Pearson eText for Finite Mathematics & Its Applications -- Instant Access (Pearson+)
12th Edition
ISBN: 9780137442966
Author: Larry Goldstein, David Schneider
Publisher: PEARSON+
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Chapter 2.3, Problem 47E
To determine
To calculate: The multiplication of the matrices
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4. Direction Fields/Phase Portraits. Use the given direction fields to plot solution curves
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Chapter 2 Solutions
Pearson eText for Finite Mathematics & Its Applications -- Instant Access (Pearson+)
Ch. 2.1 - 1. Determine whether the following systems of...Ch. 2.1 - Give the meaning of each of the following...Ch. 2.1 - 3. Perform the indicated elementary row...Ch. 2.1 - State the next elementary row operation that...Ch. 2.1 - In Exercises 1–8, perform the indicated elementary...Ch. 2.1 - Prob. 2ECh. 2.1 - In Exercises 1–8, perform the indicated elementary...Ch. 2.1 - In Exercises 1–8, perform the indicated elementary...Ch. 2.1 - In Exercises 18, perform the indicated elementary...Ch. 2.1 - In Exercises 18, perform the indicated elementary...
Ch. 2.1 - In Exercises 18, perform the indicated elementary...Ch. 2.1 - In Exercises 1–8, perform the indicated elementary...Ch. 2.1 - In Exercises 9–12, write the augmented matrix...Ch. 2.1 - In Exercises 912, write the augmented matrix...Ch. 2.1 - In Exercises 9–12, write the augmented matrix...Ch. 2.1 - In Exercises 912, write the augmented matrix...Ch. 2.1 - In Exercises 13–16, write the system of linear...Ch. 2.1 - In Exercises 1316, write the system of linear...Ch. 2.1 - In Exercises 1316, write the system of linear...Ch. 2.1 - In Exercises 1316, write the system of linear...Ch. 2.1 - In Exercises 17–22, describe in your own words the...Ch. 2.1 - In Exercises 17–22, describe in your own words the...Ch. 2.1 - In Exercises 17–22, describe in your own words the...Ch. 2.1 - In Exercises 1722, describe in your own words the...Ch. 2.1 - In Exercises 1722, describe in your own words the...Ch. 2.1 - In Exercises 17–22, describe in your own words the...Ch. 2.1 - In Exercises 2328, carry out the indicated...Ch. 2.1 - In Exercises 2328, carry out the indicated...Ch. 2.1 - In Exercises 23–28, carry out the indicated...Ch. 2.1 - In Exercises 2328, carry out the indicated...Ch. 2.1 - In Exercises 2328, carry out the indicated...Ch. 2.1 - In Exercises 2328, carry out the indicated...Ch. 2.1 - In Exercises 2936, state the next elementary row...Ch. 2.1 - In Exercises 29–36, state the next elementary row...Ch. 2.1 - In Exercises 29–36, state the next elementary row...Ch. 2.1 - Prob. 32ECh. 2.1 - In Exercises 29–36, state the next elementary row...Ch. 2.1 - In Exercises 29–36, state the next elementary row...Ch. 2.1 - In Exercises 29–36, state the next elementary row...Ch. 2.1 - Prob. 36ECh. 2.1 - In Exercises 37 and 38, two steps of the...Ch. 2.1 - In Exercises 37 and 38, two steps of the...Ch. 2.1 - The screen captures in Exercises 3946 show a...Ch. 2.1 - Prob. 40ECh. 2.1 - The screen captures in Exercises 3946 show a...Ch. 2.1 - Prob. 42ECh. 2.1 - The screen captures in Exercises 39–46 show a...Ch. 2.1 - Prob. 44ECh. 2.1 - The screen captures in Exercises 39–46 show a...Ch. 2.1 - The screen captures in Exercises 39–46 show a...Ch. 2.1 - In Exercises 47-60, solve