5 2 index. e e. Prime numbers. Prime factors and factor trees. Powers. worked example 10. base. power


 Hilary Brown
 1 years ago
 Views:
Transcription
1 Prim numbrs W giv spcial nams to numbrs dpnding on how many factors thy hav. A prim numbr has xactly two factors: itslf and 1. A composit numbr has mor than two factors. 1 is a spcial numbr nithr prim nor composit. Prim factors and factor trs A prim factor of a numbr is a factor that is also prim. Evry composit numbr can b xprssd as a product of prim numbrs. A factor tr is a good way to find ths prim factors. workd xampl 10 Writ 24 as a product of prim factors. Stps 1. Brak th numbr into a pair of factors (not using 1), thn brak ach subsqunt factor into a pair of factors. Circl any prim factors as thy appar, and stop th branch at this point. (Two possibl trs ar shown.) 2. Writ th numbr as a product of th circld factors. Solution = or Powrs Powrs ar a short way of writing rpatd factors. 5 2 is an xampl of a powr. Th small 2 is th indx and tlls us how many factors of 5 thr ar. Th 5 is calld th bas. For xampl: 4 2 = = = = bas Tutorial Tutorial 5 2 indx powr 1 whol NUMBERS 17
2 For 4 2 w say four squard or four to th powr of two or four to th scond powr. For 5 w say fiv cubd or fiv to th powr of thr or fiv to th third powr. For 7 4 w say svn to th powr of four or just svn to th fourth. Powr Man to bas can you har m? Anothr word for indx is xponnt. Numbrs writtn using indx notation ar in indx form or xponntial form. 4 is in indx form is in xpandd form. workd xampl 11 (a) Writ out 4 in xpandd form and work out th answr. (b) Writ out 7 4 in xpandd form and work out th answr. Stps Solutions (a) 1. Writ 4 in xpandd form. (a) 4 = Writ down th answr. = 64 (b) 1. Writ 7 4 in xpandd form. (b) 7 4 = Writ down th answr. = 2401 Powrs on calculators Many calculators hav a ky to hlp you work quickly with powrs, usually x y or ^. For xampl, if you want to work out 12, prss 1 2 x y = 5 x 2. To work out 5 2, simply prss. Tutorial Squars and squar roots A numbr is calld a prfct squar if it can b found by multiplying anothr numbr by itslf (i.. by squaring th othr numbr). Finding th squar root is th opposit to squaring a numbr. For xampl, to find th squar root of 16, you hav to think of a numbr that whn multiplid by itslf givs you 16. Th numbr is 4 sinc 4 4 = 16. This mans th squar root of 16 is 4. W writ this as 16 = 4. You can us your calculator to hlp with som calculations. Your calculator will hav a ky lik this:. To find 204, prss = or dpnding on th typ of calculator. Thn rad off th answr: 48. Tutorial Tutorial Tutorial 18 Hinmann MATHS ZONE
3 xrcis Prims, powrs and squar roots Prparation: Exrcis 1 Complt ths factor trs, thn writ ach numbr as a product of its prim factors. (a) 16 (b) = 50 = (c) 100 (d) 96 Worksht C = 96 = 2 Exprss ach numbr as a product of its prim factors. (a) 8 (b) 12 (c) 18 (d) 26 () 20 (f) 48 (g) 68 (h) 44 (i) 64 (j) 72 (k) 108 (l) 144 (m) 140 (n) 1000 (o) 800 (p) 400 Find thr diffrnt numbrs that can ach b xprssd as a product of four prim factors. (Th product may contain rpatd factors.) 4 Simplify ths with your calculator, using th shortst mthod possibl. (a) 21 2 (b) 18 2 (c) 48 2 (d) 61 2 () 75 2 (f) 88 2 (g) (h) 49 2 (i) (j) (k) (l) (m) (n) (o) (p) What numbr do you hav to squar to gt ach of ths? (a) 9 (b) 4 (c) 49 (d) 64 () 81 (f) 25 (g) 144 (h) Evaluat th following. (a) (c) () (g) (i) (k) (m) (o) 25 (b) 49 6 (d) (f) (h) (j) (l) (n) (p) Writ ach of ths in indx form. (Don t work out th answr.) (a) (b) (c) (d) What numbr tims itslf givs 25? Intractiv Qustions Qustions Worksht C1.9 Qustions Qustions 1 whol NUMBERS 19
4 () (f) (g) (h) (i) (j) (k) svntn cubd (l) thirtn to th powr of svn (m) ight to th fourth powr (n) nin to th sixth (o) lvn to th svnth (p) nin to th third 8 Writ ach of ths out in xpandd form, thn work out th answr. (a) 2 (b) 2 4 (c) 2 6 (d) 2 5 () 1 8 (f) 0 7 (g) 0 6 (h) 1 7 (i) 10 (j) 10 5 (k) 6 4 (l) 8 4 (m) 11 (n) 12 4 (o) 4 6 (p) What numbr do you hav to cub to gt ach of ths? (a) 1 (b) 27 (c) 8 (d) 64 () 8000 (f) 1000 (g) 125 (h) mans cub root. Th cub root of 27 is bcaus = 27. Evaluat, without using a calculator. (a) 8 (b) 64 (c) 1000 (d) 1 () 0 (f) 125 (g) 8000 (h) (a) Arrang ths numbrs in ascnding ordr (smallst to largst). 4 5, 5 4, 1 200, 10, 4 6, 5 5 (b) Arrang ths numbrs in dscnding ordr (largst to smallst) , 10 5, , 0 100, 2, 2 12 (a) Copy and complt: 10 1 = = = = = = 10 5 = (b) Th numbr was calld a googol by th mathmatician Edward Kasnr. (i) How many tims is 10 multiplid by itslf to gt a googol? (ii) Look at th pattrn in part (a). If you wr to work out what a googol is qual to, how many zros would follow th 1? (c) If you rais th numbr 10 to th powr of a googol, you gt a numbr calld a googolplx. (i) How many tims is 10 multiplid by itslf to gt a googolplx? (ii) If you wr to work out what a googolplx is qual to, how many zros would follow th 1? How much tim do you think you sav by writing a googolplx in indx form? Qustions Qustions hi.com.au 20 Hinmann MATHS ZONE
