EBK COLLEGE ALGEBRA & TRIGONOMETRY
1st Edition
ISBN: 9780077538538
Author: Miller
Publisher: VST
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Textbook Question
Chapter 9.6, Problem 22PE
Guyton makes $24/hr tutoring chemistry and $20/hr tutoring math.
Let x represent the number of hours per week he spends tutoring chemistry. Let y represent the number of hours per week he spends tutoring math.
- Write an objective function representing his weekly income for tutoring x hours of chemistry and y hours of math.
- The time that Guyton devotes to tutoring is limited by the following constraints. Write a system of inequalities representing the constraints.
- The number of hours spent tutoring each subject cannot be negative.
- Due to the academic demands ofhis own classes he tutors at most 18 hr per week.
- The tutoring center requires that he tutors math at least 4 hr per week.
- The demand for math tutors is greater than the demand for chemistry tutors, Therefore, the number of hours he spends tutoring math must be at least twice the number of hours he spends tutoring chemistry.
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Chapter 9 Solutions
EBK COLLEGE ALGEBRA & TRIGONOMETRY
Ch. 9.1 - For Exercises R.1-R.4, solve the equation. R.1...Ch. 9.1 - Prob. R.2PECh. 9.1 - For Exercises R.1-R.4, solve the equation. R.3...Ch. 9.1 - Prob. R.4PECh. 9.1 - Graph the equation and identify the x and y-...Ch. 9.1 - Prob. R.6PECh. 9.1 - Prob. 1PECh. 9.1 - Prob. 2PECh. 9.1 - Prob. 3PECh. 9.1 - Prob. 4PE
Ch. 9.1 - A system of equations that has no solution is...Ch. 9.1 - A system of linear equations in two variables may...Ch. 9.1 - For Exercises 7-10, determine if the ordered pair...Ch. 9.1 - Prob. 8PECh. 9.1 - For Exercises 7-10, determine if the ordered pair...Ch. 9.1 - Prob. 10PECh. 9.1 - For Exercises 11-14, a system of equations is...Ch. 9.1 - For Exercises 11-14, a system of equations is...Ch. 9.1 - Prob. 13PECh. 9.1 - Prob. 14PECh. 9.1 - For Exercises 15-20, solve the system of equations...Ch. 9.1 - Prob. 16PECh. 9.1 - For Exercises 15-20, solve the system of equations...Ch. 9.1 - Prob. 18PECh. 9.1 - For Exercises 15-20, solve the system of equations...Ch. 9.1 - Prob. 20PECh. 9.1 - For Exercises 21-28, solve the system of equations...Ch. 9.1 - Prob. 22PECh. 9.1 - For Exercises 21-28, solve the system of equations...Ch. 9.1 - Prob. 24PECh. 9.1 - For Exercises 21-28, solve the system of equations...Ch. 9.1 - Prob. 26PECh. 9.1 - For Exercises 21-28, solve the system of equations...Ch. 9.1 - Prob. 28PECh. 9.1 - For Exercises 2934, solve the system by using any...Ch. 9.1 - Prob. 30PECh. 9.1 - For Exercises 2934, solve the system by using any...Ch. 9.1 - Prob. 32PECh. 