Solutions 1.4Page 40


 Todd May
 1 years ago
 Views:
Transcription
1 Soluions.4Pag 40 Problm Find gnral soluions (implici if ncssary, plici if convnin) of h diffrnial quaions. dy = d ( 4y) / Sparaing h variabls yilds: / / / y dy = 4 d y / dy = 4 / d Ingraing boh sids o obain / / y dy = 4 d / y 4 / = + / 4 / y = + y() yilds: 4 / y ( ) = ( + ) / Whr =
2 Problm 9 Find gnral soluions (implici if ncssary, plici if convnin) of h diffrnial quaions. dy ( ) = y d Sparaing h variabls yilds: dy d = y Ingraing boh sids o obain dy d = y can b dcomposd ino Th abov ingral bcoms dy d d = y + + ln y = + ) ) + y = y = + ) ) + ln ( + ) + y( ) = Whr = ) y() yilds: + +
3 Problm 5 Find plici paricular soluions of h iniial valu problm. dy y = y, y( ) = d Th variabls in h diffrnial quaion ar sparad as follows. dy = y( + ) d dy ( + ) d = = ( + )d y Ingraing boh sids o obain dy = ( + ) d y ln y = + ln + y = y = Whr = + ln + y() yilds: Th iniial condiion is usd o solv for h consan. y() = = = () y () bcoms y( ) = Simplifying givs ( y ( ) = )
4 Problm 9 (Populaion growh) A crain ciy had a populaion of 5000 in 90 and a populaion of 0000 in 90. Assum ha is populaion will coninu o grow ponnially a a consan ra. Wha populaion can is ciy plannrs pc in h yar 000? k From pg., P( ) = P0, whr is h im in yars. Assuming 90 is h iniial im, h givn informaion is as follows: P = P(0) = 0000 k is solvd for using h givn informaion as follows: k (0) P(0) = 0000 = 5000 k (0) = 5 5) k = 0 Now h populaion in h yar 000 or, P (40) = (40) 0 P( 40) = 5,840 popl = P(40), can b found.
5 Problm (Radiocarbon daing) arbon racd from an ancin skull conaind only onsih as much 4 as carbon racd from prsnday bon. How old is h skull? Th govrning diffrnial quaion is givn on pg.5 dn = kn d Th soluion of h diffrnial quaion is k N( ) N = 0 N I is givn ha a h currn im, N = 0. From pg.5, k = if is in yars. Th quaion o b solvd is: N 0 (0.000 = N ) 0 Dividing boh sids by (0.000) = = givs N 0 = 4,5 yars
6 Problm 9 A pichr of burmilk iniially a 5 is o b coold by sing i on h fron porch, whr h mpraur is 0. Suppos ha h mpraur of h burmilk has droppd o 5 afr 0 min. Whn will i b a 5. Th govrning diffrnial quaion is Eq.9 pg.. dt = k( A T ) d A is h mdium mpraur and im is masurd in minus for his problm. I is givn ha A is 0, so h diffrnial quaion bcoms dt = kt d Sparaing variabls yilds: dt = kd T Ingraing boh sids o g T () yilds: dt = kd T ln T = k + k+ T = k T = Whr = Th iniial condiion is givn as T ( 0) = 5. Subsiuing h iniial condiion ino h abov quaion givs T (0) = 5 = () = 5 T = 5 k I is also givn ha T ( 0) = 5. This informaion is usd o solv for k. T (0) = 5 = 5 5) k = 0 k (0) Th im whn h mpraur rachs 5 can b solvd for as follows:
7 T ( ) = 5 = = 5 5) 5) = 0 = min 5 0
8 Problm 44 According o on cosmological hory, hr wr qual amouns of h wo uranium isoops 5 U and 8 U a h craion of h univrs in h big bang. A prsn hr ar. aoms of 8 U for ach aom of 5 U. Using h halflivs yars for 8 U and yars for 5 U, calcula h ag of h univrs. M will dno h numbr of aoms of 5 U and N will dno h numbr of aoms of 8 U. Th form of h govrning quaion is N = N 0 k I can b shown ha h halflif, τ, is ln τ = (s pg.) k Th consan, k, can b solvd for bcaus h halflivs ar givn. ln k = τ k =.540 k 8 5 = 9.0 N = N 0 M = M Th iniial im is h bginning of h univrs. Dividing boh quaions a h prsn im givs N ( ) =. = M ln. = ( ) = 5.99 billion yars
