Finite Mathematics and Applied Calculus (MindTap Course List)
7th Edition
ISBN: 9781337274203
Author: Stefan Waner, Steven Costenoble
Publisher: Cengage Learning
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Textbook Question
Chapter 8.5, Problem 3E
In Exercises 1–10, compute the indicated quantity.
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(7) (12 points) Let F(x, y, z) = (y, x+z cos yz, y cos yz).
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(b) (4 points) Find a potential f for the vector field F.
(c) (4 points) Let S be a surface in R3 for which the Stokes' Theorem is valid. Use
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as denotes the boundary of S. Explain your answer.
(3) (16 points) Consider
z = uv,
u = x+y,
v=x-y.
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T(x, y) = (x, y, ƒ (g(x, y))
(x, y) = R².
Give a parametric description of the tangent plane to S at the point p = T(x, y).
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Q(x,y) F(a+x,b+y).
=
(6) (8 points) Change the order of integration and evaluate
(z +4ry)drdy .
So S√ ²
0
Chapter 8 Solutions
Finite Mathematics and Applied Calculus (MindTap Course List)
Ch. 8.1 - In Exercises 118, describe the sample space S of...Ch. 8.1 - Prob. 2ECh. 8.1 - In Exercises 118, describe the sample space S of...Ch. 8.1 - Prob. 4ECh. 8.1 - In Exercises 118, describe the sample space S of...Ch. 8.1 - Prob. 6ECh. 8.1 - In Exercises 118, describe the sample space S of...Ch. 8.1 - Prob. 8ECh. 8.1 - In Exercises 118, describe the sample space S of...Ch. 8.1 - Prob. 10E
Ch. 8.1 - In Exercises 118, describe the sample space S of...Ch. 8.1 - Prob. 12ECh. 8.1 - In Exercises 118, describe the sample space S of...Ch. 8.1 - Prob. 14ECh. 8.1 - In Exercises 118, describe the sample space S of...Ch. 8.1 - Prob. 16ECh. 8.1 - In Exercises 118, describe the sample space S of...Ch. 8.1 - Prob. 18ECh. 8.1 - A packet of gummy candy contains four strawberry...Ch. 8.1 - Prob. 20ECh. 8.1 - Prob. 21ECh. 8.1 - Prob. 22ECh. 8.1 - Prob. 23ECh. 8.1 - Suppose two dice (one red, one green) are rolled....Ch. 8.1 - Suppose two dice (one red, one green) are rolled....Ch. 8.1 - Suppose two dice (one red, one green) are rolled....Ch. 8.1 - Prob. 27ECh. 8.1 - Prob. 28ECh. 8.1 - Prob. 29ECh. 8.1 - Prob. 30ECh. 8.1 - Let W be the event that you will use the books...Ch. 8.1 - Prob. 32ECh. 8.1 - Let W be the event that you will use the books...Ch. 8.1 - Prob. 34ECh. 8.1 - Let W be the event that you will use the books...Ch. 8.1 - Let W be the event that you will use the books...Ch. 8.1 - Let W be the event that you will use the books...Ch. 8.1 - Prob. 38ECh. 8.1 - In Exercises 3942, Pablo randomly picks three...Ch. 8.1 - Prob. 40ECh. 8.1 - In Exercises 3942, Pablo randomly picks three...Ch. 8.1 - In Exercises 3942, Pablo randomly picks