Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN: 9781337111348
Author: Bruce Crauder, Benny Evans, Alan Noell
Publisher: Cengage Learning
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Chapter 2.6, Problem 8E
Enclosing a field You have 16 miles of fence that you will use to enclose a rectangle field.
a. Draw a picture to show that you can arrange the 16 miles fence into a rectangle of width 3 miles and length 5 miles. What is the area of this rectangle?
b. Draw a picture to show that you can arrange the 16 miles fence into a rectangle of width 2 miles and length 6 miles. What is the area of this rectangle?
c. The first two parts of this exercise are designed to show you that you can get different areas for the rectangle of the sane perimeter, 16 miles. In general, if you arrange the 16 miles of fence into a rectangle of width w miles, then it will enclose an area of
(i) Make a graph of the area enclosed as a function of w, and explain what the graph is showing.
(ii) What width w should you use to enclose the most area?
(iii) What is the length of the maximum-area rectangle that you made, and what kind of figure do you have?
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For what values of a, b will the saystem have infinitely many solutions?
Chapter 2 Solutions
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Ch. 2.1 - If a coffee filter is dropped, its velocity after...Ch. 2.1 - Suppose one canoe rents for 40,and2 is taken off...Ch. 2.1 - A Saving Account You deposit money into a savings...Ch. 2.1 - Savings with regular Deposits Suppose you deposit...Ch. 2.1 - Paying Off a Credit Card Suppose you owe 15, 000...Ch. 2.1 - Buying Power The inflation rate tells us the...Ch. 2.1 - Economic Efficiency Marginal cost is the...Ch. 2.1 - Flesch Reading Ease The Flesch Reading Ease Test...Ch. 2.1 - Spache Readability Formula The Spache Readability...Ch. 2.1 - Weight Lifting Brzyckis formula is used by weight...
Ch. 2.1 - Harvard Step Test The Harvard Step Test was...Ch. 2.1 - Public High School Enrollment One model for the...Ch. 2.1 - Later Public High School Enrollment Here is a...Ch. 2.1 - Species-Area Relation The number of species of...Ch. 2.1 - Competition Two friends enjoy competing with each...Ch. 2.1 - Profit The profit P, in thousands of dollars that...Ch. 2.1 - Prob. 15ECh. 2.1 - Counting when Order Does Not Matter This is a...Ch. 2.1 - APR and EAR Recall that the APR the annual...Ch. 2.1 - An Amortization Table Suppose you borrow P dollars...Ch. 2.1 - Prob. 19ECh. 2.1 - Renting Motel Rooms You own a motel with 30 rooms,...Ch. 2.1 - Prob. 21ECh. 2.1 - A Population of Foxes A breeding group of foxes is...Ch. 2.1 - Falling with a parachute If an average-sized man...Ch. 2.1 - Rolling 4 Sixes If you roll N dice, then the...Ch. 2.1 - Prob. 25ECh. 2.1 - Profit with Varying Price The background for this...Ch. 2.1 - A Precocious Child and Her Blocks A child has 64...Ch. 2.1 - Renting Paddleboats An enterprise rents out...Ch. 2.1 - Growth in Length of Haddock D.S. Raitt found that...Ch. 2.1 - Discharge from a Fire Hose The discharge from a...Ch. 2.1 - Prob. 31ECh. 2.1 - Terminal Velocity Revisited In one of the early...Ch. 2.1 - Research Project Find a function given by formula...Ch. 2.1 - Making Tables and Comparing Functions In Exercises...Ch. 2.1 - Prob. 2SBECh. 2.1 - Prob. 3SBECh. 2.1 - Prob. 4SBECh. 2.1 - Prob. 5SBECh. 2.1 - Prob. 6SBECh. 2.1 - Prob. 7SBECh. 2.1 - Prob. 8SBECh. 2.1 - Prob. 9SBECh. 2.1 - Prob. 10SBECh. 2.1 - Prob. 11SBECh. 2.1 - Finding Limiting Values In Exercises S-11 through...Ch. 2.1 - Prob. 13SBECh. 2.1 - Prob. 14SBECh. 2.1 - Prob. 15SBECh. 2.1 - Prob. 16SBECh. 2.1 - Prob. 17SBECh. 2.1 - Prob. 18SBECh. 2.1 - Prob. 19SBECh. 2.1 - Prob. 20SBECh. 2.1 - Prob. 21SBECh. 2.1 - Prob. 22SBECh. 2.1 - Finding Limiting Values In Exercises S-11 through...Ch. 2.1 - Prob. 24SBECh. 2.1 - Finding Maxima and Minima In Exercises S-25...Ch. 2.1 - Prob. 26SBECh. 2.1 - Prob. 27SBECh. 2.1 - Prob. 28SBECh. 2.1 - Prob. 29SBECh. 2.1 - Prob. 30SBECh. 2.1 - Prob. 31SBECh. 2.1 - Prob. 32SBECh. 2.2 - TEST TOUR UNDERSTANDING FOR EXAMPLE 2.3 Suppose a...Ch. 2.2 - TEST TOUR UNDERSTANDING FOR EXAMPLE 2.4 Changes in...Ch. 2.2 - Continuous Compounding A certain investment is...Ch. 2.2 - Present Value: The present value P is the...Ch. 2.2 - Equity: When you use a mortgage to purchase a...Ch. 2.2 - Buying a Car: If you buy a 25,000 car at an APR of...Ch. 2.2 - Adult Weight from Puppy Weight There is a formula...Ch. 2.2 - Mosteller Formula for Body Surface Area: Body...Ch. 2.2 - Weekly Cost: The weekly cost of running a small...Ch. 2.2 - Average Speed: A commuter regularly drives 70...Ch. 2.2 - Resale Value: The resale value V, in dollars, of a...Ch. 2.2 - Profit The yearly profit P for a widget producer...Ch. 2.2 - Baking a Potato: A potato is placed in a preheated...Ch. 2.2 - Functional Response: The amount C of food consumed...Ch. 2.2 - Population Growth: The growth G of a population...Ch. 2.2 - Ohms Law: says that when electric current is...Ch. 2.2 - Prob. 15ECh. 2.2 - Monthly Payment for a Home: If you borrow 120,000...Ch. 2.2 - Prob. 17ECh. 2.2 - Alexanders Formula One interesting problem in the...Ch. 2.2 - Prob. 18.2ECh. 2.2 - Prob. 19ECh. 2.2 - Planet Growth The amount of growth of plants in an...Ch. 2.2 - Prob. 21ECh. 2.2 - Viewing Earth: Astronauts looking at Earth from a...Ch. 2.2 - Magazine Circulation: The circulation C of a...Ch. 2.2 - Prob. 24ECh. 2.2 - Buffalo: Waterton Lakes National Park of Canada,...Ch. 2.2 - Prob. 26ECh. 2.2 - Prob. 27ECh. 2.2 - Prob. 1SBECh. 2.2 - Prob. 2SBECh. 2.2 - Prob. 3SBECh. 2.2 - Prob. 4SBECh. 