5 1 Without using your calculator, find btwn which two conscutiv whol numbrs ach of th following lis. (a) 10 (b) 5 (c) 20 (d) 62 () 99 (f) 2 (g) 70 (h) Without using your calculator, find btwn which two conscutiv whol numbrs ach of th following lis. (a) 10 (b) 52 (c) 1001 (d) 0 () 5 (f) 71 (g) 120 (h) 2 15 (a) Us your calculator to answr TRUE or FALSE to ach statmnt. (i) 4 6 is biggr than 6 4. (ii) 2 10 is biggr than (iii) 9 is biggr than 9. (iv) 19 2 is biggr than (b) Look at your answrs for part (a) and without using your calculator answr TRUE or FALSE to ach of ths statmnts. (i) 9 8 is biggr than 8 9. (ii) is biggr than Us your calculator to find th following through trial and rror. (a) A numbr that whn multiplid by itslf thr tims givs 4 (b) A numbr that whn multiplid by itslf thr tims givs 1728 (c) A numbr that whn multiplid by itslf thr tims givs 2744 (d) A numbr that whn multiplid by itslf thr tims givs 9 04 () A numbr that whn multiplid by itslf four tims givs 4096 (f) A numbr that whn multiplid by itslf fiv tims givs (a) Copy th following pattrn and complt it using your calculator = = = (b) Look at th pattrn in part (a) and without using a calculator copy and complt th following = = = Worksht C1.10 Homwork 1.2 Do ths in your had as quickly as you can and writ down th answrs $ $ What tim is it 5 hours and 40 minuts aftr 9.17 a.m.? of $ How many odd numbrs ar thr btwn 20 and 6? 10 Find th missing numbr: 816, 408,, 102. Tim targt: 2 minuts 1 whol NUMBERS 21
6 Prim numbrs vrsus trrorism Trrorism has cost many innocnt livs so far this cntury, and mathmatics has a rol to play in stopping trrorist acts bfor thy happn. Trrorists ar abl to commit ths acts bcaus thy can plan and communicat in scrt. Govrnmnt intllignc agncis all ovr th world try to intrcpt trrorist computr mails and dcod thm. At th tim of th trrorist attacks in 2001, ncryption or coding tchniqus xistd that couldn t b crackd. Ths ncryption tchniqus ar basd on prim numbrs. All ncryption is basd on a ky, which is a word or a numbr. Ths kys giv th information ndd to dcod or dcrypt th mssag. Th kys currntly most commonly usd to ncrypt mails ar numbrs that ar th products of two prim numbrs. To crack th cod, you hav to work out th original two prim numbrs. Whn th numbrs involvd ar vry larg, this is almost impossibl to do bcaus thr ar so many possibilitis. Th largst prim vr found has ovr 2 million digits in it, and thr ar always nw prims bing found. Evn th most powrful computrs in th world would tak cnturis to find th two prims involvd in ncryption. Multiplying two prims is an ffctiv ky for ncryption bcaus it is asy to do in on dirction (multiplication), but xtrmly difficult to do in th othr dirction (finding factors). Govrnmnts ar hoping that in th futur quantum computrs that can procss calculations simultanously will b abl to find th two prim numbrs quickly and nabl thm to crack th trrorists cods. Braking an ncryption cod is calld dcryption. 22 Hinmann MATHS ZONE
7 Qustions 1 Which two prim numbrs wr multiplid togthr to giv ach of ths ncryption kys? (a) 77 (b) 8 (c) 65 (d) 202 () 14 (f) Multiply th following prim numbrs togthr to gt ncryption kys. (a) and 17 (b) 7 and 1 (c) 47 and 7 (d) 101 and 10 () 11 and 727 (f) 1 and 9 19 (a) Writ out th first fiv prim numbrs. (b) Writ out th six smallst kys that you can crat by multiplying two prims. (c) How many factors dos ach ky hav? (d) Do you think vry ky cratd by multiplying two prims togthr will hav this numbr of factors? Why? 4 Hr s a simplifid vrsion of how dcryption using prim numbrs works. Suppos th ncryptd mssag is W L R G Y S B E M R K C R E B J C V and you know th ky is 71. You hav to find th two prim numbrs that multiply togthr to giv 71. This is rasonably asy for such a small numbr. Th answr is 2 and 1. Ths digits tll you how much th lttrs in th original mssag hav bn shiftd backwards along th alphabt to giv th codd mssag.you match ths digits to th cod as follows: W L R G Y S B E M R K C R E B J C V Th way dcrypting this cod works is that th numbr tlls you how many lttrs to shift ach lttr forwards along th alphabt. Th 2 undr th W mans shift two lttrs forward through th alphabt from W, so th uncodd mssag, usually calld th plaintxt, has Y as its first lttr. For th scond lttr you find th lttr thr placs on from L in th alphabt, which givs O as th scond lttr of th plaintxt. (a) Continu dcrypting th cod to gt th ntir original plaintxt mssag. (b) Dscrib what you did with Y 2. (c) Why couldn t you us any numbr (.g. 120) as a ky? 5 Dcod this mssag givn th ky 94. K X P G Q F O N D M N H K B E L N L N S Y K Z D Not that you nd to work out which ordr to put th two prims in. Only on will giv you th mssag. 6 Encrypt your own mssag using th prim numbr systm. Us only prim numbrs undr 100 and kp th mssag undr 25 lttrs. Giv your codd mssag and ky to somon to dcrypt. Rsarch hi.com.au Find out about th GIMPS (Grat Intrnt Mrsnn Prim Sarch) projct and prsnt a rport on how prim numbrs ar usd in mail ncryption. Discuss whthr govrnmnts should ban ncryption and mak it possibl for intllignc agncis to rad all mails. 1 whol NUMBERS 2