the linear system by the...Ch. 2.1 - In Exercises 47-60, solve the linear system by the...Ch. 2.1 - In Exercises 47-60, solve the linear system by the...Ch. 2.1 - In Exercises 47-60, solve the linear system by the...Ch. 2.1 - In Exercises 47-60, solve the linear system by the...Ch. 2.1 - In Exercises 47-60, solve the linear system by the...Ch. 2.1 - In Exercises 47-60, solve the linear system by the...Ch. 2.1 - In Exercises 47-60, solve the linear system by the...Ch. 2.1 - In Exercises 47-60, solve the linear system by the...Ch. 2.1 - In Exercises 47-60, solve the linear system by the...Ch. 2.1 - In Exercises 47-60, solve the linear system by the...Ch. 2.1 - In Exercises 47-60, solve the linear system by the...Ch. 2.1 - In Exercises 47-60, solve the linear system by the...Ch. 2.1 - In Exercises 47-60, solve the linear system by the...Ch. 2.1 - A baked potato smothered with cheddar cheese...Ch. 2.1 - A high school math department purchased brand A...Ch. 2.1 - Exercises 63 and 64 are multiple choice exercises...Ch. 2.1 - Exercises 63 and 64 are multiple choice exercises...Ch. 2.1 - Sales A street vendor has a total of 350 short-...Ch. 2.1 - Sales A grocery store carries two brands of...Ch. 2.1 - Movie tickets A 275-seat movie theater charges...Ch. 2.1 - Batting average A baseball players batting average...Ch. 2.1 - 69. Areas of countries The United States and...Ch. 2.1 - College Majors The bar graph in Fig. 6 gives the...Ch. 2.1 - Coffee Blends A one-pound blend of coffee uses...Ch. 2.1 - 72. Nut Mixture A one-pound mixture of nuts...Ch. 2.1 - 73. Investment planning A bank wishes to invest a...Ch. 2.1 - Nutrition planning A dietitian wishes to plan a...Ch. 2.1 - Prob. 75ECh. 2.1 - Prob. 76ECh. 2.1 - In Exercises 77–80, use technology to put the...Ch. 2.1 - Prob. 78ECh. 2.1 - Prob. 79ECh. 2.1 - Prob. 80ECh. 2.1 - Prob. 81ECh. 2.1 - Prob. 82ECh. 2.1 - Prob. 83ECh. 2.1 - Prob. 84ECh. 2.2 - Find a specific solution to a system of linear...Ch. 2.2 - 2. Find all solutions of this system of linear...Ch. 2.2 - In Exercises 1–8, pivot the matrix about the...Ch. 2.2 - In Exercises 1–8, pivot the matrix about the...Ch. 2.2 - In Exercises 1–8, pivot the matrix about the...Ch. 2.2 - In Exercises 1–8, pivot the matrix about the...Ch. 2.2 - In Exercises 1–8, pivot the matrix about the...Ch. 2.2 - In Exercises 1–8, pivot the matrix about the...Ch. 2.2 - In Exercises 18, pivot the matrix about the...Ch. 2.2 - In Exercises 18, pivot the matrix about the...Ch. 2.2 - The screen captures in Exercises 9–16 show a...Ch. 2.2 - The screen captures in Exercises 9–16 show a...Ch. 2.2 - The screen captures in Exercises 916 show a...Ch. 2.2 - The screen captures in Exercises 916 show a...Ch. 2.2 - The screen captures in Exercises 916 show a...Ch. 2.2 - The screen captures in Exercises 9–16 show a...Ch. 2.2 - Prob. 15ECh. 2.2 - Prob. 16ECh. 2.2 - In Exercise 1736, use the Gauss-Jordan elimination...Ch. 2.2 - In Exercise 1736, use the Gauss-Jordan elimination...Ch. 2.2 - In Exercise 1736, use the Gauss-Jordan elimination...Ch. 2.2 - In Exercise 1736, use the Gauss-Jordan elimination...Ch. 2.2 - In Exercise 1736, use the Gauss-Jordan elimination...Ch. 2.2 - In Exercise 17–36, use the Gauss-Jordan...Ch. 2.2 - In Exercise 17–36, use the Gauss-Jordan...Ch. 2.2 - In Exercise 1736, use the Gauss-Jordan elimination...Ch. 2.2 - In Exercise 