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All Textbook Solutions for Precalculus Enhanced with Graphing Utilities

In Problems 5-24, graph each equation of the system. Then solve the system to find the points of intersection. { x 2 + y 2 =16 x 2 2y=8 In Problems 5-24, graph each equation of the system. Then solve the system to find the points of intersection. { xy=4 x 2 + y 2 =8 In Problems 5-24, graph each equation of the system. Then solve the system to find the points of intersection. { x 2 =y xy=1 In Problems 5-24, graph each equation of the system. Then solve the system to find the points of intersection. { x 2 + y 2 =4 y= x 2 9 In Problems 5-24, graph each equation of the system. Then solve the system to find the points of intersection. { xy=1 y=2x+1 In Problems 5-24, graph each equation of the system. Then solve the system to find the points of intersection. { y= x 2 4 y=6x13 In Problems 5-24, graph each equation of the system. Then solve the system to find the points of intersection. { x 2 + y 2 =10 xy=3 In Problems 25-54, solve each system. Use any method you wish. { 2 x 2 + y 2 =18 xy=4 In Problems 25-54, solve each system. Use any method you wish. { x 2 y 2 =21 x+y=7 In Problems 25-54, solve each system. Use any method you wish. { y=2x+1 2 x 2 + y 2 =1 In Problems 25-54, solve each system. Use any method you wish. { x 2 4 y 2 =16 2yx=2 In Problems 25-54, solve each system. Use any method you wish. { x+y+1=0 x 2 + y 2 +6yx=5 In Problems 25-54, solve each system. Use any method you wish. { 2 x 2 xy+ y 2 =8 xy=4 In Problems 25-54, solve each system. Use any method you wish. { 4 x 2 3xy+9 y 2 =15 2x+3y=5 In Problems 25-54, solve each system. Use any method you wish. { 2 y 2 3xy+6y+2x+4=0 2x3y+4=0 In Problems 25-54, solve each system. Use any method you wish. { x 2 4 y 2 +7=0 3 x 2 + y 2 =31 In Problems 25-54, solve each system. Use any method you wish. { 3 x 2 2 y 2 +5=0 2 x 2 y 2 +2=0 In Problems 25-54, solve each system. Use any method you wish. { 7 x 2 3 y 2 +5=0 3 x 2 +5 y 2 =12 In Problems 25-54, solve each system. Use any method you wish. { x 2 3 y 2 +1=0 2 x 2 7 y 2 +5=0 In Problems 25-54, solve each system. Use any method you wish. { x 2 +2xy=10 3 x 2 xy=2 In Problems 25-54, solve each system. Use any method you wish. { 5xy+13 y 2 +36=0 xy+7 y 2 =6 In Problems 25-54, solve each system. Use any method you wish. { 2 x 2 + y 2 =2 x 2 2 y 2 +8=0 In Problems 25-54, solve each system. Use any method you wish. { y 2 x 2 +4=0 2 x 2 +3 y 2 =6 In Problems 25-54, solve each system. Use any method you wish. { x 2 +2 y 2 =16 4 x 2 y 2 =24 In Problems 25-54, solve each system. Use any method you wish. { 4 x 2 +3 y 2 =4 2 x 2 6 y 2 =3 In Problems 25-54, solve each system. Use any method you wish. { 5 x 2 2 y 2 +3=0 3 x 2 + 1 y 2 =7 In Problems 25-54, solve each system. Use any method you wish. { 2 x 2 3 y 2 +1=0 6 x 2 7 y 2 +2=0 In Problems 25-54, solve each system. Use any method you wish. { 1 x 4 + 6 y 4 =6 2 x 4 2 y 4 =19 In Problems 25-54, solve each system. Use any method you wish. { 1 x 4 1 y 4 =1 1 x 4 + 1 y 4 =4 In Problems 25-54, solve each system. Use any method you wish. { x 2 3xy+2 y 2 =0 x 2 +xy=6 In Problems 25-54, solve each system. Use any method you wish. { x 2 xy2 y 2 =0 xy+x+6=0 In Problems 25-54, solve each system. Use any method you wish. { y 2 +y+ x 2 x2=0 y+1+ x2 y =0 In Problems 25-54, solve each system. Use any method you wish. { x 3 2 x 2 + y 2 +3y4=0 x2+ y 2 y x 2 =0 In Problems 25-54, solve each system. Use any method you wish. { log x y=3 log x ( 4y )=5 In Problems 25-54, solve each system. Use any method you wish. { log x ( 2y )=3 log x ( 4y )=2 In Problems 25-54, solve each system. Use any method you wish. { lnx=4lny log 3 x=2+2 log 3 y In Problems 25-54, solve each system. Use any method you wish. { lnx=5lny log 2 x=3+2 log 2 y Graph the equations given in Example 4. Solve: { x 2 +x+ y 2 3y+2=0 x+1+ y 2 y x =0 Graph the equations given in problem 49. In Problems 25-54, solve each system. Use any method you