8 Simplify th following with th hlp of a calculator, and brak th cod to find th caption. R W C C O (8 + 5 ) 16 T 4 10 A O L A 6 5 U Hinmann MATHS ZONE
9 Summary St out solutions to wordd problms by putting hadings and writing calculations in logical squnc. Estimat products and quotints by rounding numbrs to th lading digit. Ordr of oprations rquirs bracktd calculations to b don first, working from innr brackts, thn multiplication and division as thy appar, thn addition and subtraction as thy appar. Prims ar numbrs with xactly 2 factors: thmslvs and 1. Indx notation is a way of writing rpatd factors as a powr of th factor. Taking a squar root is th opposit of squaring a numbr. FAQs What is th largst multipl of 9? Numbrs don t hav largst multipls. Th multipls of 9 continu forvr: 9, 18, 27, 6, Is 1 a prim numbr? No. A prim numbr has two factors. 1 is nithr composit nor prim. Skills 1 Us rounding to th first digit to stimat ths products. (a) (b) (c) Us rounding to th first digit to stimat ths quotints. (a) (b) (c) Us rounding to th first digit to stimat ths, and thn us a calculator to work out how far off your stimat was from th xact answr. (a) (b) (c) Work ths out using your calculator. (a) 258 (21 162) (b) [(82 94) 41] Find, without using a calculator: (a) 9 (2 + 1) 2 (b) (c) (1 5 2) + (20 10) (d) [5 (9 + 1)] 6 Choos th corrct answr. In th calculation of 2 [0 (4 1)] + 6 th first opration to do is: A + B C D E any of ths symbols 7 Choos th corrct answr. (5 + 6) 2 + (15 2) 6 is qual to: A 40 B 20 C 2 D 25 E , whol NUMBERS 25
10 8 Find th first thr multipls of: (a) 7 (b) 10 (c) 12 (d) 52 9 Find th LCM of: (a) and 8 (b) 4 and 16 (c) 6 and 9 (d) 20 and Choos th corrct answr. Th LCM of 2, 5 and 9 is: A 10 B 18 C 45 D 90 E Find all th factors of: (a) 5 (b) 1 (c) 44 (d) 48 () 51 (f) Find th HCF for ach of ths. (a) 11 and 55 (b) 90 and 60 (c) 72 and 64 1 Choos th corrct answr. Th HCF of 14, 28 and 56 is: A 14 B 1 C 7 D 56 E Writ factor trs and xprss ach numbr as a product of prim factors. (a) 24 (b) 0 (c) 88 (d) Writ ach of ths numbrs in indx form. (a) (b) tn cubd (c) fiv squard (d) 12 to th powr of 8 16 Writ ach of ths out in xpandd form, thn work out th answr. (a) 5 (b) 8 4 (c) ( 2 2 ) Evaluat th following. (a) 64 (b) 900 (c) 225 Applications 18 Put brackts into ths statmnts, whr ncssary, to mak thm tru. (a) = (b) = 7 19 (a) Copy th following pattrn and complt it using your calculator = = = (b) Look at th pattrn in part (a) and without using a calculator copy and complt th following = = = 20 (a) Look at this pattrn: 2 2 = Now copy and complt ths. (i) 2 = (ii) 4 2 = 2 + (iii) 5 2 = (b) Dscrib th rlationship btwn a squar numbr and th squar numbr bfor it. (c) Using th rlationship stablishd in part (b), complt ths. (i) 12 2 = (ii) 20 2 = Is 2 10 largr or smallr than 1000? Writ th diffrnc. 1.,, 26 Hinmann MATHS ZONE
11 22 Put ths numbrs in ascnding ordr: 2 4, 121, 10 2,, Writ ach numbr as a product of its prim factors, in indx form. (a) 81 (b) 128 (c) 144 (d) Simplify ths with your calculator, using th shortst mthod possibl. (a) 6 5 (b) 1 6 (c) 15 (d) 25 () 2 (f) 2 7 (g) 6 (h) 4 5 (i) (j) (k) (l) 6 5 (m) (n) (o) (p) St out ths calculations in your normal way and work out th answrs. (a) (b) (c) List th numbrs if you count by nins, starting at 0 and nding at 75. Copy and complt th following by writing < or > btwn th numbrs. (a) (b).9.8 (c) Copy and complt ach of th following by finding th pattrn. (a) 9, 15, 22, 0,,, (b) 1,, 7, 15,,, 5 Calculat: (a) (b) (c) Find th missing numbr that maks ach of th following tru. (a) + 7 = 24 (b) 4 = 15 (c) 7 0 = 15 7 Prform th following divisions. (a) 768 (b) (c) List all numbrs that 8 gos into that ar gratr than 70 and lss than Simplify: (a) (b) 18 6 (c) 8 (15 5) 10 Which whol numbr is ach of th following dcimals closst to? (a) 1.9 (b) (c) Calculat: (a) (b) (c) If Cln purchass thr tops at $15.50 ach, how much chang will sh rciv from a $50 not? 4 6 Worksht R1.7 Worksht R1.8 Worksht R1.9 Worksht R1.10 Worksht R1.11 Worksht R1.12 Worksht R1.1 Worksht R1.14 Worksht R1.15 Worksht R1.16 Worksht R1.17 Worksht R1.18 Worksht C1.11 Worksht C1.12 Assignmnt 1 1 whol NUMBERS 27
NonHomogeneous Systems, Euler s Method, and Exponential Matrix
NonHomognous Systms, Eulr s Mthod, and Exponntial Matrix W carry on nonhomognous firstordr linar systm of diffrntial quations. W will show how Eulr s mthod gnralizs to systms, giving us a numrical approach
More informationChiSquare. Hypothesis: There is an equal chance of flipping heads or tails on a coin. Coin A. Expected (e) (o e) (o e) 2 (o e) 2 e
Why? ChiSquar How do you know if your data is th rsult of random chanc or nvironmntal factors? Biologists and othr scintists us rlationships thy hav discovrd in th lab to prdict vnts that might happn
More informationQUANTITATIVE METHODS CLASSES WEEK SEVEN
QUANTITATIVE METHODS CLASSES WEEK SEVEN Th rgrssion modls studid in prvious classs assum that th rspons variabl is quantitativ. Oftn, howvr, w wish to study social procsss that lad to two diffrnt outcoms.
More informationThe example is taken from Sect. 1.2 of Vol. 1 of the CPN book.
