College Mathematics for Business, Economics, Life Sciences, and Social Sciences + Mylab Math With Pearson Etext Title-specific Access Card:
14th Edition
ISBN: 9780134862613
Author: Barnett, Raymond A.
Publisher: Pearson College Div
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Chapter 4.6, Problem 24E
To determine
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4. Direction Fields/Phase Portraits. Use the given direction fields to plot solution curves
to each of the given initial value problems.
(a)
x = x+2y
1111
y = -3x+y
with x(0) = 1, y(0) = -1
(b) Consider the initial value problem corresponding to the given phase portrait.
x = y
y' = 3x + 2y
Draw two "straight line solutions"
passing through (0,0)
(c) Make guesses for the equations of the straight line solutions: y = ax.
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Chapter 4 Solutions
College Mathematics for Business, Economics, Life Sciences, and Social Sciences + Mylab Math With Pearson Etext Title-specific Access Card:
Ch. 4.1 - Solve by graphing and check:
2x − y = −3
x + 2y =...Ch. 4.1 - Solve each of the following systems by graphing:
x...Ch. 4.1 - Prob. 3MPCh. 4.1 - Prob. 4MPCh. 4.1 - Prob. 5MPCh. 4.1 - Prob. 6MPCh. 4.1 - Prob. 7MPCh. 4.1 - Prob. 1EDCh. 4.1 - Prob. 2EDCh. 4.1 - In Problems 1–6, find the x and y coordinates of...
Ch. 4.1 - Prob. 2ECh. 4.1 - Prob. 3ECh. 4.1 - Prob. 4ECh. 4.1 - Prob. 5ECh. 4.1 - In Problems 1–6, find the x and y coordinates of...Ch. 4.1 - Prob. 7ECh. 4.1 - Prob. 8ECh. 4.1 - Prob. 9ECh. 4.1 - Prob. 10ECh. 4.1 - Prob. 11ECh. 4.1 - Match each system in Problems 9–12 with one of the...Ch. 4.1 - Solve Problems 13–16 by graphing.
13.
Ch. 4.1 - Solve Problems 13–16 by graphing.
14.
Ch. 4.1 - Prob. 15ECh. 4.1 - Prob. 16ECh. 4.1 - Prob. 17ECh. 4.1 - Prob. 18ECh. 4.1 - Prob. 19ECh. 4.1 - Prob. 20ECh. 4.1 - Prob. 21ECh. 4.1 - Prob. 22ECh. 4.1 - Prob. 23ECh. 4.1 - Prob. 24ECh. 4.1 - Prob. 25ECh. 4.1 - Prob. 26ECh. 4.1 - Prob. 27ECh. 4.1 - Prob. 28ECh. 4.1 - Prob. 29ECh. 4.1 - Prob. 30ECh. 4.1 - Prob. 31ECh. 4.1 - Prob. 32ECh. 4.1 - Prob. 33ECh. 4.1 - Prob. 34ECh. 4.1 - Prob. 35ECh. 4.1 - Prob. 36ECh. 4.1 - Prob. 37ECh. 4.1 - Prob. 38ECh. 4.1 - Prob. 39ECh. 4.1 - Prob. 40ECh. 4.1 - Prob. 41ECh. 4.1 - Prob. 42ECh. 4.1 - Prob. 43ECh. 4.1 - In a free competitive market, if the demand for a...Ch. 4.1 - Problems 45−48 are concerned with the linear...Ch. 4.1 -
Problems 45−48 are concerned with the linear...Ch. 4.1 - Problems 45−48 are concerned with the linear...Ch. 4.1 - Problems 45–48 are concerned with the linear...Ch. 4.1 - Prob. 49ECh. 4.1 - Prob. 50ECh. 4.1 - Prob. 51ECh. 4.1 - Prob. 52ECh. 4.1 - Prob. 53ECh. 4.1 - Prob. 54ECh. 4.1 - Prob. 55ECh. 4.1 - Prob. 56ECh. 4.1 - Prob. 57ECh. 4.1 - Prob. 58ECh. 4.1 - Prob. 59ECh. 4.1 - In Problems 57−62, graph the equations in the same...Ch. 4.1 - In Problems 57−62, graph the equations in the same...Ch. 4.1 -