9.1 - Prob. 33PECh. 9.1 - Prob. 34PECh. 9.1 - For Exercises 3536, Write the general solution....Ch. 9.1 - For Exercises 3536, Write the general solution....Ch. 9.1 - Prob. 37PECh. 9.1 - Prob. 38PECh. 9.1 - For Exercises 3750, solve the system using any...Ch. 9.1 - Prob. 40PECh. 9.1 - Prob. 41PECh. 9.1 - Prob. 42PECh. 9.1 - Prob. 43PECh. 9.1 - Prob. 44PECh. 9.1 - Prob. 45PECh. 9.1 - Prob. 46PECh. 9.1 - Prob. 47PECh. 9.1 - Prob. 48PECh. 9.1 - Prob. 49PECh. 9.1 - Prob. 50PECh. 9.1 - One antifreeze solution is 36% alcohol and another...Ch. 9.1 - Prob. 52PECh. 9.1 - A radiator has 16 L of a 36% antifreeze solution....Ch. 9.1 - Prob. 54PECh. 9.1 - Michelle borrows a total of $5000 in student loans...Ch. 9.1 - Prob. 56PECh. 9.1 - Prob. 57PECh. 9.1 - A total of $6000 is invested for 5 yr with a total...Ch. 9.1 - Monique and Tara each make an ice cream sundae....Ch. 9.1 - Prob. 60PECh. 9.1 - Prob. 61PECh. 9.1 - The average of an electrician's hourly wage and a...Ch. 9.1 - A moving sidewalk in an airport moves people...Ch. 9.1 - Prob. 64PECh. 9.1 - Prob. 65PECh. 9.1 - Prob. 66PECh. 9.1 - A cleaning company charges $100 for each office it...Ch. 9.1 - Prob. 68PECh. 9.1 - For Exercises 6970, refer to Figure 9-1 and the...Ch. 9.1 - Prob. 70PECh. 9.1 - Prob. 71PECh. 9.1 - Prob. 72PECh. 9.1 - Prob. 73PECh. 9.1 - Prob. 74PECh. 9.1 - Two angles are complementary. The measure of one...Ch. 9.1 - Prob. 76PECh. 9.1 - For Exercises 7778, find the measure of angles x...Ch. 9.1 - Prob. 78PECh. 9.1 - Prob. 79PECh. 9.1 - Prob. 80PECh. 9.1 - Prob. 81PECh. 9.1 - Prob. 82PECh. 9.1 - Prob. 83PECh. 9.1 - Prob. 84PECh. 9.1 - Prob. 85PECh. 9.1 - Prob. 86PECh. 9.1 - Prob. 87PECh. 9.1 - Prob. 88PECh. 9.1 - Prob. 89PECh. 9.1 - Prob. 90PECh. 9.1 - Prob. 91PECh. 9.1 - Prob. 92PECh. 9.1 - Prob. 93PECh. 9.1 - Prob. 94PECh. 9.1 - Prob. 95PECh. 9.1 - Prob. 96PECh. 9.1 - Prob. 97PECh. 9.1 - Prob. 98PECh. 9.1 - Prob. 99PECh. 9.2 - How much interest will Roxanne have to pay if she...Ch. 9.2 - Prob. R.2PECh. 9.2 - Prob. R.3PECh. 9.2 - Prob. 1PECh. 9.2 - Prob. 2PECh. 9.2 - Prob. 3PECh. 9.2 - Prob. 4PECh. 9.2 - For Exercises 5-8, determine if the ordered triple...Ch. 9.2 - Prob. 6PECh. 9.2 - Prob. 7PECh. 9.2 - Prob. 8PECh. 9.2 - For Exercises 9-32, solve the system. If a system...Ch. 9.2 - Prob. 10PECh. 9.2 - For Exercises 9-32, solve the system. If a system...Ch. 9.2 - Prob. 12PECh. 9.2 - For Exercises 9-32, solve the system. If a system...Ch. 9.2 - Prob. 14PECh. 9.2 - For Exercises 9-32, solve the system. If a system...Ch. 9.2 - Prob. 16PECh. 9.2 - For Exercises 9-32, solve the system. If a system...Ch. 9.2 - Prob. 18PECh. 9.2 - For Exercises 9-32, solve the system. If a system...Ch. 9.2 - Prob. 20PECh. 9.2 - For Exercises 9-32, solve the system. If a system...Ch. 9.2 - Prob. 22PECh. 9.2 - Prob. 23PECh. 9.2 - Prob. 24PECh. 9.2 - For Exercises 9-32, solve the system. If a system...Ch. 9.2 - Prob. 26PECh. 9.2 - Prob. 27PECh. 9.2 - Prob. 28PECh. 9.2 - Prob. 29PECh. 9.2 - Prob. 30PECh. 9.2 - Prob. 31PECh. 9.2 - Prob. 32PECh. 9.2 - Prob. 33PECh. 9.2 - Prob. 34PECh. 9.2 - Prob. 35PECh. 9.2 - Prob. 36PECh. 9.2 - Prob. 37PECh. 9.2 - Prob. 38PECh. 9.2 - Devon invested $8000 in three different mutual...Ch. 9.2 - Prob. 40PECh. 9.2 - A basketball player scored 26 points in one game....Ch. 9.2 - Prob. 42PECh. 9.2 - Prob. 43PECh. 9.2 - Prob. 44PECh. 9.2 - Prob. 45PECh. 9.2 - Prob. 46PECh. 9.2 - The measure of the largest angle in a triangle is...Ch. 9.2 - Prob. 48PECh. 9.2 - a. Show that the points (l, 0), (3, 10), and (-2,...Ch. 9.2 - Prob. 50PECh. 9.2 - For Exercises 51-52, find an equation of the form...Ch. 9.2 - For Exercises 51-52, find an equation of the form...Ch. 9.2 - Prob. 53PECh. 9.2 - Prob. 54PECh. 9.2 - Prob. 55PECh. 9.2 - Many statistics courses cover a topic called...Ch. 9.2 - Prob. 57PECh. 9.2 - Prob. 58PECh. 9.2 - Prob. 59PECh. 9.2 - Prob. 60PECh. 9.2 - Prob. 61PECh. 9.2 - Prob. 62PECh. 9.2 - Prob. 63PECh. 9.2 - Prob. 64PECh. 9.2 - Prob. 65PECh. 9.2 - Prob. 66PECh. 9.2 - Prob. 67PECh. 9.2 - Prob. 68PECh. 9.3 - Prob. R.1PECh. 9.3 - Prob. R.2PECh. 9.3 - Prob. R.3PECh. 9.3 - Prob. R.4PECh. 9.3 - Prob. R.5PECh. 9.3 - Prob. 1PECh. 9.3 - Prob. 2PECh. 9.3 - Prob. 3PECh. 9.3 - Prob. 4PECh. 9.3 - Prob. 5PECh. 9.3 - Prob. 6PECh. 9.3 - Prob. 7PECh. 9.3 - Prob. 8PECh. 9.3 - Prob. 9PECh. 9.3 - Prob. 10PECh. 9.3 - Prob. 11PECh. 9.3 - Prob. 12PECh. 9.3 - Prob. 13PECh. 9.3 - Prob. 14PECh. 9.3 - Prob. 15PECh. 9.3 - Prob. 16PECh. 9.3 - Prob. 17PECh. 9.3 - Prob. 18PECh. 9.3 - Prob. 19PECh. 9.3 - Prob. 20PECh. 9.3 - Prob. 21PECh. 9.3 - Prob. 22PECh. 9.3 - Prob. 23PECh. 9.3 - Prob. 24PECh. 9.3 - Prob. 25PECh. 9.3 - Prob. 26PECh. 9.3 - Prob. 27PECh. 9.3 - Prob. 28PECh. 9.3 - Prob. 29PECh. 9.3 - Prob. 30PECh. 9.3 - Prob. 31PECh. 9.3 - Prob. 32PECh. 9.3 - Prob. 33PECh. 9.3 - Prob. 34PECh. 9.3 - Prob. 35PECh. 9.3 - Prob. 36PECh. 9.3 - Prob. 37PECh. 9.3 - Prob. 38PECh. 9.3 - Prob. 39PECh. 9.3 - Prob. 40PECh. 9.3 - Prob. 41PECh. 9.3 - Prob. 42PECh. 9.3 - Prob. 43PECh. 9.3 - Prob. 44PECh. 9.3 - Prob. 45PECh. 9.3 - Prob. 46PECh. 9.3 - Prob. 47PECh. 9.3 - Prob. 48PECh. 9.3 - Prob. 49PECh. 9.3 - Prob. 50PECh. 9.3 - Prob. 51PECh. 9.3 - Prob. 52PECh. 9.3 - Prob. 53PECh. 9.3 - Prob. 54PECh. 9.3 - Prob. 55PECh. 9.3 - Prob. 56PECh. 9.4 - For Exercises R.1-R.3, graph the equation. R.1....Ch. 9.4 - Prob. R.2PECh. 9.4 - Prob. R.3PECh. 9.4 - Prob. R.4PECh. 9.4 - Prob. R.5PECh. 9.4 - Prob. 1PECh. 9.4 - Prob. 2PECh. 9.4 - For Exercises 3-14, a. Graph the equations in the...Ch. 9.4 - Prob. 4PECh. 9.4 - Prob. 5PECh. 9.4 - Prob. 6PECh. 9.4 - For Exercises 3-14, a. Graph the equations in the...Ch. 9.4 - Prob. 8PECh. 9.4 - Prob. 9PECh. 9.4 - Prob. 10PECh. 9.4 - For Exercises 3-14, a. Graph the equations in the...Ch. 9.4 - Prob. 12PECh. 9.4 - For Exercises 3-14, a. Graph the equations in the...Ch. 9.4 - Prob. 14PECh. 9.4 - Prob. 15PECh. 9.4 - Prob. 16PECh. 9.4 - For Exercises 15-22, solve the system by using the...Ch. 9.4 - Prob. 18PECh. 9.4 - Prob. 19PECh. 9.4 - Prob. 20PECh. 9.4 - Prob. 21PECh. 9.4 - Prob. 22PECh. 9.4 - Prob. 23PECh. 9.4 - Prob. 24PECh. 9.4 - Prob. 25PECh. 9.4 - Prob. 26PECh. 9.4 - Prob. 27PECh. 9.4 - Prob. 28PECh. 9.4 - Prob. 29PECh. 9.4 - Prob. 30PECh. 9.4 - Prob. 31PECh. 9.4 - Prob. 32PECh. 9.4 - Prob. 33PECh. 9.4 - Prob. 34PECh. 9.4 - Prob. 35PECh. 9.4 - Prob. 36PECh. 9.4 - Find two numbers whose sum is 12 and whose product...Ch. 9.4 - Prob. 38PECh. 9.4 - Prob. 39PECh. 9.4 - Prob. 40PECh. 9.4 - Prob. 41PECh. 9.4 - Prob. 42PECh. 9.4 - Prob. 43PECh. 9.4 - Prob. 44PECh. 9.4 - Prob. 45PECh. 9.4 - Prob. 46PECh. 9.4 - Prob. 47PECh. 9.4 - Prob. 48PECh. 9.4 - Prob. 49PECh. 9.4 - Prob. 50PECh. 9.4 - Prob. 51PECh. 9.4 - Prob. 52PECh. 9.4 - Prob. 53PECh. 9.4 - Prob. 54PECh. 9.4 - Prob. 55PECh. 9.4 - Prob. 56PECh. 9.4 - Prob. 57PECh. 9.4 - Prob. 58PECh. 9.4 - Prob. 59PECh. 9.4 - Prob. 60PECh. 9.4 - Prob. 61PECh. 9.4 - Prob. 62PECh. 9.4 - Prob. 63PECh. 9.4 - Prob. 64PECh. 9.4 - Prob. 65PECh. 9.4 - Prob. 66PECh. 9.4 - Prob. 67PECh. 9.4 - Prob. 68PECh. 9.4 - Prob. 69PECh. 9.4 - Prob. 70PECh. 9.4 - Prob. 71PECh. 9.4 - Prob. 72PECh. 9.4 - Prob. 73PECh. 9.4 - Prob. 74PECh. 9.4 - Prob. 75PECh. 9.4 - Prob. 76PECh. 9.4 - Prob. 77PECh. 9.4 - Prob. 78PECh. 9.4 - Prob. 79PECh. 9.4 - Prob. 80PECh. 9.5 - Use the graph to solve the equation and...Ch. 9.5 - Prob. 1PECh. 9.5 - Prob. 2PECh. 9.5 - Prob. 3PECh. 9.5 - Prob. 4PECh. 9.5 - Prob. 5PECh. 9.5 - Prob. 6PECh. 9.5 - Prob. 7PECh. 9.5 - Prob. 8PECh. 9.5 - Prob. 9PECh. 9.5 - Prob. 10PECh. 9.5 - Prob. 11PECh. 9.5 - Prob. 12PECh. 9.5 - Prob. 13PECh. 9.5 - Prob. 14PECh. 9.5 - Prob. 15PECh. 9.5 - Prob. 16PECh. 9.5 - Prob. 17PECh. 9.5 - Prob. 18PECh. 9.5 - Prob. 19PECh. 9.5 - Prob. 20PECh. 9.5 - Prob. 21PECh. 9.5 - Prob. 22PECh. 9.5 - Prob. 23PECh. 9.5 - Prob. 24PECh. 9.5 - Prob. 25PECh. 9.5 - Prob. 26PECh. 9.5 - Prob. 27PECh. 9.5 - Prob. 28PECh. 9.5 - Prob. 29PECh. 9.5 - Prob. 30PECh. 9.5 - Prob. 31PECh. 9.5 - Prob. 32PECh. 9.5 - Prob. 33PECh. 9.5 - Prob. 34PECh. 9.5 - Prob. 35PECh. 9.5 - Prob. 36PECh. 9.5 - Prob. 37PECh. 9.5 - Prob. 38PECh. 9.5 - Prob. 39PECh. 9.5 - Prob. 40PECh. 9.5 - Prob. 41PECh. 9.5 - Prob. 42PECh. 9.5 - Prob. 43PECh. 9.5 - Prob. 44PECh. 9.5 - Prob. 45PECh. 9.5 - Prob. 46PECh. 9.5 - Prob. 47PECh. 9.5 - Prob. 48PECh. 9.5 - Prob. 49PECh. 9.5 - Prob. 50PECh. 9.5 - Prob. 51PECh. 9.5 - Prob. 52PECh. 9.5 - Prob. 53PECh. 9.5 - For Exercises 41-58, graph the solution set. If...Ch. 9.5 - For Exercises 41-58, graph the solution set. If...Ch. 9.5 - Prob. 56PECh. 9.5 - For Exercises 41-58, graph the solution set. If...Ch. 9.5 - For Exercises 41-58, graph the solution set. If...Ch. 9.5 - Prob. 59PECh. 9.5 - Prob. 60PECh. 9.5 - Prob. 61PECh. 9.5 - Prob. 62PECh. 9.5 - Prob. 63PECh. 9.5 - Prob. 64PECh. 9.5 - Prob. 65PECh. 9.5 - Prob. 66PECh. 9.5 - Prob. 67PECh. 9.5 - Prob. 68PECh. 9.5 - Prob. 69PECh. 9.5 - Prob. 70PECh. 9.5 - Prob. 71PECh. 9.5 - Prob. 72PECh. 9.5 - Prob. 73PECh. 9.5 - Prob. 74PECh. 9.5 - Prob. 75PECh. 9.5 - Explain how test points are used to determine the...Ch. 9.5 - Prob. 77PECh. 9.5 - Prob. 78PECh. 9.5 - Prob. 79PECh. 9.5 - Prob. 80PECh. 9.5 - Prob. 81PECh. 9.5 - Prob. 82PECh. 9.6 - A salesperson makes a base salary of $500 per week...Ch. 9.6 - A luxury car rental company charges $123 per day...Ch. 9.6 - The process that maximizes or minimizes a function...Ch. 9.6 - The function to be optimized in a linear...Ch. 9.6 - The region in the plane that represents the...Ch. 9.6 - The points of intersection of a feasible region...Ch. 9.6 - Prob. 5PECh. 9.6 - Prob. 6PECh. 9.6 - Prob. 7PECh. 9.6 - Prob. 8PECh. 9.6 - Prob. 9PECh. 9.6 - Prob. 10PECh. 9.6 - Prob. 11PECh. 9.6 - Prob. 12PECh. 9.6 - Prob. 13PECh. 9.6 - Prob. 14PECh. 9.6 - Prob. 15PECh. 9.6 - Prob. 16PECh. 9.6 - Prob. 17PECh. 9.6 - Prob. 18PECh. 9.6 - Prob. 19PECh. 9.6 - Prob. 20PECh. 9.6 - Prob. 21PECh. 9.6 - Guyton makes $24/hr tutoring chemistry and $20/hr...Ch. 9.6 - A plant nursery sells two sizes of oak trees to...Ch. 9.6 - A sporting goods store sells two types of exercise...Ch. 9.6 - Prob. 25PECh. 9.6 - A large department store needs at least 3600 labor...Ch. 9.6 - A manufacturer produces two models of a gas grill....Ch. 9.6 - Prob. 28PECh. 9.6 - A farmer has 1200 acres ofland and plans to plant...Ch. 9.6 - Prob. 30PECh. 9.6 - Prob. 31PECh. 9.6 - Prob. 32PECh. 9.6 - Prob. 33PECh. 9.6 - Prob. 34PECh. 9 - For Exercises 1-2, for parts (a) and (b), graph...Ch. 9 - For Exercises 1-2, for parts (a) and (b), graph...Ch. 9 - Prob. 3PRECh. 9 - Prob. 4PRECh. 