wish. { y 2 +y+ x 2 x2=0 y+1+ x2 y =0 In Problems 57-64, use a graphing utility to solve each system of equations.Express the solution(s) rounded to two decimal places. { y= x 2/3 y= e x In Problems 57-64, use a graphing utility to solve each system of equations.Express the solution(s) rounded to two decimal places. { y= x 3/2 y= e x In Problems 57-64, use a graphing utility to solve each system of equations.Express the solution(s) rounded to two decimal places. { x 2 + y 3 =2 x 3 y=4 In Problems 57-64, use a graphing utility to solve each system of equations.Express the solution(s) rounded to two decimal places. { x 3 + y 2 =2 x 2 y=4 In Problems 57-64, use a graphing utility to solve each system of equations.Express the solution(s) rounded to two decimal places. { x 4 + y 4 =12 x y 2 =2 In Problems 57-64, use a graphing utility to solve each system of equations.Express the solution(s) rounded to two decimal places. { x 4 + y 4 =6 xy=1 In Problems 57-64, use a graphing utility to solve each system of equations.Express the solution(s) rounded to two decimal places. { xy=2 y=lnx In Problems 57-64, use a graphing utility to solve each system of equations.Express the solution(s) rounded to two decimal places. { x 2 + y 2 =4 y=lnx In Problems 65-70, graph each equation and find the point(s) of intersection, if any. The circle x+2y=0 and the circle ( x1 ) 2 + ( y1 ) 2 =5 In Problems 65-70, graph each equation and find the point(s) of intersection, if any. The circle x+2y+6=0 and the parabola ( x+1 ) 2 + ( y+1 ) 2 =5 In Problems 65-70, graph each equation and find the point(s) of intersection, if any. The circle ( x1 ) 2 + ( y+2 ) 2 =4 and the parabola y 2 +4yx+1=0 In Problems 65-70, graph each equation and find the point(s) of intersection, if any. The circle ( x+2 ) 2 + ( y1 ) 2 =4 and the parabola y 2 2yx5=0 In Problems 65-70, graph each equation and find the point(s) of intersection, if any. y= 4 x3 and the circle x 2 6x+ y 2 +1=0 In Problems 65-70, graph each equation and find the point(s) of intersection, if any. y= 4 x+2 and the circle x 2 +4x+ y 2 4=0 The difference of two numbers is 2 and the sum of their squares is 10. Find the numbers.The sum of two numbers is 7 and the difference of their squares is 21. Find the numbers.The product of two numbers is 4 and the sum of their squares is 8. Find the numbers.The product of two numbers is 10 and the difference of their squares is 21. Find the numbers.The difference of two numbers is the same as their product, and the sum of their reciprocals is 5. Find the numbers.The sum of two numbers is the same as their product, and the difference of their reciprocals is 3. Find the numbers.The ratio of a to b is 2 3 . The sum of a and b is 10. What is the ratio of a+b to ba ?The ratio of a to b is 4:3 . The sum of a and b is 14. What is the ratio of ab to a+b ?Geometry The perimeter of a rectangle is 16 inches and its area is 15 square inches. What are its dimensions?Geometry An area of 52 square feet is to be enclosed by two squares whose sides are in the ratio of 2:3 . Find the sides of the squares.Geometry The altitude of an isosceles triangle drawn to its base is 3 centimeters, and its perimeter is 18 centimeters. Find the length of its base.Geometry The altitude of an isosceles triangle drawn to its base is 3 centimeters, and its perimeter is 18 centimeters. Find the length of its base.The Tortoise and the Hare In a 21-meter race between a tortoise and a hare, the tortoise leaves 9 minutes before the hare. The hare, by running at an average speed of 0.5 meter per hour faster than the tortoise, crosses the finish line 3 minutes before the tortoise. What are the average speeds of the tortoise and the hare?Running a Race In a 1-mile race, the winner crosses the finish line 10 feet ahead of the second-place runner and 20 feet ahead of the third-place runner. Assuming that each runner maintains a constant speed throughout the race, by how many feet does the second-place runner beat the third-place runner?Constructing