FINITE MATHEMATICS >PRINT UPGRADE<
7th Edition
ISBN: 9780357667286
Author: Waner
Publisher: CENGAGE L
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Textbook Question
Chapter 1.3, Problem 7E
In Exercises 7-10, first find
| x | –2 | 0 | 2 | 4 |
|
|
–1 | –2 | –3 | –4 |
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Problem 11 (a) A tank is discharging water through an orifice at a depth of T
meter below the surface of the water whose area is A m². The
following are the values of a for the corresponding values of A:
A 1.257 1.390
x 1.50 1.65
1.520 1.650 1.809 1.962 2.123 2.295 2.462|2.650
1.80 1.95 2.10 2.25 2.40 2.55 2.70
2.85
Using the formula
-3.0
(0.018)T =
dx.
calculate T, the time in seconds for the level of the water to drop
from 3.0 m to 1.5 m above the orifice.
(b) The velocity of a train which starts from rest is given by the fol-
lowing table, the time being reckoned in minutes from the start
and the speed in km/hour:
| † (minutes) |2|4 6 8 10 12
14 16 18 20
v (km/hr) 16 28.8 40 46.4 51.2 32.0 17.6 8 3.2 0
Estimate approximately the total distance ran in 20 minutes.
-
Let n = 7, let p = 23 and let S be the set of least positive residues mod p of the first (p − 1)/2
multiple of n, i.e.
n mod p, 2n mod p, ...,
p-1
2
-n mod p.
Let T be the subset of S consisting of those residues which exceed p/2.
Find the set T, and hence compute the Legendre symbol (7|23).
23
32
how come?
The first 11 multiples of 7 reduced mod 23 are
7, 14, 21, 5, 12, 19, 3, 10, 17, 1, 8.
The set T is the subset of these residues exceeding
So T = {12, 14, 17, 19, 21}.
By Gauss' lemma (Apostol Theorem 9.6),
(7|23) = (−1)|T| = (−1)5 = −1.
Let n = 7, let p = 23 and let S be the set of least positive residues mod p of the first (p-1)/2
multiple of n, i.e.
n mod p, 2n mod p, ...,
2
p-1
-n mod p.
Let T be the subset of S consisting of those residues which exceed p/2.
Find the set T, and hence compute the Legendre symbol (7|23).
The first 11 multiples of 7 reduced mod 23 are
7, 14, 21, 5, 12, 19, 3, 10, 17, 1, 8.
23
The set T is the subset of these residues exceeding
2°
So T = {12, 14, 17, 19, 21}.
By Gauss' lemma (Apostol Theorem 9.6),
(7|23) = (−1)|T| = (−1)5 = −1.
how come?
Chapter 1 Solutions
FINITE MATHEMATICS >PRINT UPGRADE<
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 - In Exercises 1-4, evaluate each expression based...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 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 - In Exercises 9-12, say whether or not f(x) is...Ch. 1.1 - Given f(x)=4x3, find a. f(1) b. f(0) c. f(1) d....Ch. 1.1 - Given f(x)=3x+4, find a. f(1) b. f(0) c. f(1) d....Ch. 1.1 - Given f(x)=x2+2x+3, find a. f(0) b. f(1) c. f(1)...Ch. 1.1 - Given g(x)=2x2x+1, find a. g(0) b. g(1) c. g(r) d....Ch. 1.1 - Given g(s)=s2+1s, find a. g(1) b. g(1) c. g(4) d....Ch. 1.1 - Given h(r)=1r+4, find a. h(0) b. h(3) c. h(5) d....Ch. 1.1 - In Exercises 19-24, graph the given functions....Ch. 1.1 - In Exercises 19-24, graph the given functions....Ch. 1.1 - In Exercises 19-24, graph the given functions....Ch. 1.1 - In Exercises 19-24, graph the given functions....Ch. 1.1 - In Exercises 19-24, graph the given functions....Ch. 1.1 - In Exercises 19-24, graph the given functions....Ch. 1.1 - In Exercises 25 and 26, match the functions to the...Ch. 1.1 - In Exercises 25 and 26, match the functions to the...Ch. 1.1 - In Exercises 27-30, first give the