Rsourc Allocation Abstract This is a small toy xampl which is wllsuitd as a first introduction to Cnts. Th CN modl is dscribd in grat dtail, xplaining th basic concpts of Cnts. Hnc, it can b rad by popl
More informationby John Donald, Lecturer, School of Accounting, Economics and Finance, Deakin University, Australia
Studnt Nots Cost Volum Profit Analysis by John Donald, Lcturr, School of Accounting, Economics and Financ, Dakin Univrsity, Australia As mntiond in th last st of Studnt Nots, th ability to catgoris costs
More informationEcon 371: Answer Key for Problem Set 1 (Chapter 1213)
con 37: Answr Ky for Problm St (Chaptr 23) Instructor: Kanda Naknoi Sptmbr 4, 2005. (2 points) Is it possibl for a country to hav a currnt account dficit at th sam tim and has a surplus in its balanc
More informationCPS 220 Theory of Computation REGULAR LANGUAGES. Regular expressions
CPS 22 Thory of Computation REGULAR LANGUAGES Rgular xprssions Lik mathmatical xprssion (5+3) * 4. Rgular xprssion ar built using rgular oprations. (By th way, rgular xprssions show up in various languags:
More informationDeer: Predation or Starvation
: Prdation or Starvation National Scinc Contnt Standards: Lif Scinc: s and cosystms Rgulation and Bhavior Scinc in Prsonal and Social Prspctiv s, rsourcs and nvironmnts Unifying Concpts and Procsss Systms,
More informationFactorials! Stirling s formula
Author s not: This articl may us idas you havn t larnd yt, and might sm ovrly complicatd. It is not. Undrstanding Stirling s formula is not for th faint of hart, and rquirs concntrating on a sustaind mathmatical
More informationMathematics. Mathematics 3. hsn.uk.net. Higher HSN23000
hsn uknt Highr Mathmatics UNIT Mathmatics HSN000 This documnt was producd spcially for th HSNuknt wbsit, and w rquir that any copis or drivativ works attribut th work to Highr Still Nots For mor dtails
More informationApplications of the compound interest formula
Applications of th compound intrst formula Quit oftn, thr of th variabls usd in th compound intrst formula ar known and th fourth nds to b found. Finding P workd xampl 6 Aunt Frda lavs Thlma a lgacy som
More information14.3 Area Between Curves
14. Ara Btwn Curvs Qustion 1: How is th ara btwn two functions calculatd? Qustion : What ar consumrs and producrs surplus? Earlir in this chaptr, w usd dfinit intgrals to find th ara undr a function and
More informationQuestion 3: How do you find the relative extrema of a function?
ustion 3: How do you find th rlativ trma of a function? Th stratgy for tracking th sign of th drivativ is usful for mor than dtrmining whr a function is incrasing or dcrasing. It is also usful for locating
More informationExponential Growth and Decay; Modeling Data
Exponntial Growth and Dcay; Modling Data In this sction, w will study som of th applications of xponntial and logarithmic functions. Logarithms wr invntd by John Napir. Originally, thy wr usd to liminat
More information7 Timetable test 1 The Combing Chart
7 Timtabl tst 1 Th Combing Chart 7.1 Introduction 7.2 Tachr tams two workd xampls 7.3 Th Principl of Compatibility 7.4 Choosing tachr tams workd xampl 7.5 Ruls for drawing a Combing Chart 7.6 Th Combing
More informationAdverse Selection and Moral Hazard in a Model With 2 States of the World
Advrs Slction and Moral Hazard in a Modl With 2 Stats of th World A modl of a risky situation with two discrt stats of th world has th advantag that it can b natly rprsntd using indiffrnc curv diagrams,
More informationFree ACA SOLUTION (IRS 1094&1095 Reporting)
Fr ACA SOLUTION (IRS 1094&1095 Rporting) Th Insuranc Exchang (301) 2791062 ACA Srvics Transmit IRS Form 1094 C for mployrs Print & mail IRS Form 1095C to mploys HR Assist 360 will gnrat th 1095 s for
More information5.4 Exponential Functions: Differentiation and Integration TOOTLIFTST:
.4 Eponntial Functions: Diffrntiation an Intgration TOOTLIFTST: Eponntial functions ar of th form f ( ) Ab. W will, in this sction, look at a spcific typ of ponntial function whr th bas, b, is.78.... This
More informationRemember you can apply online. It s quick and easy. Go to www.gov.uk/advancedlearningloans. Title. Forename(s) Surname. Sex. Male Date of birth D
24+ Advancd Larning Loan Application form Rmmbr you can apply onlin. It s quick and asy. Go to www.gov.uk/advancdlarningloans About this form Complt this form if: you r studying an ligibl cours at an approvd
More informationGenetic Drift and Gene Flow Illustration
Gntic Drift and Gn Flow Illustration This is a mor dtaild dscription of Activity Ida 4, Chaptr 3, If Not Rac, How do W Explain Biological Diffrncs? in: How Ral is Rac? A Sourcbook on Rac, Cultur, and Biology.
More informationCategory 7: Employee Commuting
7 Catgory 7: Employ Commuting Catgory dscription This catgory includs missions from th transportation of mploys 4 btwn thir homs and thir worksits. Emissions from mploy commuting may aris from: Automobil
More informationMaking and Using the Hertzsprung  Russell Diagram
Making and Using th Hrtzsprung  Russll Diagram Nam In astronomy th HrtzsprungRussll Diagram is on of th main ways that w organiz data dscribing how stars volv, ags of star clustrs, masss of stars tc.
More informationintro Imagine that someone asked you to describe church using only the bible. What would you say to them?
intro Imagin that somon askd you to dscrib church using only th bibl. What would you say to thm? So many of th things w'v mad church to b arn't ssntial in scriptur. W'r on a journy of rimagining what
More informationCloud and Big Data Summer School, Stockholm, Aug., 2015 Jeffrey D. Ullman
Cloud and Big Data Summr Scool, Stockolm, Aug., 2015 Jffry D. Ullman Givn a st of points, wit a notion of distanc btwn points, group t points into som numbr of clustrs, so tat mmbrs of a clustr ar clos
More informationThe Matrix Exponential
Th Matrix Exponntial (with xrciss) 92.222  Linar Algbra II  Spring 2006 by D. Klain prliminary vrsion Corrctions and commnts ar wlcom! Th Matrix Exponntial For ach n n complx matrix A, dfin th xponntial
More informationModelling and Solving TwoStep Equations: ax + b = c
Modlling and Solving ToStp Equations: a + b c Focus on Aftr this lsson, you ill b abl to φ modl problms φ ith tostp linar quations solv tostp linar quations and sho ho you ord out th ansr Cali borrod
More informationSPECIAL VOWEL SOUNDS
SPECIAL VOWEL SOUNDS Plas consult th appropriat supplmnt for th corrsponding computr softwar lsson. Rfr to th 42 Sounds Postr for ach of th Spcial Vowl Sounds. TEACHER INFORMATION: Spcial Vowl Sounds (SVS)
More informationHardware Modules of the RSA Algorithm
SERBIAN JOURNAL OF ELECTRICAL ENGINEERING Vol. 11, No. 1, Fbruary 2014, 121131 UDC: 004.3`142:621.394.14 DOI: 10.2298/SJEE140114011S Hardwar Moduls of th RSA Algorithm Vlibor Škobić 1, Branko Dokić 1,
More informationLecture 20: Emitter Follower and Differential Amplifiers
Whits, EE 3 Lctur 0 Pag of 8 Lctur 0: Emittr Followr and Diffrntial Amplifirs Th nxt two amplifir circuits w will discuss ar ry important to lctrical nginring in gnral, and to th NorCal 40A spcifically.
