill The table gives the wind chill...Ch. 2.5 - Developing economies The developing economies’...Ch. 2.5 - Prob. 31ECh. 2.5 - Prob. 32ECh. 2.5 - Prob. 33ECh. 2.5 - Prob. 34ECh. 2.5 - Prob. 35ECh. 2.5 - National health care The table shows the national...Ch. 2.5 - Prob. 37ECh. 2.5 - Prob. 38ECh. 2 - In Problem 1-10, find the real solutions to each...Ch. 2 - In Problem 1-10, find the real solutions to each...Ch. 2 - In Problem 1-10, find the real solutions to each...Ch. 2 - Prob. 4RECh. 2 - Prob. 5RECh. 2 - Prob. 6RECh. 2 - Prob. 7RECh. 2 - Prob. 8RECh. 2 - Prob. 9RECh. 2 - Prob. 10RECh. 2 - Prob. 11RECh. 2 - Prob. 12RECh. 2 - Prob. 13RECh. 2 - Prob. 14RECh. 2 - Prob. 15RECh. 2 - Prob. 16RECh. 2 - Prob. 17RECh. 2 - Prob. 18RECh. 2 - Prob. 19RECh. 2 - Prob. 20RECh. 2 - Prob. 21RECh. 2 - For each function in Problems 19-24, find the...Ch. 2 - For each function in Problems 19-24, find the...Ch. 2 - Prob. 24RECh. 2 - Prob. 25RECh. 2 - [Type here]
In Problems 25-30, use a graphing...Ch. 2 - Prob. 27RECh. 2 - Prob. 28RECh. 2 - Prob. 29RECh. 2 - In Problems 25-30, use a graphing calculator to...Ch. 2 - The supply function for a product is 2pq10=0,...Ch. 2 - The supply and demand for a product are given by...Ch. 2 - 33.For the product in Problem 31,if a $22 tax is...Ch. 2 - Prob. 34RECh. 2 - In Problems 33-36, a graph is given. Use the graph...Ch. 2 - Prob. 36RECh. 2 - 37. Sketch a graph of each of the following basic...Ch. 2 - Prob. 38RECh. 2 - Prob. 39RECh. 2 - In Problems 40 and 41 ,graph each function.
40. ...Ch. 2 - Prob. 41RECh. 2 - Prob. 42RECh. 2 - Prob. 43RECh. 2 - Prob. 44RECh. 2 - Prob. 45RECh. 2 - Prob. 46RECh. 2 - Prob. 47RECh. 2 - Prob. 48RECh. 2 - 49.Profit The profit for a product is given by...Ch. 2 - Prob. 50RECh. 2 - Prob. 51RECh. 2 - Prob. 52RECh. 2 - Prob. 53RECh. 2 - 54. Market equilibrium
(a) Suppose the supply...Ch. 2 - Prob. 55RECh. 2 - Prob. 56RECh. 2 - Break-even points If total costs for a product are...Ch. 2 - Break-even points If total costs for a commodity...Ch. 2 - Prob. 59RECh. 2 - Prob. 60RECh. 2 - Maximum profit Given and , find the level of...Ch. 2 - Break-even and profit maximization A certain...Ch. 2 - 63. Diabetes The rise of adult diabetes in the...Ch. 2 - Prob. 64RECh. 2 - Prob. 65RECh. 2 - Prob. 66RECh. 2 - Prob. 67RECh. 2 - 68. Average annual wage The tables below give...Ch. 2 - Prob. 69RECh. 2 - Prob. 70RECh. 2 - Prob. 1TCh. 2 - Prob. 2TCh. 2 - Prob. 3TCh. 2 - Prob. 4TCh. 2 - Which of the following three graphs is the graph...Ch. 2 - Prob. 6TCh. 2 - Prob. 7TCh. 2 - Prob. 8TCh. 2 - Prob. 9TCh. 2 - Prob. 10TCh. 2 - Prob. 11TCh. 2 - Prob. 12TCh. 2 - Prob. 13TCh. 2 - Prob. 14TCh. 2 - Prob. 15TCh. 2 - Prob. 16TCh. 2 - Suppose the supply and demand functions for a...Ch. 2 - Suppose a company’s total cost a product is given...Ch. 2 - Prob. 19TCh. 2 - Prob. 20TCh. 2 - Prob. 1EAGP1Ch. 2 - Prob. 2EAGP1Ch. 2 - Prob. 3EAGP1Ch. 2 - Prob. 4EAGP1Ch. 2 - Prob. 5EAGP1Ch. 2 - Prob. 6EAGP1Ch. 2 - Prob. 7EAGP1Ch. 2 - Prob. 1EAGP2Ch. 2 - Prob. 2EAGP2Ch. 2 - Prob. 3EAGP2Ch. 2 - Prob. 4EAGP2Ch. 2 - Prob. 5EAGP2Ch. 2 - Prob. 6EAGP2Ch. 2 - Prob. 7EAGP2Ch. 2 - Prob. 8EAGP2
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