Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for College Algebra (MindTap Course List)
9EPractice Graph each inequality x-2y511E12E13E14E15E16EPractice Graph each inequality. yx218EPractice Graph each inequality. x2+y2420E21E22E23E24E25E26E27E28E29E30E31E32E33E34E35E36E37E38E39E40E41E42E43E44E45EApplications Installing video Each week, Prime Time Video and Audio has 90 hours of labor to install satellite dishes d and some theatre systems t. On average, it takes 5 hours to install a satellite dish and 6 hours to install a home theatre system. Write a system of inequalities that provides the restrictions on the variables. Hint: Remember that a negative number of units cannot be installed.Applications Fundraising A college club is selling baskets of fruit and blocks of cheese to raise at least 600 for a local childrens hospital. a. If the profit for selling a basket of fruit is 5 and for selling a block of cheese 6, write a system of inequalities that describes when x boxes of fruit and y blocks of cheese will cause the fundraising goal to be reached. Hint: Remember that a negative number of baskets of fruit or blocks of cheese cannot be sold. b. Graph the system of inequalities.Applications Fundraising A cheerleading team is selling cookie dough and pizza kits to raise at least 3600 for their summer camp expenses. a.If the profit for selling a tub of cookie dough is 6 and for selling a pizza kit is 8, write a system of inequalities that describes when x tubs of cookie dough and y pizza kits will cause the fundraising goal to be reached. Hint: Remember that a negative number of cookie dough or pizza kits cannot be sold. b.Graph the system of inequalities.Discovery and Writing Explain how to graph an inequality in two variables.50E51E52E53E54E55E56E57E58E59E60E61E62EFind the maximum value of P=4x+3y subject to the constraints of Example 1. {x+y42x+y6x0y02SCIn Example 3, if the accountant earns a profit of 100 on each individual return and a profit of 175 on each business return, find the maximum profit. An accountant prepares tax returns for individuals and for small businesses. On average, each individual return requires 3 hours of her time and 1 hour of computer time. Each business return requires 4 hours of her time and 2 hours of computer time. Because of other business considerations, her time is limited to 240 hours, and the computer time is limited to 100 hours. If she earns a profit of 80 on each individual return and a profit of 150 on each business return, how many returns of each type should she prepare to maximize her profit?If the cost of each Robust tablet increases to 75 c and the cost of each Vigortab increases to 80 c , find the minimum cost.If during the following year it is predicted that each comedy skit will generate 30 thousand and each musical number 20 thousand, find the maximum income for the year. A television program director must schedule comedy skits and musical numbers for prime-time variety shows. Each comedy skit requires 2 hours of rehearsal time, costs 3000, and brings in 20,000 from the shows sponsors. Each musical number requires 1 hour of rehearsal time, costs 6000, and generates 12,000. If 250 hours are available for rehearsal and 600,000 is budgeted for comedy and music, how many segments of each type should be produced to maximize income? Find the maximum income.1EFill in the blanks. Ordered pairs that satisfy the constraints of a linear program are called _________ solutions.Fill in the blanks. The function to be maximized or minimized in a linear program is called the _________ function.4E5EMaximize P subject to the following constraints. P=3x+2y{x0y0x+y47EMaximize P subject to the following constraints. P=4yx{x2y0x+y12yx19E10EMaximize P subject to the following constraints. P=3x2y{x1x1yx1xy112E13E14E15E16E17EMinimize P subject to the following constraints. P=2yx {x0y0x+y5x+2y219E20EMaking furniture Two woodworkers, Chase and Devin, get 100 for making a table and 80 for making a chair. On average, Chase must work 3 hours and Devin 2 hours to make a chair. Chase must work 2 hours and Devin 6 hours to make a table. If neither wishes to work more than 42 hours per week, how many tables and how many chairs should they make each week to maximize their income? Find the maximum income. Table Chair Time Available Devins Time hr 6 2 42 Chases Time hr 2 3 42 Income 100 80Making crafts Two artists, Nine and Rob, make yard ornaments. They get 80 for each wooden snowman they make and 64 for each wooden Santa Claus. On average, Nina must work 4 hours and Rob 2 hours to make a snowman. Nina must work 3 hours and Rob 4 hours to make a Santa Claus. If neither wishes to work more than 20 hours per week, how many of each ornament should they make each week to maximize their income? Find the maximum income. Snowman Santa Claus Time Available Robs Time hr 2 4 20 Ninas Time hr 4 3 20 Income 80 64Inventories An electronics store manager stocks from 20 to 30 IBM-compatible computers and from 30 to 50 Apple computers. There is room in the store to stock up to 60 computers. The manager receives a commission of 50 on the sale of each IBM-compatible computer and 40 on the sale of each Apple computer. If the manager can sell all of