three...Ch. 8.1 - Prob. 43ECh. 8.1 - Prob. 44ECh. 8.1 - Prob. 45ECh. 8.1 - Prob. 46ECh. 8.1 - Housing Prices Exercises 4348 are based on the map...Ch. 8.1 - Housing Prices Exercises 4348 are based on the map...Ch. 8.1 - Prob. 49ECh. 8.1 - Prob. 50ECh. 8.1 - Prob. 51ECh. 8.1 - Prob. 52ECh. 8.1 - Prob. 53ECh. 8.1 - Publishing Exercises 4956 are based on the...Ch. 8.1 - Prob. 55ECh. 8.1 - Prob. 56ECh. 8.1 - Prob. 57ECh. 8.1 - Prob. 58ECh. 8.1 - Prob. 59ECh. 8.1 - Prob. 60ECh. 8.1 - Prob. 61ECh. 8.1 - Prob. 62ECh. 8.1 - Prob. 63ECh. 8.1 - Prob. 64ECh. 8.1 - Prob. 65ECh. 8.1 - Prob. 66ECh. 8.1 - Prob. 67ECh. 8.1 - Prob. 68ECh. 8.1 - Exercises 6972 use counting arguments from the...Ch. 8.1 - Prob. 70ECh. 8.1 - Exercises 6972 use counting arguments from the...Ch. 8.1 - Exercises 6972 use counting arguments from the...Ch. 8.1 - Prob. 73ECh. 8.1 - Prob. 74ECh. 8.1 - Prob. 75ECh. 8.1 - Prob. 76ECh. 8.1 - Prob. 77ECh. 8.1 - Prob. 78ECh. 8.1 - Prob. 79ECh. 8.1 - Prob. 80ECh. 8.1 - Prob. 81ECh. 8.1 - Prob. 82ECh. 8.1 - Prob. 83ECh. 8.1 - Prob. 84ECh. 8.2 - Prob. 1ECh. 8.2 - Prob. 2ECh. 8.2 - Prob. 3ECh. 8.2 - In Exercises 16, calculate the relative frequency...Ch. 8.2 - Prob. 5ECh. 8.2 - Prob. 6ECh. 8.2 - Prob. 7ECh. 8.2 - Exercises 712 are based on the following table,...Ch. 8.2 - Prob. 9ECh. 8.2 - Exercises 712 are based on the following table,...Ch. 8.2 - Prob. 11ECh. 8.2 - Exercises 712 are based on the following table,...Ch. 8.2 - Prob. 13ECh. 8.2 - Prob. 14ECh. 8.2 - Prob. 15ECh. 8.2 - Prob. 16ECh. 8.2 - Prob. 17ECh. 8.2 - Prob. 18ECh. 8.2 - Prob. 19ECh. 8.2 - Prob. 20ECh. 8.2 - Prob. 21ECh. 8.2 - Prob. 22ECh. 8.2 - Prob. 23ECh. 8.2 - Prob. 24ECh. 8.2 - Latin Music Sales: 2013 In a survey of 500 Latin...Ch. 8.2 - Prob. 26ECh. 8.2 - Prob. 27ECh. 8.2 - Prob. 28ECh. 8.2 - Population Age in Mexico The following table shows...Ch. 8.2 - Prob. 30ECh. 8.2 - Prob. 31ECh. 8.2 - Prob. 32ECh. 8.2 - Prob. 33ECh. 8.2 - Internet Connections The following pie chart shows...Ch. 8.2 - Prob. 35ECh. 8.2 - Prob. 36ECh. 8.2 - Prob. 37ECh. 8.2 - Prob. 38ECh. 8.2 - Prob. 39ECh. 8.2 - Prob. 40ECh. 8.2 - Prob. 41ECh. 8.2 - Prob. 42ECh. 8.2 - Prob. 43ECh. 8.2 - Prob. 44ECh. 8.2 - Prob. 45ECh. 8.2 - Publishing Exercises 3746 are based on the...Ch. 8.2 - Prob. 47ECh. 8.2 - Prob. 48ECh. 8.2 - Prob. 49ECh. 8.2 - Prob. 50ECh. 8.2 - Steroids Testing A pharmaceutical company is...Ch. 8.2 - Prob. 52ECh. 8.2 - Prob. 55ECh. 8.2 - Prob. 56ECh. 8.2 - Prob. 57ECh. 8.2 - Prob. 58ECh. 8.2 - Prob. 59ECh. 8.2 - Juan tells you that when you roll a pair of fair...Ch. 8.2 - How would you measure the relative frequency that...Ch. 8.2 - Prob. 62ECh. 8.3 - Complete the following probability distribution...Ch. 8.3 - Repeat Exercise 1 using the following table....Ch. 8.3 - In Exercises 38, calculate the (modeled)...Ch. 8.3 - Prob. 4ECh. 8.3 - Prob. 5ECh. 8.3 - Prob. 6ECh. 8.3 - Prob. 7ECh. 8.3 - In Exercises 38, calculate the (modeled)...Ch. 8.3 - In Exercises 918 an experiment is given together...Ch. 8.3 - Prob. 10ECh. 8.3 - In Exercises 918 an experiment is given together...Ch. 8.3 - Prob. 12ECh. 8.3 - In Exercises 918 an experiment is given together...Ch. 8.3 - In Exercises 918 an experiment is given together...Ch. 8.3 - In Exercises 918 an experiment is given together...Ch. 8.3 - Prob. 16ECh. 8.3 - In Exercises 918 an experiment is given together...Ch. 8.3 - Prob. 18ECh. 8.3 - Prob. 19ECh. 8.3 - If two indistinguishable dice are rolled, what is...Ch. 8.3 - A die is weighted in such a way that each of 2, 4,...Ch. 8.3 - Prob. 22ECh. 8.3 - Prob. 23ECh. 8.3 - Adodecahedraldiehas12faces, numbered112. If the...Ch. 8.3 - In Exercises 2540, use the given information to...Ch. 8.3 - Prob. 26ECh. 8.3 - In Exercises 2540, use the given information to...Ch. 8.3 - Prob. 28ECh. 8.3 - In Exercises 2540, use the given information to...Ch. 8.3 - Prob. 30ECh. 8.3 - In Exercises 2540, use the given information to...Ch. 8.3 - Prob. 32ECh. 8.3 - In Exercises 2540, use the given information to...Ch. 8.3 - Prob. 34ECh. 8.3 - In Exercises 2540, use the given information to...Ch. 8.3 - Prob. 36ECh. 8.3 - In Exercises 2540, use the given information to...Ch. 8.3 - Prob. 38ECh. 8.3 - In Exercises 2540, use the given information to...Ch. 8.3 - Prob. 40ECh. 8.3 - Prob. 41ECh. 8.3 - Prob. 42ECh. 8.3 - Prob. 43ECh. 8.3 - Prob. 44ECh. 8.3 - Prob. 45ECh. 8.3 - Prob. 46ECh. 8.3 - Prob. 47ECh. 8.3 - Prob. 48ECh. 8.3 - Ethnic Diversity The following pie chart shows the...Ch. 8.3 - Prob. 50ECh. 8.3 - Internet Investments in the 1990s The following...Ch. 8.3 - Prob. 52ECh. 8.3 - Prob. 53ECh. 8.3 - Prob. 54ECh. 8.3 - Prob. 55ECh. 8.3 - Prob. 56ECh. 8.3 - Prob. 57ECh. 8.3 - Prob. 58ECh. 8.3 - Prob. 59ECh. 8.3 - Gambling In Exercises 5562 are detailed some of...Ch. 8.3 - Prob. 61ECh. 8.3 - Prob. 62ECh. 8.3 - Astrology The astrology software package Turbo...Ch. 8.3 - Prob. 64ECh. 8.3 - Prob. 65ECh. 8.3 - Polls According to The New York Times/CBS poll of...Ch. 8.3 - Electric Car Sales In 2014 the probability that a...Ch. 8.3 - Hybrid Auto Sales In 2010 the probability that a...Ch. 8.3 - Student Admissions Exercises 6984 are based on the...Ch. 8.3 - Student Admissions Exercises 6984 are based on the...Ch. 8.3 - Prob. 71ECh. 8.3 - Prob. 72ECh. 8.3 - Prob. 73ECh. 8.3 - Prob. 74ECh. 8.3 - Student Admissions Exercises 6984 are based on the...Ch. 8.3 - Prob. 76ECh. 8.3 - Prob. 77ECh. 8.3 - Student Admissions Exercises 6984 are based on the...Ch. 8.3 - Prob. 79ECh. 8.3 - Student Admissions Exercises 6984 are based on the...Ch. 8.3 - Prob. 81ECh. 8.3 - Prob. 82ECh. 8.3 - Prob. 83ECh. 8.3 - Prob. 84ECh. 8.3 - Prob. 85ECh. 8.3 - Prob. 86ECh. 8.3 - Prob. 87ECh. 8.3 - Swords and Sorcery Lance the