In Problems 57−62, graph the equations in the...Ch. 4.1 - 63. The coefficients of the three systems given...Ch. 4.1 - Repeat problem 63 for the following systems:
...Ch. 4.1 - Supply and demand for T-shirts. Suppose that the...Ch. 4.1 - Supply and demand for baseball caps. Suppose that...Ch. 4.1 - Supply and demand for soybeans. At $4.80 per...Ch. 4.1 - Supply and demand for corn. At $2.13 per bushel,...Ch. 4.1 - Prob. 69ECh. 4.1 - Prob. 70ECh. 4.1 - Prob. 71ECh. 4.1 - Prob. 72ECh. 4.1 - Delivery charges. United Express, a national...Ch. 4.1 - Delivery charges. Refer to Problem 73. Federated...Ch. 4.1 - Prob. 75ECh. 4.1 - Prob. 76ECh. 4.1 - Animal diet. Animals in an experiment are to be...Ch. 4.1 - Prob. 78ECh. 4.1 - Prob. 79ECh. 4.1 - Prob. 80ECh. 4.1 - Prob. 81ECh. 4.1 - Prob. 82ECh. 4.1 - Prob. 83ECh. 4.1 - Prob. 84ECh. 4.1 - Prob. 85ECh. 4.2 - Solve using augmented matrix methods:
2x1 − x2 =...Ch. 4.2 - Prob. 2MPCh. 4.2 - Prob. 3MPCh. 4.2 - Prob. 4MPCh. 4.2 - Prob. 1EDCh. 4.2 - Prob. 2EDCh. 4.2 - Prob. 1ECh. 4.2 - Prob. 2ECh. 4.2 - Prob. 3ECh. 4.2 - Prob. 4ECh. 4.2 - Problems 1–14 refer to the following matrices: (If...Ch. 4.2 - Prob. 6ECh. 4.2 - Prob. 7ECh. 4.2 - Problems 1–14 refer to the following matrices: (If...Ch. 4.2 - Problems 1–14 refer to the following matrices: (If...Ch. 4.2 - Prob. 10ECh. 4.2 - Prob. 11ECh. 4.2 - Problems 1–14 refer to the following matrices: (If...Ch. 4.2 - Prob. 13ECh. 4.2 - Problems 1–14 refer to the following matrices: (If...Ch. 4.2 - Prob. 15ECh. 4.2 - Prob. 16ECh. 4.2 - Prob. 17ECh. 4.2 - Prob. 18ECh. 4.2 - Prob. 19ECh. 4.2 - Prob. 20ECh. 4.2 - Prob. 21ECh. 4.2 - Prob. 22ECh. 4.2 - Prob. 23ECh. 4.2 - Perform the row operations indicated in problems...Ch. 4.2 - Prob. 25ECh. 4.2 - Prob. 26ECh. 4.2 - Prob. 27ECh. 4.2 - Perform the row operations indicated in problem...Ch. 4.2 - Prob. 29ECh. 4.2 - Prob. 30ECh. 4.2 - Prob. 31ECh. 4.2 - Prob. 32ECh. 4.2 - Prob. 33ECh. 4.2 - Prob. 34ECh. 4.2 - Prob. 35ECh. 4.2 - Each of the matrices in Problems 35–42 is the...Ch. 4.2 - Prob. 37ECh. 4.2 - Prob. 38ECh. 4.2 - Prob. 39ECh. 4.2 - Prob. 40ECh. 4.2 - Prob. 41ECh. 4.2 - Prob. 42ECh. 4.2 - Prob. 43ECh. 4.2 - Prob. 44ECh. 4.2 - Prob. 45ECh. 4.2 - Prob. 46ECh. 4.2 - Prob. 47ECh. 4.2 - Solve Problems 47 and 48 using augmented matrix...Ch. 4.2 - Prob. 49ECh. 4.2 - Prob. 50ECh. 4.2 - Prob. 51ECh. 4.2 - Prob. 52ECh. 4.2 - Prob. 53ECh. 4.2 - Prob. 54ECh. 