a Box A rectangular piece of cardboard, whose area is 216 square centimeters, is made into an open box by cutting a 2-centimeter square from each corner and turning up the sides. See the figure. If the box is to have a volume of 224 cubic centimeters, what size cardboard should you start with?86AYU Fencing A farmer has 300 feet of fence available to enclose a 4500-square-foot region in the shape of adjoining squares, with sides of length x and y . See the figure. Find x and y .88AYU 89AYU 90AYU 91AYU 92AYU 93AYU 94AYU 95AYU 96AYU 97AYU 98AYU 99AYU A circle and a line intersect at most twice. A circle and a parabola intersect at most four times. Deduce that a circle and the graph of a polynomial of degree 3 intersect at most six times. What do you conjecture about a polynomial of degree 4? What about a polynomial of degree n ? Can you explain your conclusions using an algebraic argument?101AYU Solve the inequality: 3x+48x (pp. A79-A80)Graph the equation: 3x2y=6 (pp. 35-37)Graph the equation: x 2 + y 2 =9 (pp. 45-47)Graph the equation: y= x 2 +4 (pp. 106-107)True or False The lines 2x+y=4 and 4x+2y=0 are parallel. (pp. 37-38)The graph of y= ( x2 ) 2 may be obtained by shifting the graph of _____ to the (left/right) a distance of _____ units.(pp. 107-108)When graphing an inequality in two variables, use _____ if the inequality is strict; if the inequality is nonstrict, use a _____ mark.The graph of the corresponding equation of a linear inequality is a line that separates the xy-plane into two regions. The two regions are called _____ mark.True or False The graph of a system of inequalities must have an overlapping region.If a graph of a system of linear inequalities cannot be contained in any circle, then it is _____ mark.In Problems 11-22, graph each inequality. x0 In Problems 11-22, graph each inequality. y0 In Problems 11-22, graph each inequality. x4 In Problems 11-22, graph each inequality. y2 In Problems 11-22, graph each inequality. 2x+y6 In Problems 11-22, graph each inequality. 3x+2y6 In Problems 11-22, graph each inequality. x 2 + y 2 1 In Problems 11-22, graph each inequality. x 2 + y 2 9 In Problems 11-22, graph each inequality. y x 2 1 In Problems 11-22, graph each inequality. y x 2 +2 In Problems 11-22, graph each inequality. xy4 In Problems 11-22, graph each inequality. xy1 In Problems 23-34, graph each system of linear inequalities. { x+y2 2x+y4 In Problems 23-34, graph each system of linear inequalities. { 3xy6 x+2y2 In Problems 23-34, graph each system of linear inequalities. { 2xy4 3x+2y6 In Problems 23-34, graph each system of linear inequalities. { 4x5y0 2xy2 In Problems 23-34, graph each system of linear inequalities. { 2x3y0 3x+2y6 In Problems 23-34, graph each system of linear inequalities. { 4xy2 x+2y2 In Problems 23-34, graph each system of linear inequalities. { x2y6 2x4y0 In Problems 23-34, graph each system of linear inequalities. { x+4y8 x+4y4 In Problems 23-34, graph each system of linear inequalities. { 2x+y2 2x+y2 In Problems 23-34, graph each system of linear inequalities. { x4y4 x4y0 In Problems 23-34, graph each system of linear inequalities. { 2x+3y6 2x+3y0 In Problems 23-34, graph each system of linear inequalities. { 2x+y0 2x+y2 In Problems 35-42, graph each system of inequalities. { x 2 + y 2 9 x+y3 In Problems 35-42, graph each system of inequalities. { x 2 + y 2 9 x+y3 In Problems 35-42, graph each system of inequalities. { y x 2 4 yx2 In Problems 35-42, graph each system of inequalities. { y 2 x yx In Problems 35-42, graph each system of inequalities. { x 2 + y 2 16 y x 2 4 In Problems 35-42, graph each system of inequalities. { x 2 + y 2 25 y x 2 5 In Problems 35-42, graph each system of inequalities. { xy4 y x 2 +1 In Problems 35-42, graph each system of inequalities. { y+ x 2 1 y x 2 1 In Problems 43-52, graph each system of linear inequalities. Tell whether the graph is bounded or unbounded, and label the corner points. { x0 y0 2x+y6 x+2y6 In Problems 43-52, graph each system of linear inequalities. Tell whether