Finite Mathematics and Applied Calculus (MindTap Course List)
Finite Mathematics and Applied Calculus (MindTap Course List)
7th Edition
ISBN: 9781337274203
Author: Stefan Waner, Steven Costenoble
Publisher: Cengage Learning
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Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…
Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …
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Chapter 1.3, Problem 53E

In Exercises 39-58, calculate the exact slope (rather than a decimal approximation) of the straight line through the given pair of points, if defined. Try to do as many as you can without writing anything down except the answer. [HINT: See Quick Example 5.]

( a ,     b ) and ( c ,     d )

( a ≠ c )

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Chapter 1 Solutions

Finite Mathematics and Applied Calculus (MindTap Course List)

Ch. 1.1 - In Exercises 1-4, evaluate each expression based...Ch. 1.1 - In Exercises 1-4, evaluate each expression based...Ch. 1.1 - In Exercises 1-4, evaluate each expression based...Ch. 1.1 - Prob. 4ECh. 1.1 - In Exercises 5-8, use the graph of the function f...Ch. 1.1 - In Exercises 5-8, use the graph of the function f...Ch. 1.1 - In Exercises 5-8, use the graph of the function f...Ch. 1.1 - In Exercises 5-8, use the graph of the function f...Ch. 1.1 - In Exercises 9-12, say whether or not f(x) is...Ch. 1.1 - In Exercises 9-12, say whether or not f(x) is...
Ch. 1.1 - In Exercises 9-12, say whether or not f(x) is...Ch. 1.1 - Prob. 12ECh. 1.1 - Given f(x)=4x3, find a. f(1) b. f(0) c. f(1) d....Ch. 1.1 - Prob. 14ECh. 1.1 - Prob. 15ECh. 1.1 - Prob. 16ECh. 1.1 - Given g(s)=s2+1s, find a. g(1) b. g(1) c. g(4) d....Ch. 1.1 - Prob. 18ECh. 1.1 - Prob. 19ECh. 1.1 - Prob. 20ECh. 1.1 - Prob. 21ECh. 1.1 - Prob. 22ECh. 1.1 - Prob. 23ECh. 1.1 - Prob. 24ECh. 1.1 - In Exercises 25 and 26, match the functions to the...Ch. 1.1 - Prob. 26ECh. 1.1 - Prob. 27ECh. 1.1 - Prob. 28ECh. 1.1 - Prob. 29ECh. 1.1 - Prob. 30ECh. 1.1 - Prob. 31ECh. 1.1 - Prob. 32ECh. 1.1 - Prob. 33ECh. 1.1 - Prob. 34ECh. 1.1 - In Exercises 31-36, sketch the graph of the...Ch. 1.1 - Prob. 36ECh. 1.1 - In Exercises 37-40, find and simplify (a)...Ch. 1.1 - Prob. 38ECh. 1.1 - Prob. 39ECh. 1.1 - Prob. 40ECh. 1.1 - Prob. 41ECh. 1.1 - Offshore Crude Oil Production: Mexico The...Ch. 1.1 - Social Website Popularity: Twitter The following...Ch. 1.1 - Social Website Popularity: Delicious The following...Ch. 1.1 - Housing Starts Exercises 45-48 refer to the...Ch. 1.1 - Housing Starts Exercises 45-48 refer to the...Ch. 1.1 - Housing Starts Exercises 