4.2 - Solve Problems 55– 74 using augmented, matrix...Ch. 4.2 - Prob. 56ECh. 4.2 - Prob. 57ECh. 4.2 - Prob. 58ECh. 4.2 - Prob. 59ECh. 4.2 - Prob. 60ECh. 4.2 - Prob. 61ECh. 4.2 - Prob. 62ECh. 4.2 - Solve Problems 55– 74 using augmented, matrix...Ch. 4.2 - Prob. 64ECh. 4.2 - Solve Problems 55– 74 using augmented, matrix...Ch. 4.2 - Prob. 66ECh. 4.2 - Solve Problems 55– 74 using augmented, matrix...Ch. 4.2 - Prob. 68ECh. 4.2 - Prob. 69ECh. 4.2 - Prob. 70ECh. 4.2 - Solve Problems 55-74 using augmented, matrix...Ch. 4.2 - Prob. 72ECh. 4.2 - Prob. 73ECh. 4.2 - Solve Problems 55-74 using augmented, matrix...Ch. 4.2 - Prob. 75ECh. 4.2 - Prob. 76ECh. 4.2 - Prob. 77ECh. 4.2 - Prob. 78ECh. 4.2 - Prob. 79ECh. 4.2 - Prob. 80ECh. 4.2 - Prob. 81ECh. 4.2 - Prob. 82ECh. 4.2 - Prob. 83ECh. 4.2 - Prob. 84ECh. 4.3 - The matrices below are not in reduced form....Ch. 4.3 - Solve by Gauss–Jordan elimination:
3x1 + x2 − 2x3...Ch. 4.3 - Solve by Gauss-Jordan elimination:
2x1 − 4x2 − x3...Ch. 4.3 - Solve by Gauss–Jordan elimination:
Ch. 4.3 - Prob. 5MPCh. 4.3 - Prob. 6MPCh. 4.3 - Prob. 1EDCh. 4.3 - Prob. 2EDCh. 4.3 - In Problems 1–4, write the augmented matrix of the...Ch. 4.3 - Prob. 2ECh. 4.3 - In Problems 1–4, write the augmented matrix of the...Ch. 4.3 - Prob. 4ECh. 4.3 - In Problems 5−8, write the system of linear...Ch. 4.3 - Prob. 6ECh. 4.3 - Prob. 7ECh. 4.3 - Prob. 8ECh. 4.3 - In Problems 9–18, if a matrix is in reduced form,...Ch. 4.3 - In Problems 9–18, if a matrix is in reduced form,...Ch. 4.3 - In Problems 9–18, if a matrix is in reduced form,...Ch. 4.3 - In Problems 9–18, if a matrix is in reduced form,...Ch. 4.3 - In Problems 9–18, if a matrix is in reduced form,...Ch. 4.3 - Prob. 14ECh. 4.3 - In Problems 9–18, if a matrix is in reduced form,...Ch. 4.3 - Prob. 16ECh. 4.3 - In Problems 9–18, if a matrix is in reduced form,...Ch. 4.3 - Prob. 18ECh. 4.3 - In Problems 19–28, write the solution of the...Ch. 4.3 - Prob. 20ECh. 4.3 - In Problems 19–28, write the solution of the...Ch. 4.3 - Prob. 22ECh. 4.3 - In Problems 19–28, write the solution of the...Ch. 4.3 - Prob. 24ECh. 4.3 - In Problems 19–28, write the solution of the...Ch. 4.3 - Prob. 26ECh. 4.3 - In Problems 19–28, write the solution of the...Ch. 4.3 - Prob. 28ECh. 4.3 - Prob. 29ECh. 4.3 - Prob. 30ECh. 4.3 - In which of Problems 19, 21, 23, 25, and 27 is the...Ch. 4.3 - Prob. 32ECh. 4.3 - In Problems 33–38, discuss the validity of each...Ch. 4.3 - Prob. 34ECh. 4.3 - Prob. 35ECh. 4.3 - Prob. 36ECh. 4.3 - Prob. 37ECh. 4.3 - Prob. 38ECh. 4.3 - Prob. 39ECh. 4.3 - Use row operations to change each matrix in...Ch. 4.3 - Prob. 41ECh. 4.3 - Prob. 42ECh. 4.3 - Prob. 43ECh. 4.3 - Prob. 44ECh. 4.3 - Prob. 45ECh. 4.3 - Prob. 46ECh. 4.3 - Solve Problems 47–62 using Gauss–Jordan...Ch. 4.3 - Prob. 48ECh. 4.3 - Prob. 49ECh. 4.3 - Prob. 50ECh. 4.3 - Solve Problems 47–62 using Gauss–Jordan...Ch. 4.3 - Prob. 52ECh. 4.3 - Solve Problems 47–62 using Gauss–Jordan...Ch. 4.3 - Prob. 54ECh. 4.3 - Solve Problems 47–62 using Gauss–Jordan...Ch. 4.3 - Prob. 56ECh. 4.3 - Prob. 57ECh. 4.3 - Prob. 58ECh. 4.3 - Solve Problems 47–62 using Gauss–Jordan...Ch. 4.3 - Prob. 60ECh. 4.3 - Prob. 61ECh. 4.3 - Prob. 62ECh. 4.3 - Consider a consistent system of three linear...Ch. 4.3 - Prob. 64ECh. 4.3 - Prob. 65ECh. 4.3 - Solve Problems 47–62 using Gauss–Jordan...Ch. 4.3 - Solve Problems 47–62 using Gauss–Jordan...Ch. 4.3 - Prob. 68ECh. 4.3 - Prob. 69ECh. 4.3 - Prob. 70ECh. 4.3 - Find a, b, and c so that the graph of the...Ch. 4.3 - Prob. 72ECh. 4.3 - Construct a mathematical model for each the...Ch. 4.3 - Prob. 74ECh. 4.3 - Construct a mathematical model for each the...Ch. 4.3 - Construct a mathematical model for each the...Ch. 4.3 - Construct a mathematical model for each of the...Ch. 4.3 - Prob. 78ECh. 4.3 - Construct a mathematical model for each the...Ch. 4.3 - Prob. 80ECh. 4.3 - Prob. 81ECh. 4.3 - Taxable income. Repeat Problem 81 if tax law is...Ch. 4.3 - Construct a mathematical model for each the...Ch. 4.3 - Prob. 84ECh. 4.3 - Prob. 85ECh. 4.3 - Prob. 86ECh. 4.3 - Construct a mathematical model for each of the...Ch. 4.3 - Prob. 88ECh. 4.3 - Population growth. The U.S. population was...Ch. 4.3 - Prob. 90ECh. 4.3 - Prob. 91ECh. 4.3 - Prob. 92ECh. 4.3 - Prob. 93ECh. 4.3 - Prob. 94ECh. 4.3 - Sociology. Two sociologists have grant money to...Ch. 4.3 - Prob. 96ECh. 4.3 - Prob. 97ECh. 4.3 - Traffic flow. Refer to Problem 97. Closing...Ch. 4.4 - Add:
Ch. 4.4 - Prob. 2MPCh. 4.4 - Prob. 3MPCh. 4.4 - Prob. 4MPCh. 4.4 - Prob. 5MPCh. 4.4 - Prob. 6MPCh. 4.4 - Prob. 7MPCh. 4.4 - Find each product, if it is...Ch. 4.4 - Prob. 9MPCh. 4.4 - Prob. 10MPCh. 4.4 - Prob. 1EDCh. 4.4 - Prob. 1ECh. 4.4 - Prob. 2ECh. 4.4 - Prob. 3ECh. 4.4 - Prob. 4ECh. 4.4 - Prob. 5ECh. 4.4 - Prob. 6ECh. 4.4 - Prob. 7ECh. 4.4 - Prob. 8ECh. 4.4 - In Problems 1–14, perform the indicated operation,...Ch. 4.4 - Prob. 10ECh. 4.4 - Prob. 11ECh. 4.4 - Prob. 12ECh. 4.4 - In Problems 1–14, perform the indicated operation,...Ch. 4.4 - Prob. 14ECh. 4.4 - Prob. 15ECh. 4.4 - Prob. 16ECh. 4.4 - In Problems 15–22, find the matrix product. Note...Ch. 4.4 - Prob. 18ECh. 4.4 - Prob. 19ECh. 4.4 - Prob. 20ECh. 4.4 - In Problems 15–22, find the matrix product. Note...Ch. 4.4 - Prob. 22ECh. 4.4 - Prob. 23ECh. 4.4 - Prob. 24ECh. 4.4 - B Find the products in Problems 23–30.
