College Mathematics for Trades and Technologies, 10th Edition Solution Manual

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RESOURCEMANUALCOLLEGEMATHEMATICSFORTRADES ANDTECHNOLOGIESTENTHEDITIONCheryl CleavesSouthwest Tennessee Community CollegeMargie HobbsSouthwest Tennessee Community College

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iiiResource Manual to accompanyCollege Mathematics for Trades and Technologies,Tenth EditionCheryl Cleaves and Margie HobbsContentsPrefacevIntroduction1Teaching Tips4Reproducible Activities13Teaching Aids69Transparency Masters94Selected Solutions161Even-Numbered Chapter Review ExercisesAll Concept Analysis ExercisesEven-NumberedPractice Test ExercisesEven-Numbered Cumulative Practice TestsChapter 1Review of Basic Concepts163Chapter 2Review of Fractions173Chapter 3Percents185Chapter 4Measurement198Chapter 5Signed Numbers and Powers of 10205Chapter 6Statistics213Chapter 7Linear Equations and Inequalities224Chapter 8Formulas, Proportion, and Variation239Chapter 9Linear Equations, Functions, and Inequalities in Two Variables245Chapter 10Systems of Linear Equations and Inequalities261

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ivChapter 11Powers and Polynomials277Chapter 12Roots and Radicals282Chapter 13Factoring288Chapter 14Rational Expressions, Equations, and Inequalities294Chapter 15Quadratic and Other Non-Linear Equations and Inequalities306Chapter 16Exponential and Logarithmic Equations336Chapter 17Geometry347Chapter 18Triangles356Chapter 19Right-Triangle Trigonometry366Chapter 20Trigonometry with Any Angle374

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4TEACHING TIPSCollege Mathematics for Trades and Technologies, Tenth Edition,and its accompanying instructionalresources have been designed to enable students to experience mathematics. Every instructor brings a differentpersonality and teaching style to the mathematics classroom. We encourage you to experiment with a wide varietyof activities and projects that are included in the text and this manual. We have found the activities that are mostbeneficial will vary with the personality of a class. A variety of approaches will help an instructor provide richmathematical experiences for students with a wide range of learning styles.Impromptu Classroom Collaborative ActivitiesCollege students often are reluctant to form study groups with their classmates. It is helpful if the instructorencourages collaboration by giving students opportunities during class time to realize its benefits and to get to knowsome fellow classmates. Mini-sets of exercises can be used during class time. The exercises can be selected from theeven-numbered Chapter Review Exercises, or Practice Test at the end of the chapter, since these answers are not inthe text. TheStop and Checkand section exercises or odd-numbered end-of-chapter exercises can be used andstudents can check their answers with the answers in the text. A plan for incorporating collaborative learning couldbe:1.Select one to three problems for students to work individually in class. Allow a reasonable amount of timefor students to complete the problems.2.Have each student compare results with a study partner and each pair should reach a consensus on thecorrect answers.3.Have each pair of students compare results with another pair of students. The four students should reach aconsensus on the correct answers.4.Record and display the answers of each group of four. If more than one answer is given for any problem,engage the class in a discussion to reach a class consensus on the correct answers.Team ProjectsSome of the activities suggested in this manual are short activities that can be completed in one class period orless or in an overnight assignment. However, others will require a longer commitment of time. We suggest that someactivities be accomplished using teamwork. Our distinction between teamwork and collaborative activities is that ateamwork activity has teammates working on individual tasks that will fit together to complete a product or report.A collaborative activity involves classmates working collectively in a group to complete a task. The text and thismanual give some guidance on forming teams and working in a team environment.We are including a plan that has been successful in our classes for building teamwork skills and for helpingstudents realize the usefulness of mathematics in the team project.Students can form their own working groups or they can be assigned to a group of three or four students. Eachteam selects from activities the instructor provides from this Instructor’s Resource Manual. Even if two teams selectthe same project, the teams generally develop an entirely different approach to the project. In the ReproducibleActivities we have included a sample handout to orient students to the team process. Following are sampleinstructions that can be used for team projects.Teams will be three to four students. Each student will have a specific responsibility in the project. Peerevaluations will be part of the total project grade (Teaching Aid 17 on p. 94).Written Report•One report for each team•Narrative portion of report will be three to five word-processed, double-spaced pages.•Narrative portion should include:1.Statement of problem2.Method for solving problem3.Explanation of each team member’s responsibility4.Findings5.Conclusion

