Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Nature of Mathematics (MindTap Course List)
46PS47PS48PS49PS50PS51PS52PS53PS54PS55PSThe perimeter of this pentagon is 280cm. Find the lengths of the sides.57PS58PS59PS60PSIN YOUR OWN WORDS What do we mean by area?2PS3PS4PS5PS6PS7PS8PS9PS10PS11PS12PS13PS14PS15PS16PS17PS18PS19PS20PS21PS22PS23PS24PS25PS26PS27PS28PS29PS30PS31PS32PS33PS34PS35PS36PS37PS38PS39PSFind the area of each shaded region in Problems 19-40. Assume that given measurements are exact, and round approximate answers to the nearest tenth of a square unit.41PS42PS43PS44PS45PS46PS47PS48PS49PS50PS51PS52PS53PS54PS55PSWhat is the area to the nearest square inch of a regular hexagon with a side equal to 10in.?Find the area to the nearest square inch of the shaded region contained 10in. squares in problems 5758. Assume that the arcs intersect the midpoints of the sides.Find the area to the nearest square inch of the shaded region contained 10in. squares in problems 5758. Assume that the arcs intersect the midpoints of the sides.IN YOUR OWN WORDS Extra square centimeter problem Figure 8.12 illustrates a strange and interesting relationship. The square in part a has an area of 65cm2 8cm by 8cm. When this same figure is cut and rearranged as shown in part b, it appears to have an area of 65cm2. Where did this extra square centimeter come from? Hint: Construct your own square 8cm on a side, and then cut it into the four pieces as shown. Place the four pieces together as illustrated. Be sure to do your measuring and cutting very carefully. Satisfy yourself that this extra square centimeter has appeared. Can you explain this relationship?IN YOUR OWN WORDS Extra square inch problem Figure 8.13 illustrates a strange and interesting relationship in a very visual way. For this problem, state a question based on this figure and then give the answer.IN YOUR OWN WORDS Contrast length, area, and volume.IN YOUR OWN WORDS What do we mean by surface area ?IN YOUR OWN WORDS Contrast volume and capacity.Compare the size of a cubic inch and a cubic centimetre.Compare the size of a quart and a liter.Compare a meter and a yard.In Problems 7-8, find the volume of each solid by counting the number of cubic centimeters in each box.In Problems 7-8, find the volume of each solid by counting the number of cubic centimeters in each box.Find the volume of each solid in Problems 9-16.Find the volume of each solid in Problems 9-16.Find the volume of each solid in Problems 9-16.Find the volume of each solid in Problems 9-16.Find the volume of each solid in Problems 9-16.Find the volume of each solid in Problems 9-16.Find the volume of each solid in Problem 9-16.Find the volume of each solid in Problems 9-16.Measure each amount given in Problems 17-21. a.Container A in cups. b.Container A in ounces.Measure each amount given in Problems 17-21. a.Container B in ounces. b.Container B in milliliters.Measure each amount given in Problems 17-21. a. Container C in ounces. b. Container C in milliliters.Measure each amount given in Problems 17-21. a. Container D in cups. b. Container D in ounces. c. Container D in milliliters.Measure each amount given in Problems 17-21. a. Container E in milliliters. b. Container F in milliliters. c. Container G in milliliters.The ability to estimate capacities is an important skill to develop. Without measuring, pick the best answer in Problems 22-32. An average cup of coffee is about A.250mLB.750mLC.1LThe ability to estimate capacities is an important skill to develop. Without measuring, pick the best answer in Problems 22-32. If you want to paint a small bookshelf, how much paint would you probably need? A.5mLB.500mLC.5LThe ability to estimate capacities is an important skill to develop. Without measuring, pick the best answer in Problems 22-32. A six-pack of beer would contain about A.2mLB.200mLC.2LThe ability to estimate capacities is an important skill to develop. Without measuring, pick the best answer in Problems 22-32. The dose of a strong cough medicine might be A.5mLB.500mLC.5LThe ability to estimate capacities is an important skill to develop. Without measuring, pick the best answer