2.2 - Prob. 5SBECh. 2.2 - Prob. 6SBECh. 2.2 - Prob. 7SBECh. 2.2 - Prob. 8SBECh. 2.2 - Prob. 9SBECh. 2.2 - Prob. 10SBECh. 2.2 - Prob. 11SBECh. 2.2 - Finding Windows and Making Graphs: In Exercises...Ch. 2.2 - Prob. 13SBECh. 2.2 - Prob. 14SBECh. 2.2 - Prob. 15SBECh. 2.2 - Prob. 16SBECh. 2.2 - Prob. 17SBECh. 2.2 - Finding Windows and Making Graphs: In Exercises...Ch. 2.2 - Prob. 19SBECh. 2.2 - Prob. 20SBECh. 2.2 - Prob. 21SBECh. 2.2 - Prob. 22SBECh. 2.2 - Prob. 23SBECh. 2.2 - Prob. 24SBECh. 2.2 - Prob. 25SBECh. 2.2 - Prob. 26SBECh. 2.2 - Prob. 27SBECh. 2.2 - Prob. 28SBECh. 2.2 - Prob. 29SBECh. 2.2 - Finding Windows and Making Graphs: In Exercises...Ch. 2.3 - In the situation of the example, how long could...Ch. 2.3 - If you travel 300 miles on the first day and then...Ch. 2.3 - Prob. 3TUCh. 2.3 - Prob. 1ECh. 2.3 - Trans Fat You are ordering fast food for your...Ch. 2.3 - Prob. 3ECh. 2.3 - Prob. 4ECh. 2.3 - Break-even Point A manufacturer of T-shirts has...Ch. 2.3 - Juice Sales The number J, in thousands, of cans of...Ch. 2.3 - Resale Value The resale value V, in thousands of...Ch. 2.3 - Aerobic Power Aerobic power can be thought of as...Ch. 2.3 - Gas Mileage The distance d, in miles, that you can...Ch. 2.3 - Isocost Equation We are to buy quantities of two...Ch. 2.3 - Supply and Demand The quantity S of barley, in...Ch. 2.3 - Stock Turnover at Retail In retail sales, an...Ch. 2.3 - Prob. 13ECh. 2.3 - Sales Strategy A small business is considering...Ch. 2.3 - Prob. 15ECh. 2.3 - Prob. 16ECh. 2.3 - Temperature Conversions In everyday experience,...Ch. 2.3 - The Ideal Gas Law A mole of a chemical is a fixed...Ch. 2.3 - Running Ants A scientist observed that the speed S...Ch. 2.3 - Tax Owed According to the Oklahoma Income Tax...Ch. 2.3 - Prob. 21ECh. 2.3 - Growth in Weight and Height Between the ages of 7...Ch. 2.3 - Prob. 23ECh. 2.3 - Prob. 24ECh. 2.3 - Prob. 25ECh. 2.3 - Prob. 26ECh. 2.3 - Prob. 27ECh. 2.3 - Prob. 1SBECh. 2.3 - Prob. 2SBECh. 2.3 - Prob. 3SBECh. 2.3 - Prob. 4SBECh. 2.3 - Prob. 5SBECh. 2.3 - Prob. 6SBECh. 2.3 - Prob. 7SBECh. 2.3 - Solving Linear Equations In Exercises S-7 through...Ch. 2.3 - Prob. 9SBECh. 2.3 - Solving Linear Equations In Exercises S-7 through...Ch. 2.3 - Prob. 11SBECh. 2.3 - Solving Linear Equations In Exercises S-7 through...Ch. 2.3 - Prob. 13SBECh. 2.3 - Prob. 14SBECh. 2.3 - Prob. 15SBECh. 2.3 - Prob. 16SBECh. 2.3 - Prob. 17SBECh. 2.3 - Prob. 18SBECh. 2.3 - Prob. 19SBECh. 2.3 - Prob. 20SBECh. 2.3 - Prob. 21SBECh. 2.3 - Prob. 22SBECh. 2.3 - Prob. 23SBECh. 2.3 - Prob. 24SBECh. 2.3 - Prob. 25SBECh. 2.3 - Prob. 26SBECh. 2.3 - Prob. 27SBECh. 2.3 - Reversing Roles of Variables In Exercises S-17...Ch. 2.3 - Prob. 29SBECh. 2.3 - Prob. 30SBECh. 