Wizard has been...Ch. 8.3 - Public Health A study shows that 80% of the...Ch. 8.3 - Prob. 90ECh. 8.3 - Prob. 91ECh. 8.3 - Prob. 92ECh. 8.3 - Prob. 93ECh. 8.3 - Prob. 94ECh. 8.3 - Prob. 95ECh. 8.3 - Prob. 96ECh. 8.3 - Prob. 97ECh. 8.3 - Prob. 98ECh. 8.3 - Prob. 99ECh. 8.3 - Prob. 100ECh. 8.3 - Prob. 101ECh. 8.3 - Prob. 102ECh. 8.3 - Prob. 103ECh. 8.3 - Prob. 104ECh. 8.4 - Recall from Example 1 that whenever Suzan sees a...Ch. 8.4 - Recall from Example 1 that whenever Suzan sees a...Ch. 8.4 - Recall from Example 1 that whenever Suzan sees a...Ch. 8.4 - Recall from Example 1 that whenever Suzan sees a...Ch. 8.4 - Recall from Example 1 that whenever Suzan sees a...Ch. 8.4 - Recall from Example 1 that whenever Suzan sees a...Ch. 8.4 - Prob. 7ECh. 8.4 - Prob. 8ECh. 8.4 - Recall from Example 1 that whenever Suzan sees a...Ch. 8.4 - Prob. 10ECh. 8.4 - Dogs of the Dow The Dogs of the Dow are the stocks...Ch. 8.4 - Prob. 12ECh. 8.4 - Prob. 13ECh. 8.4 - Prob. 14ECh. 8.4 - Dogs of the Dow The Dogs of the Dow are the stocks...Ch. 8.4 - Dogs of the Dow The Dogs of the Dow are the stocks...Ch. 8.4 - Prob. 17ECh. 8.4 - Prob. 18ECh. 8.4 - Prob. 19ECh. 8.4 - Poker In Exercises 1924 you are asked to calculate...Ch. 8.4 - Poker In Exercises 1924 you are asked to calculate...Ch. 8.4 - Prob. 22ECh. 8.4 - Prob. 23ECh. 8.4 - Prob. 24ECh. 8.4 - The Monkey at the Typewriter Suppose that a monkey...Ch. 8.4 - The Cat on the Piano A standard piano keyboard has...Ch. 8.4 - Prob. 27ECh. 8.4 - Prob. 28ECh. 8.4 - Lotteries The Sorry State Lottery requires you to...Ch. 8.4 - Lotteries The Sad State Lottery requires you to...Ch. 8.4 - Transfers Your company is considering offering 400...Ch. 8.4 - Prob. 32ECh. 8.4 - Prob. 33ECh. 8.4 - Prob. 34ECh. 8.4 - Prob. 35ECh. 8.4 - Elimination Tournaments In a (fictitious) soccer...Ch. 8.4 - Prob. 37ECh. 8.4 - Prob. 38ECh. 8.4 - Prob. 39ECh. 8.4 - Prob. 40ECh. 8.4 - Prob. 41ECh. 8.4 - Prob. 42ECh. 8.4 - Graph Searching A graph consists of a collection...Ch. 8.4 - Prob. 44ECh. 8.4 - Prob. 45ECh. 8.4 - Prob. 46ECh. 8.4 - Committees An investigatory committee in the...Ch. 8.4 - Committees A committee is to consist of a chair,...Ch. 8.4 - Prob. 49ECh. 8.4 - Prob. 50ECh. 8.4 - Prob. 51ECh. 8.4 - Prob. 52ECh. 8.4 - Prob. 53ECh. 8.4 - Prob. 54ECh. 8.5 - In Exercises 110, compute the indicated quantity....Ch. 8.5 - Prob. 2ECh. 8.5 - In Exercises 110, compute the indicated quantity....Ch. 8.5 - Prob. 4ECh. 8.5 - In Exercises 110, compute the indicated quantity....Ch. 8.5 - Prob. 6ECh. 8.5 - In Exercises 110, compute the indicated quantity....Ch. 8.5 - Prob. 8ECh. 8.5 - In Exercises 110, compute the indicated quantity....Ch. 8.5 - Prob. 10ECh. 8.5 - In Exercises 1116, fill in the blanks using the...Ch. 8.5 - Prob. 12ECh. 8.5 - In Exercises 1116, fill in the blanks using the...Ch. 8.5 - Prob. 14ECh. 