9 Problm 4 A crain pic of dubious informaion abou phnylhylamin in h drinking war bgan o sprad on day in a ciy wih a populaion of 00,000. Wihin a wk, 0000 popl had hard his rumor. Assum ha h ra of incras of h numbr who hav hard h rumor is proporional o h numbr who hav no y hard i. How long will i b unil half h populaion of h ciy has hard h rumor? An ODE mus b formd o fi h abov informaion. L N b h numbr of popl, in housands, who hav hard h rumor. Th ODE is: dn = k( 00 N) d Th abov ODE sas ha h ra of incras of h numbr who hav hard h rumor is proporional o h numbr who hav no y hard i, as sad in h problm samn. Tim is masurd in days. 00N is h oal populaion minus h popl who hav hard h rumor, and hus h numbr of popl who hav no hard h rumor. Sparaing variabls yilds: dn = kd 00 N Ingraing boh sids o obain dn = kd 00 N 00 N) = k + 00 N = 00 N = Whr = ( k+ ) k N() yilds: Iniially, no on has hard h rumor, so N(0) = 0. This iniial condiion is usd o solv for = () = 00 N() = 0 is givn and is usd o solv for k. k () N() = 0 = = 00 k = k 9 0 )
10 Now h im whn half h populaion has hard h rumor can b found. 50 = = = 9 0 ) = Solving for givs: = 4 days
RC (ResistorCapacitor) Circuits. AP Physics C
(RsisrCapacir Circuis AP Physics C Circui Iniial Cndiins An circui is n whr yu hav a capacir and rsisr in h sam circui. Supps w hav h fllwing circui: Iniially, h capacir is UNCHARGED ( = 0 and h currn
More informationDIFFERENTIAL EQUATIONS with TI89 ABDUL HASSEN and JAY SCHIFFMAN. A. Direction Fields and Graphs of Differential Equations
DIFFERENTIAL EQUATIONS wih TI89 ABDUL HASSEN and JAY SCHIFFMAN W will assum ha h radr is familiar wih h calculaor s kyboard and h basic opraions. In paricular w hav assumd ha h radr knows h funcions of
More informationSection 7.4: Exponential Growth and Decay
1 Sction 7.4: Exponntial Growth and Dcay Practic HW from Stwart Txtbook (not to hand in) p. 532 # 117 odd In th nxt two ction, w xamin how population growth can b modld uing diffrntial quation. W tart
More informationName: Algebra II Review for Quiz #13 Exponential and Logarithmic Functions including Modeling
Name: Algebra II Review for Quiz #13 Exponenial and Logarihmic Funcions including Modeling TOPICS: Solving Exponenial Equaions (The Mehod of Common Bases) Solving Exponenial Equaions (Using Logarihms)
More informationTransient Thermoelastic Behavior of Semiinfinite Cylinder by Using MarchiZgrablich and Fourier Transform Technique
Inrnaional Journal of Mahmaical Enginring and Scinc ISSN : 77698 Volum 1 Issu 5 (May 01) hp://www.ijms.com/ hps://sis.googl.com/si/ijmsjournal/ Transin Thrmolasic Bhavior of Smiinfini Cylindr by Using
More informationChapter 7. Response of FirstOrder RL and RC Circuits
Chaper 7. esponse of FirsOrder L and C Circuis 7.1. The Naural esponse of an L Circui 7.2. The Naural esponse of an C Circui 7.3. The ep esponse of L and C Circuis 7.4. A General oluion for ep and Naural
More informationMathematics in Pharmacokinetics What and Why (A second attempt to make it clearer)
Mahemaics in Pharmacokineics Wha and Why (A second aemp o make i clearer) We have used equaions for concenraion () as a funcion of ime (). We will coninue o use hese equaions since he plasma concenraions
More informationcooking trajectory boiling water B (t) microwave 0 2 4 6 8 101214161820 time t (mins)
Alligaor egg wih calculus We have a large alligaor egg jus ou of he fridge (1 ) which we need o hea o 9. Now here are wo accepable mehods for heaing alligaor eggs, one is o immerse hem in boiling waer
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 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 informationMorningstar Investor Return
Morningsar Invesor Reurn Morningsar Mehodology Paper Augus 31, 2010 2010 Morningsar, Inc. All righs reserved. The informaion in his documen is he propery of Morningsar, Inc. Reproducion or ranscripion
More informationAP Calculus AB 2013 Scoring Guidelines
AP Calculus AB 1 Scoring Guidelines The College Board The College Board is a missiondriven noforprofi organizaion ha connecs sudens o college success and opporuniy. Founded in 19, he College Board was
More informationCircuit Types. () i( t) ( )
Circui Types DC Circuis Idenifying feaures: o Consan inpus: he volages of independen volage sources and currens of independen curren sources are all consan. o The circui does no conain any swiches. All