More informationINTRO. DVD projection equipment Life in 6 Words: The GOSPEL Explored DVD Participant Guides one for each group member Pens/pencils Bibles
GO OUR SINS PAYING EVERYONE LIFE v i GREAT STORIES Ky Scriptur: 1 Corinthians 15:34 Supplis: V projction quipmnt Lif in 6 Words: Th GOSPEL Explord V Pticipant Guids on for ach group mmbr Pns/pncils Bibls
More informationSimulated Radioactive Decay Using Dice Nuclei
Purpos: In a radioactiv sourc containing a vry larg numbr of radioactiv nucli, it is not possibl to prdict whn any on of th nucli will dcay. Although th dcay tim for any on particular nuclus cannot b prdictd,
More informationC H A P T E R 1 Writing Reports with SAS
C H A P T E R 1 Writing Rports with SAS Prsnting information in a way that s undrstood by th audinc is fundamntally important to anyon s job. Onc you collct your data and undrstand its structur, you nd
More informationStatistical Machine Translation
Statistical Machin Translation Sophi Arnoult, Gidon Mailltt d Buy Wnnigr and Andra Schuch Dcmbr 7, 2010 1 Introduction All th IBM modls, and Statistical Machin Translation (SMT) in gnral, modl th problm
More informationSOFTWARE ENGINEERING AND APPLIED CRYPTOGRAPHY IN CLOUD COMPUTING AND BIG DATA
Intrnational Journal on Tchnical and Physical Problms of Enginring (IJTPE) Publishd by Intrnational Organization of IOTPE ISSN 077358 IJTPE Journal www.iotp.com ijtp@iotp.com Sptmbr 015 Issu 4 Volum 7
More informationBasis risk. When speaking about forward or futures contracts, basis risk is the market
Basis risk Whn spaking about forward or futurs contracts, basis risk is th markt risk mismatch btwn a position in th spot asst and th corrsponding futurs contract. Mor broadly spaking, basis risk (also
More informationSigmoid Functions and Their Usage in Artificial Neural Networks
Sigmoid Functions and Thir Usag in Artificial Nural Ntworks Taskin Kocak School of Elctrical Enginring and Computr Scinc Applications of Calculus II: Invrs Functions Eampl problm Calculus Topic: Invrs
More informationNew Basis Functions. Section 8. Complex Fourier Series
Nw Basis Functions Sction 8 Complx Fourir Sris Th complx Fourir sris is prsntd first with priod 2, thn with gnral priod. Th connction with th ralvalud Fourir sris is xplaind and formula ar givn for convrting
More informationLecture notes: 160B revised 9/28/06 Lecture 1: Exchange Rates and the Foreign Exchange Market FT chapter 13
Lctur nots: 160B rvisd 9/28/06 Lctur 1: xchang Rats and th Forign xchang Markt FT chaptr 13 Topics: xchang Rats Forign xchang markt Asst approach to xchang rats Intrst Rat Parity Conditions 1) Dfinitions
More informationImproving Managerial Accounting and Calculation of Labor Costs in the Context of Using Standard Cost
Economy Transdisciplinarity Cognition www.ugb.ro/tc Vol. 16, Issu 1/2013 5054 Improving Managrial Accounting and Calculation of Labor Costs in th Contxt of Using Standard Cost Lucian OCNEANU, Constantin
More informationGateway 125,126,130 Fall 2006 Exam 1 KEY p1
Gatway 125,126,130 Fall 2006 Exam 1 KEY p1 Q16 (1 point ach) Plas plac th corrct lttr/s in th box. 1) How many lctrons can th third principal quantum lvl (n = 3) hold? a. 2 b. 8 c. 16 d. 18. 32 2) Arrang
More informationA Project Management framework for Software Implementation Planning and Management
PPM02 A Projct Managmnt framwork for Softwar Implmntation Planning and Managmnt Kith Lancastr Lancastr Stratgis Kith.Lancastr@LancastrStratgis.com Th goal of introducing nw tchnologis into your company
More informationII. Equipment. Magnetic compass, magnetic dip compass, Helmholtz coils, HP 6212 A power supply, Keithley model 169 multimeter
Magntic fild of th arth I. Objctiv: Masur th magntic fild of th arth II. Equipmnt. Magntic compass, magntic dip compass, Hlmholtz s, HP 6212 A powr supply, Kithly modl 169 multimtr III Introduction. IIIa.