17–36, use the Gauss-Jordan...Ch. 2.2 - In Exercise 17–36, use the Gauss-Jordan...Ch. 2.2 - In Exercise 1736, use the Gauss-Jordan elimination...Ch. 2.2 - In Exercise 17–36, use the Gauss-Jordan...Ch. 2.2 - In Exercise 17–36, use the Gauss-Jordan...Ch. 2.2 - In Exercise 17–36, use the Gauss-Jordan...Ch. 2.2 - Prob. 31ECh. 2.2 - In Exercise 17–36, use the Gauss-Jordan...Ch. 2.2 - In Exercise 1736, use the Gauss-Jordan elimination...Ch. 2.2 - In Exercise 1736, use the Gauss-Jordan elimination...Ch. 2.2 - In Exercise 17–36, use the Gauss-Jordan...Ch. 2.2 - Prob. 36ECh. 2.2 - In Exercises 37–40, find three solutions to the...Ch. 2.2 - In Exercises 37–40, find three solutions to the...Ch. 2.2 - In Exercises 3740, find three solutions to the...Ch. 2.2 - In Exercises 37–40, find three solutions to the...Ch. 2.2 - 41. Nutrition planning In a laboratory experiment,...Ch. 2.2 - Nutrition planning Rework Exercise 41 with the...Ch. 2.2 - Nutrition planning The nutritional content of...Ch. 2.2 - 44. Nutrition planning Refer to Exercise 43. Show...Ch. 2.2 - Furniture Manufacturing A furniture manufacturer...Ch. 2.2 - Computer equipment An office manager placed an...Ch. 2.2 - 47. Quilting Granny’s Custom Quilts receives an...Ch. 2.2 - 48. Purchasing Options Amanda is decorating her...Ch. 2.2 - 49. For what values(s) of k will the following...Ch. 2.2 - For what value of k will the following system of...Ch. 2.2 - Figure 5 shows the graphs of the equations from a...Ch. 2.2 - Prob. 52ECh. 2.2 - In Exercises 53–56, graph the three equations...Ch. 2.2 - Prob. 54ECh. 2.2 - Prob. 55ECh. 2.2 - Prob. 56ECh. 2.2 - Apply rref or row reduce to the matrix in Example...Ch. 2.2 - Prob. 58ECh. 2.3 - Compute [3121012041][710542604].Ch. 2.3 - 2. Give the system of linear equations that is...Ch. 2.3 - Give a matrix equation equivalent to this system...Ch. 2.3 - In Exercises 16, give the size and special...Ch. 2.3 - Prob. 2ECh. 2.3 - In Exercises 16, give the size and special...Ch. 2.3 - Prob. 4ECh. 2.3 - In Exercises 16, give the size and special...Ch. 2.3 - In Exercises 1–6, give the size and special...Ch. 2.3 - Exercises 7–10 refer to the matrix .
7. Find and...Ch. 2.3 - Exercises 710 refer to the 23 matrix A=[246031]....Ch. 2.3 - Exercises 710 refer to the 23 matrix A=[246031]....Ch. 2.3 - Exercises 7–10 refer to the matrix .
10. For what...Ch. 2.3 - In Exercises 11-26, perform the indicated matrix...Ch. 2.3 - In Exercises 11-26, perform the indicated matrix...Ch. 2.3 - In Exercises 11-26, perform the indicated matrix...Ch. 2.3 - In Exercises 11-26, perform the indicated matrix...Ch. 2.3 - In Exercises 11-26, perform the indicated matrix...Ch. 2.3 - In Exercises 11-26, perform the indicated matrix...Ch. 2.3 - In Exercises 11-26, perform the indicated matrix...Ch. 2.3 - In Exercises 11-26, perform the indicated matrix...Ch. 2.3 - In Exercises 11-26, perform the indicated matrix...Ch. 2.3 - In Exercises 11-26, perform the indicated matrix...Ch. 2.3 - In Exercises 11-26, perform the indicated matrix...Ch. 2.3 - In Exercises 11-26, perform the indicated matrix...Ch. 2.3 - In Exercises 11-26, perform the indicated matrix...Ch. 2.3 - In Exercises 11-26, perform the indicated matrix...Ch. 2.3 - In Exercises 11-26, perform the indicated matrix...Ch. 2.3 - In Exercises 11-26, perform the indicated matrix...Ch. 2.3 - In Exercises 27–32, the sizes of