More informationAnswer, Key Homework 2 David McIntyre 45123 Mar 25, 2004 1
Answer, Key Homework 2 Daid McInyre 4123 Mar 2, 2004 1 This prinou should hae 1 quesions. Muliplechoice quesions may coninue on he ne column or page find all choices before making your selecion. The
More informationNumerical Algorithm for the Stochastic Present Value of Aggregate Claims in the Renewal Risk Model
Gn. Mah. Nos, Vol. 9, No. 2, Dcmbr, 23, pp. 4 ISSN 229784; Copyrigh ICSRS Publicaion, 23 www.icsrs.org Availabl fr onlin a hp://www.gman.in Numrical Algorihm for h Sochasic Prsn Valu of Aggrga Claims
More informationDensity Dependence. births are a decreasing function of density b(n) and deaths are an increasing function of density d(n).
FW 662 Densiydependen populaion models In he previous lecure we considered densiy independen populaion models ha assumed ha birh and deah raes were consan and no a funcion of populaion size. Longerm
More informationMTBF: Understanding Its Role in Reliability
Modul MTBF: Undrsanding Is Rol in Rliabiliy By David C. Wilson Foundr / CEO March 4, Wilson Consuling Srvics, LLC dav@wilsonconsulingsrvics.n www.wilsonconsulingsrvics.n Wilson Consuling Srvics, LLC Pag
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 informationQUALITY OF DYING AND DEATH QUESTIONNAIRE FOR NURSES VERSION 3.2A
UNIVERSITY OF WASHINGTON SCHOOL OF MEDICINE QUALITY OF DYING AND DEATH QUESTIONNAIRE FOR NURSES VERSION 3.2A Plas rurn your compld qusionnair in h nclosd nvlop o: [Rurn Addrss] RNID PID Copyrigh by h Univrsiy
More informationChapter 28 Magnetic Induction
Chapr 8 Magnic nducion Forad Concpual Probls (a) Th agnic quaor is a lin on h surfac of Earh on which Earh s agnic fild is horizonal. A h agnic quaor, how would you orin a fla sh of papr so as o cra h
More informationImagine a Source (S) of sound waves that emits waves having frequency f and therefore
heoreical Noes: he oppler Eec wih ound Imagine a ource () o sound waes ha emis waes haing requency and hereore period as measured in he res rame o he ource (). his means ha any eecor () ha is no moing
More informationDifferential Equations. Solving for Impulse Response. Linear systems are often described using differential equations.
Differenial Equaions Linear sysems are ofen described using differenial equaions. For example: d 2 y d 2 + 5dy + 6y f() d where f() is he inpu o he sysem and y() is he oupu. We know how o solve for y given
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 informationTHERMODYNAMICS TUTORIAL 7 COMPRESSIBLE FLOW
HERMODYNAMICS UORIAL 7 COMPRESSIBLE FLOW On comlion of his uorial you should b abl o do h following. Dfin nroy Driv xrssions for nroy changs in fluids Driv Brnoulli's quaion for gas Driv quaions for comrssibl
More informationChapter 2 Kinematics in One Dimension
Chaper Kinemaics in One Dimension Chaper DESCRIBING MOTION:KINEMATICS IN ONE DIMENSION PREVIEW Kinemaics is he sudy of how hings moe how far (disance and displacemen), how fas (speed and elociy), and how
More informationFullwave rectification, bulk capacitor calculations Chris Basso January 2009
ullwave recificaion, bulk capacior calculaions Chris Basso January 9 This shor paper shows how o calculae he bulk capacior value based on ripple specificaions and evaluae he rms curren ha crosses i. oal
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 informationTwo Compartment Body Model and V d Terms by Jeff Stark
Two Comparmen Body Model and V d Terms by Jeff Sark In a onecomparmen model, we make wo imporan assumpions: (1) Linear pharmacokineics  By his, we mean ha eliminaion is firs order and ha pharmacokineic
More informationRC, RL and RLC circuits
Name Dae Time o Complee h m Parner Course/ Secion / Grade RC, RL and RLC circuis Inroducion In his experimen we will invesigae he behavior of circuis conaining combinaions of resisors, capaciors, and inducors.