More informationCHAPTER 88 THE BINOMIAL AND POISSON DISTRIBUTIONS
CHAPTER 88 THE BINOMIAL AND POISSON DISTRIBUTIONS EXERCISE Pag 97 1. Concrt blocks ar tstd and it is found that on avrag 7% fail to mt th rquird spcification. For a batch of nin blocks dtrmin th probabilitis
More informationWORKERS' COMPENSATION ANALYST, 1774 SENIOR WORKERS' COMPENSATION ANALYST, 1769
081685 WORKERS' COMPENSATION ANALYST, 1774 SENIOR WORKERS' COMPENSATION ANALYST, 1769 Summary of Dutis : Dtrmins City accptanc of workrs' compnsation cass for injurd mploys; authorizs appropriat tratmnt
More informatione = C / electron Q = Ne
Physics 0 Modul 01 Homwork 1. A glass rod that has bn chargd to +15.0 nc touchs a mtal sphr. Aftrword, th rod's charg is +8.00 nc. What kind of chargd particl was transfrrd btwn th rod and th sphr, and
More informationChapter 9 Nuclear Radiation Radioactive Isotopes 9.1 radioactive isotope Natural Radioactivity
Chaptr 9 Nuclar Radiation 9. Natural Radioactivity Radioactiv Isotops A radioactiv isotop has an unstabl nuclus. mits radiation to bcom mor stabl. can b on or mor of th isotops of an lmnt 2 Nuclar Radiation
More informationTELL YOUR STORY WITH MYNEWSDESK The world's leading allinone brand newsroom and multimedia PR platform
TELL YOUR STORY WITH MYNEWSDESK Th world's lading allinon brand nwsroom and multimdia PR platform SO WHAT'S THE STORY WITH MYNEWSDESK? Th world s lading allinon nwsroom and digital PR platform. Usd
More informationA Derivation of Bill James Pythagorean WonLoss Formula
A Drivation of Bill Jams Pythagoran WonLoss Formula Ths nots wr compild by John Paul Cook from a papr by Dr. Stphn J. Millr, an Assistant Profssor of Mathmatics at Williams Collg, for a talk givn to th
More informationSolutions to Homework 8 chem 344 Sp 2014
1. Solutions to Homwork 8 chm 44 Sp 14 .. 4. All diffrnt orbitals mans thy could all b paralll spins 5. Sinc lctrons ar in diffrnt orbitals any combination is possibl paird or unpaird spins 6. Equivalnt
More informationTIME MANAGEMENT. 1 The Process for Effective Time Management 2 Barriers to Time Management 3 SMART Goals 4 The POWER Model e. Section 1.
Prsonal Dvlopmnt Track Sction 1 TIME MANAGEMENT Ky Points 1 Th Procss for Effctiv Tim Managmnt 2 Barrirs to Tim Managmnt 3 SMART Goals 4 Th POWER Modl In th Army, w spak of rsourcs in trms of th thr M
More informationKey Management System Framework for Cloud Storage Singa Suparman, Eng Pin Kwang Temasek Polytechnic {singas,engpk}@tp.edu.sg
Ky Managmnt Systm Framwork for Cloud Storag Singa Suparman, Eng Pin Kwang Tmask Polytchnic {singas,ngpk}@tp.du.sg Abstract In cloud storag, data ar oftn movd from on cloud storag srvic to anothr. Mor frquntly
More informationA Theoretical Model of Public Response to the Homeland Security Advisory System
A Thortical Modl of Public Rspons to th Homland Scurity Advisory Systm Amy (Wnxuan) Ding Dpartmnt of Information and Dcision Scincs Univrsity of Illinois Chicago, IL 60607 wxding@uicdu Using a diffrntial
More informationCPU. Rasterization. Per Vertex Operations & Primitive Assembly. Polynomial Evaluator. Frame Buffer. Per Fragment. Display List.
Elmntary Rndring Elmntary rastr algorithms for fast rndring Gomtric Primitivs Lin procssing Polygon procssing Managing OpnGL Stat OpnGL uffrs OpnGL Gomtric Primitivs ll gomtric primitivs ar spcifid by
More informationunion scholars program APPLICATION DEADLINE: FEBRUARY 28 YOU CAN CHANGE THE WORLD... AND EARN MONEY FOR COLLEGE AT THE SAME TIME!
union scholars YOU CAN CHANGE THE WORLD... program AND EARN MONEY FOR COLLEGE AT THE SAME TIME! AFSCME Unitd Ngro Collg Fund Harvard Univrsity Labor and Worklif Program APPLICATION DEADLINE: FEBRUARY 28
More informationhttp://www.wwnorton.com/chemistry/tutorials/ch14.htm Repulsive Force
ctivation nrgis http://www.wwnorton.com/chmistry/tutorials/ch14.htm (back to collision thory...) Potntial and Kintic nrgy during a collision + + ngativly chargd lctron cloud Rpulsiv Forc ngativly chargd
More informationEntityRelationship Model
EntityRlationship Modl Kuanghua Chn Dpartmnt of Library and Information Scinc National Taiwan Univrsity A Company Databas Kps track of a company s mploys, dpartmnts and projcts Aftr th rquirmnts collction
More informationData Encryption and Decryption Using RSA Algorithm in a Network Environment
IJCSNS Intrnational Journal of Computr Scinc and Ntwork Scurity, VOL.13 No.7, July 2013 9 Data Encryption and Dcryption Using RSA Algorithm in a Ntwork Environmnt Nntaw Y. Goshw. Dpartmnt of Elctrical/Elctronics
More informationME 612 Metal Forming and Theory of Plasticity. 6. Strain
Mtal Forming and Thory of Plasticity mail: azsnalp@gyt.du.tr Makin Mühndisliği Bölümü Gbz Yüksk Tknoloji Enstitüsü 6.1. Uniaxial Strain Figur 6.1 Dfinition of th uniaxial strain (a) Tnsil and (b) Comprssiv.
More informationLecture 3: Diffusion: Fick s first law
Lctur 3: Diffusion: Fick s first law Today s topics What is diffusion? What drivs diffusion to occur? Undrstand why diffusion can surprisingly occur against th concntration gradint? Larn how to dduc th
More informationPrinciples of Humidity Dalton s law
Principls of Humidity Dalton s law Air is a mixtur of diffrnt gass. Th main gas componnts ar: Gas componnt volum [%] wight [%] Nitrogn N 2 78,03 75,47 Oxygn O 2 20,99 23,20 Argon Ar 0,93 1,28 Carbon dioxid
More informationSample Lesson. Intensive, Multisensory Reading Intervention with Proven Results Grades PreK 8+ RTI. Level 1: Introductory Lesson 5: Short e
ORTON GILLINGHAM Sampl Lsson Intnsiv, Multisnsory Rading Intrvntion with Provn Rsults Grads PrK 8+ RTI Lvl 1: Introductory Lsson 5: Short BASED PROGRAM tl 8002255750 psbookscom fax 8884402665 From Tachr
More informationImportant Information Call Through... 8 Internet Telephony... 6 two PBX systems... 10 Internet Calls... 3 Internet Telephony... 2
Installation and Opration Intrnt Tlphony Adaptr Aurswald Box Indx C I R 884264 03 02/05 Call Duration, maximum...10 Call Through...7 Call Transportation...7 Calls Call Through...7 Intrnt Tlphony...3 two
More informationFinancial Mathematics
Financial Mathatics A ractical Guid for Actuaris and othr Businss rofssionals B Chris Ruckan, FSA & Jo Francis, FSA, CFA ublishd b B rofssional Education Solutions to practic qustions Chaptr 7 Solution
More informationSample Copy. Student Objectives. 71a. Chapter 4. Lesson 1. Lesson 4. Lesson 5. Lesson 2. Lesson 3. Level 3 Grammar. Recite the Pronoun Jingle (13).
