Finite Mathematics and Calculus with Applications (10th Edition)
10th Edition
ISBN: 9780321979407
Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey
Publisher: PEARSON
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Chapter 2.5, Problem 57E
To determine
To solve: The matrix equation
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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 2 Solutions
Finite Mathematics and Calculus with Applications (10th Edition)
Ch. 2.1 - Solve the system 2x+3y=123x4y=1.Ch. 2.1 - Prob. 2YTCh. 2.1 - Prob. 3YTCh. 2.1 - Prob. 1ECh. 2.1 - Prob. 2ECh. 2.1 - Prob. 3ECh. 2.1 - Prob. 4ECh. 2.1 - Prob. 5ECh. 2.1 - Prob. 6ECh. 2.1 - Prob. 7E
Ch. 2.1 - Prob. 8ECh. 2.1 - Use the echelon method to solve each system of two...Ch. 2.1 - Prob. 10ECh. 2.1 - Use the echelon method to solve each system of two...Ch. 2.1 - Prob. 12ECh. 2.1 - Prob. 13ECh. 2.1 - Prob. 14ECh. 2.1 - Prob. 15ECh. 2.1 - Prob. 16ECh. 2.1 - Prob. 17ECh. 2.1 - Prob. 18ECh. 2.1 - Prob. 19ECh. 2.1 - Prob. 20ECh. 2.1 - Prob. 21ECh. 2.1 - Prob. 22ECh. 2.1 - Prob. 23ECh. 2.1 - Prob. 24ECh. 2.1 - Prob. 25ECh. 2.1 - Solve each system of equations. Let z be the...Ch. 2.1 - Prob. 27ECh. 2.1 - Prob. 28ECh. 2.1 - For each of the following systems of equations in...Ch. 2.1 - For each of the following systems of equations in...Ch. 2.1 - Prob. 31ECh. 2.1 - Prob. 32ECh. 2.1 - Prob. 33ECh. 2.1 - Prob. 34ECh. 2.1 - Prob. 35ECh. 2.1 - Prob. 36ECh. 2.1 - Prob. 37ECh. 2.1 - Prob. 38ECh. 2.1 - Prob. 39ECh. 2.1 - Prob. 40ECh. 2.1 - Prob. 41ECh. 2.1 - Prob. 42ECh. 2.1 - Prob. 43ECh. 2.1 - Prob. 44ECh. 2.1 - Life Sciences 45. Birds The date of the first...Ch. 2.1 - Prob. 46ECh. 2.1 - Prob. 47ECh. 2.1 - Flight Time A flight leaves New York at 8 P.M. and...Ch. 2.1 - Prob. 49ECh. 2.2 - Prob. 1YTCh. 2.2 - Use the Gauss-Jordan method to solve the system...Ch. 2.2 - Prob. 3YTCh. 2.2 - Prob. 1WECh. 2.2 - Prob. 2WECh. 2.2 - Prob. 1ECh. 2.2 - Prob. 2ECh. 2.2 - Prob. 3ECh. 2.2 - Prob. 4ECh. 2.2 - Prob. 5ECh. 2.2 - Prob. 6ECh. 2.2 - Prob. 7ECh. 2.2 - Prob. 8ECh. 2.2 - Prob. 9ECh. 2.2 - Prob. 10ECh. 2.2 - Prob. 11ECh. 2.2 - Prob. 12ECh. 2.2 - Prob. 13ECh. 2.2 - Prob. 14ECh. 2.2 - Prob. 15ECh. 2.2 - Prob. 16ECh. 2.2 - Prob. 17ECh. 2.2 - Prob. 18ECh. 2.2 - Prob. 19ECh. 2.2 - Prob. 20ECh. 2.2 - Prob. 21ECh. 2.2 - Use the Gauss-Jordan method to solve each system...Ch. 2.2 - Prob. 23ECh. 2.2 - Prob. 24ECh. 2.2 - Prob. 25ECh. 2.2 - Prob. 26ECh. 2.2 - Use the Gauss-Jordan method to solve each system...Ch. 2.2 - Prob. 28ECh. 2.2 - Prob. 29ECh. 2.2 - Prob. 30ECh. 2.2 - Prob. 31ECh. 2.2 - Prob. 32ECh. 2.2 - Prob. 33ECh. 2.2 - Prob. 34ECh. 2.2 - Prob. 35ECh. 2.2 - Prob. 36ECh. 2.2 - Prob. 37ECh. 2.2 - Prob. 38ECh. 2.2 - Prob. 39ECh. 2.2 - Use the Gauss-Jordan method to solve each system...Ch. 