Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Precalculus
In Problems 5-24, graph each equation of the system. Then solve the system to find the points of intersection. { x 2 + y 2 =8 x 2 + y 2 +4y=0In Problems 5-24, graph each equation of the system. Then solve the system to find the points of intersection. { y=3x5 x 2 + y 2 =5In Problems 5-24, graph each equation of the system. Then solve the system to find the points of intersection. { x 2 + y 2 =10 y=x+2In 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 2 x=4In 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=8In 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 =8In Problems 5-24, graph each equation of the system. Then solve the system to find the points of intersection. { x 2 =y xy=1In 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 9In Problems 5-24, graph each equation of the system. Then solve the system to find the points of intersection. { xy=1 y=2x+1In Problems 5-24, graph each equation of the system. Then solve the system to find the points of intersection. { y= x 2 4 y=6x13In 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=325AYU26AYU27AYU28AYUIn Problems 25-54, solve each system. Use any method you wish. { x+y+1=0 x 2 + y 2 +6yx=530AYU31AYU32AYU33AYU34AYU35AYU36AYU37AYU38AYU39AYU40AYU41AYU42AYU43AYU44AYU45AYU46AYUIn Problems 25-54, solve each system. Use any method you wish. { x 2 3xy+2 y 2 =0 x 2 +xy=648AYU49AYU50AYU51AYU52AYU53AYU54AYU55AYU56AYU57AYU58AYU59AYU60AYU61AYU62AYU63AYU64AYU65AYU66AYU67AYU68AYU69AYU70AYUThe difference of two numbers is 2 and the sum of their squares is 10. Find the numbers.72AYU73AYU74AYU75AYU76AYUThe 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 ?78AYU79AYUGeometry 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.81AYUGeometry 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?84AYUConstructing 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?86AYU87AYU88AYU89AYU90AYU91AYU92AYU93AYU94AYU95AYU96AYU97AYU98AYU99AYU100AYU101AYUSolve the inequality: 3x+48x (pp. A79-A80)2AYU3AYU4AYU5AYU6AYU7AYU8AYU9AYU10AYU11AYU12AYU13AYU14AYU15AYU16AYU17AYU18AYUIn Problems 11-22, graph each inequality. y x 2 120AYU21AYU22AYU23AYU24AYU25AYU26AYU27AYU28AYU29AYU30AYU31AYU32AYU33AYU34AYU35AYU36AYU37AYU38AYU39AYU40AYU41AYU42AYU43AYU44AYU45AYUIn 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+y247AYU48AYU49AYU50AYU51AYU52AYUIn problems 53-56, write a system of linear inequalities for the given graph.54AYU55AYU56AYU57AYU58AYUBlending 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.60AYU61AYUA 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+y4AYU5AYU6AYU7AYU8AYU9AYU10AYU11AYU12AYU13AYUIn Problems 9-18, solve each linear programming problem. Maximize z=5x+3y subject to x0,y0,x+y2,x+y8,2x+y1015AYU16AYU17AYUIn Problems 9-18, solve each linear programming problem. Maximize z=2x+4y subject to x0,y0,2x+y4,x+y9Maximizing 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.eduSpring 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.comReturn 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.htmlMaximizing 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?29AYUAnimal 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.1RE2RE3RE4RE5RE6RE7RE8RE9RE10RE11RE12RE13RE14RE15RE16RE17RE18RE19RE20RE21RE22RE23RE24RE25RE26RE27RE28RE29RE30RE31RE32RE33RE34RE35RE36RE37RE38RE39RE40RE41RE42RE43RE44RE45RE46RE47RE48RE49RE50RE51RE52RE53RE54RE55RE56RE57RE58RE59RE60RE61RE62RE63RE64RE65RE66RE67RE68RE69RE70RE1CT2CT3CT4CT5CT6CT7CT8CT9CT10CT11CT12CT13CT14CT15CTA weightlifter begins his routine by benching pounds and increases the weight by pounds for each set. If he does repetitions in each set, what is the total weight lifted after sets?
1CR2CR3CR4CR5CR6CR7CR8CR9CR10CR11CR12CRFor 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)3AYUTrue or False The notation a 5 represents the fifth term of a sequence.True or False If is am integer, then
The sequence a 1 =5 , a n =3 a n1 is an example of a( n ) _____ sequence. (a) alternating(b) recursive (c) Fibonacci(d) summationThe notation a 1 + a 2 + a 3 ++ a n = k=1 n a k is an example of ______ notation.8AYUIn Problems 11-16, evaluate each factorial expression. 10!10AYU11AYUIn Problems 11-16, evaluate each factorial expression. 12! 10!In Problems 914, evaluate each factorial expression. 4!11!7!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 }16AYUIn 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 }