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COLLEGE MATHEMATICS5Presentation•Ten to fifteen minutes•Share the five components of the written report with the class. Do NOT read the writtenreport. Summarize the written report and use appropriate visual aids for the class.•Presentation does not have to involve all team members; but each team member must beprepared to answer questions about the project.Deadlines•(Date)Brief description of project, team members, and team assignments•(Date)Draft of written report•(Date)Final copy of written report Oral presentationChapter-by-Chapter SuggestionsFor many of us, our workload is so demanding that we may not always have quality time for developingnew ideas or activities. We are providing some chapter-by-chapter suggestions for presenting the concepts of thechapters.CHAPTER 1: Review of Basic ConceptsThe purpose of this chapter is to review or develop the student’s number sense and to increase the student’sunderstanding of some very important basic mathematical concepts while focusing on whole numbers and decimals.Mathematical concepts introduced in this chapter form the foundation for many of the topics found later in the text.By encountering the concepts of exponents, roots, and powers of 10 while working with whole numbers anddecimals, students can make a smoother transition to the symbolic representations and manipulations involving theseconcepts later in the text.If your course does not allow time to include this chapter, it is advisable to encourage your students toindependently study the Chapter Review of Key Concept and assess themselves using the Practice Test or adiagnostic test or assignment in MyLab Math.The authors strongly encourage the early introduction of the scientific or graphing calculator. Students whodevelop proficiency with these tools while increasing estimating skills and mental arithmetic skills will have a betterunderstanding of the mathematical concepts and will have more confidence in their own mathematical abilities.Understanding of concepts will need to be emphasized while proficiency in manipulation skills will need to be de-emphasized.A structured problem-solving approach is introduced in this chapter so that students can become familiar withthe steps needed to analyze and solve a problem. Even though students may not be required to use a structuredformat in writing solutions of a problem, they should be directed to at least mentally consider each step in theprocess. This process will help in developing the necessary problem-solving skills for more complex problems.ActivitiesThe100-Cell Grid for Multiplication and Fraction Activities(Teaching Aid 4) can be used to introduce one-digit multiplication facts. As an in-class discussion, students can see that basic concepts like the commutativeproperty of multiplication, zero property of multiplication, multiplication by 1, and multiplication as repeatedaddition reduce the amount of rote memorization necessary to learn one-digit multiplication facts. Students shouldbe encouraged to examine in detail the grid to identify numerous patterns involving the products of two one-digitnumbers. This activity encourages the student’s development of number sense.Transposing Digitsgives an opportunity for students to investigate a property of numbers that they may or maynot have known before. Students can experience an often used research technique of verifying a suspected pattern orproperty.Factoring Into Pairs of Factorshelps students strengthen their recall of multiplication facts and recognize therelationship between multiplication and division. This activity is sometimes repeated in later chapters to helpstudents make a connection between previously learned skills and new concepts of reducing fractions, findingcommon denominators, factoring polynomials, etc.Estimating Radicalsis a powerful activity that helps studentsdevelop some number sense with square roots. For the adult student who is experiencing low self-esteem forbeginning a study of college mathematics, this activity can be a real morale booster. Many advanced students canimprove their number sense with square roots.