More informationCHARGE AND DISCHARGE OF A CAPACITOR
REFERENCES RC Circuis: Elecrical Insrumens: Mos Inroducory Physics exs (e.g. A. Halliday and Resnick, Physics ; M. Sernheim and J. Kane, General Physics.) This Laboraory Manual: Commonly Used Insrumens:
More informationPhysics 111 Fall 2007 Electric Currents and DC Circuits
Physics 111 Fall 007 Elecric Currens and DC Circuis 1 Wha is he average curren when all he sodium channels on a 100 µm pach of muscle membrane open ogeher for 1 ms? Assume a densiy of 0 sodium channels
More informationNonHomogeneous 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 informationDerivations and Applications of Greek Letters Review and
Rvi //008 Chap 0 Divaion an Applicaion of Gk L Rviw an Ingaion By HongYi Chn, Rug Univiy, USA ChngFw L, Rug Univiy, USA Wikang Shih, Rug Univiy, USA Abac In hi chap, w inouc h finiion of Gk l. W alo
More informationKrebs (1972). A group of organisms of the same species occupying a particular space at a particular time
FW 662 Lcur 1  Dnsiyindpndn populaion modls Tx: Golli, 21, A Primr of Ecology Wha is a populaion? Krbs (1972). A group of organisms of h sam spcis occupying a paricular spac a a paricular im Col (1957).
More informationAcceleration Lab Teacher s Guide
Acceleraion Lab Teacher s Guide Objecives:. Use graphs of disance vs. ime and velociy vs. ime o find acceleraion of a oy car.. Observe he relaionship beween he angle of an inclined plane and he acceleraion
More informationChapter 2 Problems. s = d t up. = 40km / hr d t down. 60km / hr. d t total. + t down. = t up. = 40km / hr + d. 60km / hr + 40km / hr
Chaper 2 Problems 2.2 A car ravels up a hill a a consan speed of 40km/h and reurns down he hill a a consan speed of 60 km/h. Calculae he average speed for he rip. This problem is a bi more suble han i
More informationChapter 4: Exponential and Logarithmic Functions
Chaper 4: Eponenial and Logarihmic Funcions Secion 4.1 Eponenial Funcions... 15 Secion 4. Graphs of Eponenial Funcions... 3 Secion 4.3 Logarihmic Funcions... 4 Secion 4.4 Logarihmic Properies... 53 Secion
More informationAP Calculus BC 2010 Scoring Guidelines
AP Calculus BC Scoring Guidelines The College Board The College Board is a noforprofi membership associaion whose mission is o connec sudens o college success and opporuniy. Founded in, he College Board
More informationDifferential Equations
31 C H A P T E R Differenial Equaions Change is inrinsic in he universe and in he world around us; he world is in moion. Aemps o undersand and predic change ofen involve creaing models reflecing raes of
More informationDifferential Equations and Linear Superposition
Differenial Equaions and Linear Superposiion Basic Idea: Provide soluion in closed form Like Inegraion, no general soluions in closed form Order of equaion: highes derivaive in equaion e.g. dy d dy 2 y
More informationEconomics Honors Exam 2008 Solutions Question 5
Economics Honors Exam 2008 Soluions Quesion 5 (a) (2 poins) Oupu can be decomposed as Y = C + I + G. And we can solve for i by subsiuing in equaions given in he quesion, Y = C + I + G = c 0 + c Y D + I
More informationSolution of a differential equation of the second order by the method of NIGAM
Tire : Résoluion d'une équaion différenielle du second[...] Dae : 16/02/2011 Page : 1/6 Soluion of a differenial equaion of he second order by he mehod of NIGAM Summarized: We presen in his documen, a
More informationMany quantities are transduced in a displacement and then in an electric signal (pressure, temperature, acceleration). Prof. B.