technology...Ch. 1.1 - In Exercises 27-30, first give the technology...Ch. 1.1 - In Exercises 27-30, first give the technology...Ch. 1.1 - In Exercises 27-30, first give the technology...Ch. 1.1 - In Exercises 31-36, sketch the graph of the...Ch. 1.1 - In Exercises 31-36, sketch the graph of the...Ch. 1.1 - In Exercises 31-36, sketch the graph of the...Ch. 1.1 - In Exercises 31-36, sketch the graph of the...Ch. 1.1 - In Exercises 31-36, sketch the graph of the...Ch. 1.1 - In Exercises 31-36, sketch the graph of the...Ch. 1.1 - In Exercises 37-40, find and simplify (a)...Ch. 1.1 - In Exercises 37-40, find and simplify (a)...Ch. 1.1 - In Exercises 37-40, find and simplify (a)...Ch. 1.1 - In Exercises 37-40, find and simplify (a)...Ch. 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 - Housing Starts Exercises 45-48 refer to the...Ch. 1.1 - For which value or values of t is f(t+5)f(t)...Ch. 1.1 - For which value of values t is f(t)f(t1) least?...Ch. 1.1 - Net Income: Casual Apparel In the following graph,...Ch. 1.1 - Net Income: Casual Apparel In the following graph,...Ch. 1.1 - Funding for NASA: 1958-1966 The percentage of the...Ch. 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 - Prob. 56ECh. 1.1 - Prob. 57ECh. 1.1 - Processor Speeds The processor speed, in megahertz...Ch. 1.1 - Income Taxes The U.S. federal income tax is a...Ch. 1.1 - Income Taxes Repeat Exercise 59 using the...Ch. 1.1 - Complete the following sentence: If the market...Ch. 1.1 - Complete the following sentence: If weekly profit...Ch. 1.1 - Complete the following: The function notation for...Ch. 1.1 - Complete the following: The equation notation for...Ch. 1.1 - True or false? Every graphically specified...Ch. 1.1 - True or false? Every algebraically specified...Ch. 1.1 - Prob. 67ECh. 1.1 - Prob. 68ECh. 1.1 - Prob. 69ECh. 1.1 - Which supplies more information about a situation:...Ch. 1.1 - Prob. 71ECh. 1.1 - Why is the following assertion false? If f(2)=2...Ch. 1.1 - How do the graphs of two functions differ if they...Ch. 1.1 - Prob. 74ECh. 1.1 - Prob. 75ECh. 1.1 - How do the graphs of two functions f and g differ...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 - 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 - 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 - Resources You now have 200 music files on your...Ch. 1.2 - Resources The amount of free space left on your...Ch. 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 - Study You study math 4 hours a day on Sunday...Ch. 1.2 - Recreation You spend 5 hours per day on Saturdays...Ch. 1.2 - Prob. 17ECh. 1.2 - Cost The cost of renting tuxes for the Choral...Ch. 1.2 - Break-Even Analysis Your college newspaper, The...Ch. 1.2 - Break-Even Analysis The Audubon Society at...Ch. 1.2 - Break-Even Analysis Gymnast Clothing manufactures...Ch. 1.2 - Break-Even Analysis Gymnast Clothing also...Ch. 1.2 - Prob. 23ECh. 1.2 - Break-Even Analysis: School Construction Costs The...Ch. 1.2 - Profit Analysis: Aviation The hourly operating...Ch. 1.2 - Prob. 26ECh. 1.2 - Prob. 27ECh. 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 - Demand: Smartphones The worldwide demand for...Ch. 1.2 - Demand: Smartphones (See Exercise 35.) Here is...Ch. 