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6TEACHING TIPSCHAPTER 2: Review of FractionsUnderstanding the concepts of fractions is best developed using fractions with small denominators. Tediouscalculations with fractions having large common denominators or fractions with no common factors can be handledefficiently using decimal equivalents or a calculator with a fraction key.Emphasis should be placed on the student’s ability to identify which of the four basic operations is needed tosolve application problems. For higher-level mathematics, an understanding of equivalent fractions and addingfractions with unlike denominators is important. However, examples and problems to be solved by hand should belimited to reasonable numbers. Concepts such as division by zero, multiplying or dividing by 1, and dividing anumber by itself should be emphasized and related to appropriate topics in fractions.ActivitiesThefractionactivities,CommonFractions,DecimalFractions,FractionsinSimplestForm,FractionRelationships,andSize of Fractionsare designed to develop the student’s number sense about fractions anddecimals and to enable students to discover the relationship between fractions and decimals. These activities can beseparated and all or some of the outcomes can be introduced. However, the series of activities helps studentsdevelop estimating skills with fractions. The activities emphasize the relationship of the numerator to thedenominator of a fraction and the effect this relationship has on the value of the fraction. The calculator is integratedinto the activities to reinforce the concept that fractions and decimals are different notations for expressing the samevalue and to increase the student’s proficiency and confidence in using the calculator.Factoring Into Pairs of Factorsis appropriate preparation for understanding prime factorization, reducingfractions, and finding common denominators.CHAPTER 3: PercentsThis chapter includes fraction and decimal equivalents. These equivalents help students to develop a numbersense with percents. Focus should be placed on the idea that a specific value can be written in three differentnotations. While memorization of some common equivalents will come automatically with practice, the authorsstress understanding the relationships rather than focusing on the memorization of the common percent-fraction-decimal equivalents as isolated facts.Various versions of percentage formulas are also introduced. These formulas are commonly used in solvingpercent problems involving applications such as interest.ActivitiesPercents is one of the most useful mathematical topics to introduce problem-solving techniques and to buildcritical thinking skills. Real-life exposure to percents creates a natural motivation for students to want to understandand use percents. Numerous in-class and out-of-class activities can be generated by using local or national dailynewspapers, technical journals, and consumer buying magazines. Projects may also compare strategies for buying orfinancing major purchases or planning and developing costs for building or decorating projects. Some students maybe interested in researching various retirement strategies. The scope of these activities could range from havingstudents develop problems from ads or news articles to extended individual or collaborative projects that incorporateskills in mathematics, written and oral communication, consumer finance, economics, marketing, and varioustechnical fields.Analyzing Nutrition LabelsandWhat Percent Tax Do I Really Pay?apply our knowledge of percents. Manystudents from a variety of career choices will be interested in these topics. These activities may be started in classand completed as out-of-class assignments or projects.CHAPTER 4: MeasurementDiscussion of measurements in this chapter should support the student’s development of spatial sense. Studentsshould be able to approximate in the metric system the length, volume, and weight measures of various objects.Verification of cross-system measurements can be made using the conversion factors for both systems. Being able touse resources to find conversion factors is more valuable than students’ memorizing these factors. The authors seeno value in having students memorize the conversion factors because when employees must convert betweensystems, specific levels of precision are required and these factors are readily available to the employee.

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COLLEGE MATHEMATICS7Reading measuring instruments is an important skill in the workplace. Detailed instructions and numerousvisual aids are given for a variety of measuring instruments in an electronic appendix. The appendix follows thesame format as the text and is reinforced with MyLab Math support.ActivitiesEstimating measures is becoming a lost art. Students should estimate the measure of an object before measuringit. Hands-on activities can be designed to enable students to verify their estimates by actually measuring variousobjects for length, volume, and weight. Students can research the measurements that are most frequently used intheir selected field of study.CHAPTER 5: Signed Numbers and Powers of 10The early introduction of signed numbers is important for many technical programs. Visualization of signednumbers on the number line and on the rectangular coordinate axes is also helpful for many students.ActivitiesActivities that simulate workplace situations reinforce the practical need for integers.Arranging GlobalInteractive Communications, Preparing a Reference Chart for Global Communications,andLocating Coordinateson a Sphereare activities included in this manual. Scientific and graphing calculators should be encouraged for usein this chapter, especially when the student is evaluating an expression with several steps. Emphasis should beplaced on making decisions about the appropriate use of the calculator. Mental calculations should be encouraged!The mind is still quicker than the hand for many calculations. A thorough understanding of the signed number rulesis very important and the calculator can be used to verify answers obtained by applying the rules.CHAPTER 6: StatisticsData interpretation and analysis is often neglected in studies of mathematics. However, it is becomingincreasingly important in the workplace, especially where statistical process control (SPC) is used. Students usuallyfind the study of data analysis very interesting and motivating because they can see applications more readily thanwith other topics.ActivitiesThe activityCircle, Bar, and Line Graphsmay be used here to strengthen the student’s ability to interpret datafrom various types of graphs. It is very beneficial for students to plan, design, and conduct an investigation in whichthe findings are reported in writing and graphically. Another interesting point to emphasize is that graphs that appearin newspapers, magazines, and other publications are not always meaningful or easy to interpret.Critiquing Graphshelps students judge the usefulness and appropriateness of graphs.CHAPTER 7: Linear Equations and InequalitiesAs students prepare for an in-depth study of solving equations, it is important that students’ skills in the basicoperations of signed numbers and the order of operations are fresh. Also, translating from words to symbols is animportant skill in preparing for problem-solving strategies.Linear equations are introduced through applications. Scales can be used to illustrate the concept of performingthe same operation on both sides of the equation in the simplification process.Problem solving is emphasized in this chapter and the six-step problem-solving strategy is used for approachingapplied problems. Students should practice their critical thinking skills to interpret problems using algebraictechniques. Students should not be penalized for devising a sequence of arithmetic calculations to solve the problem;however, students should be encouraged to express this sequence of arithmetic calculations algebraically. This oftenhelps to bridge the gap from arithmetic to algebra and to see the usefulness of expressing problems symbolically andusing systematic steps to solve an equation. Many times, easy problems are used to demonstrate the algebraicprocess. Once the algebraic process is mastered, it can then be used to solve more complex problems.The concepts for solving equations are extended to equations containing fractions and decimals. Rate, time, andwork problems are also included.

