Student Solutions Manual for Waner/Costenoble's Finite Math and Applied Calculus, 7th
7th Edition
ISBN: 9781337275972
Author: Waner, Stefan; Costenoble, Steven
Publisher: Cengage Learning
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Chapter 7.4, Problem 83E
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Question 1. (10 points)
A researcher is studying tumours in mice. The growth rate for the volume of the tumour V(t) in cm³ is given by
dV
=
1.45V(2 In(V+1)).
dt
(a) (4 pts) Find all the equilibria and determine their stability using the stability condition.
(b) (2 pts) Draw the phase plot f(V) versus V where f(V) = V'. You may find it helpful to use Desmos or Wolfram Alpha to plot the graph of
f(V) versus V (both are free to use online), or you can plot it by hand if you like. On the plot identify each equilibrium as stable or unstable.
(c) (4 pts) Draw direction arrows for the case where the tumour starts at size 3cm³ and for the case where the tumour starts at size 9cm³. Explain
in biological terms what happens to the size of each of these tumours at time progresses.
For the system consisting of the two planes:plane 1: -x + y + z = 0plane 2: 3x + y + 3z = 0a) Are the planes parallel and/or coincident? Justify your answer. What does this tell you about the solution to the system?b) Solve the system (if possible). Show a complete solution. If there is a line of intersection express it in parametric form.
Question 2: (10 points) Evaluate the definite integral.
Use the following form of the definition of the integral to evaluate the integral:
Theorem: Iff is integrable on [a, b], then
where Ax = (ba)/n and x₂ = a + i^x.
You might need the following formulas.
IM³
L² (3x²
(3x²+2x-
2x - 1)dx.
n
[f(z)dz lim f(x)Az
a
n→∞
i=1
n(n + 1)
2
n
i=1
n(n+1)(2n+1)
6
Chapter 7 Solutions
Student Solutions Manual for Waner/Costenoble's Finite Math and Applied Calculus, 7th
Ch. 7.1 - Prob. 1ECh. 7.1 - Prob. 2ECh. 7.1 - Prob. 3ECh. 7.1 - Prob. 4ECh. 7.1 - Prob. 5ECh. 7.1 - Prob. 6ECh. 7.1 - Prob. 7ECh. 7.1 - Prob. 8ECh. 7.1 - Prob. 9ECh. 7.1 - Prob. 10E
Ch. 7.1 - Prob. 11ECh. 7.1 - Prob. 12ECh. 7.1 - Prob. 13ECh. 7.1 - Prob. 14ECh. 7.1 - Prob. 15ECh. 7.1 - Prob. 16ECh. 7.1 - In Exercises 1720, draw a Venn diagram that...Ch. 7.1 - Prob. 18ECh. 7.1 - In Exercises 1720, draw a Venn diagram that...Ch. 7.1 - Prob. 20ECh. 7.1 - Prob. 21ECh. 7.1 - Prob. 22ECh. 7.1 - Prob. 23ECh. 7.1 - Prob. 24ECh. 7.1 - Prob. 25ECh. 7.1 - Prob. 26ECh. 7.1 - Prob. 27ECh. 7.1 - Prob. 28ECh. 7.1 - Prob. 29ECh. 7.1 - Prob. 30ECh. 7.1 - Prob. 31ECh. 7.1 - Prob. 32ECh. 7.1 - Prob. 33ECh. 7.1 - Prob. 34ECh. 7.1 - In Exercises 3542, A={small,medium,large},...Ch. 7.1 - In Exercises 3542, A={small,medium,large},...Ch. 7.1 - Prob. 37ECh. 7.1 - In Exercises 3542, A={small,medium,large},...Ch. 7.1 - Prob. 39ECh. 7.1 - In Exercises 3542, A={small,medium,large},...Ch. 7.1 - Prob. 41ECh. 7.1 - In Exercises 