the computers, how many should she stock to maximize her commissions? Find the maximum commission. Inventory IBM Apple Minimum 20 30 Maximum 30 50 Commission 50 40Diet problems A diet requires at least 16 units of vitamin C and at least 34 units of vitamin B complex. Two food supplements are available that provide these nutrients in the amounts and costs shown in the table. How much of each should be used to minimize the cost? Supplement Vitamin C Vitamin B Cost A 3 units/g 2 units/g 3 c /g B 2 units/g 6 units/g 4 c /gProduction Manufacturing DVRs and TVs requires the use of the electronics, assembly, and finishing departments of a factory, according to the following schedule: Hours for DVR Hours for TV Hours Available per Week Electronics 3 4 180 Assembly 2 3 120 Finishing 2 1 60 Each DVR has a profit of 40, and each TV has profit of 32. How many DVRs and TVs should be manufactured weekly to maximize profit? Find the maximum profit.Production problems A company manufactures one type of computer chip that runs at 2.0 GHz and another that runs at 2.8 GHz. The company can make a maximum of 50 fast chips per day and a maximum of 100 slow chips per day. It takes 6 hours to make a fast chip and 3 hours to make a slow chip, and the companys employees can provide up to 360 hours of labor per day. If the company makes a profit of 20 on each 2.8-GHz chip and 27 on each 2.0-GHz chip, how many of each type should be manufactured to earn the maximum profit?27EProduction A small country exports soybeans and flowers. Soybeans require 8 workers per acre, flowers require 12 workers per acre, and 100, 000 workers are available. Government contracts require that there be at least 3 times as many acres of soybeans as flowers planted. It costs 250 per acre to plant soybeans and 300 per acre to plant flowers, and there is a budget of 3 million. If the profit from soybeans is 1600 per acre and the profit from flowers is 2000 per acre, how many acres of each crop should be planted to maximize profit? Find the maximum profit.29EMarking ice cream An ice cream store sells two new flavors: Fantasy and Excess. Each barrel of Fantasy requires 4 pounds of nuts and 3 pounds of chocolate and has a profit of 500. Each barrel of Excess requires 4 pounds of nuts and 2 pounds of chocolate and has a profit of 400. There are 16 pounds of nuts and 18 pounds of chocolate in stock, and the owner does not want to buy more for this batch. How many barrels of each should be made for a maximum profit? Find the maximum profit.31E32E33E34E35E36E37E38E39E40E1E2E3E4E5E6E7E8E9E10E11E12E13E14E15E16E17E18EDepartment store order The buyer for a large department store must order 40 coats, some fake fur and some leather. He is unsure of the expected sales. He can buy 25 fur coats and the rest leather for 9300, or 10 fur coats and the rest leather for 12,600. How much does he pay if he decides to split the order evenly?Ticket sales Adult tickets for the championship game are usually 5, but on Seniors Day, seniors paid 4. Childrens tickets were 2.50. Sales of 1800 tickets totaled 7425, and children and seniors accounted for one-half of the tickets sold. How many of each were sold?21E22E23E24E25E26E27E28E29E30E31E32E33E34E35E36E37E38EFind the inverse of each matrix, if possible. [2335]40E41E42E43E44E45E46E47E48E49E50E51E52E53E54E55E56EIf |abcdefghi|=7,evaluate each determinant. |abcd+ge+hf+ighi|58EDecompose into partial fractions. 4x3+3x+x2+2x4+x260E61E62E63E64E65E66E67E68E69EA company manufactures two fertilizers, x and y. Each 50-pound bag of fertilizer requires three ingredients, which are available in the limited quantities shown in the table. The profit on each bag of fertilizer x is 6 and on each bag of y is 5. How many bags of each product should be produced to maximize the profit? Ingredient Number of Pounds in Fertilizer x Number of Pounds in Fertilizer y Total number of Pounds Available Nitrogen 6 10 20,000 Phosphorus 8 6 16,400 Potash 6 4 12,0001CT2CT3CT4CTMixing solutions A chemist has two solutions; one has a 20 concentration and the other a 45 concentration. How many liters of each must she mix to obtain 10 liters of 30 concentration?Wholesale distribution Ace Electronics, Hi-Fi Stereo, and CD World buy a total of 175 DVD players from the same distributor each month. Because CD World buys 25 more units than the other two stores combined, CD Worlds cost is only 160 per unit. The players cost Hi-Fi 165 each and Ace 170 each. How many players does each retailer buy each month if the distributor receives 28,500 each month from the sale of the players to the three stores?7CT8CT9CT10CT11CT12CT13CT14CT15CT16CT17CT18CTUse Cramers Rule to solve each system for y. {3x5y=33x+y=220CT21CT22CT23CT24CT25CT26CT1SC2SC3SC4SC5SC6SCFind the vertex and yintercepts of the parabola with an equation of y2x+2y=3. Then graph it.8SC9SC1E2E3E4E5EDetermine whether the graph of the parabola opens upward, downward, to the left, or to the right. y2=10x:opens7EDetermine whether the graph of the parabola opens upward, downward, to the left, or to the right. (x2)2=(y+3):opensFill in the blanks. A parabola is the set of all points in a plane equidistant from a line, called the ______, and a fixed point not on the line, called