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8TEACHING TIPSMaking connections between methods for solving equations and inequalities is important in this chapter.Understanding the “and” and “or” relationships is also important. However, it is NOT important that studentsmemorize the symbols for the various sets of numbers. Rather, it is more important that they understand how thevarious sets of numbers relate to each other.Students should realize that they are only extending their knowledge of the linear equations to include theconcept of inequalities.ActivitiesChapter 7 is the first opportunity that many students will have to translate the conditions of a word problem toan algebraic equation. Many students come to our classes with preconceived notions that they cannot work appliedproblems. For the math-anxious student it is very important to experience success with problem solving. We suggestthat students be allowed to work in groups to solve the applied problems in this chapter. There will be opportunitiesin later chapters for students to concentrate on their individual problem-solving skills.To emphasize the parallels between equations and inequalities, have students reword some of the wordproblems in the sections for equations to require the use of inequalities. Phrases such as “at least” or “at most” canbe substituted for “equal.”CHAPTER 8: Formulas, Proportion, and VariationProportions are presented with a wider variety of applications. This chapter offers many opportunities to helpstudents make connections with outcomes from earlier chapters. Situations that are directly or inversely proportionalprovide a good opportunity for using common sense to predict a reasonable answer. This approach to estimatingallows students to find their own errors in setting up a proportion problem.ActivitiesIn formula rearrangement, students can increase their proficiency with the calculator by verifying that the newformula is equivalent to the original formula. To do this they can assign values for each variable in the formula.These values are used to evaluate both the original and new formulas. When the results are not the same, studentswill be able to revise their work in rearranging the formula or in using the calculator.Analyzing Nutrition Labelscan be used to strengthen proportion concepts and to illustrate direct proportions.A good application of proportions used in the workplace is found in working with blueprints. Projects oractivities can be planned around actual blueprints for various industries. Students could be asked to design ablueprint for a home project.The potential for developing activities in this section is extensive and activities can easily be customized to thestudent’s interest. A team or individual project that has students investigate the common formulas of a particularcareer will greatly enhance this chapter. Oral presentations of the findings of the students will give the entire classan overview of the power of mathematics in broadening career choices.CHAPTER 9: Linear Equations, Functions, and Inequalities in Two VariablesCritical thinking skills can be strengthened by allowing students to make decisions about which graphingmethod is best to graph equations with various characteristics. Students should be able to visualize the graph of anequation by looking at the various components of the equation. Students should be able to write an equation byexamining the visual graph of the equation. Graphing calculators or computer software may be used to electronicallygraph equations.First, we examine the graphs of equations. Then, we examine the equations of graphs.The definition of slope should be visualized by graphing the two points and drawing the line that passes throughthe two points. Students should be able to predict the value of the slope from the graph BEFORE they calculate theslope. That is, they should be able to predict if the graph rises or falls from left to right or if the graph is more steepor more flat. Also, students should be encouraged to make the calculation first, then predict what the graph of theline connecting these points should “look like.” Finally, graph the two points to confirm their prediction.Similarities and differences between equations of parallel lines and perpendicular lines should be presented in avisual format. Students should be able to see examples of pairs of equations and their parallel graphs. They shouldalso be able to see examples of pairs of lines that are perpendicular and compare them with their equations.Comparison of the equation pairs that graph into parallel and perpendicular lines will help students makeconnections between the relationship of the equations and their graphs.