two matrices are...Ch. 2.3 - In Exercises 27–32, the sizes of two matrices are...Ch. 2.3 - In Exercises 27–32, the sizes of two matrices are...Ch. 2.3 - In Exercises 27–32, the sizes of two matrices are...Ch. 2.3 - In Exercises 27–32, the sizes of two matrices are...Ch. 2.3 - In Exercises 2732, the sizes of two matrices are...Ch. 2.3 - In Exercises 33-52, perform the...Ch. 2.3 - In Exercises 33-52, perform the multiplication....Ch. 2.3 - In Exercises 33-52, perform the multiplication....Ch. 2.3 - In Exercises 33-52, perform the multiplication....Ch. 2.3 - In Exercises 33-52, perform the...Ch. 2.3 - In Exercises 33-52, perform the multiplication....Ch. 2.3 - In Exercises 33-52, perform the...Ch. 2.3 - In Exercises 33-52, perform the multiplication....Ch. 2.3 - In Exercises 33-52, perform the multiplication....Ch. 2.3 - In Exercises 33-52, perform the...Ch. 2.3 - In Exercises 33-52, perform the multiplication....Ch. 2.3 - Prob. 44ECh. 2.3 - In Exercises 33-52, perform the multiplication....Ch. 2.3 - In Exercises 33-52, perform the...Ch. 2.3 - Prob. 47ECh. 2.3 - Prob. 48ECh. 2.3 - Prob. 49ECh. 2.3 - In Exercises 33-52, perform the multiplication....Ch. 2.3 - In Exercises 33-52, perform the...Ch. 2.3 - In Exercises 33-52, perform the...Ch. 2.3 - In Exercises 53-56, give the system of linear...Ch. 2.3 - In Exercises 53-56, give the system of linear...Ch. 2.3 - In Exercises 53-56, give the system of linear...Ch. 2.3 - In Exercises 53-56, give the system of linear...Ch. 2.3 - In Exercises 5760, write the given system of...Ch. 2.3 - In Exercises 57–60, write the given system of...Ch. 2.3 - In Exercises 57–60, write the given system of...Ch. 2.3 - In Exercises 57–60, write the given system of...Ch. 2.3 - Prob. 61ECh. 2.3 - Prob. 62ECh. 2.3 - Prob. 63ECh. 2.3 - Prob. 64ECh. 2.3 - Wardrobe costs The quantities of pants, shirts,...Ch. 2.3 - Retail Sales Two stores sell the exact same brand...Ch. 2.3 - Retail Sales A candy shop sells various items for...Ch. 2.3 - Wholesale and retail Sales A company has three...Ch. 2.3 - Prob. 69ECh. 2.3 - 70. Semester Grades A professor bases semester...Ch. 2.3 - Prob. 71ECh. 2.3 - Prob. 72ECh. 2.3 - 73. Labor Costs Suppose that a contractor employs...Ch. 2.3 - Prob. 74ECh. 2.3 - Nutrition Analysis Mikeys diet consists of food X...Ch. 2.3 - Bakery Sales A bakery makes three types of...Ch. 2.3 - Revenue A community fitness center has a pool and...Ch. 2.3 - Prob. 78ECh. 2.3 - 79. Production Planning A bakery sells Boston...Ch. 2.3 - Prob. 80ECh. 2.3 - Prob. 81ECh. 2.3 - MP3 Sales A store sells three types of MP3...Ch. 2.3 - Prob. 83ECh. 2.3 - Prob. 84ECh. 2.3 - Prob. 85ECh. 2.3 - Prob. 86ECh. 2.3 - Prob. 87ECh. 2.3 - Prob. 88ECh. 2.3 - Prob. 89ECh. 2.3 - Prob. 90ECh. 2.3 - Prob. 91ECh. 2.3 - Prob. 92ECh. 2.3 - Prob. 93ECh. 2.3 - Prob. 94ECh. 2.3 - Prob. 95ECh. 2.3 - Prob. 96ECh. 2.3 - Prob. 97ECh. 2.3 - Prob. 98ECh. 2.4 - Show that the inverse of...Ch. 2.4 - 2. Use the method of this section to solve the...Ch. 2.4 - In Exercises 1 and 2, use the fact that...Ch. 2.4 - In Exercises 1 and 2, use the fact that...Ch. 2.4 - In Exercises 310, find the inverse of the given...Ch. 2.4 - In Exercises 310, find the inverse of the given...Ch. 2.4 - In Exercises 3–10, find the inverse of the given...Ch. 2.4 - In Exercises 3–10, find the inverse of the given...Ch. 2.4 - In Exercises 3–10, find the