45-48 refer to the...Ch. 1.1 - Prob. 48ECh. 1.1 - Prob. 49ECh. 1.1 - Prob. 50ECh. 1.1 - Net Income: Casual Apparel In the following graph,...Ch. 1.1 - Prob. 52ECh. 1.1 - Prob. 53ECh. 1.1 - Funding for NASA: 1966-2015 The percentage of the...Ch. 1.1 - Acquisition of Language The percentage p(t) of...Ch. 1.1 - Acquisition of Language The percentage p(t)...Ch. 1.1 - Prob. 57ECh. 1.1 - Processor Speeds The processor speed, in megahertz...Ch. 1.1 - Prob. 59ECh. 1.1 - Prob. 60ECh. 1.1 - Prob. 61ECh. 1.1 - Prob. 62ECh. 1.1 - Prob. 63ECh. 1.1 - Complete the following: The equation notation for...Ch. 1.1 - Prob. 65ECh. 1.1 - Prob. 66ECh. 1.1 - Prob. 67ECh. 1.1 - Prob. 68ECh. 1.1 - True or false? Every function can be specified...Ch. 1.1 - Prob. 70ECh. 1.1 - Why is the following assertion false? If f(x)=x21,...Ch. 1.1 - Why is the following assertion false? If f(2)=2...Ch. 1.1 - Prob. 73ECh. 1.1 - Prob. 74ECh. 1.1 - Prob. 75ECh. 1.1 - Prob. 76ECh. 1.2 - Exercises 1-8 are based on the following...Ch. 1.2 - Prob. 2ECh. 1.2 - Prob. 3ECh. 1.2 - Prob. 4ECh. 1.2 - Exercises 1-8 are based on the following...Ch. 1.2 - Exercises 1-8 are based on the following...Ch. 1.2 - Exercises 1-8 are based on the following...Ch. 1.2 - Prob. 8ECh. 1.2 - Resources You now have 200 music files on your...Ch. 1.2 - Prob. 10ECh. 1.2 - Soccer My rectangular soccer field site has a...Ch. 1.2 - Cabbage My rectangular cabbage patch has a total...Ch. 1.2 - Vegetables I want to fence in a square vegetable...Ch. 1.2 - Orchids My square orchid garden abuts my house so...Ch. 1.2 - Prob. 15ECh. 1.2 - Recreation You spend 5 hours per day on Saturdays...Ch. 1.2 - Prob. 17ECh. 1.2 - Prob. 18ECh. 1.2 - Break-Even Analysis Your college newspaper, The...Ch. 1.2 - Break-Even Analysis The Audubon Society at...Ch. 1.2 - Prob. 21ECh. 1.2 - Break-Even Analysis Gymnast Clothing also...Ch. 1.2 - Break-Even Analysis: School Construction Costs The...Ch. 1.2 - Break-Even Analysis: School Construction Costs The...Ch. 1.2 - Profit Analysis: Aviation The hourly operating...Ch. 1.2 - Profit Analysis: Aviation The hourly operating...Ch. 1.2 - Break-Even Analysis (based on a question from a...Ch. 1.2 - Prob. 28ECh. 1.2 - Prob. 29ECh. 1.2 - Prob. 30ECh. 1.2 - Break-Even Analysis: Organized Crime The organized...Ch. 1.2 - Break-Even Analysis: Disorganized Crime Butch...Ch. 1.2 - Demand: E-Readers The demand for Amazon's Kindle...Ch. 1.2 - Demand for Monorail Service: Mars The demand for...Ch. 1.2 - Prob. 35ECh. 1.2 - Prob. 36ECh. 1.2 - Equilibrium Price: Skateboards The demand for your...Ch. 1.2 - Equilibrium Price: Skateboards The demand