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COLLEGE MATHEMATICS9The graphing calculator is a very helpful tool in visualization of these concepts.ActivitiesActivities 1 through 3 ofGraphing Equationscan be used to help students expand their understanding ofpatterns associated with linear equations. Instructions for using the activities as a group assignment are given to usewith the activity sheets.Commodities Market Investingillustrates the use of graphing in consumer applications.Students should be encouraged to work together and discuss the visualization activities that are important for aclear understanding of algebraic concepts in this chapter.CHAPTER 10: Systems of Linear Equations and InequalitiesThe notion of systems of equations can be compared to finding the overlapping regions or intersection of morethan one condition in a problem. The idea is to determine if all the conditions of the problem can be metsimultaneously.There are numerous applications for systems of equations. Students may be encouraged to write appliedproblems that would be appropriate for a given system of equations. This strengthens the students’ critical thinkingskills and writing skills.An electronic appendix on Matrices and Determinants that includes Cramer’s rule for solving systems ofequations is available in MyLab Math.ActivitiesWhile most of the conditions of problems in the text are designed so that all the conditions can be metsimultaneously, students may investigate situations where the conditions cannot be met simultaneously. When thisoccurs, they should list the various ranges, if any, under which the conditions may be acceptable.Making Business Choicescan be used to show how systems of equations can be used in decision-making.Applications problems in this chapter also can be solved using equations with one variable. Students shouldinvestigate a wide range of strategies for solving the problems.CHAPTER 11: Powers and PolynomialsStudents should treat the laws of exponents like the signed number rules. These rules are used with manyconcepts in mathematics. Practice should be sufficient so that applications of the laws of exponents become mentaltools that students use instinctively.Students often confuse the two wordsexponentandpower. In informal language they are sometimes usedinterchangeably. However, the formal mathematical definitions distinguish between these two concepts. Using themathematical definition, 24 and 16 are both powers. The 24 is a power written in exponential form and the 16 is apower written in ordinary number form. A power in exponential form includes a base and an exponent.The definition of exponent and the way we visualize exponents depend on the kind of number used as theexponent.Forexample,withpositivewholenumbers,theexponentisvisualizedasimplyingrepeatedmultiplication. When the exponent is zero, the value of the expression is defined to be one (when the base is otherthan zero). When the exponent is a negative integer, the student should visualize the exponent as indicating thereciprocal of the power with an exponent of the same absolute value. Students should also understand that thereciprocal of any power can be formed by writing the power with the opposite of the original exponent. Forexample, the reciprocal of3x−is3xjust like the reciprocal of23is32. We use this property to change the sign ofan exponent when necessary. For example, we can rewrite12a−as2aThese two expressions are equal.Emphasis should be placed on connections between the notations for expressing roots with radicals and withfractional exponents. Students should understand that the laws of exponents are the same for fractional exponents asthey are for integer exponents.As with any discussion involving fractions, it should be noted that the exceptions to rules are always madewhen denominators are zero. With powers, exceptions to rules are made when the base is zero.