the graph is bounded or unbounded, and label the corner points. { x0 y0 x+y4 2x+3y6 In Problems 43-52, graph each system of linear inequalities. Tell whether the graph is bounded or unbounded, and label the corner points. { x0 y0 x+y2 2x+y4 In Problems 43-52, graph each system of linear inequalities. Tell whether the graph is bounded or unbounded, and label the corner points. { x0 y0 3x+y6 2x+y2 In Problems 43-52, graph each system of linear inequalities. Tell whether the graph is bounded or unbounded, and label the corner points. { x0 y0 x+y2 2x+3y12 3x+y12 In Problems 43-52, graph each system of linear inequalities. Tell whether the graph is bounded or unbounded, and label the corner points. { x0 y0 x+y1 x+y7 2x+y10 In Problems 43-52, graph each system of linear inequalities. Tell whether the graph is bounded or unbounded, and label the corner points. { x0 y0 x+y2 x+y8 2x+y10 In Problems 43-52, graph each system of linear inequalities. Tell whether the graph is bounded or unbounded, and label the corner points. { x0 y0 x+y2 x+y8 x+2y1 In Problems 43-52, graph each system of linear inequalities. Tell whether the graph is bounded or unbounded, and label the corner points. { x0 y0 x+2y1 x+2y10 In Problems 43-52, graph each system of linear inequalities. Tell whether the graph is bounded or unbounded, and label the corner points. { x0 y0 x+2y1 x+2y10 x+y2 x+y8 In problems 53-56, write a system of linear inequalities for the given graph.In problems 53-56, write a system of linear inequalities for the given graph.In problems 53-56, write a system of linear inequalities for the given graph.In problems 53-56, write a system of linear inequalities for the given graph.Financial Planning A retired couple has up to 50,000 to invest. As their financial adviser, you recommend that they place at least 35,000 in Treasury bills yielding 3 and at most 10,000 in corporate bonds yielding 3 . a. Using x to denote the amount of money invested in Treasury bills and y to denote the amount invested in corporate bonds, write a system of linear inequalities that describes the possible amounts of each investment. b. Graph the system and label the corner points.Manufacturing Trucks Mikes Toy Truck Company manufactures two models of toy trucks, a standard model and a deluxe model. Each standard model requires 2 hours (h) for painting and 3 h for detail work; each deluxe model requires 3 h for painting and 4 h for detail work. Two painters and three detail workers are employed by the company, and each works 40 h per week. a. Using x to denote the number of standard-model trucks and y to denote the number of deluxe-model trucks, write a system of linear inequalities that describes the possible numbers of each model of truck that can be manufactured in a week. b. Graph the system and label the corner points.Blending Coffee Bills Coffee House, a store that specializes in coffee, has available 75 pounds ( lb ) of A grade coffee and 120 lb of B grade coffee. These will be blended into 1-lb packages as follows: an economy blend that contains 4 ounces ( oz ) of A grade coffee and 12 oz of B grade coffee, and a superior blend that contains 8 oz of A grade coffee and 8 oz of B grade coffee. a. Using x to denote the number of packages of the economy blend and y to denote the number of packages of the superior blend, write a system of linear inequalities that describes the possible numbers of packages of each kind of blend. b. Graph the system and label the corner points.Mixed Nuts Nolas Nuts, a store that specializes in selling nuts, has available 90 pounds (lb) of cashews and 120 lb of peanuts. These are to be mixed in 12-ounce (oz) packages as follows: a lower-priced package containing 8 oz of peanuts and 4 oz of cashews, and a quality package containing 6 oz of peanuts and 6 oz of cashews. a. Using x to denote the number of lower-priced packages, and use y to denote the number of quality packages. Write a system of linear inequalities that describes the possible numbers of each kind