in Problems 22-32. A glass of water served at a restaurant is about A.200mLB.2mLC.2LThe ability to estimate capacities is an important skill to develop. Without measuring, pick the best answer in Problems 22-32. Enough gas to fill your cars empty tank would be about A.15mLB.200mLC.70L28PS29PS30PS31PS32PS33PS34PS35PS36PS37PS38PS39PS40PS41PS42PS43PS44PS45PS46PS47PS48PS49PS50PS51PS52PS53PS54PSThe exterior dimensions of a refrigerator/freezer are shown in Figure 8.19 a. How many cubic feet are contained within the refrigerator/freezer? b. If it is advertised as a 19-cu-ft refrigerator, how much space is taken up by the motor, insulation, and so on?56PS57PSUse the plot shown in Figure 8.20 and give your answers to the nearest cubic yard. a. How many cubic yard of sawdust are needed for preparation of the lawn area if it is to be spread to a depth of six inches? b. How many cubic yards of gravel are necessary for the walk-way if it is to be placed to a depth of three inches? c. How much compost is available if the pit is four inches deep? d. Suppose that you wish to pave the driveway. How much concrete is needed if it is to be poured to a depth of four inches.59PSa. Guess what percentage of the worlds population could be packed into a cubical box measuring 12mi on each side. Hint: The volume of a typical person is about 2cuft b. Now calculate the answer to part a, using the earths populations as given in problem 59 59. The total human population of the earth is about 6.2109. The total human population of the earth is about 6.2109. a. If each person has the room of a prison cell (50sqft), and if there are about 2.8107sqft in a square mile, how many people could fit into a square mile? b. How many square miles would be required to accommodate the entire human population of the earth? c. If the total land area of the earth is about 5.2107sqmi, and if all the land area were divided equally, how many acres of land would each person be allocated (1sqmi=640acres)?1PS2PS3PS4PSName the metric units you would use to measure each of the quantities in Problems 5-10. a.The distance from New York to Chicago. b.The distance around your waist.6PS7PS8PS9PS10PS11PS12PS13PS14PS15PS16PSWithout measuring, pick the best choice in Problems 1724 by estimating. A hamburger patty would weigh about A. 170g B. 240mg C. 2kg18PS19PS20PS21PS22PS23PS24PS25PS26PS27PS28PS29PS30PSWrite each measurement given in Problems 3138 using all of the metric prefixes.sssss kilometer(km)hectometer(hm)dekameter(dkm)meter(m)decimeter(dm)centimeter(cm)millimeter(mm)932PS33PS34PS35PS36PS37PS38PS39PS40PS41PS42PS43PS44PS45PS46PS47PS48PS49PS50PS51PS52PS53PS54PS55PSIf the length of a box is doubled, the width is tripled, and the height is doubled, what effect does that have on the volume?57PS58PS59PSA polyhedron is a simple closed surface in space whose boundary is composed of polygonal regions see Figure 8.31.A rather surprising relationship exists among the number of vertices, edges, and faces of polyhedra. See if you can discover it by looking for patterns in the figures and filling in the blanks. FigureofFacesofVerticesofEdgesa.Triangularpyramid446b.Quadrilateralpyramid58c.Pentagonalpyramid610d.Regulartetrahedron44e.Cube12f.Regularoctahedron6g.Regulardodehedron30h.Regularicosahedron301CR2CR3CR4CR5CR6CR7CR8CR9CR10CR11CR12CR13CR14CR15CR16CR17CR18CR19CRJohn is bragging about his new 40-inch measured diagonally flat screen TV with an aspect ratio of 3:4. Bill, who doesnt like such bragging, claims that he could build a larger 45-inch flat screen with only half as many square inches as Johns set. How is this possible?Level 1 IN YOUR OWN WORDS Describe the Konigsberg bridge problem.2PSLevel 1 IN YOUR OWN WORDS Describe the solution to the Konigsberg bridge problem.4PS5PS6PS7PS8PS9PS10PSWhich of the networks in Problem 6-11 have Euler circuit? If a network can be traversed show how.12PS13PS14PS15PS16PS17PS18PS19PS20PS21PS22PS23PS24PS25PS26PS27PS28PS29PS30PS31PS32PSHISTORICAL QUEST Travelers Dodecahedron This problem was sold in the last half of the 19th century as a puzzle known as the Travelers Dodecahedron or A Voyage Round the World. It consisted of 