for your...Ch. 1.2 - Equilibrium Price: Cell Phones Worldwide quarterly...Ch. 1.2 - Equilibrium Price: Cell Phones Worldwide annual...Ch. 1.2 - Demand: E-Readers The demand for Amuons Kindle...Ch. 1.2 - Prob. 42ECh. 1.2 - Toxic Waste Treatment The cost of treating waste...Ch. 1.2 - Prob. 44ECh. 1.2 - Spending on Corrections in the 1990s The following...Ch. 1.2 - Prob. 46ECh. 1.2 - Prob. 47ECh. 1.2 - Prob. 48ECh. 1.2 - Prob. 49ECh. 1.2 - Prob. 50ECh. 1.2 - Prob. 51ECh. 1.2 - Prob. 52ECh. 1.2 - Prob. 53ECh. 1.2 - Prob. 54ECh. 1.2 - Investments In August 2013, E*TRADE Financial was...Ch. 1.2 - Prob. 56ECh. 1.2 - Prob. 57ECh. 1.2 - Prob. 58ECh. 1.2 - Carbon Dating A fossil originally contained 104...Ch. 1.2 - Prob. 60ECh. 1.2 - Prob. 61ECh. 1.2 - Prob. 62ECh. 1.2 - Radium Decay The amount of radium 226 remaining in...Ch. 1.2 - Prob. 64ECh. 1.2 - If the population of the lunar station at Clavius...Ch. 1.2 - Prob. 66ECh. 1.2 - Prob. 67ECh. 1.2 - Prob. 68ECh. 1.2 - Prob. 69ECh. 1.2 - Prob. 70ECh. 1.2 - Prob. 71ECh. 1.2 - Complete the following sentence: In a linear cost...Ch. 1.2 - Prob. 73ECh. 1.2 - What would happen to the price of a certain...Ch. 1.2 - Prob. 75ECh. 1.2 - Prob. 76ECh. 1.2 - If f and g are functions with f(x)g(x) for every...Ch. 1.2 - Prob. 78ECh. 1.2 - Prob. 79ECh. 1.2 - Prob. 80ECh. 1.3 - In Exercises 1-6, a table of values for a linear...Ch. 1.3 - In Exercises 1-6, a table of values for a linear...Ch. 1.3 - Prob. 3ECh. 1.3 - Prob. 4ECh. 1.3 - Prob. 5ECh. 1.3 - Prob. 6ECh. 1.3 - In Exercises 7-10, first find f(0), if not...Ch. 1.3 - Prob. 8ECh. 1.3 - Prob. 9ECh. 1.3 - Prob. 10ECh. 1.3 - In Exercises 11-14, decide which of the two given...Ch. 1.3 - In Exercises 11-14, decide which of the two given...Ch. 1.3 - Prob. 13ECh. 1.3 - Prob. 14ECh. 1.3 - Prob. 15ECh. 1.3 - Prob. 16ECh. 1.3 - In Exercises 15-24, find the slope of the given...Ch. 1.3 - Prob. 18ECh. 1.3 - In Exercises 15-24, find the slope of the given...Ch. 1.3 - Prob. 20ECh. 1.3 - In Exercises 15-24, find the slope of the given...Ch. 1.3 - Prob. 22ECh. 1.3 - In Exercises 15-24, find the slope of the given...Ch. 1.3 - Prob. 24ECh. 1.3 - In Exercises 2538, graph the given equation.[HINT:...Ch. 1.3 - Prob. 26ECh. 1.3 - Prob. 27ECh. 1.3 - Prob. 28ECh. 1.3 - Prob. 29ECh. 1.3 - Prob. 30ECh. 1.3 - Prob. 31ECh. 1.3 - Prob. 32ECh. 1.3 - In Exercises 2538, graph the given equation.