Solution Manual Computer Math Problem Solving for Information Technology 2nd Edition Charles Marchant Reeder Instant download and all chapters Solution Manual Computer Math Problem Solving for Information Technology 2nd Edition Charles Marchant Reeder https://testbankdata.com/download/solution-manual-computer-mathproblem-solving-information-technology-2nd-edition-charles-marchantreeder/
Contents Chapter 1:
Problem Solving
Chapter 2:
Exponents
1
36
Chapter 3:
Number Systems
49
Chapter 4:
Unit Analysis
67
Chapter 5:
A Little Alge bra
96
Chapter 6:
Gr a phing
116
Cha pter 7: 7:
Computer Programming Conce p pts ts
133
Cha pter 8:
Computer Logic
159
Chapter 9:
Structured Program Design
172
A p pendix A :
hmeet ic R eview Arithm
19 3
Appendix B:
More Algebr a
209
Appendix C:
Geometry
242
Chapter 1: Problem Solving Introductory Pro blem This cha pter 's introductory problem requires a team of two per sons. String Handcuff s •
•
•
Each person needs to make a set of "handcuff s" from a piece of string string about 3 feet long. Tie slipknots at each end of the string. (If you don't know how, ask your instructor .) The first person puts the handcuff s on by placing a slipknot around each wrist and drawing it snug, but not tight. N tight. Notice the handcuff s complete an unbroken "ring" that incl clud udees the shoulder s and both arms. The next person puts the handcuff s on by putting one hand in a slipknot and passing the o ther slipknot through the partner's "ring" before putting it on the remaining wrist. Again, pull both sli p pknots close over the wrist, but not tight.
ing" formed by at111, body, arm, and Each team member is connected to the other by an unbroken "r in string. The ring of one person is interlocked with that of the other . It's somewhat lik e those br ass rings that magicians so mysteriously snap a part.
To solve the problem you must separate the two "rings" so you and your partner are no longer connected. Do this without breaking the string or removing any slipknot from around any wrist. Random trial and error is a good way to begin. But at some point it will be helpful to carefully think about your situation and try to examine things systematically. You may break the rules to gain insight. But your final solution you must follow the ru les. From time to time, as you try to solve the pr o blem, your instructor may give you hints.
After You Haye Solved the Pro blem Write a detailed set of instructions instructions telling how to solve the pro blem. Then have another team carry out your instruction onss. Correct and refine your instructions if some parts are incorr ect or unclear . f some Answer the following questions: •
What insight let you discover the solution?
•
What was slightly slightly misleading about the wording of the the pro blem?
Af ter Your Written Solution Has Been Tested At the end, your instructor will present you with a formal solution to compare with your own.
Instructions to Separate the String Handcuff s
1.
Identify the team members as person A and person B.
2.
Place a section of person person A's str ing over person B s wrist, just on the elbow side of the sli p kno ot. pkn
3.
Reach under person B s sli pknot pknot and pull a loo p of person person A's string through, toward the fingers of person person B.
4.
Without twisting it, pass the loop completely over person B s hand.
'
'
'
5. Now the string can be pulled free and the partners can se parate. N ot e:
The five steps above are diagramed in figure 1.1 on the following page.
What insight led you to this solution? bilit ies: Diff er ent insights are lik ely ely. Here are some possi b •
The string, arm, and body forms what at first seemed to be an unbroken ri rin ng.
•
Without a break in this ring se para rati tion is not po possi b ble.
•
The only possible break in the ring is at the slipknot. Examine that point closely.
•
Because the string is flexible it can be passed around the hand.
•
This can be clearly seen by removing the sli pkn pknot from the hand A to a po p osition just away from the fingertips. Although this violates the rules, it does allow you see how B's string can be passed over A 's hand to allow se paration.
What part of the problem statement led you to the final insight above? The statement statement:: "You may break the rules to to gain insight." What was slightly misleading about the wording of the pro blem? The statement: "It's somewhat like the brass rings that magicians snap a part."
2
The five steps needed to separate the string han hand dcuff s are shown below.
1.
5
3
.
.