2.4 - The number N of deer expected to be present on the...Ch. 2.4 - Prob. 2TUCh. 2.4 - Doubling Time An investment grows according to the...Ch. 2.4 - You Win the Lottery Congratulations You have just...Ch. 2.4 - Prob. 3ECh. 2.4 - Your Childs Education You want to begin making...Ch. 2.4 - Engine Displacement The displacement for an...Ch. 2.4 - Altmans z-score Altmans z-score is a financial...Ch. 2.4 - Admiralty Coefficient The Admiralty Coefficent A...Ch. 2.4 - Properller Size An ideal diameter d, in feet, of a...Ch. 2.4 - A Population of Foxes A breeding group of foxes is...Ch. 2.4 - Profit The monthly profit P for a widget producer...Ch. 2.4 - Prob. 11ECh. 2.4 - The Skydiver Again When a skydiver jumps from an...Ch. 2.4 - Falling with a Parachute If an average-sized man...Ch. 2.4 - A Cup of Cofee The temperature C of a fresh cup of...Ch. 2.4 - Reaction Rates In a chemical reaction, the...Ch. 2.4 - Population Growth The growth G of a population of...Ch. 2.4 - Van der Waals Equation In Exercise 18 at the end...Ch. 2.4 - Radioactive Decay The half-life of a radioactive...Ch. 2.4 - Prob. 19ECh. 2.4 - Prob. 20ECh. 2.4 - Grazing Kangaroos The amount of vegetation eaten...Ch. 2.4 - Grazing Rabbits and Sheep This is a continuation...Ch. 2.4 - Prob. 23ECh. 2.4 - Hosting a Convention You are hosting a convention...Ch. 2.4 - Breaking Even The background for this exercise can...Ch. 2.4 - Prob. 26ECh. 2.4 - Water Flea F. 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Smith has studied population...Ch. 2.6 - Prob. 26ECh. 2.6 - Prob. 27ECh. 2.6 - Maximum and Minimum Values In Exercise S-1 through...Ch. 2.6 - Maximum and Minimum Values In Exercise S-1 through...Ch. 2.6 - Prob. 3SBECh. 2.6 - Prob. 4SBECh. 2.6 - Prob. 5SBECh. 2.6 - Finding Maxima and Minima In Exercises S-5 through...Ch. 2.6 - Finding Maxima and Minima In Exercises S-5 through...Ch. 2.6 - Prob. 8SBECh. 2.6 - Finding Maxima and Minima In Exercises S-5 through...Ch. 2.6 - Prob. 10SBECh. 2.6 - Finding Maxima and Minima In Exercises S-5 through...Ch. 2.6 - Prob. 12SBECh. 2.6 - Prob. 13SBECh. 2.6 - Prob. 14SBECh. 2.6 - Prob. 15SBECh. 2.6 - Finding Maxima and Minima In Exercises S-5 through...Ch. 2.6 - Prob. 17SBECh. 2.6 - Finding Maxima and Minima In Exercises S-5 through...Ch. 2.6 - Finding Maxima and Minima In Exercises S-5 through...Ch. 2.6 - Prob. 20SBECh. 2.6 - Finding Maxima and Minima In Exercises S-5 through...Ch. 2.6 - Prob. 22SBECh. 2.6 - Prob. 23SBECh. 2.6 - Prob. 24SBECh. 2.6 - Prob. 25SBECh. 2.6 - Prob. 26SBECh. 