25.
Ch. 4.4 - Prob. 26ECh. 4.4 - Prob. 27ECh. 4.4 - Prob. 28ECh. 4.4 -
Find the products in problems 23–30.
29.
Ch. 4.4 - Prob. 30ECh. 4.4 - Problems 31–48 refer to the following...Ch. 4.4 - Problems 31–48 refer to the following...Ch. 4.4 - Problems 31–48 refer to the following...Ch. 4.4 - Problems 31–48 refer to the following...Ch. 4.4 - Problems 31–48 refer to the following...Ch. 4.4 - Prob. 36ECh. 4.4 - Problems 31–48 refer to the following...Ch. 4.4 - Prob. 38ECh. 4.4 - Prob. 39ECh. 4.4 - Prob. 40ECh. 4.4 - Problems 31–48 refer to the following...Ch. 4.4 - Prob. 42ECh. 4.4 - Prob. 43ECh. 4.4 - Problems 31–48 refer to the following...Ch. 4.4 - Problems 31–48 refer to the following...Ch. 4.4 - Prob. 46ECh. 4.4 - Prob. 47ECh. 4.4 - Prob. 48ECh. 4.4 - If a and b are nonzero real numbers,
find AB and...Ch. 4.4 - Prob. 50ECh. 4.4 - Prob. 51ECh. 4.4 - Prob. 52ECh. 4.4 - Prob. 53ECh. 4.4 - Prob. 54ECh. 4.4 - If a, b, c, and d so that
Ch. 4.4 - Prob. 56ECh. 4.4 - If a, b, c, and d, so that
Ch. 4.4 - Prob. 58ECh. 4.4 - Prob. 59ECh. 4.4 - Prob. 60ECh. 4.4 - Prob. 61ECh. 4.4 - Prob. 62ECh. 4.4 - Prob. 63ECh. 4.4 - Prob. 64ECh. 4.4 - Prob. 65ECh. 4.4 - Prob. 66ECh. 4.4 - Markup. An import car dealer sells three models of...Ch. 4.4 - Prob. 68ECh. 4.4 - Labor costs. A company with manufacturing plants...Ch. 4.4 - Inventory value. A personal computer retail...Ch. 4.4 - Prob. 71ECh. 4.4 - Prob. 72ECh. 4.4 - Prob. 73ECh. 4.4 - Prob. 74ECh. 4.5 - Prob. 1MPCh. 4.5 - Prob. 2MPCh. 4.5 - Prob. 3MPCh. 4.5 - Prob. 4MPCh. 4.5 - Prob. 5MPCh. 4.5 - Prob. 1EDCh. 4.5 - Prob. 2EDCh. 4.5 - Prob. 3EDCh. 4.5 - In Problems 1-4, find the additive inverse and the...Ch. 4.5 - Prob. 2ECh. 4.5 - Prob. 3ECh. 4.5 - Prob. 4ECh. 4.5 - Prob. 5ECh. 4.5 - Prob. 6ECh. 4.5 - Prob. 7ECh. 4.5 - Prob. 8ECh. 4.5 - Prob. 9ECh. 4.5 - Prob. 10ECh. 4.5 - Prob. 11ECh. 4.5 - Prob. 12ECh. 4.5 - Prob. 13ECh. 4.5 - Prob. 14ECh. 4.5 - Prob. 15ECh. 4.5 - Prob. 16ECh. 4.5 - Prob. 17ECh. 4.5 - Prob. 18ECh. 4.5 - Prob. 19ECh. 4.5 - Prob. 20ECh. 4.5 - In Problems 19–28, examine the product of the two...Ch. 4.5 - Prob. 22ECh. 4.5 - In Problems 19–28, examine the product of the two...Ch. 4.5 - Prob. 24ECh. 4.5 - In Problems 19–28, examine the product of the two...Ch. 4.5 - Prob. 26ECh. 4.5 - Prob. 27ECh. 4.5 - Prob. 28ECh. 4.5 - Without performing any row operations, explain why...Ch. 4.5 - Prob. 30ECh. 4.5 - Prob. 31ECh. 