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10TEACHING TIPSCHAPTER 12: Roots and RadicalsEmphasis should be placed on connections between notations for expressing roots with radicals and withfractional exponents. Students should understand that the laws of exponents covered in Chapter 11 are the same asthose used for fractional exponents. This is an excellent opportunity to show students MANY ways to find powersand roots using a scientific or graphing calculator.See teaching tips for Chapter 11 for a discussion of the meaning of exponents depending upon the kind ofnumber represented by the exponent.As with any discussion involving fractions, it should be noted that the exceptions to rules are always madewhen denominators are zero. With powers, exceptions to rules are made when the base is zero.The introduction of imaginary and complex numbers is optional. However, this brief treatment helps students tounderstand why even roots of negative numbers are undefined when restricted to real numbers. Applications ofcomplex numbers are included in the discussion on vectors in Chapter 21.ActivitiesEstimating Radicalsis an activity that is designed to expand the student’s number sense to include irrationalnumbers. It distinguishes between squares and square roots and between rational and irrational numbers. Thisactivity also enables the students to determine the proper placement of irrational numbers on the number line.CHAPTER 13: FactoringThe presentation and emphasis for the topic of factoring are in transition due to the various curriculum andpedagogy standards initiatives and due to the integration of technology in the teaching and learning of mathematics.The concepts of factoring are still beneficial in recognizing patterns and in understanding the simplifying process forrational expressions. However, the focus should be on expressions that are relatively easy to factor. The timerequired in factoring difficult expressions could be more beneficially spent in having the student use the graphingcalculator to investigate alternative strategies for solving problems that we currently use factoring to solve. Thischapter also presents a number of special products.ActivitiesFactoring into Pairs of Factorscan be used as an introduction to factoring trinomials. Many manipulatives thatcan be used to illustrate or reinforce factoring are commercially available.Graphing calculators and computer algebra software offer the potential for many activities. Trinomials can begraphed as functions. By examining where the graph crosses thexaxis (wheny= 0), the students can determine thefactors of the trinomial.x2– 5x +6 can be graphed as the functiony=x2– 5x+ 6. The graph of this function crossesthex-axis at 2 and 3. This indicates that the trinomial can be factored into (x– 2)(x– 3). Students will naturallyquestion why the factors have signs opposite the signs of the coordinates of the points where the graph crosses thex-axis. This curiosity will give the instructor an opportunity to lead into the next chapter, which includes the zeroproperty of multiplication and the solutions for equations like (x– 2)(x– 3) = 0.CHAPTER 14: Rational Expressions, Equations, and InequalitiesThis is a topic that will receive decreased emphasis in the transition to the curriculum and pedagogy standards.This chapter currently serves to integrate several mathematical concepts and to use these concepts in a different setof circumstances from those in which they have been previously used. For example, students will strengthen theirunderstanding of the concepts of basic arithmetic such as reducing fractions and finding common denominators.Emphasis in this chapter should be placed upon the student’s understanding of the concept of excluded values.Students often find it difficult to conceptualize this idea and often omit that constraint in giving the solution.ActivitiesPatient Charting Efficiencyis an activity that uses rational equations in career applications. Students can usegraphing calculators to graph rational expressions. Some graphing calculators will show the “holes” or excludedvalues and some will not. Whether the excluded values are shown sometimes depends on the range settings of aparticular calculator.