[HINT:...Ch. 1.3 - Prob. 34ECh. 1.3 - Prob. 35ECh. 1.3 - Prob. 36ECh. 1.3 - Prob. 37ECh. 1.3 - Prob. 38ECh. 1.3 - Prob. 39ECh. 1.3 - Prob. 40ECh. 1.3 - Prob. 41ECh. 1.3 - Prob. 42ECh. 1.3 - In Exercises 39-58, calculate the exact slope...Ch. 1.3 - Prob. 44ECh. 1.3 - In Exercises 39-58, calculate the exact slope...Ch. 1.3 - Prob. 46ECh. 1.3 - Prob. 47ECh. 1.3 - Prob. 48ECh. 1.3 - Prob. 49ECh. 1.3 - Prob. 50ECh. 1.3 - Prob. 51ECh. 1.3 - Prob. 52ECh. 1.3 - In Exercises 39-58, calculate the exact slope...Ch. 1.3 - Prob. 54ECh. 1.3 - Prob. 55ECh. 1.3 - Prob. 56ECh. 1.3 - Prob. 57ECh. 1.3 - Prob. 58ECh. 1.3 - In the following figure, estimate the slopes of...Ch. 1.3 - Prob. 60ECh. 1.3 - In Exercises 61-80, find a linear equation whose...Ch. 1.3 - In Exercises 61-80, find a linear equation whose...Ch. 1.3 - Prob. 63ECh. 1.3 - Prob. 64ECh. 1.3 - In Exercises 61-80, find a linear equation whose...Ch. 1.3 - Prob. 66ECh. 1.3 - In Exercises 61-80, find a linear equation whose...Ch. 1.3 - Prob. 68ECh. 1.3 - Prob. 69ECh. 1.3 - Prob. 70ECh. 1.3 - Prob. 71ECh. 1.3 - In Exercises 61-80, find a linear equation whose...Ch. 1.3 - Prob. 73ECh. 1.3 - Prob. 74ECh. 1.3 - Prob. 75ECh. 1.3 - Prob. 76ECh. 1.3 - Prob. 77ECh. 1.3 - Prob. 78ECh. 1.3 - Prob. 79ECh. 1.3 - Prob. 80ECh. 1.3 - Prob. 81ECh. 1.3 - Cost A soft-drink manufacturer can produce 1,000...Ch. 1.3 - Cost: iPhone 5 (16 GB) If it costs Apple $2,070 to...Ch. 1.3 - Prob. 84ECh. 1.3 - Demand Sales figures show that your company sold...Ch. 1.3 - Demand A large department store is prepared to buy...Ch. 1.3 - Demand for Smartphones The following table shows...Ch. 1.3 - Prob. 88ECh. 1.3 - Demand for Monorail Service: Las Vegas In 2005 the...Ch. 1.3 - Demand/or Monorail Service: Mars The Utarek...Ch. 1.3 - Pasta Imports in the 1990s During the period...Ch. 1.3 - Prob. 92ECh. 1.3 - Net Income The net income of Amazon decreased from...Ch. 1.3 - Operating Expenses The operating expenses of...Ch. 1.3 - Prob. 95ECh. 1.3 - Prob. 96ECh. 1.3 - Prob. 97ECh. 1.3 - Prob. 98ECh. 1.3 - Textbook Sizes The second edition of Applied...Ch. 1.3 - Prob. 100ECh. 1.3 - Prob. 101ECh. 1.3 - Prob. 102ECh. 1.3 - Prob. 103ECh. 1.3 - Prob. 104ECh. 1.3 - Prob. 105ECh. 1.3 - Prob. 106ECh. 1.3 - Processor Speeds The processor speed, in megahertz...Ch. 1.3 - Processor Speeds The processor speed, in megahertz...Ch. 1.3 - Prob. 109ECh. 1.3 - Prob. 110ECh. 1.3 - Prob. 111ECh. 1.3 - Prob. 112ECh. 1.3 - Prob. 113ECh. 1.3 - Prob. 114ECh. 1.3 - Prob. 115ECh. 1.3 - Prob. 116ECh. 1.3 - Prob. 117ECh. 1.3 - Prob. 118ECh. 1.3 - Prob. 119ECh. 1.3 - Prob. 120ECh. 1.3 - Prob. 121ECh. 1.3 - Prob. 122ECh. 1.3 - Prob. 123ECh. 1.3 - Prob. 124ECh. 1.3 - Prob. 125ECh. 1.3 - Prob. 126ECh. 1.3 - Prob. 127ECh. 1.3 - Prob. 128ECh. 1.3 - Prob. 129ECh. 1.3 - Prob. 130ECh. 1.3 - Prob. 131ECh. 1.3 - Prob. 132ECh. 1.3 - Prob. 133ECh. 1.3 - Prob. 134ECh. 1.4 - In Exercises 1-4, compute the sum-of-squares error...Ch. 1.4 - In Exercises 1-4, compute the sum-of-squares error...Ch. 1.4 - Prob. 3ECh. 1.4 - Prob. 4ECh. 1.4 - Prob. 5ECh. 1.4 - Prob. 6ECh. 1.4 - In Exercises 5-8, use technology to compute the...Ch. 1.4 - In Exercises 5-8, use technology to compute the...Ch. 1.4 - Prob. 9ECh. 1.4 - In Exercises 9-12, find the regression line...Ch. 1.4 - In Exercises 9-12, find the regression line...Ch. 1.4 - Prob. 12ECh. 1.4 - In Exercises 13 and 14, use correlation...Ch. 1.4 - Prob. 14ECh. 1.4 - Mobile Broadband Subscriptions The following table...Ch. 1.4 - Fixed-Line Telephone Subscriptions The following...Ch. 1.4 - Demand for Smartphones The following table shows...Ch. 1.4 - Demand for Smartphones The following table shows...Ch. 1.4 - Oil Recovery The Texas Bureau of Economic Geology...Ch. 1.4 - Prob. 20ECh. 1.4 - Profit: Amazon The following table shows Amazons...Ch. 1.4 - Operating Expenses: Amazon The following table...Ch. 1.4 - Prob. 23ECh. 1.4 - Prob. 24ECh. 1.4 - Prob. 25ECh. 1.4 - Prob. 26ECh. 1.4 - Prob. 27ECh. 1.4 - Prob. 28ECh. 1.4 - Prob. 29ECh. 1.4 - Prob. 30ECh. 1.4 - Prob. 31ECh. 1.4 - Prob. 32ECh. 1.4 - Prob. 33ECh. 1.4 - Prob. 34ECh. 1.4 - New York City Housing Costs at the Turn of the...Ch. 1.4 - Fiber-Optic Connections at the Turn of the Century...Ch. 1.4 - Prob. 37ECh. 1.4 - Prob. 38ECh. 1.4 - Prob. 39ECh. 1.4 - Prob. 40ECh. 1.4 - Prob. 41ECh. 1.4 - Prob. 42ECh. 1.4 - Prob. 43ECh. 1.4 - Prob. 44ECh. 1.4 - Prob. 45ECh. 1.4 - Prob. 46ECh. 1 - In Exercises 1-4, use the graph of the function f...Ch. 1 - In Exercises 1-4, use the graph of the function f...Ch. 1 - Prob. 3RECh. 1 - Prob. 4RECh. 1 - Prob. 5RECh. 1 - Prob. 6RECh. 1 - Prob. 7RECh. 1 - Prob. 8RECh. 1 - Prob. 9RECh. 1 - Prob. 10RECh. 1 - Prob. 11RECh. 1 - Prob. 12RECh. 1 - Prob. 13RECh. 1 - Prob. 14RECh. 1 - Prob. 15RECh. 1 - Prob. 16RECh. 1 - Prob. 17RECh. 1 - Prob. 18RECh. 1 - Prob. 19RECh. 1 - Prob. 20RECh. 1 - Prob. 21RECh. 1 - Prob. 22RECh. 1 - Prob. 23RECh. 1 - Prob. 24RECh. 1 - Prob. 25RECh. 1 - Prob. 26RECh. 1 - Prob. 27RECh. 1 - Prob. 28RECh. 1 - Prob. 29RECh. 1 - Prob. 30RECh. 1 - Prob. 31RECh. 1 - Prob. 32RECh. 1 - Internet Advertising Several months ago, John...Ch. 1 - Prob. 34RECh. 1 - Internet Advertising When OHaganBooks.com actually...Ch. 1 - Prob. 36RECh. 1 - Prob. 37RECh. 1 - Prob. 38RECh. 1 - Prob. 39RECh. 1 - Break-Even Analysis OHaganBooks.com also generates...Ch. 1 - Demand and Profit To generate a profit from its...Ch. 1 - Prob. 42RECh. 1 - Prob. 43RECh. 1 - Prob. 44RE
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