inverse of the given...Ch. 2.4 - In Exercises 3–10, find the inverse of the given...Ch. 2.4 - In Exercises 3–10, find the inverse of the given...Ch. 2.4 - In Exercises 310, find the inverse of the given...Ch. 2.4 - In Exercises 11–14, use a matrix equation to solve...Ch. 2.4 - In Exercises 1114, use a matrix equation to solve...Ch. 2.4 - In Exercises 1114, use a matrix equation to solve...Ch. 2.4 - In Exercises 1114, use a matrix equation to solve...Ch. 2.4 - Marriage Trends It is found that the number of...Ch. 2.4 - Epidemiology A flu epidemic is spreading through a...Ch. 2.4 - 17. Housing Trends Statistics show that, at a...Ch. 2.4 - Performance on Tests A teacher estimates that, of...Ch. 2.4 - In Exercises 19–22, use the fact that the...Ch. 2.4 - In Exercises 19–22, use the fact that the...Ch. 2.4 - In Exercises 19–22, use the fact that the...Ch. 2.4 - In Exercises 19–22, use the fact that the...Ch. 2.4 - In Exercises 23–26, use the fact that the...Ch. 2.4 - In Exercises 2326, use the fact that the following...Ch. 2.4 - In Exercises 23–26, use the fact that the...Ch. 2.4 - In Exercises 2326, use the fact that the following...Ch. 2.4 - 27. Show that if and , then the inverse of is...Ch. 2.4 - (True or False) If B is the inverse of A, then A...Ch. 2.4 - Prob. 29ECh. 2.4 - 30. If and , what is A?
Ch. 2.4 - 31. Show that, if AB is a matrix of all zeros and...Ch. 2.4 - Consider the matrices A=[3152] and B=[6252]. Show...Ch. 2.4 - Find a 22 matrix A and a 21 column matrix B for...Ch. 2.4 - 34. Find a matrix A and a column matrix B for...Ch. 2.4 - In Exercises 3538, use the inverse operation to...Ch. 2.4 - In Exercises 35–38, use the inverse operation to...Ch. 2.4 - In Exercises 35–38, use the inverse operation to...Ch. 2.4 - In Exercises 35–38, use the inverse operation to...Ch. 2.4 - In Exercises 3942, calculate the solution by using...Ch. 2.4 - In Exercises 39–42, calculate the solution by...Ch. 2.4 - In Exercises 3942, calculate the solution by using...Ch. 2.4 - In Exercises 39–42, calculate the solution by...Ch. 2.4 - 43. Try finding the inverse of a matrix that does...Ch. 2.5 - 1. Use the Gauss–Jordan method to calculate the...Ch. 2.5 - Solve the system of linear equations...Ch. 2.5 - In Exercises 1–12, use the Gauss–Jordan method to...Ch. 2.5 - In Exercises 1–12, use the Gauss–Jordan method to...Ch. 2.5 - In Exercises 1–12, use the Gauss–Jordan method to...Ch. 2.5 - In Exercises 1–12, use the Gauss–Jordan method to...Ch. 2.5 - In Exercises 1–12, use the Gauss–Jordan method to...Ch. 2.5 - In Exercises 1–12, use the Gauss–Jordan method to...Ch. 2.5 - In Exercises 112, use the GaussJordan method to...Ch. 2.5 - In Exercises 1–12, use the Gauss–Jordan method to...Ch. 2.5 - In Exercises 112, use the GaussJordan method to...Ch. 2.5 - In Exercises 112, use the GaussJordan method to...Ch. 2.5 - In Exercises 112, use the GaussJordan method to...Ch. 2.5 - In Exercises 1–12, use the Gauss–Jordan method to...Ch. 2.5 - In Exercises 13–18, use an inverse matrix to solve...Ch. 2.5 - In Exercises 13–18, use an inverse matrix to solve...Ch. 2.5 - In Exercises 1318, use an inverse matrix to solve...Ch. 2.5 - In Exercises 13–18, use an inverse matrix to solve...Ch. 2.5 - In Exercises 13–18, use an inverse matrix to solve...Ch. 2.5 - In Exercises 1318, use an inverse matrix to solve...Ch. 2.5 - 19. Find a matrix A for which
.