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COLLEGE MATHEMATICS11CHAPTER 15: Quadratic and Other Non-Linear Equations and InequalitiesThe various strategies for solving quadratic equations give a good opportunity to develop critical thinking skills.Students should be encouraged to examine the advantages and disadvantages of the various methods and to selectthe most appropriate method for the particular problem.While the text focuses on approximating the roots of solutions for quadratic equations for technical applications,students should understand that the solution in simplest radical form is the exact number solution and is desired insome situations.An electronic appendix on Conics is available in MyLab Math if you need to expand your coverage to parabolasthat are not a function, ellipses, circles, and hyperbolas.ActivitiesActivities 4 through 6 ofGraphing Equationscan be used to enable students to visualize patterns associatedwith graphs of quadratic equations.Calculating Vehicular Speed from Skid Marks and Road Conditionsshows theusefulness of quadratic equations in career applications. Graphing calculators can be used to visualize the solutionsof quadratic equations. Students may also be encouraged to research technical literature for applications of quadraticequations.CHAPTER 16: Exponential and Logarithmic EquationsThis chapter comes after three chapters with several abstract concepts but few motivational applications. Moststudents are interested in money and how it grows. The business and investment formulas help students see thepower of mathematics and its usefulness in making life and business decisions.The section on logarithms is intended to be an introduction to the concept and not a thorough comprehensivestudy of the topic. The formula for finding the amount of time necessary for achievement of an investment goalhelps to illustrate the relationship between logarithmic and exponential equations.ActivitiesSeveral activities are available for this chapter.What is the Natural Exponential e?should be used to enable thestudent to understand how the constanteis derived. This is also the student’s first experience with the concept oflimits and this activity enables the student to discover the effect of using increasingly large values in the expression11.nn§·+¨¸©¹The activity,Compounded Amount and Compound Interest, enables students to see applications ofeand alsoillustrates the effect of frequency of compounding on the compounded amount or compound interest.Many business applications have formulas with variable exponents. Many students get interested in investmentformulas and it can easily lead to a discussion of planned investment programs.The investment formulas that are given provide the tools for many investigative activities. They also open thedoor for some personal finance discussions that are useful for college students.CHAPTER 17: GeometryMany areas of work require knowledge and understanding of geometric principles. While many concepts havebeen integrated throughout the text, the authors think this chapter is very important to the overall development of thestudents’ mathematical knowledge base. It is also essential for students who study trigonometry, calculus, and othermathematical topics.Emphasis should be placed on understanding and using formulas rather than memorizing them.ActivitiesThese topics are rich with real-world applications. Students should be encouraged to make connections in avariety of real-world situations.Students may estimate the number of degrees in a given radian measure and estimate the number of radians in agiven degree measure. Also, students may sketch angles with given degree or radian measures.

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12TEACHING TIPSCHAPTER 18: TrianglesTriangles play a very important role in the study of mathematics. The Pythagorean theorem, similar triangles,and special right triangles such as the 30°, 60°, 90° triangle and the 45°, 45°, 90° right triangle are used in solvingmany real-world applications. The distance formula is an application of the Pythagorean theorem.ActivitiesIndividual and team projects can be designed to find missing measures with similar triangles. Students caninvestigate careers that use geometry and trigonometry. A good understanding of the properties of triangles is animportant prerequisite for the study of trigonometry.CHAPTER 19: Right-Triangle TrigonometryUse the trigonometric ratios to solve applied problems. Classroom discussion should focus on why one functionis used rather than another, different ways a problem can be solved, why one way may be more advantageous thanothers, and why answers may vary significantly especially when using rounded calculated values to find othervalues. The number of places an answer should be rounded to should also be discussed. Students should researchsituations where varying levels of accuracy are desired.Students should also be encouraged to develop spatial sense by sketching figures to show proper relationshipsamong the sides and angles. Estimation skills should be developed by encouraging students to predict the result ofcalculations and compare the predicted values with the calculated values.ActivitiesStudents should measure the sides and angles of various right triangles, then confirm measures and thetrigonometric ratios by using the ratios to calculate various angles and sides. The triangles that are measured can befigures drawn by students or objects in the real world.CHAPTER 20: Trigonometry with Any AngleSection 20-1 should be related to graphing ordered pairs from Chapter 9.Students should be encouraged to critically examine problems to decide whether to use the law of sines or thelaw of cosines.ActivitiesStudents should measure the sides and angles of various oblique triangles, then confirm measures by using thelaws of sines and cosines to calculate various angles and sides. The triangles that are measured can be figures drawnby students or objects in the real world.Surveying technology offers many rich experiences for applying the concepts of this chapter.