4.5 - Prob. 32ECh. 4.5 - Without performing any row operations, explain why...Ch. 4.5 - Prob. 34ECh. 4.5 - Prob. 35ECh. 4.5 - Prob. 36ECh. 4.5 - Without performing any row operations, explain why...Ch. 4.5 - Prob. 38ECh. 4.5 - Prob. 39ECh. 4.5 - Prob. 40ECh. 4.5 - Given M in problems 39–48, find M−1 and show that...Ch. 4.5 - Prob. 42ECh. 4.5 - Prob. 43ECh. 4.5 - Prob. 44ECh. 4.5 - Given M in Problems 39–48, find M–1and show that...Ch. 4.5 - Prob. 46ECh. 4.5 - Prob. 47ECh. 4.5 - Prob. 48ECh. 4.5 - Find the inverse of each matrix in Problems 49–56,...Ch. 4.5 - Prob. 50ECh. 4.5 - Find the inverse of each matrix in problem 49–56,...Ch. 4.5 - Given M in problem 39–48, find M–1 and show that...Ch. 4.5 - Find the inverse of each matrix in problems 49–56,...Ch. 4.5 - Prob. 54ECh. 4.5 - Prob. 55ECh. 4.5 - Prob. 56ECh. 4.5 - In Problems 57–60, find the inverse. Note that...Ch. 4.5 - Prob. 58ECh. 4.5 - Prob. 59ECh. 4.5 - Prob. 60ECh. 4.5 - Find the inverse of each matrix in problems 61–68,...Ch. 4.5 - Find the inverse of each matrix in problems 61–68,...Ch. 4.5 - Find the inverse of each matrix in problems 61–68,...Ch. 4.5 - Prob. 64ECh. 4.5 - Find the inverse of each matrix in problems 61–68,...Ch. 4.5 - Find the inverse of each matrix in problems 61–68,...Ch. 4.5 - Prob. 67ECh. 4.5 - Prob. 68ECh. 4.5 - Show that (A–1)–1 = A for: A =
Ch. 4.5 - Prob. 70ECh. 4.5 - Prob. 71ECh. 4.5 - Prob. 72ECh. 4.5 - Prob. 73ECh. 4.5 - Prob. 74ECh. 4.5 - Prob. 75ECh. 4.5 - Prob. 76ECh. 4.5 - Prob. 77ECh. 4.5 - Prob. 78ECh. 4.5 - Cryptography. The following message was encoded...Ch. 4.5 - Prob. 80ECh. 4.5 - Prob. 81ECh. 4.5 - Prob. 82ECh. 4.5 - Prob. 83ECh. 4.5 - Prob. 84ECh. 4.5 - Prob. 85ECh. 4.5 - Prob. 86ECh. 4.5 - Prob. 87ECh. 4.5 - Prob. 88ECh. 4.6 - Given an n × n matrix A and n × 1 column matrices...Ch. 4.6 - Prob. 2MPCh. 4.6 - Prob. 3MPCh. 4.6 - Prob. 4MPCh. 4.6 - Prob. 1EDCh. 4.6 - Prob. 1ECh. 4.6 - Prob. 2ECh. 4.6 - Prob. 3ECh. 4.6 - Prob. 4ECh. 4.6 - Prob. 5ECh. 4.6 - Prob. 6ECh. 4.6 - Prob. 7ECh. 4.6 - Prob. 8ECh. 4.6 - Write Problems 9–12 as systems of linear equations...Ch. 4.6 - Prob. 10ECh. 4.6 - Write problems 9–12 as system of linear equations...Ch. 4.6 - Prob. 12ECh. 4.6 - Write each system on Problems 13–16 as a matrix...Ch. 4.6 - Prob. 14ECh. 4.6 - Write each system in Problems 13–16 as a matrix...Ch. 4.6 - Prob. 16ECh. 4.6 - Find x1 and x2 in problems 17–20.