Ch. 2.5 - Find a 22 matrix A for which [2513]A=[1042].Ch. 2.5 - College Degrees Figure 1 gives the responses of a...Ch. 2.5 - 22. College Choices Figure 2 gives the responses...Ch. 2.5 - 23. High School attended Figure 3 gives the...Ch. 2.5 - Placement Tests Figure 4 gives the responses of a...Ch. 2.6 - Let...Ch. 2.6 - Prob. 2CYUCh. 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 - Prob. 8ECh. 2.6 - Prob. 9ECh. 2.6 - Prob. 10ECh. 2.6 - Prob. 11ECh. 2.6 - Three-Sector Economy In Exercises 112, suppose...Ch. 2.6 - 13. Industrial Production Suppose that, in the...Ch. 2.6 - Conglomerate Suppose that the conglomerate of...Ch. 2.6 - Prob. 15ECh. 2.6 - 16. Industrial Production Suppose that the economy...Ch. 2.6 - Industrial Production In the economy of Example 1,...Ch. 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 - Three-Sector Economy An economy consists of the...Ch. 2.6 - 27. Localized Economy A town has a merchant, a...Ch. 2.6 - Prob. 28ECh. 2.6 - Prob. 29ECh. 2.6 - Prob. 30ECh. 2.6 - Prob. 31ECh. 2.6 - Prob. 32ECh. 2 - What is meant by a solution to a system of linear...Ch. 2 - What is a matrix?Ch. 2 - 3. State the three elementary row operations on...Ch. 2 - Prob. 4FCCECh. 2 - What is meant by pivoting a matrix about a nonzero...Ch. 2 - 6. State the Gauss–Jordan elimination method for...Ch. 2 - 7. What is a row matrix? Column matrix? Square...Ch. 2 - Prob. 8FCCECh. 2 - Define the sum and difference of two matrices.Ch. 2 - Define the product of two matrices.Ch. 2 - Prob. 11FCCECh. 2 - Prob. 12FCCECh. 2 - Prob. 13FCCECh. 2 - 14. Explain how to use the inverse of a matrix to...Ch. 2 - Prob. 15FCCECh. 2 - Prob. 16FCCECh. 2 - Prob. 17FCCECh. 2 - Prob. 1RECh. 2 - Prob. 2RECh. 2 - Prob. 3RECh. 2 - In Exercises 3–8, use the Gauss–Jordan elimination...Ch. 2 - Prob. 5RECh. 2 - Prob. 6RECh. 2 - Prob. 7RECh. 2 - Prob. 8RECh. 2 - Prob. 9RECh. 2 - Prob. 10RECh. 2 - Prob. 11RECh. 2 - Prob. 12RECh. 2 - Prob. 13RECh. 2 - Prob. 14RECh. 2 - Prob. 15RECh. 2 - Prob. 16RECh. 2 - Prob. 17RECh. 2 - Prob. 18RECh. 2 - Crop Allocation Farmer Brown has 1000 acres of...Ch. 2 - Equipment Sales A company makes backyard...Ch. 2 - Prob. 21RECh. 2 - 22. Job Earnings Sara, Quinn, Tamia, and Zack are...Ch. 2 - Prob. 23RECh. 2 - Prob. 24RECh. 2 - Two-Sector Economy The economy of a small country...Ch. 2 - Coins Joe has $3.30 in his pocket, made up of...Ch. 2 - Identify each statement as true or false. (a) If a...Ch. 2 - Identify each statement as true or false. (a)...Ch. 2 - Prob. 29RECh. 2 - Prob. 30RECh. 2 - Prob. 31RECh. 2 - Prob. 32RECh. 2 - Prob. 33RECh. 2 - Population Dynamics In 1991, the U.S. Fish and...Ch. 2 - Population Dynamics In 1991, the U.S. Fish and...Ch. 2 - Population Dynamics In 1991, the U.S. Fish and...Ch. 2 - Prob. 4PCh. 2 - Prob. 5PCh. 2 - Prob. 6PCh. 2 - Prob. 7PCh. 2 - Prob. 8P
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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_forwardAnswer the following questions related to the following matrix A = 3 ³).arrow_forward
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