3542, A={small,medium,large},...Ch. 7.1 - Prob. 43ECh. 7.1 - Let A={H, T} be the set of outcomes when a coin is...Ch. 7.1 - Prob. 45ECh. 7.1 - Let A={H, T} be the set of outcomes when a coin is...Ch. 7.1 - Prob. 47ECh. 7.1 - Prob. 48ECh. 7.1 - Prob. 49ECh. 7.1 - Prob. 50ECh. 7.1 - Prob. 51ECh. 7.1 - Prob. 52ECh. 7.1 - Prob. 53ECh. 7.1 - Prob. 54ECh. 7.1 - Prob. 55ECh. 7.1 - Prob. 56ECh. 7.1 - Prob. 57ECh. 7.1 - Prob. 58ECh. 7.1 - Prob. 59ECh. 7.1 - Prob. 60ECh. 7.1 - Databases A freelance computer consultant keeps a...Ch. 7.1 - Databases A freelance computer consultant keeps a...Ch. 7.1 - Databases A freelance computer consultant keeps a...Ch. 7.1 - Databases A freelance computer consultant keeps a...Ch. 7.1 - Databases A freelance computer consultant keeps a...Ch. 7.1 - Prob. 66ECh. 7.1 - Databases A freelance computer consultant keeps a...Ch. 7.1 - Databases A freelance computer consultant keeps a...Ch. 7.1 - You sell iPads and jPads. Let I be the set of all...Ch. 7.1 - Prob. 72ECh. 7.1 - You are searching online for techno music that is...Ch. 7.1 - Prob. 74ECh. 7.1 - Prob. 75ECh. 7.1 - Prob. 76ECh. 7.1 - Prob. 77ECh. 7.1 - Prob. 78ECh. 7.1 - Prob. 79ECh. 7.1 - Prob. 80ECh. 7.1 - Prob. 81ECh. 7.1 - Prob. 82ECh. 7.1 - When this book was being written, the copy editor...Ch. 7.1 - Prob. 84ECh. 7.2 - Let A={Drink,Johan,Frans,Sarie},...Ch. 7.2 - Let A={Drink,Johan,Frans,Sarie},...Ch. 7.2 - Let A={Drink,Johan,Frans,Sarie},...Ch. 7.2 - Let A={Drink,Johan,Frans,Sarie},...Ch. 7.2 - Let A={Drink,Johan,Frans,Sarie},...Ch. 7.2 - Let A={Drink,Johan,Frans,Sarie},...Ch. 7.2 - Verify that n(AB)=n(A)+n(B)n(AB) with A and B as...Ch. 7.2 - Verify that n(AC)=n(A)+n(C)n(AC) with A and C as...Ch. 7.2 - Let A={H,T},B={1,2,3,4,5,6}, and...Ch. 7.2 - Let A={H,T},B={1,2,3,4,5,6}, and...Ch. 7.2 - Let A={H,T},B={1,2,3,4,5,6}, and...Ch. 7.2 - Let A={H,T},B={1,2,3,4,5,6}, and...Ch. 7.2 - Let A={H,T},B={1,2,3,4,5,6}, and...Ch. 7.2 - Let A={H,T},B={1,2,3,4,5,6}, and...Ch. 7.2 - If n(A)=43,n(B)=20, and n(AB)=3, find n(AB).Ch. 7.2 - If n(A)=60, n(B)=20, and n(AB)=1 find n(AB).Ch. 7.2 - If n(AB)=100andn(A)=n(B)=60, fi0nd n(AB).Ch. 7.2 - If n(A)=100,n(AB)=150, and n(AB)=40, find n(B).Ch. 7.2 - Prob. 19ECh. 7.2 - Prob. 20ECh. 7.2 - Prob. 21ECh. 7.2 - Prob. 22ECh. 7.2 - Prob. 23ECh. 7.2 - Prob. 24ECh. 7.2 - Prob. 25ECh. 7.2 - With S,A,andB as above, verify that...Ch. 7.2 - Prob. 27ECh. 7.2 - In Exercises 2730, use the given information to...Ch. 7.2 - In Exercises 2730, use the given information to...Ch. 7.2 - Prob. 30ECh. 7.2 - Web Searches In November 2011 a search using the...Ch. 7.2 - Web Searches In November 2011 a search using the...Ch. 7.2 - Amusement On a particularly boring transatlantic...Ch. 7.2 - Restaurant Menus While scanning through the...Ch. 7.2 - Mobile Gamers Of a total of 132 million mobile...Ch. 7.2 - Mobile Gamers Of a total of 208 million mobile...Ch. 7.2 - Prob. 37ECh. 7.2 - Prob. 38ECh. 