2.2 - Prob. 41ECh. 2.2 - Prob. 42ECh. 2.2 - On National Public Radio, the Weekend Edition...Ch. 2.2 - Prob. 44ECh. 2.2 - Investments Katherine Chong invests 10,000...Ch. 2.2 - Prob. 46ECh. 2.2 - Prob. 47ECh. 2.2 - Prob. 48ECh. 2.2 - Loans To get the necessary funds for a planned...Ch. 2.2 - Manufacturing Nadir, Inc. produces three models of...Ch. 2.2 - Deliveries An electronics company produces three...Ch. 2.2 - Tents L.L. Bean makes three sizes of Ultra Dome...Ch. 2.2 - Prob. 53ECh. 2.2 - APPLY IT Transportation An auto manufacturer sends...Ch. 2.2 - Prob. 55ECh. 2.2 - Prob. 56ECh. 2.2 - Prob. 57ECh. 2.2 - Prob. 58ECh. 2.2 - Prob. 59ECh. 2.2 - Prob. 60ECh. 2.2 - Prob. 61ECh. 2.2 - Health The U.S. National Center for Health...Ch. 2.2 - Prob. 63ECh. 2.2 - Prob. 64ECh. 2.2 - Prob. 65ECh. 2.2 - Prob. 66ECh. 2.2 - Baseball Ichiro Suzuki holds the American League...Ch. 2.2 - Prob. 69ECh. 2.2 - Snack Food According to the nutrition labels on...Ch. 2.2 - Lights Out The Tiger Electronics game, Lights Out,...Ch. 2.2 - Prob. 72ECh. 2.2 - Prob. 73ECh. 2.3 - Prob. 1YTCh. 2.3 - Prob. 2YTCh. 2.3 - Prob. 1ECh. 2.3 - Prob. 2ECh. 2.3 - Decide whether each statement is true or false. If...Ch. 2.3 - Prob. 4ECh. 2.3 - Prob. 5ECh. 2.3 - Prob. 6ECh. 2.3 - Prob. 7ECh. 2.3 - Prob. 8ECh. 2.3 - Prob. 9ECh. 2.3 - Prob. 10ECh. 2.3 - Prob. 11ECh. 2.3 - Prob. 12ECh. 2.3 - Prob. 13ECh. 2.3 - Prob. 14ECh. 2.3 - Prob. 15ECh. 2.3 - Prob. 16ECh. 2.3 - Prob. 17ECh. 2.3 - Prob. 18ECh. 2.3 - Prob. 19ECh. 2.3 - Prob. 20ECh. 2.3 - Prob. 21ECh. 2.3 - Prob. 22ECh. 2.3 - Prob. 23ECh. 2.3 - Prob. 24ECh. 2.3 - Prob. 25ECh. 2.3 - Prob. 26ECh. 2.3 - Prob. 27ECh. 2.3 - Prob. 28ECh. 2.3 - Prob. 29ECh. 2.3 - Prob. 30ECh. 2.3 - Prob. 31ECh. 2.3 - Prob. 32ECh. 2.3 - Prob. 33ECh. 2.3 - Prob. 34ECh. 2.3 - Prob. 35ECh. 2.3 - Prob. 36ECh. 2.3 - Prob. 37ECh. 2.3 - Prob. 38ECh. 2.3 - Prob. 39ECh. 2.3 - Prob. 40ECh. 2.3 - Prob. 41ECh. 2.3 - Prob. 42ECh. 2.3 - Prob. 43ECh. 2.3 - Prob. 44ECh. 2.3 - Prob. 45ECh. 2.3 - Prob. 46ECh. 2.3 - Life Expectancy The following table gives the life...Ch. 2.3 - Prob. 48ECh. 2.3 - Educational Attainment The following table gives...Ch. 2.3 - Prob. 50ECh. 2.4 - Prob. 1YTCh. 2.4 - Prob. 2YTCh. 2.4 - Prob. 1ECh. 2.4 - Prob. 2ECh. 2.4 - Prob. 3ECh. 2.4 - Prob. 4ECh. 2.4 - Prob. 5ECh. 2.4 - Prob. 6ECh. 2.4 - Prob. 7ECh. 2.4 - Prob. 8ECh. 2.4 - Prob. 9ECh. 2.4 - Prob. 10ECh. 2.4 - Prob. 11ECh. 2.4 - Prob. 12ECh. 2.4 - Prob. 13ECh. 2.4 - The product matrix AB has the same number of...Ch. 2.4 - Prob. 15ECh. 2.4 - Prob. 16ECh. 2.4 - Prob. 17ECh. 2.4 - Prob. 18ECh. 2.4 - Prob. 19ECh. 2.4 - Prob. 20ECh. 2.4 - Prob. 21ECh. 2.4 - Prob. 22ECh. 2.4 - Prob. 23ECh. 2.4 - Prob. 24ECh. 2.4 - Prob. 25ECh. 2.4 - Prob. 26ECh. 2.4 - Prob. 27ECh. 2.4 - Prob. 28ECh. 2.4 - Prob. 29ECh. 2.4 - Prob. 