2.6 - Endpoint Maximum Find the maximum value of...Ch. 2.6 - Maximum and Minimum Find the maximum and minimum...Ch. 2.CR - Finding a Minimum Suppose the function...Ch. 2.CR - Population of Foxes A breeding group of foxes is...Ch. 2.CR - Prob. 3CRCh. 2.CR - Water Jug If a completely full 5-gallon water jug...Ch. 2.CR - Maxima and Minima Find the maximum and minimum...Ch. 2.CR - George Reserve Population The number of deer on...Ch. 2.CR - Prob. 7CRCh. 2.CR - Forming a Pen We want to form a free-standing...Ch. 2.CR - The Crossing-Graphs Method Solve using the...Ch. 2.CR - Prob. 10CRCh. 2.CR - Prob. 11CRCh. 2.CR - Prob. 12CRCh. 2.CR - Linear Equations Solve for W:L=98.42+1.08W4.14A.Ch. 2.CR - Growth of North Sea Sole The length of North Sea...Ch. 2.CR - Minimum Find the minimum value of x2+20/(x+1) on...Ch. 2.CR - Prob. 16CRCh. 2.CR - Prob. 17CRCh. 2.CR - Temperature Conversions The three principal...Ch. 2.CR - Lidocaine Lidocaine is a drug used to treat...Ch. 2.CR - The Single-Graph Method Use the single-graph...Ch. 2.CR - Prob. 21CRCh. 2.FR1 - Prob. 1ECh. 2.FR1 - Prob. 2ECh. 2.FR1 - Prob. 3ECh. 2.FR1 - Prob. 4ECh. 2.FR1 - Prob. 5ECh. 2.FR1 - Prob. 6ECh. 2.FR1 - Prob. 7ECh. 2.FR1 - Prob. 8ECh. 2.FR1 - Prob. 9ECh. 2.FR1 - Prob. 10ECh. 2.FR1 - Prob. 11ECh. 2.FR1 - Prob. 12ECh. 2.FR1 - Prob. 13ECh. 2.FR1 - Prob. 14ECh. 2.FR1 - Prob. 15ECh. 2.FR2 - Prob. 1ECh. 2.FR2 - Prob. 2ECh. 2.FR2 - Prob. 3ECh. 2.FR2 - Prob. 4ECh. 2.FR2 - Prob. 5ECh. 2.FR2 - Prob. 6ECh. 2.FR2 - Prob. 7ECh. 2.FR2 - Prob. 8ECh. 2.FR2 - Prob. 9ECh. 2.FR2 - Prob. 10ECh. 2.FR2 - Prob. 11ECh. 2.FR2 - Prob. 12ECh. 2.FR2 - Prob. 13ECh. 2.FR2 - Prob. 14ECh. 2.FR2 - Prob. 15ECh. 2.FR3 - Locating the Vertex of a Parabola In Exercises 1...Ch. 2.FR3 - Prob. 2ECh. 2.FR3 - Prob. 3ECh. 2.FR3 - Prob. 4ECh. 2.FR3 - Prob. 5ECh. 2.FR3 - Prob. 6ECh. 2.FR3 - Applications Exercises 5 through 13 illustrate...Ch. 2.FR3 - Prob. 8ECh. 2.FR3 - Prob. 9ECh. 2.FR3 - Prob. 10ECh. 2.FR3 - Prob. 11ECh. 2.FR3 - Prob. 12ECh. 2.FR3 - Prob. 13E
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Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Elementary Geometry For College Students, 7e
Geometry
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Cengage,
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Trigonometry (MindTap Course List)
Trigonometry
ISBN:9781337278461
Author:Ron Larson
Publisher:Cengage Learning
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Big Ideas Math A Bridge To Success Algebra 1: Stu...
Algebra
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:Houghton Mifflin Harcourt
ALGEBRAIC EXPRESSIONS & EQUATIONS | GRADE 6; Author: SheenaDoria;https://www.youtube.com/watch?v=fUOdon3y1hU;License: Standard YouTube License, CC-BY
Algebraic Expression And Manipulation For O Level; Author: Maths Solution;https://www.youtube.com/watch?v=MhTyodgnzNM;License: Standard YouTube License, CC-BY
Algebra for Beginners | Basics of Algebra; Author: Geek's Lesson;https://www.youtube.com/watch?v=PVoTRu3p6ug;License: Standard YouTube License, CC-BY
Introduction to Algebra | Algebra for Beginners | Math | LetsTute; Author: Let'stute;https://www.youtube.com/watch?v=VqfeXMinM0U;License: Standard YouTube License, CC-BY