7.2 - Prob. 39ECh. 7.2 - Prob. 40ECh. 7.2 - Prob. 41ECh. 7.2 - Prob. 42ECh. 7.2 - Housing Starts Exercises 4348 are based on the...Ch. 7.2 - Housing Starts Exercises 4348 are based on the...Ch. 7.2 - Housing Starts Exercises 4348 are based on the...Ch. 7.2 - Housing Starts Exercises 4348 are based on the...Ch. 7.2 - Housing Starts Exercises 4348 are based on the...Ch. 7.2 - Housing Starts Exercises 4348 are based on the...Ch. 7.2 - Stocks Exercises 4954 are based on the following...Ch. 7.2 - Stocks Exercises 4954 are based on the following...Ch. 7.2 - Stocks Exercises 4954 are based on the following...Ch. 7.2 - Stocks Exercises 4954 are based on the following...Ch. 7.2 - Stocks Exercises 4954 are based on the following...Ch. 7.2 - Stocks Exercises 4954 are based on the following...Ch. 7.2 - Medicine In a study of Tibetan children,10 a total...Ch. 7.2 - Medicine In a study of Tibetan children,11 a total...Ch. 7.2 - Entertainment According to a survey of 100 people...Ch. 7.2 - Athletics Of the 4,700 students at Medium Suburban...Ch. 7.2 - Entertainment In a survey of 100 Enormous State...Ch. 7.2 - Entertainment Refer back to Exercise 59. You are...Ch. 7.2 - Prob. 61ECh. 7.2 - Prob. 62ECh. 7.2 - Why is the Cartesian product referred to as a...Ch. 7.2 - Refer back to your answer to Exercise 63. What set...Ch. 7.2 - Formulate an interesting application whose answer...Ch. 7.2 - Formulate an interesting application whose answer...Ch. 7.2 - When is n(AB)n(A)+n(B)?Ch. 7.2 - When is n(AB)=n(A)?Ch. 7.2 - When is n(AB)=n(A)?Ch. 7.2 - When is n(AB)=n(A)?Ch. 7.2 - Use a Venn diagram or some other method to obtain...Ch. 7.2 - Prob. 72ECh. 7.3 - An experiment requires a choice among three...Ch. 7.3 - Prob. 2ECh. 7.3 - An experiment requires a sequence of three steps....Ch. 7.3 - Prob. 4ECh. 7.3 - Prob. 5ECh. 7.3 - Prob. 6ECh. 7.3 - Prob. 7ECh. 7.3 - Prob. 8ECh. 7.3 - Prob. 9ECh. 7.3 - Prob. 10ECh. 7.3 - Prob. 11ECh. 7.3 - Prob. 12ECh. 7.3 - How many different four-letter sequences can be...Ch. 7.3 - Prob. 14ECh. 7.3 - Ice Cream When Baskin-Robbins was founded in 1945,...Ch. 7.3 - Prob. 16ECh. 7.3 - Prob. 17ECh. 7.3 - Ternary Codes A ternary digit is either 0, 1, or...Ch. 7.3 - Ternary Codes A ternary digit is either 0, 1, or...Ch. 7.3 - Binary Codes A binary digit, or bit, is either 0...Ch. 7.3 - Reward While selecting candy for students in his...Ch. 7.3 - Productivity Professor Oger must choose between an...Ch. 7.3 - Prob. 23ECh. 7.3 - Radar Detectors Radar detectors are either powered...Ch. 7.3 - Multiple-Choice Tests Professor Easys final...Ch. 7.3 - Multiple-Choice Tests Professor Toughs final...Ch. 7.3 - Tests A test requires that you answer either Part...Ch. 7.3 - Tests A test requires that you answer first Part A...Ch. 7.3 - Stock Portfolios Your broker has suggested that...Ch. 7.3 - Prob. 30ECh. 7.3 - Computer Codes A computer byte consists of eight...Ch. 7.3 - Prob. 