of package. b. Graph the system and label the corner points.Transporting Goods A small truck can carry no more than 1600 pounds (lb) of cargo and no more than 150 cubic feet ( f t 3 ) of cargo. A printer weighs 20 lb and occupies 3f t 3 of space. A microwave oven weighs 30 lb and occupies 2f t 3 of space. a. Using x to represent the number of microwave ovens and y to represent the number of printers, write a system of linear inequalities that describes the number of ovens and printers that can be hauled by the truck. b. Graph the system and label the corner points.A linear programming problem requires that a linear expression, called the ________, be maximized or minimized.True or False If a linear programming problem has a solution, it is located at a corner point of the graph of the feasible points.In problems 3-8, find the maximum and minimum value of the given objective function of a linear programming problem. The figure illustrates the graph of the feasible points. z=x+y In problems 3-8, find the maximum and minimum value of the given objective function of a linear programming problem. The figure illustrates the graph of the feasible points. z=2x+3y In problems 3-8, find the maximum and minimum value of the given objective function of a linear programming problem. The figure illustrates the graph of the feasible points. z=x+10y In problems 3-8, find the maximum and minimum value of the given objective function of a linear programming problem. The figure illustrates the graph of the feasible points. z=10x+y In problems 3-8, find the maximum and minimum value of the given objective function of a linear programming problem. The figure illustrates the graph of the feasible points. z=5x+7y In problems 3-8, find the maximum and minimum value of the given objective function of a linear programming problem. The figure illustrates the graph of the feasible points. z=7x+5y In Problems 9-18, solve each linear programming problem. Maximize z=2x+y subject to x0,y0,x+y6,x+y1 In Problems 9-18, solve each linear programming problem. Maximize z=x+3y subject to x0,y0,x+y3,x5,y7 In Problems 9-18, solve each linear programming problem. Maximize z=2x+5y subject to x0,y0,x+y2,x5,y3 In Problems 9-18, solve each linear programming problem. Maximize z=3x+4y subject to x0,y0,2x+3y6,x+y8 In Problems 9-18, solve each linear programming problem. Maximize z=3x+5y subject to x0,y0,x+y2,2x+3y12,3x+2y12 In Problems 9-18, solve each linear programming problem. Maximize z=5x+3y subject to x0,y0,x+y2,x+y8,2x+y10 In Problems 9-18, solve each linear programming problem. Maximize z=5x+4y subject to x0,y0,x+y2,2x+3y12,3x+y12 In Problems 9-18, solve each linear programming problem. Maximize z=2x+3y subject to x0,y0,x+y3,x+y9,x+3y6 In Problems 9-18, solve each linear programming problem. Maximize z=5x+2y subject to x0,y0,x+y10,2x+y10,x+2y10 In Problems 9-18, solve each linear programming problem. Maximize z=2x+4y subject to x0,y0,2x+y4,x+y9 Maximizing Profit A manufacturer of skis produces two types: downhill and cross-country. Use the following table to determine how many of each kind of ski should be produced to achieve a maximum profit. What is the maximum profit? What would the maximum profit be if the time available for manufacturing were increased to 48 hours?Farm Management A farmer has 70 acres of land available for planting either soybeans or wheat. The cost of preparing the soil, the workdays required, and the expected profit per acre planted for each type of crop are given in the following table. The farmer cannot spend more than 1800 in preparation costs and cannot use a total of more than 120 workdays. How many acres of each crop should be planted to maximize the profit? What is the maximum profit? What is the maximum profit if the farmer is willing to spend no more than 2400 on preparation?Banquet Seating A banquet hall offers two types of tables for rent: 6-person rectangular tables at a cost of 28 each and 10-person round tables at a cost of 52 each. Kathleen would like to