8.5 - In Exercises 1116, fill in the blanks using the...Ch. 8.5 - Prob. 16ECh. 8.5 - Prob. 17ECh. 8.5 - In Exercises 1722, find the conditional...Ch. 8.5 - Prob. 19ECh. 8.5 - Prob. 20ECh. 8.5 - In Exercises 1722, find the conditional...Ch. 8.5 - In Exercises 1722, find the conditional...Ch. 8.5 - Prob. 23ECh. 8.5 - Prob. 24ECh. 8.5 - Prob. 25ECh. 8.5 - Exercises 2328 require the use of counting...Ch. 8.5 - Exercises 2328 require the use of counting...Ch. 8.5 - Exercises 2328 require the use of counting...Ch. 8.5 - In Exercises 2932, supply the missing quantities....Ch. 8.5 - Prob. 30ECh. 8.5 - In Exercises 2932, supply the missing quantities....Ch. 8.5 - In Exercises 2932, supply the missing quantities....Ch. 8.5 - In Exercises 3336, say whether the given pair of...Ch. 8.5 - Prob. 34ECh. 8.5 - In Exercises 3336, say whether the given pair of...Ch. 8.5 - In Exercises 3336, say whether the given pair of...Ch. 8.5 - Prob. 37ECh. 8.5 - Prob. 38ECh. 8.5 - Prob. 39ECh. 8.5 - Prob. 40ECh. 8.5 - Prob. 41ECh. 8.5 - Prob. 42ECh. 8.5 - If a coin is tossed 11 times, find the probability...Ch. 8.5 - Prob. 44ECh. 8.5 - Personal Bankruptcy In 2004 the probability that a...Ch. 8.5 - Prob. 46ECh. 8.5 - Existing Home Sales During the year ending April...Ch. 8.5 - Existing Home Sales Refer to the data given in...Ch. 8.5 - Prob. 49ECh. 8.5 - Prob. 50ECh. 8.5 - Marketing A market survey shows that 40% of the...Ch. 8.5 - Marketing A market survey shows that 60% of the...Ch. 8.5 - Road Safety In 1999 the probability that a...Ch. 8.5 - Prob. 54ECh. 8.5 - Publishing Exercises 5562 are based on the...Ch. 8.5 - Prob. 56ECh. 8.5 - Prob. 57ECh. 8.5 - Prob. 58ECh. 8.5 - Prob. 59ECh. 8.5 - Prob. 60ECh. 8.5 - Prob. 61ECh. 8.5 - Publishing Exercises 5562 are based on the...Ch. 8.5 - Prob. 63ECh. 8.5 - In Exercises 6368, draw an appropriate tree...Ch. 8.5 - In Exercises 6368, draw an appropriate tree...Ch. 8.5 - Prob. 66ECh. 8.5 - Prob. 67ECh. 8.5 - Prob. 68ECh. 8.5 - Education and Employment Exercises 6978 are based...Ch. 8.5 - Prob. 70ECh. 8.5 - Prob. 71ECh. 8.5 - Prob. 72ECh. 8.5 - Prob. 73ECh. 8.5 - Prob. 74ECh. 8.5 - Prob. 75ECh. 8.5 - Prob. 76ECh. 8.5 - Prob. 77ECh. 8.5 - Prob. 78ECh. 8.5 - Prob. 79ECh. 8.5 - Prob. 80ECh. 8.5 - Prob. 81ECh. 8.5 - Prob. 82ECh. 8.5 - Internet Use in 2000 The following pie chart shows...Ch. 8.5 - Prob. 84ECh. 8.5 - Prob. 85ECh. 8.5 - Prob. 86ECh. 8.5 - Prob. 87ECh. 8.5 - Prob. 88ECh. 8.5 - Prob. 89ECh. 8.5 - Prob. 90ECh. 8.5 - Prob. 91ECh. 8.5 - Prob. 92ECh. 8.5 - Prob. 93ECh. 8.5 - Prob. 94ECh. 8.5 - Prob. 95ECh. 8.5 - Prob. 96ECh. 8.5 - Ultimate Hockey Cyber Video Games, Inc., the...Ch. 8.5 - Prob. 98ECh. 8.5 - Prob. 99ECh. 8.5 - Prob. 100ECh. 8.5 - Prob. 101ECh. 8.5 - Prob. 102ECh. 8.5 - Prob. 103ECh. 8.5 - Prob. 104ECh. 8.5 - Prob. 105ECh. 8.5 - Prob. 106ECh. 8.5 - Prob. 107ECh. 8.5 - Prob. 