32ECh. 7.3 - Prob. 33ECh. 7.3 - Prob. 34ECh. 7.3 - Prob. 35ECh. 7.3 - Prob. 36ECh. 7.3 - Tournaments How many ways are there of filling in...Ch. 7.3 - Prob. 38ECh. 7.3 - Prob. 39ECh. 7.3 - Prob. 40ECh. 7.3 - Prob. 41ECh. 7.3 - Prob. 42ECh. 7.3 - DNA Chains: Life in Nature DNA (deoxyribonucleic...Ch. 7.3 - Prob. 44ECh. 7.3 - Prob. 45ECh. 7.3 - Telephone Numbers In the past, a local telephone...Ch. 7.3 - Romeo and Juliet Here is a list of the main...Ch. 7.3 - Prob. 48ECh. 7.3 - Prob. 49ECh. 7.3 - Prob. 50ECh. 7.3 - Mazes a. How many four-letter sequences are...Ch. 7.3 - Prob. 52ECh. 7.3 - Prob. 53ECh. 7.3 - Prob. 54ECh. 7.3 - Prob. 55ECh. 7.3 - Combination Locks Dripping wet after your shower,...Ch. 7.3 - Prob. 57ECh. 7.3 - Prob. 58ECh. 7.3 - Prob. 59ECh. 7.3 - Prob. 60ECh. 7.3 - Prob. 61ECh. 7.3 - Programming in Java Script (Some programming...Ch. 7.3 - Prob. 63ECh. 7.3 - Prob. 64ECh. 7.3 - Prob. 65ECh. 7.3 - Numbers How many odd numbers between 10 and 99...Ch. 7.3 - Prob. 67ECh. 7.3 - Prob. 68ECh. 7.3 - Prob. 69ECh. 7.3 - Prob. 70ECh. 7.3 - Prob. 71ECh. 7.3 - Find an interesting application that requires a...Ch. 7.4 - In Exercises 116, evaluate the number. [HINT: See...Ch. 7.4 - Prob. 2ECh. 7.4 - Prob. 3ECh. 7.4 - In Exercises 116, evaluate the number. [HINT: See...Ch. 7.4 - Prob. 5ECh. 7.4 - Prob. 6ECh. 7.4 - Prob. 7ECh. 7.4 - Prob. 8ECh. 7.4 - Prob. 9ECh. 7.4 - Prob. 10ECh. 7.4 - Prob. 11ECh. 7.4 - Prob. 12ECh. 7.4 - Prob. 13ECh. 7.4 - Prob. 14ECh. 7.4 - Prob. 15ECh. 7.4 - Prob. 16ECh. 7.4 - How many ordered lists are there of four items...Ch. 7.4 - Prob. 18ECh. 7.4 - Prob. 19ECh. 7.4 - Prob. 20ECh. 7.4 - Prob. 21ECh. 7.4 - Prob. 22ECh. 7.4 - Prob. 23ECh. 7.4 - Prob. 24ECh. 7.4 - Prob. 25ECh. 7.4 - Prob. 26ECh. 7.4 - How many six-letter sequences are possible that...Ch. 7.4 - Prob. 28ECh. 7.4 - Prob. 29ECh. 7.4 - Prob. 30ECh. 7.4 - Prob. 31ECh. 7.4 - Prob. 32ECh. 7.4 - Prob. 33ECh. 7.4 - Prob. 34ECh. 7.4 - Prob. 35ECh. 7.4 - Marbles For Exercises 2942, a bag contains three...Ch. 7.4 - Prob. 37ECh. 7.4 - Prob. 38ECh. 7.4 - Prob. 39ECh. 7.4 - Prob. 40ECh. 7.4 - Prob. 41ECh. 7.4 - Prob. 42ECh. 7.4 - Prob. 43ECh. 7.4 - Prob. 44ECh. 7.4 - Prob. 45ECh. 7.4 - Prob. 46ECh. 7.4 - Prob. 47ECh. 7.4 - In Exercises 4752, calculate how many different...Ch. 7.4 - Prob. 49ECh. 7.4 - Prob. 50ECh. 7.4 - Prob. 51ECh. 7.4 - Prob. 52ECh. 7.4 - Prob. 53ECh. 7.4 - Prob. 54ECh. 7.4 - Poker Hands A poker hand consists of 5 cards from...Ch. 7.4 - Prob. 56ECh. 7.4 - Prob. 57ECh. 7.4 - Prob. 58ECh. 7.4 - Prob. 59ECh. 7.4 - Prob. 60ECh. 7.4 - Dogs of the Dow The Dogs of the Dow are the stocks...Ch. 7.4 - Dogs of the Dow The Dogs of the Dow are the stocks...Ch. 7.4 - Day Trading Day traders typically buy and sell...Ch. 7.4 - Day Trading Day traders typically buy and sell...Ch. 7.4 - Elimination Tournaments In an elimination...Ch. 7.4 - Elimination Tournaments In an elimination...Ch. 7.4 - Prob. 