rent the hall for a wedding banquet and needs tables for 250 people. The hall can have a maximum of 35 tables, and the hall has only 15 rectangular tables available. How many of each type of table should be rented to minimize cost and what is the minimum cost? Source: facilities.princeton.edu Spring Break The student activities department of a community college plans to rent buses and vans for a spring-break trip. Each bus has 40 regular seats and 1 special seat designed to accommodate travelers with disabilities. Each van has 8 regular seats and 3 special seats. The rental cost is 350 for each van and 975 for each bus. If 320 regular and 36 special seats are required for the trip, how many vehicles of each type should be rented to minimize cost? Source: www.busrates.com Return on Investment An investment broker is instructed by her client to invest up to 20,000 , some in a junk bond yielding 9 per annum and some in Treasury bills yielding 7 per annum. The client wants to invest at least 8,000 in T-bills and no more than 12,000 in the junk bond. (a) How much should the broker recommend that the client place in each investment to maximize income if the client insists that the amount invested in T-bills must equal or exceed the amount placed in the junk bond? (b) How much should the broker recommend that the client place in each investment to maximize income if the client insists that the amount invested in T-bills must not exceed the amount placed in the junk bond?Production Scheduling In a factory, machine 1 produces 8-inch (in.) pliers at the rate of 60 units per hour (h) and 6-in. pliers at the rate of 70 units/h. Machine 2 produces 8-in. pliers at the rate of 40 units/h and 6-in. pliers at the rate of 20 units/h. It costs 50/h to operate machine 1, and machine 2 costs 30/h to operate. The production schedule requires that at least 240 units of 8-in. pliers and at least 140 units of 6-in. pliers be produced during each 10-h day. Which combination of machines will cost the least money to operate?Managing a Meat Market A meat market combines ground beef and ground pork in a single package for meat loaf. The ground beef is 75 lean ( 75 beef, 25 fat) and costs the market 0.75 per pound (lb). The ground pork is 60 lean and costs the market 0.45/lb . The meat loaf must be at least 70 lean. If the market wants to use at least 50 lb of its available pork, but no more than 200 lb of its available ground beef, how much ground beef should be mixed with ground pork so that the cost is minimized?Ice Cream The Mom and Pop Ice Cream Company makes two kinds of chocolate ice cream: regular and premium. The properties of 1 gallon (gal) of each type are shown in the table: In addition, current commitments require the company to make at least 1 gal of premium for every 4 gal of regular. Each day, the company has available 725 pounds (lb) of flavoring and 425 lb of milk-fat products. If the company can ship no more than 3000 lb of product per day, how many gallons of each type should be produced daily to maximize profit? Source: www.scitoys.com/ingredients/ice_cream.html Maximizing Profil on Ice Skates A factory manufactures two kinds of ice skates: racing skates and figure skates. The racing skates require 6 work-hours in the fabrication department, whereas the figure skates require 4 work-hours there. The racing skates require 1 work-hour in the finishing department, whereas the figure skates require 2 work-hours there. The fabricating department has available at most 120 work-hours per day, and the finishing department has no more than 40 work-hours per day available. If the profit on each racing skate is 10 and the profit on each figure skate is 12 , how many of each should be manufactured each day to maximize profit? (Assume that all skates made are sold.)Financial Planning A retired couple have up to 50,000 to place in fixed-income securities. Their financial adviser suggests two securities to them: one is an AAA bond that yields 8 per annum; the other is a certificate