9 - Prob. 1RECh. 9 - Prob. 2RECh. 9 - Prob. 3RECh. 9 - Prob. 4RECh. 9 - Prob. 5RECh. 9 - Prob. 6RECh. 9 - Prob. 7RECh. 9 - Prob. 8RECh. 9 - Prob. 9RECh. 9 - Prob. 10RECh. 9 - Prob. 11RECh. 9 - Prob. 12RECh. 9 - Prob. 13RECh. 9 - Prob. 14RECh. 9 - Prob. 15RECh. 9 - Prob. 16RECh. 9 - Prob. 17RECh. 9 - Prob. 18RECh. 9 - Emily receives an inheritance of $20,000 and...Ch. 9 - Prob. 20RECh. 9 - For Exercises 20-21, use a system of linear...Ch. 9 - Prob. 22RECh. 9 - Prob. 23RECh. 9 - Prob. 24RECh. 9 - Prob. 25RECh. 9 - Prob. 26RECh. 9 - Prob. 27RECh. 9 - Prob. 28RECh. 9 - Prob. 29RECh. 9 - Prob. 30RECh. 9 - Prob. 31RECh. 9 - Prob. 32RECh. 9 - Prob. 33RECh. 9 - Prob. 34RECh. 9 - Prob. 35RECh. 9 - Prob. 36RECh. 9 - Prob. 37RECh. 9 - The sum of the squares of two negative numbers is...Ch. 9 - Prob. 39RECh. 9 - Prob. 40RECh. 9 - Prob. 41RECh. 9 - Prob. 42RECh. 9 - Prob. 43RECh. 9 - Prob. 44RECh. 9 - Prob. 45RECh. 9 - Prob. 46RECh. 9 - Prob. 47RECh. 9 - Prob. 48RECh. 9 - Prob. 49RECh. 9 - Prob. 50RECh. 9 - Prob. 51RECh. 9 - Prob. 52RECh. 9 - Prob. 53RECh. 9 - Prob. 54RECh. 9 - Prob. 55RECh. 9 - Prob. 56RECh. 9 - Prob. 57RECh. 9 - A fitness instructor wants to mix two brands...Ch. 9 - Prob. 1TCh. 9 - Prob. 2TCh. 9 - Prob. 3TCh. 9 - Prob. 4TCh. 9 - Prob. 5TCh. 9 - Prob. 6TCh. 9 - Prob. 7TCh. 9 - Prob. 8TCh. 9 - Prob. 9TCh. 9 - Prob. 10TCh. 9 - Prob. 11TCh. 9 - Prob. 12TCh. 9 - Prob. 13TCh. 9 - Prob. 14TCh. 9 - Prob. 15TCh. 9 - Prob. 16TCh. 9 - Prob. 17TCh. 9 - Prob. 18TCh. 9 - Prob. 19TCh. 9 - Prob. 20TCh. 9 - Use a system of linear equations in three...Ch. 9 - Prob. 22TCh. 9 - Prob. 23TCh. 9 - Prob. 24TCh. 9 - Prob. 25TCh. 9 - Prob. 26TCh. 9 - Prob. 27TCh. 9 - Prob. 28TCh. 9 - Prob. 29TCh. 9 - Prob. 30TCh. 9 - Prob. 31TCh. 9 - Prob. 32TCh. 9 - Prob. 33TCh. 9 - Prob. 34TCh. 9 - Prob. 35TCh. 9 - Prob. 36TCh. 9 - A weight lifter wants to mix two types of protein...Ch. 9 - Prob. 1CRECh. 9 - Prob. 2CRECh. 9 - Prob. 3CRECh. 9 - Prob. 4CRECh. 9 - Prob. 5CRECh. 9 - Prob. 6CRECh. 9 - Prob. 7CRECh. 9 - Prob. 8CRECh. 9 - Prob. 9CRECh. 9 - Prob. 10CRECh. 9 - Prob. 11CRECh. 9 - Prob. 12CRECh. 9 - Prob. 13CRECh. 9 - Prob. 14CRECh. 9 - Prob. 15CRECh. 9 - Prob. 16CRECh. 9 - Prob. 17CRECh. 9 - Prob. 18CRECh. 9 - Prob. 19CRECh. 9 - Prob. 20CRECh. 9 - Prob. 21CRECh. 9 - Prob. 22CRE
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- Select the best statement. A. If a set of vectors includes the zero vector 0, then the set of vectors can span R^ as long as the other vectors are distinct. n B. If a set of vectors includes the zero vector 0, then the set of vectors spans R precisely when the set with 0 excluded spans Rª. ○ C. If a set of vectors includes the zero vector 0, then the set of vectors can span Rn as long as it contains n vectors. ○ D. If a set of vectors includes the zero vector 0, then there is no reasonable way to determine if the set of vectors spans Rn. E. If a set of vectors includes the zero vector 0, then the set of vectors cannot span Rn. F. none of the abovearrow_forwardWhich of the following sets of vectors are linearly independent? (Check the boxes for linearly independent sets.) ☐ A. { 7 4 3 13 -9 8 -17 7 ☐ B. 0 -8 3 ☐ C. 0 ☐ D. -5 ☐ E. 3 ☐ F. 4 THarrow_forward3 and = 5 3 ---8--8--8 Let = 3 U2 = 1 Select all of the vectors that are in the span of {u₁, u2, u3}. (Check every statement that is correct.) 