30ECh. 2.4 - Prob. 31ECh. 2.4 - Prob. 32ECh. 2.4 - Prob. 33ECh. 2.4 - Prob. 34ECh. 2.4 - Prob. 35ECh. 2.4 - Prob. 36ECh. 2.4 - Prob. 37ECh. 2.4 - Prob. 38ECh. 2.4 - Prob. 39ECh. 2.4 - Prob. 40ECh. 2.4 - Prob. 41ECh. 2.4 - Prob. 42ECh. 2.4 - Prob. 43ECh. 2.4 - Prob. 44ECh. 2.4 - Prob. 45ECh. 2.4 - Prob. 46ECh. 2.4 - Prob. 47ECh. 2.4 - Cost Analysis The Mundo Candy Company makes three...Ch. 2.4 - Shoe Sales Sals Shoes and Freds Footwear both have...Ch. 2.4 - Prob. 50ECh. 2.4 - Prob. 51ECh. 2.4 - Prob. 52ECh. 2.4 - Prob. 53ECh. 2.4 - Prob. 54ECh. 2.4 - Prob. 55ECh. 2.4 - Prob. 56ECh. 2.4 - Prob. 57ECh. 2.5 - Prob. 1YTCh. 2.5 - Prob. 2YTCh. 2.5 - Prob. 3YTCh. 2.5 - Prob. 1WECh. 2.5 - Prob. 2WECh. 2.5 - Prob. 3WECh. 2.5 - Prob. 4WECh. 2.5 - Prob. 1ECh. 2.5 - Prob. 2ECh. 2.5 - Prob. 3ECh. 2.5 - Prob. 4ECh. 2.5 - Prob. 5ECh. 2.5 - Prob. 6ECh. 2.5 - Prob. 7ECh. 2.5 - Prob. 8ECh. 2.5 - Prob. 9ECh. 2.5 - Prob. 10ECh. 2.5 - Prob. 11ECh. 2.5 - Prob. 12ECh. 2.5 - Prob. 13ECh. 2.5 - Prob. 14ECh. 2.5 - Prob. 15ECh. 2.5 - Prob. 16ECh. 2.5 - Prob. 17ECh. 2.5 - Prob. 18ECh. 2.5 - Prob. 19ECh. 2.5 - Prob. 20ECh. 2.5 - Prob. 21ECh. 2.5 - Prob. 22ECh. 2.5 - Prob. 23ECh. 2.5 - Prob. 24ECh. 2.5 - Prob. 25ECh. 2.5 - Prob. 26ECh. 2.5 - Prob. 27ECh. 2.5 - Prob. 28ECh. 2.5 - Prob. 29ECh. 2.5 - Prob. 30ECh. 2.5 - Solve each system of equations by using the...Ch. 2.5 - Prob. 32ECh. 2.5 - Prob. 33ECh. 2.5 - Prob. 34ECh. 2.5 - Prob. 35ECh. 2.5 - Prob. 36ECh. 2.5 - Prob. 37ECh. 2.5 - Prob. 38ECh. 2.5 - Prob. 39ECh. 2.5 - Prob. 40ECh. 2.5 - Prob. 41ECh. 2.5 - Prob. 42ECh. 2.5 - Prob. 43ECh. 2.5 - Prob. 44ECh. 2.5 - Prob. 45ECh. 2.5 - Prob. 46ECh. 2.5 - Prob. 47ECh. 2.5 - Prob. 48ECh. 2.5 - Prob. 49ECh. 2.5 - Prob. 50ECh. 2.5 - Prob. 51ECh. 2.5 - Prob. 52ECh. 2.5 - Prob. 53ECh. 2.5 - Prob. 54ECh. 2.5 - Prob. 55ECh. 2.5 - Prob. 56ECh. 2.5 - Prob. 57ECh. 2.5 - Prob. 58ECh. 2.5 - Solve each exercise by using the inverse of the...Ch. 2.5 - Prob. 60ECh. 2.5 - Solve each exercise by using the inverse of the...Ch. 2.5 - Prob. 62ECh. 2.5 - Prob. 63ECh. 2.5 - Encryption Use the matrices presented in Example 7...Ch. 2.5 - Prob. 65ECh. 2.5 - Prob. 66ECh. 2.6 - Prob. 1YTCh. 2.6 - Prob. 2YTCh. 2.6 - Prob. 1WECh. 2.6 - Prob. 2WECh. 2.6 - Prob. 1ECh. 2.6 - Prob. 2ECh. 2.6 - Prob. 3ECh. 2.6 - Prob. 4ECh. 2.6 - Prob. 5ECh. 2.6 - Prob. 6ECh. 2.6 - Prob. 7ECh. 2.6 - Find the ratios of products A, B, and C using a...Ch. 2.6 - Prob. 9ECh. 2.6 - Prob. 10ECh. 2.6 - Business and Economics Input-Output Open Model In...Ch. 2.6 - Prob. 12ECh. 2.6 - Prob. 13ECh. 2.6 - Prob. 14ECh. 2.6 - Prob. 15ECh. 2.6 - Prob. 16ECh. 2.6 - Prob. 17ECh. 2.6 - Prob. 18ECh. 2.6 - Prob. 19ECh. 2.6 - Prob. 20ECh. 2.6 - Prob. 21ECh. 2.6 - Prob. 22ECh. 2.6 - Prob. 23ECh. 2.6 - Prob. 24ECh. 2.6 - Prob. 25ECh. 2.6 - Prob. 26ECh. 2.6 - Prob. 27ECh. 2.6 - Prob. 28ECh. 2.6 - Prob. 29ECh. 2 - Determine whether each of the following statements...Ch. 2 - Prob. 2RECh. 2 - Determine whether each of the following statements...Ch. 2 - Prob. 4RECh. 2 - Prob. 6RECh. 2 - Determine whether each of the following statements...Ch. 2 - Prob. 8RECh. 2 - Determine whether each of the following statements...Ch. 2 - Prob. 10RECh. 2 - Determine whether each of the following statements...Ch. 2 - Prob. 12RECh. 2 - Determine whether each of the following statements...Ch. 2 - Prob. 14RECh. 2 - Determine whether each of the following statements...Ch. 2 - Prob. 16RECh. 2 - What is true about the number of solutions to a...Ch. 2 - Prob. 18RECh. 2 - Solve each system by the echelon method. 19....Ch. 2 - Prob. 20RECh. 2 - Solve each system by the echelon method. 21....Ch. 2 - Prob. 22RECh. 2 - Use the Gauss-Jordan method to solve each system...Ch. 2 - Prob. 24RECh. 2 - Use the Gauss-Jordan method to solve each system...Ch. 2 - Prob. 26RECh. 2 - Use the Gauss-Jordan method to solve each system...Ch. 2 - Prob. 28RECh. 2 - Find the size of each matrix, find the values of...Ch. 2 - Prob. 30RECh. 2 - Find the size of each matrix, find the values of...Ch. 2 - Prob. 32RECh. 2 - Given the matrices...Ch. 2 - Prob. 34RECh. 2 - Given the matrices...Ch. 2 - Prob. 36RECh. 2 - Given the matrices...Ch. 2 - Prob. 38RECh. 2 - Given the matrices...Ch. 2 - Prob. 40RECh. 2 - Given the matrices...Ch. 2 - Prob. 42RECh. 2 - Given the matrices...Ch. 2 - Prob. 44RECh. 2 - Given the matrices...Ch. 2 - Prob. 46RECh. 2 - Find the inverse, if it exists, for each matrix....Ch. 2 - Prob. 48RECh. 2 - Find the inverse, if it exists, for each matrix....Ch. 2 - Prob. 50RECh. 2 - Find the inverse, if it exists, for each matrix....Ch. 2 - Prob. 52RECh. 2 - Find the inverse, if it exists, for each matrix....Ch. 2 - Prob. 54RECh. 2 - Solve the matrix equation AX = B for X using the...Ch. 2 - Prob. 56RECh. 2 - Solve the matrix equation AX = B for X using the...Ch. 2 - Prob. 58RECh. 2 - Solve each system of equations by inverses. 59....Ch. 2 - Prob. 60RECh. 2 - Prob. 61RECh. 2 - Prob. 62RECh. 2 - Prob. 63RECh. 2 - Prob. 64RECh. 2 - Prob. 65RECh. 2 - Prob. 66RECh. 2 - Production Requirements The Waputi Indians make...Ch. 2 - Prob. 68RECh. 2 - Prob. 69RECh. 2 - Prob. 70RECh. 2 - Prob. 71RECh. 2 - Prob. 72RECh. 2 - Input-Output An economy depends on two...Ch. 2 - Nebraska The 1970 economy of the state of Nebraska...Ch. 2 - Prob. 75RECh. 2 - Prob. 76RECh. 2 - CAT Scans (Refer to Exercise 76.) Four X-ray beams...Ch. 2 - Prob. 78RECh. 2 - Prob. 79RECh. 2 - Prob. 80RECh. 2 - Prob. 81RECh. 2 - Prob. 82RECh. 2 - Prob. 83RECh. 2 - Baseball In the 2009 Major League Baseball season,...Ch. 2 - Prob. 85RE
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