67ECh. 7.4 - Elimination Tournaments In an elimination...Ch. 7.4 - Prob. 69ECh. 7.4 - Prob. 70ECh. 7.4 - Prob. 71ECh. 7.4 - Prob. 72ECh. 7.4 - Prob. 73ECh. 7.4 - Prob. 74ECh. 7.4 - Prob. 75ECh. 7.4 - Prob. 76ECh. 7.4 - Prob. 77ECh. 7.4 - Prob. 78ECh. 7.4 - Prob. 79ECh. 7.4 - Prob. 80ECh. 7.4 - Prob. 81ECh. 7.4 - Prob. 82ECh. 7.4 - Prob. 83ECh. 7.4 - Prob. 84ECh. 7.4 - Prob. 85ECh. 7.4 - Prob. 86ECh. 7.4 - Prob. 87ECh. 7.4 - Complete the following: If a counting procedure...Ch. 7.4 - Prob. 89ECh. 7.4 - Prob. 90ECh. 7 - Prob. 1RECh. 7 - Prob. 2RECh. 7 - Prob. 3RECh. 7 - Prob. 4RECh. 7 - Prob. 5RECh. 7 - Prob. 6RECh. 7 - Prob. 7RECh. 7 - Prob. 8RECh. 7 - Prob. 9RECh. 7 - Prob. 10RECh. 7 - Prob. 11RECh. 7 - Prob. 12RECh. 7 - Prob. 13RECh. 7 - Prob. 14RECh. 7 - Prob. 15RECh. 7 - Prob. 16RECh. 7 - Prob. 17RECh. 7 - Prob. 18RECh. 7 - In Exercises 1924, consider a bag containing four...Ch. 7 - Prob. 20RECh. 7 - Prob. 21RECh. 7 - Prob. 22RECh. 7 - Prob. 23RECh. 7 - Prob. 24RECh. 7 - Prob. 25RECh. 7 - Inventories OHaganBooks.com currently operates...Ch. 7 - Prob. 27RECh. 7 - Inventories OHaganBooks.com currently operates...Ch. 7 - Inventories OHaganBooks.com currently operates...Ch. 7 - Prob. 30RECh. 7 - Prob. 31RECh. 7 - Prob. 32RECh. 7 - Prob. 33RECh. 7 - Prob. 34RECh. 7 - Prob. 35RECh. 7 - Prob. 36RECh. 7 - Prob. 37RECh. 7 - Prob. 38RECh. 7 - Online IDs As the customer base at OHaganBooks.com...Ch. 7 - Online IDs As the customer base at OHaganBooks.com...Ch. 7 - Prob. 41RECh. 7 - Prob. 42RECh. 7 - Prob. 43RE
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- For the system consisting of the three planes:plane 1: -4x + 4y - 2z = -8plane 2: 2x + 2y + 4z = 20plane 3: -2x - 3y + z = -1a) Are any of the planes parallel and/or coincident? Justify your answer.b) Determine if the normals are coplanar. What does this tell you about the system?c) Solve the system if possible. Show a complete solution (do not use matrix operations). Classify the system using the terms: consistent, inconsistent, dependent and/or independent.arrow_forwardFor the system consisting of the three planes:plane 1: -4x + 4y - 2z = -8plane 2: 2x + 2y + 4z = 20plane 3: -2x - 3y + z = -1a) Are any of the planes parallel and/or coincident? Justify your answer.b) Determine if the normals are coplanar. What does this tell you about the system?c) Solve the system if possible. Show a complete solution (do not use matrix operations). Classify the system using the terms: consistent, inconsistent, dependent and/or independent.arrow_forwardOpen your tool box and find geometric methods, symmetries of even and odd functions and the evaluation theorem. Use these to calculate the following definite integrals. Note that you should not use Riemann sums for this problem. (a) (4 pts) (b) (2 pts) 3 S³ 0 3-x+9-dz x3 + sin(x) x4 + cos(x) dx (c) (4 pts) L 1-|x|dxarrow_forward
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