Ch. 4.6 - Prob. 18ECh. 4.6 - Prob. 19ECh. 4.6 - Prob. 20ECh. 4.6 - In Problems 21–24, find x1 and x2.
Ch. 4.6 - Prob. 22ECh. 4.6 - Prob. 23ECh. 4.6 - In Problems 21–24, find x1 and x2.
Ch. 4.6 - In Problems 25–30, solve for x1 and x2.
Ch. 4.6 - In Problems 25–30, solve for x1 and x2.
Ch. 4.6 - Prob. 27ECh. 4.6 - Prob. 28ECh. 4.6 - In problems 25–30, solve for x1 and x2.
Ch. 4.6 - Prob. 30ECh. 4.6 - In Problems 31–38, write each system as a matrix...Ch. 4.6 - Prob. 32ECh. 4.6 - Prob. 33ECh. 4.6 - Prob. 34ECh. 4.6 - In Problems 31–38, write each system as a matrix...Ch. 4.6 - Prob. 36ECh. 4.6 - Prob. 37ECh. 4.6 - Prob. 38ECh. 4.6 - Prob. 39ECh. 4.6 - Prob. 40ECh. 4.6 - Prob. 41ECh. 4.6 - Prob. 42ECh. 4.6 - Prob. 43ECh. 4.6 - Prob. 44ECh. 4.6 - In Problems 45–50, explain why the system cannot...Ch. 4.6 - Prob. 46ECh. 4.6 - In Problems 45–50, explain why the system cannot...Ch. 4.6 - Prob. 48ECh. 4.6 - In Problems 45–50, explain why the system cannot...Ch. 4.6 - Prob. 50ECh. 4.6 - Prob. 51ECh. 4.6 - Prob. 52ECh. 4.6 - Prob. 53ECh. 4.6 - Prob. 54ECh. 4.6 - Prob. 55ECh. 4.6 - Prob. 56ECh. 4.6 - Prob. 57ECh. 4.6 - Prob. 58ECh. 4.6 - In Problems 59–62, write each system as a matrix...Ch. 4.6 - Prob. 60ECh. 4.6 - Prob. 61ECh. 4.6 - Prob. 62ECh. 4.6 - Concert tickets. A concert hall has 10,000 seats...Ch. 4.6 - Prob. 64ECh. 4.6 - Production scheduling. A supplier manufactures car...Ch. 4.6 - Prob. 66ECh. 4.6 - Prob. 67ECh. 4.6 - Prob. 68ECh. 4.6 - Prob. 69ECh. 4.6 - Prob. 70ECh. 4.7 - An economy is based on three sectors, coal, oil,...Ch. 4.7 - Prob. 1EDCh. 4.7 - Prob. 1ECh. 4.7 - Prob. 2ECh. 4.7 - Prob. 3ECh. 4.7 - Prob. 4ECh. 4.7 - Prob. 5ECh. 4.7 - Prob. 6ECh. 4.7 - Prob. 7ECh. 4.7 - Prob. 8ECh. 4.7 - Problems 9–14 pertain to the following...Ch. 4.7 - Problems 9–14 pertain to the following input-...Ch. 4.7 - Prob. 11ECh. 4.7 - Prob. 12ECh. 4.7 - Prob. 13ECh. 4.7 - Prob. 14ECh. 4.7 - Prob. 15ECh. 4.7 - Prob. 16ECh. 4.7 - Prob. 17ECh. 4.7 - Prob. 18ECh. 4.7 - Prob. 19ECh. 4.7 - Problems 15–20 pertain to the following input-...Ch. 4.7 - Prob. 21ECh. 4.7 - Prob. 22ECh. 4.7 - Prob. 23ECh. 4.7 - Prob. 24ECh. 4.7 - Prob. 25ECh. 4.7 - Prob. 26ECh. 4.7 - Prob. 27ECh. 4.7 - Prob. 28ECh. 4.7 - Prob. 29ECh. 4.7 - Prob. 30ECh. 4.7 - Prob. 31ECh. 4.7 - Prob. 32ECh. 4.7 - Prob. 33ECh. 4.7 - Prob. 34ECh. 4.7 - Prob. 35ECh. 4.7 - Prob. 36ECh. 4.7 - Prob. 37ECh. 4.7 - Prob. 38ECh. 4.7 - Prob. 39ECh. 4.7 - Prob. 40ECh. 4.7 - Prob. 41ECh. 4.7 - Repeat Problem 41 with the following table:
Four...Ch. 4 - Prob. 1RECh. 4 - Prob. 2RECh. 4 - Prob. 3RECh. 4 - Prob. 4RECh. 4 - Prob. 5RECh. 4 - Prob. 6RECh. 4 - Prob. 7RECh. 4 - Prob. 8RECh. 4 - Prob. 9RECh. 4 - Prob. 10RECh. 4 - Prob. 11RECh. 4 - Prob. 12RECh. 4 - Prob. 13RECh. 4 - Prob. 14RECh. 4 - Prob. 15RECh. 4 - Prob. 16RECh. 4 - Prob. 17RECh. 4 - Prob. 18RECh. 4 - Prob. 19RECh. 4 - Prob. 20RECh. 4 - Prob. 21RECh. 4 - Prob. 22RECh. 4 - Prob. 23RECh. 4 - Prob. 24RECh. 4 - Prob. 25RECh. 4 - Prob. 26RECh. 4 - Prob. 27RECh. 4 - Prob. 28RECh. 4 - Prob. 29RECh. 4 - Prob. 30RECh. 4 - Prob. 31RECh. 4 - Prob. 32RECh. 4 - Prob. 33RECh. 4 - Prob. 34RECh. 4 - Prob. 35RECh. 4 - Prob. 36RECh. 4 - Prob. 37RECh. 4 - Prob. 38RECh. 4 - Prob. 39RECh. 4 - Prob. 40RECh. 4 - Prob. 41RECh. 4 - Prob. 42RECh. 4 - Prob. 43RECh. 4 - Prob. 44RECh. 4 - Prob. 45RECh. 4 - Prob. 46RECh. 4 - Prob. 47RECh. 4 - Prob. 48RECh. 4 - Prob. 49RECh. 4 - Prob. 50RECh. 4 - Prob. 51RECh. 4 - Prob. 52RECh. 4 - Prob. 53RE
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- (7) (12 points) Let F(x, y, z) = (y, x+z cos yz, y cos yz). Ꮖ (a) (4 points) Show that V x F = 0. (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 Stokes' Theorem to calculate the line integral Jos F.ds; as denotes the boundary of S. Explain your answer.arrow_forward(3) (16 points) Consider z = uv, u = x+y, v=x-y. (a) (4 points) Express z in the form z = fog where g: R² R² and f: R² → R. (b) (4 points) Use the chain rule to calculate Vz = (2, 2). Show all intermediate steps otherwise no credit. (c) (4 points) Let S be the surface parametrized by 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). (d) (4 points) Calculate the second Taylor polynomial Q(x, y) (i.e. the quadratic approximation) of F = (fog) at a point (a, b). Verify that Q(x,y) F(a+x,b+y). =arrow_forward(6) (8 points) Change the order of integration and evaluate (z +4ry)drdy . So S√ ² 0arrow_forward
- (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_forwardAnswer the following questions related to the following matrix A = 3 ³).arrow_forward
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