Figure 1.1 Separating String Handcuff s Illustrati on by Emily Reeder
3
Practice Pr o blems Section 1-2 Introductory Pr o blems For the following problems, merely identify the data, condition, and unknown (Polya's components). Every problem need not have a condition, but if i itt does, it will of ten be preceded by the word if. For now there is no need to develop a plan or carry out the solution. so lution. You will have an opportunity to do that later . 1-2.1
A computer-generat computer-generated ed report incl clud udes inventory information for 200 items. The information for each item is given on a se par ate line. If 50 lines will fit on a page of pr inter printer paper will it take print the r ep eport? pa per , how many pages of printer
Answer :
Data: Condition: Unknown:
1- 2.2
A box contains 30 coo c ookie kiess. If each cookie weighs 1/2 ounce, what is the weight o f the cookies?
Answer :
1- 2.3
ms.. The report contains information for 200 items Information for each item takes one line. pe er . 50 lines will fit on a page of printer pa p The number of pages pages in the report is unknown.
Data: Condition on:: Unknown:
A box contains 30 cookies. Each cookie weighs 1/ 2 ounce. The weight of the the cookies is unknown.
A box contains 30 cookies. If the empty box weighs 2 ounces and each cookie cook ie weighs 1/2 ounce, what is the weight of the box full of cookies?
Answer :
Data: Condition:
nknown Unknow n:
The box contains 30 cook ies. The empty box weighs 2 ounces. Each cookie weighs 1/2 ounce. The weight of the the full box of cookies cookies is unknown.
Intermediate Pro blems 1-2.4
A box of cookies cookies contained 30 cook ies when pu pur chased. The empty box weighs 2 oun uncces and each cook ie weighs 1 /2 ounce. If one thir d of the cook ies have been eaten, what is the combined weight of the the box and the r emaining cook ies?
Answer :
Data:
Condition: Unknown:
4
A box contains 30 cook ies. The empty box weighs 2 ounces. Each cookie weighs 1/2 ounce. One third of the cookies have been eaten. The weight of the the box and the remaining cookies is unknown.
5
1-2.5
A computercomputer-generated generated report includes inventory information on for 220 items. The information for each item is given on a se parate li ne. If 50 lines will fit on a page ge,, how many pages will it take to pr p r int the r e port?
Answer :
Data: Condition: Unknown wn::
1-2.6
A report generated by a computer includes information for 1000 customers. There are two types of customer s, regular and pr and pr ef err ed. The information for each regular customer tak es es one line on the r e p po ort. The information for each preferred customer takes two lines es on on the r e port. Each page can contain up to 50 lines. If the number ofr egular customers customers is thr ee times the number of preferred preferred customers, how many pages will the report r equir e? e?
Answer :
Data:
Condition on::
Unkn kno own: 1-2. 7
Report contains information on for 220 items. Information for each item takes one line. 50 lines will fit on a page of printer p a per. The number of pages pages in the report is unknown.
The report contains 10 00 customer s. There are two types of customers: customers: regular and pr ef err ed. Information for each regular customer takes one line. Information for each preferred customer takes two lines. f the Each page of the report can contain 50 lines. The number of regular regular customers is three times times the number of preferred customer s. wn.. The number of pages pages in the report report is the unknown
Students in the CIS department can receive intern rnsshi p credit p credit for work experience in a position related to information technology. At the beginning of the term, each student w it h an approved internship position enrolls for a s p pecified number of credits. At the end of the term each student su b ng the the number of hours wor k k ed. Credit is bm mits a time sheet showing awarded at the rate of one one credit for each 30 hours wor k ke d. Credits are rounded to the f credit. nearest half credit. (For example, values in the range 1. 75 and up to but not including ng 2.25 2.25 will round to 2.0. Values in the range 2.25 and up to but not including 2.75 will round to 2.5.) The credits awarded can never exceed the credits enrolled, regardless of the number of hours wor k k ed. Compute the number of credits credits awarded to each student from the fo foll llowing enrollment data: Credits E nr oll ed
Adams, Jane Beck , Carl Jones, Michael Smith, Mary Walk er , William Data: sweer : Answ
1
2 2 2 5
Condition on:: Unknown:
4
ke d Hours wor k
30 15 90 50 75 Each student enrolls for a specified specified number of cr edits. Each student submits time sheet showing hours wor k k ed. Each student earns one cr edit for each 30 hours wor k k ed. Credits earned are rounded to the nearest nearest 1/ 2 credit. Credits awarded can not exceed credits enr olled. The number of credits credits earned by each student is u nknown.