108ECh. 8.5 - Prob. 109ECh. 8.5 - Prob. 110ECh. 8.5 - Prob. 111ECh. 8.5 - Prob. 112ECh. 8.6 - In Exercises 18, use Bayes theorem or a tree...Ch. 8.6 - Prob. 2ECh. 8.6 - In Exercises 18, use Bayes theorem or a tree...Ch. 8.6 - Prob. 4ECh. 8.6 - In Exercises 18, use Bayes theorem or a tree...Ch. 8.6 - Prob. 6ECh. 8.6 - In Exercises 18, use Bayes theorem or a tree...Ch. 8.6 - Prob. 8ECh. 8.6 - Music Downloading According to a study on the...Ch. 8.6 - Prob. 10ECh. 8.6 - Weather It snows in Greenland an average of once...Ch. 8.6 - Prob. 12ECh. 8.6 - University Admissions In fall 2014, 34% of...Ch. 8.6 - Prob. 14ECh. 8.6 - Side-Impact Hazard In 2004, 45.4% of all light...Ch. 8.6 - Prob. 16ECh. 8.6 - Athletic Fitness Tests Any athlete who fails the...Ch. 8.6 - Academic Testing Professor Frank Nabarro insists...Ch. 8.6 - Side-Impact Hazard (Compare Exercise 15.) In 2004,...Ch. 8.6 - Side-Impact Hazard In 1986, 23.9% of all light...Ch. 8.6 - University Admissions In fall 2008, UCLA admitted...Ch. 8.6 - Prob. 22ECh. 8.6 - Internet Use (Historical) In 2000, 86% of all...Ch. 8.6 - Prob. 24ECh. 8.6 - Market Surveys A New York Times survey of...Ch. 8.6 - Prob. 26ECh. 8.6 - Prob. 27ECh. 8.6 - Prob. 28ECh. 8.6 - Employment in the 1980s In a 1987 survey of...Ch. 8.6 - Prob. 30ECh. 8.6 - Prob. 31ECh. 8.6 - Prob. 32ECh. 8.6 - Benefits of Exercise According to a study in The...Ch. 8.6 - Prob. 34ECh. 8.6 - Prob. 35ECh. 8.6 - Prob. 36ECh. 8.6 - Prob. 37ECh. 8.6 - Prob. 38ECh. 8.6 - Prob. 39ECh. 8.6 - Prob. 40ECh. 8.6 - Prob. 41ECh. 8.6 - Prob. 42ECh. 8.6 - Prob. 43ECh. 8.6 - Prob. 44ECh. 8.7 - In Exercises 110, write down the transition matrix...Ch. 8.7 - Prob. 2ECh. 8.7 - Prob. 3ECh. 8.7 - In Exercises 110, write down the transition matrix...Ch. 8.7 - Prob. 5ECh. 8.7 - Prob. 6ECh. 8.7 - Prob. 7ECh. 8.7 - Prob. 8ECh. 8.7 - In Exercises 110, write down the transition matrix...Ch. 8.7 - Prob. 10ECh. 8.7 - Prob. 11ECh. 8.7 - Prob. 12ECh. 8.7 - Prob. 13ECh. 8.7 - Prob. 14ECh. 8.7 - Prob. 15ECh. 8.7 - Prob. 16ECh. 8.7 - Prob. 17ECh. 8.7 - Prob. 18ECh. 8.7 - Prob. 19ECh. 8.7 - Prob. 20ECh. 8.7 - Prob. 21ECh. 8.7 - Prob. 22ECh. 8.7 - Prob. 23ECh. 8.7 - Prob. 24ECh. 8.7 - Prob. 25ECh. 8.7 - Prob. 26ECh. 8.7 - Prob. 27ECh. 8.7 - Prob. 28ECh. 8.7 - Prob. 29ECh. 8.7 - Prob. 30ECh. 8.7 - Prob. 31ECh. 8.7 - Prob. 32ECh. 8.7 - Prob. 33ECh. 8.7 - Prob. 34ECh. 8.7 - In Exercises 2536, you are given a transition...Ch. 8.7 - Prob. 36ECh. 8.7 - Prob. 37ECh. 8.7 - Prob. 38ECh. 8.7 - Pest Control In an experiment to test the...Ch. 8.7 - Employment You have worked for the Department of...Ch. 8.7 - Risk Analysis An auto insurance company classifies...Ch. 8.7 - Prob. 42ECh. 8.7 - Textbook Adoptions College instructors who adopt...Ch. 8.7 - Confidence Level Tommy the Dunkers performance on...Ch. 8.7 - Prob. 45ECh. 8.7 - Prob. 46ECh. 8.7 - Prob. 51ECh. 8.7 - Prob. 53ECh. 8.7 - Prob. 54ECh. 8.7 - Prob. 55ECh. 8.7 - Prob. 56ECh. 8.7 - Prob. 57ECh. 8.7 - Prob. 58ECh. 8.7 - Prob. 59ECh. 8.7 - Prob. 60ECh. 8.7 - Prob. 61ECh. 8.7 - Prob. 62ECh. 8.7 - Prob. 63ECh. 8.7 - Prob. 64ECh. 8.7 - Prob. 65ECh. 8.7 - If higher and higher powers of P approach a fixed...Ch. 8 - Prob. 1RECh. 8 - Prob. 2RECh. 8 - Prob. 3RECh. 8 - In Exercises 16, say how many elements are in the...Ch. 8 - Prob. 5RECh. 8 - Prob. 6RECh. 8 - In Exercises 710, calculate the relative frequency...Ch. 8 - Prob. 8RECh. 8 - In Exercises 710, calculate the relative frequency...Ch. 8 - In Exercises 710, calculate the relative frequency...Ch. 8 - In Exercises 1114, calculate the probability P(E)....Ch. 8 - Prob. 12RECh. 8 - In Exercises 1114, calculate the probability P(E)....Ch. 8 - Prob. 14RECh. 8 - Prob. 15RECh. 8 - Prob. 16RECh. 8 - Prob. 17RECh. 8 - A bag contains four red marbles, two green ones,...Ch. 8 - Prob. 19RECh. 8 - A bag contains four red marbles, two green ones,...Ch. 8 - Prob. 21RECh. 8 - Prob. 22RECh. 8 - Prob. 23RECh. 8 - Prob. 24RECh. 8 - Prob. 25RECh. 8 - Prob. 26RECh. 8 - Prob. 27RECh. 8 - Prob. 28RECh. 8 - Prob. 29RECh. 8 - Prob. 30RECh. 8 - Two dice, one green and one yellow, are rolled. In...Ch. 8 - Two dice, one green and one yellow, are rolled. In...Ch. 8 - Prob. 33RECh. 8 - Prob. 34RECh. 8 - Prob. 35RECh. 8 - Prob. 36RECh. 8 - Prob. 37RECh. 8 - Prob. 38RECh. 8 - Prob. 39RECh. 8 - Prob. 40RECh. 8 - Prob. 41RECh. 8 - Prob. 42RECh. 8 - Prob. 43RECh. 8 - Prob. 44RECh. 8 - Prob. 45RECh. 8 - Prob. 46RECh. 8 - Prob. 47RECh. 8 - Prob. 48RECh. 8 - Prob. 49RECh. 8 - Marketing To gauge the effectiveness of the...Ch. 8 - Prob. 51RECh. 8 - Prob. 52RECh. 8 - Prob. 53RECh. 8 - Prob. 54RECh. 8 - Prob. 55RECh. 8 - Prob. 56RECh. 8 - Prob. 57RECh. 8 - Prob. 58RE
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- (10) (16 points) Let R>0. Consider the truncated sphere S given as x² + y² + (z = √15R)² = R², z ≥0. where F(x, y, z) = −yi + xj . (a) (8 points) Consider the vector field V (x, y, z) = (▼ × F)(x, y, z) Think of S as a hot-air balloon where the vector field V is the velocity vector field measuring the hot gasses escaping through the porous surface S. The flux of V across S gives the volume flow rate of the gasses through S. Calculate this flux. Hint: Parametrize the boundary OS. Then use Stokes' Theorem. (b) (8 points) Calculate the surface area of the balloon. To calculate the surface area, do the following: Translate the balloon surface S by the vector (-15)k. The translated surface, call it S+ is part of the sphere x² + y²+z² = R². Why do S and S+ have the same area? ⚫ Calculate the area of S+. What is the natural spherical parametrization of S+?arrow_forward(1) (8 points) Let c(t) = (et, et sint, et cost). Reparametrize c as a unit speed curve starting from the point (1,0,1).arrow_forward(9) (16 points) Let F(x, y, z) = (x² + y − 4)i + 3xyj + (2x2 +z²)k = - = (x²+y4,3xy, 2x2 + 2²). (a) (4 points) Calculate the divergence and curl of F. (b) (6 points) Find the flux of V x F across the surface S given by x² + y²+2² = 16, z ≥ 0. (c) (6 points) Find the flux of F across the boundary of the unit cube E = [0,1] × [0,1] x [0,1].arrow_forward