20 pegs called cities, and the point of the puzzle was to use string to connect each peg only once, arriving back to the same peg you started from. Find a route starting at Brussels-labeled 1 that visits each of the 20 cities on the dodecahedron shown in Figure 9.8. FIGURE 9.8Hamiltons Travelers DodecahedronHISTORICAL QUEST Is there an Euler circuit for the Travelers Dodecahedron shown in Figure 9.8? If so, show it. FIGURE 9.8Hamiltons Travelers Dodecahedron35PS36PS37PS38PS39PS40PSThe edges of a cube form a three-dimensional network. Are the edges of a cube traversable?A saleswoman wants to visit eastern cities, New York City, Boston, Cleveland, and Washington, D.C. Driving distances are as shown in Figure 9.14. What is the shortest trip starting in New York that visits each of these cities? FIGURE 9.14TSP for four cities Find a solution using the brute-force method.43PS44PSRepeat Problem 44 using the brute-force method. 44. A salesperson wants to visit each of the cities Denver, St. Louis, Los Angeles, and New Orleans. Driving distances are as shown in Figure 9.15. What is the shortest trip starting in Denver that visits each of these cities? FIGURE 9.15TSP for four cities a. Find a solution, if possible, using the nearest-neighbor method. b. Find a solution, if possible, using the sorted-edge method.Count the number of vertices, edges arcs, and regions for each of Problems 617. Let V=numberofvertices, E=numberofedges, and R=numberofregions. Compare V+R with E. Make a conjecture relating V, R, and E. This relationship is called Eulers formula for networks.The saleswoman in Problem 42 needs to add Atlanta to her itinerary. Driving distances are shown. What is the shortest trip starting in New York that visits each of these cities? A B C NYC D.C. A 1,115 780 887 634 B 1,115 667 216 441 C 780 667 481 375 NYC 887 216 481 235 D.C. 634 441 375 233 42. A saleswoman wants to visit eastern cities, New York City, Boston, Cleveland, and Washington, D.C. Driving distances are as shown in Figure 9.14. What is the shortest trip starting in New York that visits each of these cities? FIGURE 9.14TSP for four cities Find a solution using the brute-force method.A quality control inspector must visit franchises in Atlanta, Boston, Chicago, Dallas, and Minneapolis. Since this inspection must be monthly, the inspector, who lives in Chicago, would like to find the most efficient route in terms of distance. Driving distances are shown. What is the most effective route? A B C D M A 1,115 691 691 1,131 B 1,115 1,013 1,845 1,619 C 717 1,013 937 420 D 691 1,845 937 963 M 1,131 1,619 420 96349PS50PSOn a planet far, far away, Luke finds himself in a strange building with hexagon-shaped rooms as shown in Figure 9.17. FIGURE 9.17Strange room arrangement In his search for the princess, Luke always moves to an adjacent room and always in a southerly direction. a.How many paths are there to room 1? to room 2? to room 3? to room 4? b. How many paths are there to room 10? c. How many paths are there to room 13?How many paths are there to room n in Problem 51? 51. On a planet far, far away, Luke finds himself in a strange building with hexagon-shaped rooms as shown in Figure 9.17. FIGURE 9.17Strange room arrangement In his search for the princess, Luke always moves to an adjacent room and always in a southerly direction. a.How many paths are there to room 1? to room 2? to room 3? to room 4? b. How many paths are there to room 10? c. How many paths are there to room 13?Emil Torday told the story of seeing some African children playing with a pattern in the sand as shown in Figure 9.18. FIGURE 9.18African sand game The children were drawing, and I was at once asked to perform certain impossible tasks; great was their joy when the white man failed to accomplish them. One task was to trace the figure in the sand with one continuous sweep of the finger. a. What is the childrens secret for successfully drawing this pattern? b. Draw this figure; why it is difficult to do this without knowing something about networks?54PS55PS56PS57PS58PS59PS60PS1PS2PS3PS4PS5PS6PS7PS8PS9PS10PS11PS12PS13PS14PS15PS16PS17PS18PS19PS20PS21PS22PS23PS24PS25PS