Solution Manual for Trigonometry, 11th Edition

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CHAPTERPROJECTS(DOWNLOADONLY)TRIGONOMETRY:AUNITCIRCLEAPPROACHELEVENTHEDITIONMichael SullivanChicago State University

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Platinum Plan:$100/month for up to 3000 K-bytesof service plus $0.04 for each addi-tional K-byte of serviceYou have been requested to write a report thatanswers the following questions in order to aid em-ployees in choosing the appropriate pricing plan.(a) IfCis the monthly charge forxK-bytes of serv-ice, expressCas a function ofxfor each of thethree plans.(b) Graph each of the three functions found inpart (a).(c) For how many K-bytes of service is the SilverPlan the best pricing option? When is the GoldPlan best? When is the Platinum Plan best?Explain your reasoning.(d) Write a report that summarizes your findings.During the past decade the availability and usageof wireless Internet services have increased. The in-dustry has developed a number of pricing proposalsfor such services. Marketing data have indicated thatsubscribers of wireless Internet services have tendedto desire flat fee rate structures as compared withrates based totally on usage.The Computer ResourceDepartment of Indigo Media (hypothetical) has en-tered into a contractual agreement for wirelessInternet services. As a part of the contractual agree-ment, employees are able to sign up for their ownwireless services. Three pricing options are available:Silver Plan:$20/month for up to 200 K-bytes ofservice plus $0.16 for each addi-tional K-byte of serviceGold Plan:$50/month for up to 1000 K-bytesof service plus $0.08 for each addi-tional K-byte of serviceP r o j e c ta tM o t o r o l a

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minimum and a maximum value as the elevatormoves up the building. This pattern is called astanding wave pattern.Calculate the ratio of themaximum to the minimum signal strength thatthe pager sees. This is called thestanding waveratio(SWR).2.Show that the distance between two consecutiveminima is 1 meter.3.Show that the distance between two consecutivemaxima is 1 meter.4.Show that the distance between a minimum andits nearby maximum is 0.5 meter.5.What should the sensitivity of the pager be toguarantee reception of the signal regardless ofthe distance of the elevator from the ground?6.Draw the graphin the complex plane ashvaries. Explain all your answers to Questions 1through 5 using this figure.EnormSignal Fades Due to InterferenceConsider an individual wearing a pager in an exterior el-evator on a high-rise building.The pager receives directsignals from a transmitting tower far away, as well astheir reflections from the flat ground (see the figure).Oversimplifying things, it can be shown that thenormalized signal received by the pager is given bywherehis the height of the pager (elevator) from theground expressed in meters.1.Show that the magnitude of the normalized sig-nal received by the pager oscillates between aE(h)normL1+0.25Ccos(2ph)+isin(2ph)DhP r o j e c ta tM o t o r o l a

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3.Cost of CableYou work for the Silver Satellite &Cable TV Company in the Research & DevelopmentDepartment. You have been asked to come up with aformula to determine the cost of running cable from aconnection box to a new cable household. The first ex-ample that you are working with involves the Stevenfamily, who own a rural home with a driveway 2 mileslong extending to the house from a nearby highway. Thenearest connection box is along the highway but 5 milesfrom the driveway.It costs the company $100 per mile to install cablealong the highway and $140 per mile to install cable offthe highway. Because the Steven’s house is surrounded byfarmland that they own, it would be possible to run thecable overland to the house directly from the connectionbox or from any point between the connection box to thedriveway.

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(a) Draw a sketch of this problem situation, assuming thatthe highway is a straight road and the driveway is alsoa straight road perpendicular to the highway. Includetwo or more possible routes for the cable.(b) Letxrepresent the distance in miles that the cableruns along the highway from the connection box be-fore turning off toward the house. Express the totalcost of installation as a function ofx. (You maychoose to answer part (c) before part (b) if you wouldlike to examine concrete instances before creatingthe equation.)(c) Make a table of the possible integral values ofxandthe corresponding cost in each instance. Does onechoice appear to cost the least?(d) If you charge the Stevens $800 for installation, wouldyou be willing to let them choose which way the cablewould go? Explain.(e) Using a graphing calculator, graph the function frompart (b) and determine the value ofxthat would makethe installation cost minimum.(f) Before proceeding further with the installation, youcheck the local regulations for cable companies andfind that there is pending state legislation that saysthat the cable cannot turn off the highway more than0.5 mile from the Steven’s driveway. If this legislationpasses, what will be the ultimate cost of installing theSteven’s cable?(g) If the cable company wishes to install cable in 5000homes in this area, and assuming that the figures forthe Steven’s installation are typical, how much willthe new legislation cost the company overall if theycannot use the cheapest installation cost, but insteadhave to follow the new state regulations?

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