5
Brainstorming Pr o blems ng.. Your instructor has Try solving these problems with careful r easoning has the solutions. 1-2.8
A bear goes for a walk . He walks 3 miles south, then 3 miles east, and finally 3 miles north. At the end of this this walk the bear has arrived a rrived back where he started. What color is the bear? Answer :
The only point on earth that a walk of three three miles south, three miles east and three miles north will return to the starting point is at the North Pole. The only type of bear that will be found at the North Pole is a polar bear . efor e, the bear must be white. Ther efo We will ignor e the issue of whether whether polar bears come as far north as the they are more lik ely to be found farther south near the edge of the pole or if they ice cap where access to food is easier . Just consider that this a str ay bear and the problem problem works very nicely.
1-2.9
You are a driving a bus on the Main Str eet line. At the start of the run down Main Str eet the pty ty. At First Avenue three passengers get on. At Second Avenue two more bus is em p passengers get on. At Fifth Avenue four passengers get on and two get off At Seventh Avenue one passenger one passenger gets off and and two get on. How old is the bus dri driv ver ? .
Answer : The age of the dr iver will be the same as your age age since you ar e dr iving. The r will fluous. pe er fl rest of the information is su p 1-2.10
A 10- pound solid iron ball is dropped from 5 feet above the surface of a lak e that is 50 feet deep. The time for the ball to disappear is measured with a sto pwatch. This measurement is made under two d iff er ent conditions as follows: Condition 1:
It is noon on a bright sunny day with the wind from the north at 4 mp h. The temperature of the lak e at the sur fa face is 40 degrees Fahrenheit. The lak e is crystal crystal clear with visibility visibility downward 25 feet.
Condition 2:
It is 2:00 PM on a cloudy day with the wind from the south at 10 mp h. The bility temperature of the lak e at the surf ace is 20 degrees Fahrenheit. Visi b downward is less than a few inches below the sur fa face.
Under which condition will the ball take the longest time to disappear? Explain. Answer :
1-2.11
6
r ccondition 2. The ball takes the longest time to disa p pear under Of all all the information information given, the temperature temperature makes the biggest diff er ence fresh water is 32 degr ees in this pro blem. Since the freezing point of fresh Fahrenheit, the lake sur fa 20 face will be frozen solid at a temperature of 20 degrees Fahrenheit. Thus, the ball ball will fall 5 feet to the surface and af ter a few bounces will to come to rest and stay put.
Three lam ps (labeled 1, 2, and 3) are sitting on a table in a room. In an ad jacent room out of sight of the lam ps ps,, are three switches (labeled A, B, B , and C). Each switch controls one of the the Thee wiring is out of sight and there is no way to see which switch is connected to lam ps. Th
7
which lamp. What is the fewest number of trips from the switch room to the lam p room that will allow you to match each switch with it s lam p?
Answer :
Only one trip to the lam p room is required to match each lam p with its switch. Here is how to do it: In the switch room tum on two lamps. After a few minutes, tum off one one of these. Then go to the lam p room. The lamp that is on matches the switch you left on. The lam p that is off but but has a warm bul b b, matches the switch you turned on then off. The remaining lam p matches the remaini remaining ng switch. •
•
•
•
•
•
1-2.12
Four men want to cross a bridge at night so they can proceed on to the town on the other side. All begin on the side opposite the town. They need a flashlight to cross the bridge, and they have only onl y one flashlight flashligh t among them. Also, a maximum of only only two men can cross the bridge at one time, and whoever crosses must share the flashlight. They can cross two at a time but someone must return the flashlight to the starting side so the next two can cross. peed and any pair crossing at the same time must walk at Each man walks at a di d iff er ent s p the slower man's pace. Here are their walking rates: Man # 1 takes 1 minute to cross the br b r idge. Man #2 takes 2 minu nuttes es to to cross the b bri ridge. Man #3 takes 5 minutes to cross the bridge. Man #4 takes 10 minutes to cross the br br idge. Can you find a strategy that th at will get all four men together on the other side of the bridge (under the above constraints) in only 17 minutes? Answer : Man #1 and 2 cross together (takes 2 minutes). Man #1 goes back alone (takes 1 more minute te)). Man #3 and 4 cross together (takes 10 minu nuttes). Man #2 takes flashlight back (tak es es 2 minutes). Man #1 and 2 cross together again (takes 2 minutes). Now all four have crossed and it took 2+ 1 + 10+2+2 = 17 minutes! Let the two slowest slow est men to go together so their times do n't add up, and let Key ideas: the two fastest men do the shuttling of the flashlight.