of deposit (CD) that yields 4 . After careful consideration of the alternatives, the couple decide to place at most 20,000 in the AAA bond and at least 15,000 in the CD. They also instruct the financial adviser to place at least as much in the CD as in the AAA bond. How should the financial adviser proceed to maximize the return on their investment?Product Design An entrepreneur is having a design group produce at least six samples of a new kind of fastener that he wants to market. It costs 9.00 to produce each metal fastener and 4.00 to produce each plastic fastener. He wants to have at least two of each version of the fastener and needs to have all the samples 24 hours (h) from now. It takes 4 h to produce each metal sample and 2 h to produce each plastic sample. To minimize the cost of the samples, how many of each kind should the entrepreneur order? What will be the cost of the samples?Animal Nutrition Kevin's dog Amadeus likes two kinds of canned dog food. Gourmet Dog costs 40 cents a can and has 20 units of a vitamin complex; the calorie content is 75 calories. Chow Hound costs 32 cents a can and has 35 units of vitamins and 50 calories. Kevin likes Amadeus to have at least 1175 units of vitamins a month and at least 2375 calories during the same time period. Kevin has space to store only 60 cans of dog food at a time. How much of each kind of dog food should Kevin buy each month to minimize his cost?Airline Revenue An airline has two classes of service: first class and coach. Management's experience has been that each aircraft should have at least 8 but no more than 16 first- class seats and at least 80 but no more than 120 coach seats (a) If management decides that the ratio of first-class seats to coach seats should never exceed 1:12 , with how many of each type of seat should an aircraft be configured to maximize revenue? (b) If management decides that the ratio of first-class seats to coach seats should never exceed 1:8 , with how many of each type of seat should an aircraft be configured to maximize revenue? (c) If you were management, what would you do? [Hint: Assume that the airline charges C for a coach seat and F for a first-class seat; C0,FC .]Explain in your own words what a linear programming problem is and how it can be solved.1RE 2RE 3RE 4RE 5RE 6RE 7RE 8RE 9RE 10RE 11RE 12RE 13RE 14RE 15RE 16RE 17RE 18RE 19RE 20RE 21RE 22RE 23RE 24RE 25RE 26RE 27RE 28RE 29RE 30RE 31RE 32RE 33RE 34RE 35RE 36RE 37RE 38RE 1CT 2CT 3CT 4CT 5CT 6CT 7CT 8CT 9CT 10CT 11CT 12CT 13CT 14CT 15CT 16CT 1CR 2CR 3CR 4CR 5CR 6CR 7CR 8CR 9CR 10CR 11CR 12CR For the function f( x )= x1 x , find f( 2 ) and f( 3 ) . (pp.60-63)True or False A function is a relation between two sets D and R so that each element x in the first set D is related to exactly one element y in the second set R . (pp. 57-60)If 1000 is invested at 4 per annum compounded semiannually, how much is in the account after 2 years? (pp. 325-327)How much do you need to invest now at 5 per annum compounded monthly so that in 1 year you will have 1000 ? (p. 329)5AYU True or False The notation a 5 represents the fifth term of a sequence.If n0 is an integer, then n!= ________ When n2 .The sequence a 1 =5 , a n =3 a n1 is an example of a( n ) _____ sequence. (a) alternating(b) recursive (c) Fibonacci(d) summation The notation a 1 + a 2 + a 3 ++ a n = k=1 n a k is an example of ______ notation.k=1 n k=1+2+3++n = ______. (a) n! (b) n( n+1 ) 2 (c) nk (d) n( n+1 )( 2n+1 ) 6 In Problems 11-16, evaluate each factorial expression. 10!In Problems 11-16, evaluate each factorial expression. 9!In Problems 11-16, evaluate each factorial expression. 9! 6!In Problems 11-16, evaluate each factorial expression. 12! 10!In Problems 11-16, evaluate each factorial expression. 3!7! 4!In Problems 11-16, evaluate each factorial expression. 5!8! 