the _______.10E11E12E13E14E15E16E17E18E19E20E21E22E23E24E25E26E27E28E29E30EFind an equation in standard form of each parabola described. Vertex at (0,0); focus at (0,3)Find an equation in standard form of each parabola described. Vertex at (0,0); focus at (0,3)Find an equation in standard form of each parabola described. Vertex at (0,0); focus at (3,0)Find an equation in standard form of each parabola described. Vertex at (0,0); focus at (3,0)Find an equation in standard form of each parabola described. Vertex at (3,5); focus at (3,2)Find an equation in standard form of each parabola described. Vertex at (3,5); focus at (3,5)Find an equation in standard form of each parabola described. Vertex at (3,5); focus at (3,2)Find an equation in standard form of each parabola described. Vertex at (3,5); focus at (6,5)Find an equation in standard form of each parabola described. Vertex at (0,2); directrix at y=3Find an equation in standard form of each parabola described. Vertex at (3,4); focus at y=2Find an equation in standard form of each parabola described. Vertex at (1,5); directrix at x=1Find an equation in standard form of each parabola described. Vertex at (3,5); directrix at x=6Find an equation in standard form of each parabola described. Vertex at (2,2); passes through (0,0)Find an equation in standard form of each parabola described. Vertex at (2,2); passes through (0,0)Find an equation in standard form of each parabola described. Vertex at (4,6); passes through (0,3)Find an equation in standard form of each parabola described. Vertex at (2,3); passes through (0,3)Find an equation in standard form of each parabola described. Vertex at (6,8); passes through (5,10) and (5,6)Find an equation in standard form of each parabola described. Vertex at (2,3); passes through (1,134) and (1,214)Find an equation in standard form of each parabola described. Vertex at (3,1); passes through (4,3) and (2,3)Find an equation in standard form of each parabola described. Vertex at (4,2); passes through (3,0) and (94,3)Write each parabola in standard form and graph it. y=x2+4x+5Write each parabola in standard form and graph it. 2x212x7y=10Write each parabola in standard form and graph it. y2+4x6y=1Write each parabola in standard form and graph it. x22y2x=7Write each parabola in standard form and graph it. y24y=4x8Write each parabola in standard form and graph it. y2+2x2y=5Write each parabola in standard form and graph it. y24y=8x+20Write each parabola in standard form and graph it. y22y=9x+17Write each parabola in standard form and graph it. x26y+22=4xWrite each parabola in standard form and graph it. 4y24y+16x=7Write each parabola in standard form and graph it. 4x24x+32y=4762E63E64E65E66E67ERipples in a pond When a stone is thrown into the center of a pond, the ripples spread out in a circular pattern, moving at a rate of 3 feet per second. If the stone is dropped at a point (0,0) in the illustration, when will the ripple reach the seagull floating at the point (15,36)?69E70EMeshing gear For design purpose, the large gear is described by the circle x2+y2=16. The smaller gear is a circle centered at (7,0) and tangent to the large circle. Find an equation in standard form of the smaller gear.72E73ESearchlight reflectors A parabolic mirror reflect light in a beam when the light source is placed at its focus. In the illustration, how far from the vertex of the parabolic reflector should the light source be placed? All the measurements are in the feetWriting equation of the parabolas Derive the equation of the parabolic arch shown.Projectiles The cannonball in the illustration follows the parabolic trajectory y=30xx2. How far short of the castle does it land?Satellite antennas The cross section of the satellite antenna in the illustration is a parabola given by the equation y=116x2, with distance measured in feet. If the dish is 8feet wide, how deep it is?Design of a satellite antenna The cross section of the satellite antenna shown is a parabola with the pickup at its focus. Find the distance d from the pickup to the centre of the dish.79EOperating a resort A resort owner plans to build and rent n cabins for d dollars per week. The price d that she can charge for each cabin depends on the number of cabin she builds, where d=45(n3212). Find the number of the cabins she should build to maximize her weekly income.Design of a parabolic reflector Find the outer diameter The length AB of the parabolic reflector shown.Design of a suspension bridge The cable between the tower of the suspension bridge shown in the illustration has the shape of a parabola with vertex 15feet above the roadway. Find an equation in standard form of the parabola.Gateway Arch The gateway Arch in St.Louis has a shape that approximates a parabola. See the illustration Find the width w of the arch 200 feet above the ground. Round to the nearest foot.Building tunnels A construction firm plans to build a tunnel whose arch is in the shape of parabola. See the illustration.The tunnel will span a two lane highway 8 meters wide. To allow safe passage for vehicles, the tunnel must be 5meter high at a distance of 1 meter from the tunnels edge. Find the maximum height of tunnel.85E86E87E88E89E90E91E92E93E94E95E96E