Chatr tudnt Objctivs Rcit th ronoun Jing (13). Rcit th ubjct ronoun Jing (1). Idntif ronouns and subjct ronouns. Rcit sam Q & Fow, adding th subjct ronoun. Idntif undrstood subjct ronouns. Rviw imrativ
More informationIntermediate Macroeconomic Theory / Macroeconomic Analysis (ECON 3560/5040) Final Exam (Answers)
Intrmdiat Macroconomic Thory / Macroconomic Analysis (ECON 3560/5040) Final Exam (Answrs) Part A (5 points) Stat whthr you think ach of th following qustions is tru (T), fals (F), or uncrtain (U) and brifly
More informationAP Calculus AB 2008 Scoring Guidelines
AP Calculus AB 8 Scoring Guidlins Th Collg Board: Conncting Studnts to Collg Succss Th Collg Board is a notforprofit mmbrship association whos mission is to connct studnts to collg succss and opportunity.
More informationLogo Design/Development 1on1
Logo Dsign/Dvlopmnt 1on1 If your company is looking to mak an imprssion and grow in th marktplac, you ll nd a logo. Fortunatly, a good graphic dsignr can crat on for you. Whil th pric tags for thos famous
More informationContinuity Cloud Virtual Firewall Guide
Cloud Virtual Firwall Guid uh6 Vrsion 1.0 Octobr 2015 Foldr BDR Guid for Vam Pag 1 of 36 Cloud Virtual Firwall Guid CONTENTS INTRODUCTION... 3 ACCESSING THE VIRTUAL FIREWALL... 4 HYPERV/VIRTUALBOX CONTINUITY
More informationSection 55 Inverse of a Square Matrix
 Invrs of a Squar Matrix 9 (D) Rank th playrs from strongst to wakst. Explain th rasoning hind your ranking. 68. Dominan Rlation. Eah mmr of a hss tam plays on math with vry othr playr. Th rsults ar givn
More informationL13: Spectrum estimation nonparametric and parametric
L13: Spctrum stimation nonparamtric and paramtric Lnnart Svnsson Dpartmnt of Signals and Systms Chalmrs Univrsity of Tchnology Problm formulation Larning objctivs Aftr today s lctur you should b abl to
More informationStandard errors for regression coefficients; Multicollinearity
Standard rror for rgrion cofficint; Multicollinarit Standard rror. Rcall that b k i a point timat of β k. Bcau of ampling variabilit, thi timat ma b too high or too low. bk, th tandard rror of b k, giv
More informationArchitecture of the proposed standard
Architctur of th proposd standard Introduction Th goal of th nw standardisation projct is th dvlopmnt of a standard dscribing building srvics (.g.hvac) product catalogus basd on th xprincs mad with th
More informationGOD CALLS MOSES. 2 Illustrations by Ken Tunell
GOD CALLS MOSES Aftr th dath of Josph and his brothrs, thir familis Mcontinud to liv in th land of Egypt. Thr thy grw grat in numbr and latr bcam known as Isralits. Aftr many yars, a nw Pharaoh bcam king
More informationA Note on Approximating. the Normal Distribution Function
Applid Mathmatical Scincs, Vol, 00, no 9, 4549 A Not on Approimating th Normal Distribution Function K M Aludaat and M T Alodat Dpartmnt of Statistics Yarmouk Univrsity, Jordan Aludaatkm@hotmailcom and
More informationLEVEL 5 S E C N D G R A D E. Decodable Reader Stories: Unit 1. Name: Week 3 Spelling Words
Practic vry Mmory Word using all fiv stps. Word Work BLM Unit 1, Lsson 11 Family: Plas kp this pag at hom and continu practicing th words with your child all wk. Childrn could writ any two words from th
More informationWho uses our services? We have a growing customer base. with institutions all around the globe.
not taking xpr Srvic Guid 2013 / 2014 NTE i an affordabl option for audio to txt convrion. Our rvic includ not or dirct trancription rvic from prviouly rcordd audio fil. Our rvic appal pcially to tudnt
More informationModule 7: Discrete State Space Models Lecture Note 3
Modul 7: Discrt Stat Spac Modls Lctur Not 3 1 Charactristic Equation, ignvalus and ign vctors For a discrt stat spac modl, th charactristic quation is dfind as zi A 0 Th roots of th charactristic quation
More informationSaving Through Trailer Tracking
SEE WHAT S HAPPENING. CUT RENTAL COSTS. Losing track of rntal trailrs is on of th worst things that can happn to you, lading to unncssary and costly rntal chargs. A Brkshir Hathaway Copany A Brkshir Hathaway
More informationIncomplete 2Port Vector Network Analyzer Calibration Methods
Incomplt Port Vctor Ntwork nalyzr Calibration Mthods. Hnz, N. Tmpon, G. Monastrios, H. ilva 4 RF Mtrology Laboratory Instituto Nacional d Tcnología Industrial (INTI) Bunos irs, rgntina ahnz@inti.gov.ar
More information3. Yes. You can put 20 of the 6V lights in series, or you can put several of the 6V lights in series with a large resistance.
CHAPTE 6: DC Circuits sponss to Qustions. Evn though th bird s ft ar at high potntial with rspct to th ground, thr is vry littl potntial diffrnc btwn thm, bcaus thy ar clos togthr on th wir. Th rsistanc
More informationVersion 1.0. General Certificate of Education (Alevel) January 2012. Mathematics MPC3. (Specification 6360) Pure Core 3. Final.
Vrsion.0 Gnral Crtificat of Education (Alvl) January 0 Mathmatics MPC (Spcification 660) Pur Cor Final Mark Schm Mark schms ar prpard by th Principal Eaminr and considrd, togthr with th rlvant qustions,
More informationTraffic Flow Analysis (2)
Traffic Flow Analysis () Statistical Proprtis. Flow rat distributions. Hadway distributions. Spd distributions by Dr. GangLn Chang, Profssor Dirctor of Traffic safty and Oprations Lab. Univrsity of Maryland,
More informationIn the previous two chapters, we clarified what it means for a problem to be decidable or undecidable.