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College Mathematics, Tenth EditionCleaves and HobbsReproducible Activities13REPRODUCIBLE ACTIVITIESThe activities in this section are designed to be self-contained units of work. They can be used in class or out ofclass, as assignments to be completed individually by students or in groups, or as long-term projects that can becompleted by students individually or in groups.The activities are intended to enrich the presentation in the textbook and to guide the students through aninvestigative or discovery process. It is hoped that, after having completed an activity, a student will have a more in-depth understanding of the underlying mathematical principles and will have developed a richer number sense.The following activities are available in this supplement. The authors are continually exploring new activitiesand as they are refined they will be made available in future editions. More information on when and how to useeach activity is given in the teaching tips.TRANSPOSING DIGITS (p. 16)Outcome: Verify that the difference between two numbers that have two digits transposed is divisible by nine.FACTORING INTO PAIRS OF FACTORS (pp. 17í20)Outcome 1: Find all possible pairs of factors of a given number.Outcome 2: Distinguish between prime and composite numbers.Outcome 3: Find numbers that are perfect squares.Outcome 4: Find the square root of a number using a calculator.LOCATING COORDINATES ON A SPHERE (pp. 21í23)Outcome: Find locations on a sphere using ordered pairs.ARRANGING GLOBAL INTERACTIVE COMMUNICATIONS (p. 24)Outcome: Determine an optimum time for a global interactive communication.PREPARING A REFERENCE CHART FOR GLOBAL COMMUNICATIONS (p. 25)Outcome: Gather and organize data to improve efficiency.COMMON FRACTIONS (p. 26)Outcome: Distinguish between proper and improper common fractions.DECIMAL FRACTIONS (p. 27)Outcome: Examine decimal equivalents of common fractions.FRACTIONS IN SIMPLEST FORM (p. 28)Outcome: Examine equivalent fractions in simplest form.FRACTION RELATIONSHIPS (pp. 29í32)Outcome: Develop a procedure for comparing fractions to11, 2or14by inspection.SIZE OF FRACTIONS (pp. 33í35)Outcome: Categorize fractions based upon their relationship to113,,424, and 1.ANALYZING NUTRITION LABELS (pp. 36í40)Outcome: Use proportions and percents to analyze nutrition labels.WHAT PERCENT TAX DO I REALLY PAY? (pp. 41í43)Outcome 1: Determine the percent of tax withheld for a given taxable income.Outcome 2: Determine the percent of income tax for a given annual taxable income.

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14REPRODUCIBLE ACTIVITIESCollege Mathematics, Tenth EditionCleaves and HobbsReproducible Activities㌇CIRCLE, BAR, AND LINE GRAPHS (p. 44)Outcome 1: Interpret data from various types of graphs.Outcome 2: Plan, design, and conduct an investigation in which the findings are reported in writing andgraphically.CRITIQUING GRAPHS (pp. 45)Outcome: Critique graphs found in recent publications.ESTIMATING RADICALS (pp. 46í47)Squares and Square RootsOutcome 1: Distinguish between squares and square roots and rational and irrational numbers.Outcome 2: Determine between which two whole numbers a given irrational number will fall.RATIONAL EQUATIONS (p. 48)Patient Charting EfficiencyOutcome: Use rational equations in career applications.QUADRATIC EQUATIONS (pp. 49í50)Calculating Vehicular Speed from Skid Marks and Road ConditionsOutcome: Use quadratic equations in career applications.WHAT IS THE NATURAL EXPONENTIALe? (p. 51)Outcome: Discover the effect of large values ofnin the expression11nn§·+¨¸©¹.COMPOUNDED AMOUNT AND COMPOUND INTEREST (p. 52)Outcome: Compare the two compound amount formulas for compound interest,1and.mmrApApen§·=+=¨¸©¹GRAPHING EQUATIONS PROJECT (pp. 53í54)Instructions for Group Projects for Five-Member GroupsGRAPHING EQUATIONS (pp. 55í63)Graphing Activity 1Outcome: Examine equations in the formy=mx.Graphing Activity 2Outcome: Examine equations in the formy=mx+b.Graphing Activity 3Outcome: Examine equations in the formy=kandx=k.Graphing Activity 4Outcome: Examine quadratic equations in the formy=ax2.Graphing Activity 5Outcome: Examine quadratic equations in the formy=ax2+b.Graphing Activity 6Outcome: Examine quadratic equations in the formy= (x+b)2.

College Mathematics for Trades and Technologies, 10th Edition Solution Manual - Page 16 preview image

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COLLEGE MATHEMATICS15College Mathematics, Tenth EditionCleaves and HobbsReproducible ActivitiesGRAPHICAL REPRESENTATION (p. 64)Commodities Market InvestingOutcome: Use graphing in consumer applications.SYSTEMS OF EQUATIONS (p. 65)Making Business ChoicesOutcome: Use systems of equations to make good business choices.ESTIMATING MEASURES (pp. 66í67)Outcome: Estimate linear and circular measure in inches.WHAT IS PI,ʌ? (p. 68)Outcome: Discover the relationship between the circumference and diameter of a circle.

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