3!In Problems 17-28, write down the first five terms of each sequence. { s n }={ n }In Problems 17-28, write down the first five terms of each sequence. { s n }={ n 2 +1 }In Problems 17-28, write down the first five terms of each sequence. { a n }={ n n+2 }In Problems 17-28, write down the first five terms of each sequence. { b n }={ 2n+1 2n }In Problems 17-28, write down the first five terms of each sequence. { c n }={ ( 1 ) n+1 n 2 }In Problems 17-28, write down the first five terms of each sequence. { d n }={ ( 1 ) n1 ( n 2n1 ) }In Problems 17-28, write down the first five terms of each sequence. { s n }={ 2 n 3 n +1 }In Problems 17-28, write down the first five terms of each sequence. { s n }={ ( 4 3 ) n }In Problems 17-28, write down the first five terms of each sequence. { t n }={ ( 1 ) n ( n+1 )( n+2 ) }In Problems 17-28, write down the first five terms of each sequence. { a n }={ 3 n n }In Problems 17-28, write down the first five terms of each sequence. { b n }={ n e n }In Problems 17-28, write down the first five terms of each sequence. { c n }={ n 2 2 n }In Problems 29-36, the given pattern continues. Write down the nth term of a sequence { a n } suggested by the pattern. 1 2 , 2 3 , 3 4 , 4 5 ,...In Problems 29-36, the given pattern continues. Write down the nth term of a sequence { a n } suggested by the pattern. 1 12 , 1 23 , 1 34 , 1 45 ,...In Problems 29-36, the given pattern continues. Write down the nth term of a sequence { a n } suggested by the pattern. 1, 1 2 , 1 4 , 1 8 ,...In Problems 29-36, the given pattern continues. Write down the nth term of a sequence { a n } suggested by the pattern. 2 3 , 4 9 , 8 27 , 16 81 ,...In Problems 29-36, the given pattern continues. Write down the nth term of a sequence { a n } suggested by the pattern. 1,1,1,1,1,1,...In Problems 29-36, the given pattern continues. Write down the nth term of a sequence { a n } suggested by the pattern. 1, 1 2 ,3, 1 4 ,5, 1 6 ,7, 1 8 ,...In Problems 29-36, the given pattern continues. Write down the nth term of a sequence { a n } suggested by the pattern. 1,2,3,4,5,6,...In Problems 29-36, the given pattern continues. Write down the nth term of a sequence { a n } suggested by the pattern. 2,4,6,8,10,...In Problems 37-50, a sequence is defined recursively. Write down the first five terms. a 1 =2 ; a n =3+ a n1 In Problems 37-50, a sequence is defined recursively. Write down the first five terms. a 1 =3 ; a n =4 a n1 In Problems 37-50, a sequence is defined recursively. Write down the first five terms. a 1 =2 ; a n =n+ a n1 In Problems 37-50, a sequence is defined recursively. Write down the first five terms. a 1 =1 ; a n =n a n1 In Problems 37-50, a sequence is defined recursively. Write down the first five terms. a 1 =5 ; a n =2 a n1 In Problems 37-50, a sequence is defined recursively. Write down the first five terms. a 1 =2 ; a n = a n1 In Problems 37-50, a sequence is defined recursively. Write down the first five terms. a 1 =3 ; a n = a n1 n In Problems 37-50, a sequence is defined recursively. Write down the first five terms. a 1 =2 ; a n =n+3 a n1 In Problems 37-50, a sequence is defined recursively. Write down the first five terms. a 1 =1 ; a 2 =2 ; a n = a n1 a n2 In Problems 37-50, a sequence is defined recursively. Write down the first five terms. a 1 =1 ; a 2 =1 ; a n = a n2 +n a n1 In Problems 37-50, a sequence is defined recursively. Write down the first five terms. a 1 =A ; a n = a n1 +d In Problems 37-50, a sequence is defined recursively. Write down the first five terms. a 1 =A ; a n =r a n1 ; r0 In Problems 37-50, a sequence is defined recursively. Write down the first five terms. a 1 = 2 ; a n = 2+ a n1 In Problems 37-50, a sequence is defined recursively. Write down the first five terms. a 1 = 2 ; a n = a n1 2 In Problems 51-60, write out each sum. k=1 n ( k+2 )In Problems 51-60, write out each sum. k=1 n ( 2k+1 )In Problems 51-60, write out each sum. k=1 n k 2 2 In Problems 51-60, write out each sum. k=1 n ( k+1 ) 2 In Problems 51-60, write out each sum. k=0 n 1 3 k In Problems 51-60, write out each sum. k=0 n ( 3 2 ) k In Problems 51-60, write out each sum. k=0 n1 1 3 k+1

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