3 ☐ A. The vector 3 is in the span. -1 3 ☐ B. The vector -5 75°1 is in the span. ГОЛ ☐ C. The vector 0 is in the span. 3 -4 is in the span. OD. The vector 0 3 ☐ E. All vectors in R³ are in the span. 3 F. The vector 9 -4 5 3 is in the span. 0 ☐ G. We cannot tell which vectors are i the span.arrow_forward
- (20 p) 1. Find a particular solution satisfying the given initial conditions for the third-order homogeneous linear equation given below. (See Section 5.2 in your textbook if you need a review of the subject.) y(3)+2y"-y-2y = 0; y(0) = 1, y'(0) = 2, y"(0) = 0; y₁ = e*, y2 = e¯x, y3 = e−2x (20 p) 2. Find a particular solution satisfying the given initial conditions for the second-order nonhomogeneous linear equation given below. (See Section 5.2 in your textbook if you need a review of the subject.) y"-2y-3y = 6; y(0) = 3, y'(0) = 11 yc = c₁ex + c2e³x; yp = −2 (60 p) 3. Find the general, and if possible, particular solutions of the linear systems of differential equations given below using the eigenvalue-eigenvector method. (See Section 7.3 in your textbook if you need a review of the subject.) = a) x 4x1 + x2, x2 = 6x1-x2 b) x=6x17x2, x2 = x1-2x2 c) x = 9x1+5x2, x2 = −6x1-2x2; x1(0) = 1, x2(0)=0arrow_forwardFind the perimeter and areaarrow_forwardAssume {u1, U2, us} spans R³. Select the best statement. A. {U1, U2, us, u4} spans R³ unless u is the zero vector. B. {U1, U2, us, u4} always spans R³. C. {U1, U2, us, u4} spans R³ unless u is a scalar multiple of another vector in the set. D. We do not have sufficient information to determine if {u₁, u2, 43, 114} spans R³. OE. {U1, U2, 3, 4} never spans R³. F. none of the abovearrow_forward
- Assume {u1, U2, 13, 14} spans R³. Select the best statement. A. {U1, U2, u3} never spans R³ since it is a proper subset of a spanning set. B. {U1, U2, u3} spans R³ unless one of the vectors is the zero vector. C. {u1, U2, us} spans R³ unless one of the vectors is a scalar multiple of another vector in the set. D. {U1, U2, us} always spans R³. E. {U1, U2, u3} may, but does not have to, span R³. F. none of the abovearrow_forwardLet H = span {u, v}. For each of the following sets of vectors determine whether H is a line or a plane. Select an Answer u = 3 1. -10 8-8 -2 ,v= 5 Select an Answer -2 u = 3 4 2. + 9 ,v= 6arrow_forwardSolve for the matrix X: X (2 7³) x + ( 2 ) - (112) 6 14 8arrow_forward
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