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 - Equilibrium Price: Mars Monorail Service The...Ch. 1.2 - Prob. 43ECh. 1.2 - Prob. 44ECh. 1.2 - Prob. 45ECh. 1.2 - Prob. 46ECh. 1.2 - Prob. 47ECh. 1.2 - Prob. 48ECh. 1.2 - Prob. 49ECh. 1.2 - Prob. 50ECh. 1.2 - Social Website Popularity: Pinterest The following...Ch. 1.2 - Social Website Popularity: Twitter The following...Ch. 1.2 - Demand for Gasoline The following table shows the...Ch. 1.2 - Demand for Mobile Data The following table shows...Ch. 1.2 - Investments In August 2013, E*TRADE Financial was...Ch. 1.2 - Investments In August 2013, Ally Bank was offering...Ch. 1.2 - Investments Refer to Exercise 55. In August of...Ch. 1.2 - Investments Refer to Exercise 56. In August of...Ch. 1.2 - Carbon Dating A fossil originally contained 104...Ch. 1.2 - Prob. 60ECh. 1.2 - Prob. 61ECh. 1.2 - Carbon Dating A fossil contains 2.8 grams of...Ch. 1.2 - Radium Decay The amount of radium 226 remaining in...Ch. 1.2 - Iodine Decay The amount of iodine 131 remaining in...Ch. 1.2 - If the population of the lunar station at Clavius...Ch. 1.2 - Prob. 66ECh. 1.2 - Classify the following model as analytical or...Ch. 1.2 - Prob. 68ECh. 1.2 - Prob. 69ECh. 1.2 - Prob. 70ECh. 1.2 - Fill in the blanks: In a linear cost function, the...Ch. 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 - Prob. 77ECh. 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 - 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. 5ECh. 1.3 - Prob. 6ECh. 1.3 - In Exercises 7-10, first find f(0), if not...Ch. 1.3 - In Exercises 7-10, first find f(0), if not...Ch. 1.3 - Prob. 9ECh. 1.3 - Prob. 10ECh. 1.3 - In Exercises 11-14, decide which of the two given...Ch. 1.3 - Prob. 12ECh. 1.3 - Prob. 13ECh. 1.3 - Prob. 14ECh. 1.3 - In Exercises 15-24, find the slope of the given...Ch. 1.3 - Prob. 16ECh. 1.3 - Prob. 17ECh. 1.3 - Prob. 18ECh. 1.3 - Prob. 19ECh. 1.3 - Prob. 20ECh. 1.3 - Prob. 21ECh. 1.3 - Prob. 22ECh. 1.3 - Prob. 23ECh. 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 - In Exercises 2538, graph the given equation.[HINT:...Ch. 1.3 - Prob. 33ECh. 1.3 - Prob. 34ECh. 1.3 - Prob. 35ECh. 1.3 - Prob. 36ECh. 1.3 - Prob. 37ECh. 1.3 - Prob. 38ECh. 1.3 - In Exercises 39-58, calculate the exact slope...Ch. 1.3 - Prob. 40ECh. 1.3 - Prob. 41ECh. 1.3 - Prob. 42ECh. 1.3 - Prob. 43ECh. 1.3 - Prob. 44ECh. 1.3 - Prob. 45ECh. 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 - Prob. 53ECh. 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 - In the following figure, estimate the slopes of...Ch. 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 - Prob. 65ECh. 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. 68ECh. 1.3 - Prob. 69ECh. 1.3 - Prob. 70ECh. 1.3 - Prob. 71ECh. 1.3 - Prob. 72ECh. 1.3 - Prob. 73ECh. 1.3 - Prob. 74ECh. 1.3 - Prob. 75ECh. 1.3 - In Exercises 61-80, find a linear equation whose...Ch. 1.3 - Prob. 77ECh. 1.3 - Prob. 78ECh. 1.3 - Prob. 79ECh. 1.3 - Prob. 80ECh. 1.3 - Prob. 81ECh. 1.3 - Prob. 82ECh. 1.3 - Cost: iPhone 5 (16 GB) If it costs Apple $2,070 to...Ch. 1.3 - Cost: Kinects If it costs Microsoft $1,230 to...Ch. 1.3 - Demand Sales figures show that your company sold...Ch. 1.3 - Prob. 86ECh. 1.3 - Demand for Smartphones The following table shows...Ch. 1.3 - Demand for Smartphones The following table shows...Ch. 