- (8) (12 points) (a) (8 points) Let C be the circle x² + y² = 4. Let F(x, y) = (2y + e²)i + (x + sin(y²))j. Evaluate the line integral JF. F.ds. Hint: First calculate V x F. (b) (4 points) Let S be the surface r² + y² + z² = 4, z ≤0. Calculate the flux integral √(V × F) F).dS. Justify your answer.arrow_forwardDetermine whether the Law of Sines or the Law of Cosines can be used to find another measure of the triangle. a = 13, b = 15, C = 68° Law of Sines Law of Cosines Then solve the triangle. (Round your answers to four decimal places.) C = 15.7449 A = 49.9288 B = 62.0712 × Need Help? Read It Watch Itarrow_forward(4) (10 points) Evaluate √(x² + y² + z²)¹⁄² exp[}(x² + y² + z²)²] dV where D is the region defined by 1< x² + y²+ z² ≤4 and √√3(x² + y²) ≤ z. Note: exp(x² + y²+ 2²)²] means el (x²+ y²+=²)²]¸arrow_forward
- (2) (12 points) Let f(x,y) = x²e¯. (a) (4 points) Calculate Vf. (b) (4 points) Given x directional derivative 0, find the line of vectors u = D₁f(x, y) = 0. (u1, 2) such that the - (c) (4 points) Let u= (1+3√3). Show that Duƒ(1, 0) = ¦|▼ƒ(1,0)| . What is the angle between Vf(1,0) and the vector u? Explain.arrow_forwardFind the missing values by solving the parallelogram shown in the figure. (The lengths of the diagonals are given by c and d. Round your answers to two decimal places.) a b 29 39 66.50 C 17.40 d 0 54.0 126° a Ꮎ b darrow_forward(5) (10 points) Let D be the parallelogram in the xy-plane with vertices (0, 0), (1, 1), (1, 1), (0, -2). Let f(x,y) = xy/2. Use the linear change of variables T(u, v)=(u,u2v) = (x, y) 1 to calculate the integral f(x,y) dA= 0 ↓ The domain of T is a rectangle R. What is R? |ǝ(x, y) du dv. |ð(u, v)|arrow_forward
- 2 Anot ined sove in peaper PV+96252 Q3// Find the volume of the region between the cylinder z = y2 and the xy- plane that is bounded by the planes x=1, x=2,y=-2,andy=2. vertical rect a Q4// Draw and Evaluate Soxy-2sin (ny2)dydx D Lake tarrow_forwardDetermine whether the Law of Sines or the Law of Cosines can be used to find another measure of the triangle. B 13 cm 97° Law of Sines Law of Cosines A 43° Then solve the triangle. (Round your answers to two decimal places.) b = x C = A = 40.00arrow_forwardFind the missing values by solving the parallelogram shown in the figure. (The lengths of the diagonals are given by c and d. Round your answers to two decimal places.) a 29 b 39 d Ꮎ 126° a Ꮎ b darrow_forward
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