1-2.13
Ten stacks of gold coins have ten coins each ch.. Nine of the stacks have coins made of pur e gold, and one stack has coins made of an an alloy that look s exactly lik e gold. Each pure gol gold coin weighs 10 grams and each alloy coin weighs 9 grams. You have an electronic scale that can display the weight of any pile of coins coins with 99.99 percent accur acy. What is the f ewest number of weighings weighings needed to determine which stack contains co ntains the alloy coins.
Answer :
6
One weighing is sufficient. Weigh a pile of 55 coins made up of one coin from the first stack, two coins from the second, three from the third and so on. If all coins weighed 10 grams, the total weight would be 550 grams. Because some of the coins are all lloy oy, the pile will weigh less. (Between 549 and 540.) The number of grams grams under 550 corresponds to the stack number of the alloy coins.
7
S e c t i o n 1- 4 Practice using the IPO method to plan, execute, and check the solut ion of the following pro blems. These problems should be solved using only simple arithmetic and caref ul reasoning .
Solution to Pra ct ice Problem 1-4.1 Problem
How many 150-foot la p pss must you swim in a 75-foot pool in order to swim a mile?
Output
Number of 150-foot laps required to swim one mile
Input
Length of pool is 75 feet. Each lap is 15 0 f eet.
Process
Notation Additiona l Information
Diagram
None needed. A mile is 5280 feet. A lap is two lengths of the poo pool. l. None needed.
To find the number ofl a ps in a m mile ile divide the number of feet in a mile by the number of feet in a la p. Number ofla ps = 5280/150 = 35.2 la ps Number of Laps 35.2 Approach
Solution
=
Check
8
Work problem in r ever se: 35.2 laps each 15 0 feet long give 35.2 * 150 feet= 5280 feet 5280 feet is one mile, the solution check s.
9
Solution to Practice Problem 1-4. 4.2 2
8
Problem
A box contains 30 cook ies. If each cookie weighs 1/2 ounce, what is the net weight of the the box when it is full? Net weight is the weight of t the he contents and excludes the weight of the container .
Output
The net weight of the the box when it is full
Input
A box contains 30 cook ies ies. Each cookie weighs 1/2 ounce. Net weight is the weight of the contents and excludes the weight of the box. f the
Process
Notation
w = net weight
Additional tio on Informati Diagram Approach
None needed. None needed. f the Compute the net weight (weight of the contents) by multi p plying o c oo . f the number cookies cookies by the weight per k ie
Solution
w (ounce)= 30 (cookies)* 1/2 (ounce/cookie)= 15 ounces w = 15 ounces
Check
Work problem in r ever se: Net weight is 15 oz. There are 2 cookies for each ounce nce:: x (cook ies)= 15 (oun uncces)* 2 (cook ies/ounce) Thus the box contains 30 cook ies. The solution check s.
9
Solution to Practice Problem
Problem
1-4.3
A computer-generated report includes inventory information for 200 items. The informat ion for each item is given on a separate line. Up to 50 lines will fit on a page ge.. The pages are num ber ed. The first page is number 1. What is the final page num ber ?
Output
The final page num ber , counting from
Input
A computer-generated report includes inventory information for 200 items. The information on for each item is given on a separate line. Up to 50 lines will fit on a page. The pages are num ber ed. The first page is number 1.
Process
Notation
None needed ded..
Additional Information Diagram
None needed.
Approach
Divide the total items by 50 to get the number of pages. If there is a r emainder , these lines will be on an additional p age.
1
None needed.
Solution
200 items I 50 lines per page = 4 pages exactly. There is no r emainder , so an additional page is not needed.
Check
The l" page contains 50 lines. The total lines so far are 50. The 2nd page contains 50 lines lines.. The total lines so far are 100 100.. The 3r d page contains 50 lines. The total lines so far are 150 . The 4th page contains 50 lines. The total lines so far are 200 . All 200 lines will fit on 4 pages exactly.
10