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 - Mercury Imports in the 2210s During the period...Ch. 1.3 - Net Income The net income of Amazon decreased from...Ch. 1.3 - Operating Expenses The operating expenses of...Ch. 1.3 - Velocity The position of a model train, in feet...Ch. 1.3 - Velocity The height of a falling sheet of paper,...Ch. 1.3 - Fast Cars A police car was traveling down Ocean...Ch. 1.3 - Fast Cars The car that was being pursued by the...Ch. 1.3 - Textbook Sizes The second edition of Applied...Ch. 1.3 - Textbook Sizes The second edition of Finite...Ch. 1.3 - Prob. 101ECh. 1.3 - Prob. 102ECh. 1.3 - Airline Net Income Exercises 103and104 are based...Ch. 1.3 - Airline Net Income Exercises 103and104 are based...Ch. 1.3 - Income The well-known romance novelist Celestine...Ch. 1.3 - Prob. 106ECh. 1.3 - Prob. 107ECh. 1.3 - Processor Speeds The processor speed, in megahertz...Ch. 1.3 - Superbowl Advertising Exercises 109 and 110 are...Ch. 1.3 - Prob. 110ECh. 1.3 - Employment in Mexico The number of workers...Ch. 1.3 - Mortgage Delinquencies The percentage of borrowers...Ch. 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 - If f and g are linear functions, then is fg...Ch. 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 - 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 - In Exercises 5-8, use technology to compute the...Ch. 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 - In Exercises 5-8, use technology to compute the...Ch. 1.4 - In Exercises 9-12, find the regression line...Ch. 1.4 - In Exercises 9-12, find the regression line...Ch. 1.4 - In Exercises 9-12, find the regression line...Ch. 1.4 - In Exercises 9-12, find the regression line...Ch. 1.4 - In Exercises 13 and 14, use correlation...Ch. 1.4 - In Exercises 13 and 14, use correlation...Ch. 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 - Textbook Sizes The following table shows the...Ch. 1.4 - Textbook Sizes Repeat Exercise 23 using the...Ch. 1.4 - Soybean Production: Cerrados The following table...Ch. 1.4 - Prob. 26ECh. 1.4 - Prob. 27ECh. 1.4 - Prob. 28ECh. 1.4 - Doctorates in Mexico Exercises 29-32 are based on...Ch. 1.4 - Doctorates in Mexico Exercises 29-32 are based on...Ch. 1.4 - Doctorates in Mexico Exercises 29-32 are based on...Ch. 1.4 - Doctorates in Mexico Exercises 29-32 are based on...Ch. 1.4 - a. Do the results of Exercises 29 and 31 suggest...Ch. 1.4 - a. Do the results of Exercises 30 and 32 suggest...Ch. 1.4 - New York City Housing Costs at the Turn of the...Ch. 1.4 - Prob. 36ECh. 1.4 - Prob. 37ECh. 1.4 - What is the smallest possible sum-of-squares error...Ch. 1.4 - Prob. 39ECh. 1.4 - Prob. 40ECh. 1.4 - Prob. 41ECh. 1.4 - Prob. 42ECh. 1.4 - Must the regression line pass through at least one...Ch. 1.4 - Why must care be taken in using mathematical...Ch. 1.4 - Your friend Imogen tells you that if r for a...Ch. 1.4 - Your other friend Mervyn tells you that if r for a...Ch. 1 - In Exercises 1-4, use the graph of the function f...Ch. 1 - Prob. 2RECh. 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 - In Exercises 15-22, find the equation of the...Ch. 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 - Production Costs Over at Duffin House, Marjory...Ch. 1 - Internet Advertising When OHaganBooks.com actually...Ch. 1 - Prob. 36RECh. 1 - Recreation John OHagan has just returned from a...Ch. 1 - Prob. 38RECh. 1 - Prob. 39RECh. 1 - Break-Even Analysis OHaganBooks.com also generates...Ch. 1 - Prob. 41RECh. 1 - Demand and Profit To generate a profit from its...Ch. 1 - Prob. 43RECh. 1 - Demand OHaganBooks.com has tried selling novels...
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