Chaptr 7 Computational Complxity 7.1 Th Class P In th prvious two chaptrs, w clarifid what it mans for a problm to b dcidabl or undcidabl. In principl, if a problm is dcidabl, thn thr is an algorithm (i..,
More informationTeaching Computer Networking with the Help of Personal Computer Networks
Taching Computr Ntworking with th Hlp of Prsonal Computr Ntworks Rocky K. C. Chang Dpartmnt of Computing Th Hong Kong Polytchnic Univrsity Hung Hom, Kowloon, Hong Kong csrchang@comp.polyu.du.hk ABSTRACT
More information(Analytic Formula for the European Normal Black Scholes Formula)
(Analytic Formula for th Europan Normal Black Schols Formula) by Kazuhiro Iwasawa Dcmbr 2, 2001 In this short summary papr, a brif summary of Black Schols typ formula for Normal modl will b givn. Usually
More informationMagic Square of Squares
Intrnatinal Jurnal f Enginring and Tchnical Rsarch (IJETR) ISSN: 232869, Vlum, Issu8, Octbr 23 Magic Squar f Squars Shubhankar Paul Abstract A n n array f intgrs is calld a magic squar whn all th rws,
More informationVersion Issue Date Reason / Description of Change Author Draft February, N/A 2009
Appndix A: CNS Managmnt Procss: OTRS POC Documnt Control Titl : CNS Managmnt Procss Documnt : (Location of Documnt and Documnt numbr) Author : Ettin Vrmuln (EV) Ownr : ICT Stratgic Srvics Vrsion : Draft
More informationFACULTY SALARIES FALL 2004. NKU CUPA Data Compared To Published National Data
FACULTY SALARIES FALL 2004 NKU CUPA Data Compard To Publishd National Data May 2005 Fall 2004 NKU Faculty Salaris Compard To Fall 2004 Publishd CUPA Data In th fall 2004 Northrn Kntucky Univrsity was among
More informationPlanning and Managing Copper Cable Maintenance through Cost Benefit Modeling
Planning and Managing Coppr Cabl Maintnanc through Cost Bnfit Modling Jason W. Rup U S WEST Advancd Tchnologis Bouldr Ky Words: Maintnanc, Managmnt Stratgy, Rhabilitation, Costbnfit Analysis, Rliability
More informationDevelopment of Financial Management Reporting in MPLS
1 Dvlopmnt of Financial Managmnt Rporting in MPLS 1. Aim Our currnt financial rports ar structurd to dlivr an ovrall financial pictur of th dpartmnt in it s ntirty, and thr is no attmpt to provid ithr
More informationWelcome! You can play the instrument while you are charging. The guitar comes with: Push the MCK back in and you are ready to play!
Wlcom! Th ark Fir is th most innovativ nw guitar in svral dcads. Whil th guitar may look vry traditional, it has many faturs that go wll past what th world has sn bfor. W hav workd vry hard so you can
More informationParallel and Distributed Programming. Performance Metrics
Paralll and Distributd Programming Prformanc! wo main goals to b achivd with th dsign of aralll alications ar:! Prformanc: th caacity to rduc th tim to solv th roblm whn th comuting rsourcs incras;! Scalability:
More informationHOMEWORK FOR UNIT 51: FORCE AND MOTION
Nam Dat Partnrs HOMEWORK FOR UNIT 51: FORCE AND MOTION 1. You ar givn tn idntial springs. Dsrib how you would dvlop a sal of for (i., a mans of produing rpatabl fors of a varity of sizs) using ths springs.
More informationUse a highlevel conceptual data model (ER Model). Identify objects of interest (entities) and relationships between these objects
Chaptr 3: Entity Rlationship Modl Databas Dsign Procss Us a highlvl concptual data modl (ER Modl). Idntify objcts of intrst (ntitis) and rlationships btwn ths objcts Idntify constraints (conditions) End
More informationMagic Message Maker Amaze your customers with this Gift of Caring communication piece
Magic Mssag Makr maz your customrs with this Gift of aring communication pic Girls larn th powr and impact of crativ markting with this attntion grabbing communication pic that will hlp thm o a World of
More informationSTATEMENT OF INSOLVENCY PRACTICE 3.2
STATEMENT OF INSOLVENCY PRACTICE 3.2 COMPANY VOLUNTARY ARRANGEMENTS INTRODUCTION 1 A Company Voluntary Arrangmnt (CVA) is a statutory contract twn a company and its crditors undr which an insolvncy practitionr
More informationCreating Your Own Coffeehouse AtHome. An Interactive Guide Brought to you by New Folgers Coffeehouse Blend
Crating Yr Own ffhs thom n Intractiv Guid Brght to y by Nw Folgrs ffhs Blnd ro Drip ff HOW DO YOU LIKE YOUR COFFEE? vr ff ld Th Folgr ff mpany rss ff ch n Icd ff B r w C o f f How to Mak ff with a Traditional
More informationMath 161 Solutions To Sample Final Exam Problems
Solutions To Sampl Final Eam Problms Mat 6 Mat 6 Solutions To Sampl Final Eam Problms. Find dy in parts a  blow. a y = + b y = c y = arctan d y +lny = y = cos + f y = +ln ln g y = +t3 dt y = g a y = b
More informationOPTIONS AND FUTURES: A TECHNICAL APPRAISAL
Pag 15 OPTIONS AND FUTURES: A TECHNICAL APPRAISAL by David J.S. Rutldg Papr prsntd to Sminar on Trading in Options: Opportunitis in th Intrnational Markt sponsord by Th Sydny Stock Exchang and Th Scuritis
More informationCryptographic Protocol Analysis of AN.ON
Cryptographic Protocol Analysis of AN.ON Bndikt Wstrmann 1, Rolf Wndolsky 2, Lxi Pimnidis 3, and Dogan Ksdogan 1,4 1 Q2S, NTNU, 7491 Trondhim, Norway 2 JonDos GmbH, 93055 Rgnsburg, Grmany 3 idv GmbH, 50672
More information