Displacmn snsors Many quaniis ar ransducd in a displacmn and hn in an lcric signal (prssur, mpraur, acclraion). Poniomrs Poniomrs i p p i o i p A poniomr is basd on a sliding conac moving on a rsisor.
More information2.5 Life tables, force of mortality and standard life insurance products
Soluions 5 BS4a Acuarial Science Oford MT 212 33 2.5 Life ables, force of moraliy and sandard life insurance producs 1. (i) n m q represens he probabiliy of deah of a life currenly aged beween ages + n
More information6.5. Modelling Exercises. Introduction. Prerequisites. Learning Outcomes
Modelling Exercises 6.5 Inroducion This Secion provides examples and asks employing exponenial funcions and logarihmic funcions, such as growh and decay models which are imporan hroughou science and engineering.
More informationINFLUENCE OF DEBT FINANCING ON THE EFFECTIVENESS OF THE INVESTMENT PROJECT WITHIN THE MODIGLIANIMILLER THEORY
VOUME 2, 2 NFUENCE OF DEBT FNANCNG ON THE EFFECTVENE OF THE NVETMENT PROJECT WTHN THE MODGANMER THEORY Pr Brusov, Taaa Flaova, Naal Orhova, Pavl Brusov, Nasa Brusova Fac Uvrsy ur h Govrm of h Russa Frao,
More informationAppendix A: Area. 1 Find the radius of a circle that has circumference 12 inches.
Appendi A: Area workedou s o OddNumbered Eercises Do no read hese workedou s before aemping o do he eercises ourself. Oherwise ou ma mimic he echniques shown here wihou undersanding he ideas. Bes wa
More informationNewton s Laws of Motion
Newon s Laws of Moion MS4414 Theoreical Mechanics Firs Law velociy. In he absence of exernal forces, a body moves in a sraigh line wih consan F = 0 = v = cons. Khan Academy Newon I. Second Law body. The
More informationOption Pricing with Constant & Time Varying Volatility
Opion Pricing wih Consan & im arying olailiy Willi mmlr Cnr for Empirical Macroconomics Bilfld Grmany; h Brnard chwarz Cnr for Economic Policy Analysis Nw York NY UA and Economics Dparmn h Nw chool for
More information5.8 Resonance 231. The study of vibrating mechanical systems ends here with the theory of pure and practical resonance.
5.8 Resonance 231 5.8 Resonance The sudy of vibraing mechanical sysems ends here wih he heory of pure and pracical resonance. Pure Resonance The noion of pure resonance in he differenial equaion (1) ()
More informationRC (ResistorCapacitor) Circuits. AP Physics C
(ResisorCapacior Circuis AP Physics C Circui Iniial Condiions An circui is one where you have a capacior and resisor in he same circui. Suppose we have he following circui: Iniially, he capacior is UNCHARGED
More informationThe Transport Equation
The Transpor Equaion Consider a fluid, flowing wih velociy, V, in a hin sraigh ube whose cross secion will be denoed by A. Suppose he fluid conains a conaminan whose concenraion a posiion a ime will be
More informationRotational Inertia of a Point Mass
Roaional Ineria of a Poin Mass Saddleback College Physics Deparmen, adaped from PASCO Scienific PURPOSE The purpose of his experimen is o find he roaional ineria of a poin experimenally and o verify ha
More informationµ r of the ferrite amounts to 1000...4000. It should be noted that the magnetic length of the + δ
Page 9 Design of Inducors and High Frequency Transformers Inducors sore energy, ransformers ransfer energy. This is he prime difference. The magneic cores are significanly differen for inducors and high
More informationIT Update  August 2006
IT Nws Saus: No Aciv Til: Da: 7726 Summay (Opional): Body: Wlcom Back! Offic of Infomaion Tchnology Upda: IT Upda  Augus 26 Rob K. Blchman, Ph.D. Associa Dico, Offic of Infomaion Tchnology Whil You W
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 informationModule 4. Singlephase AC circuits. Version 2 EE IIT, Kharagpur
Module 4 Singlephase A circuis ersion EE T, Kharagpur esson 5 Soluion of urren in A Series and Parallel ircuis ersion EE T, Kharagpur n he las lesson, wo poins were described:. How o solve for he impedance,
More informationAP Calculus AB 2007 Scoring Guidelines
AP Calculus AB 7 Scoring Guidelines The College Board: Connecing Sudens o College Success The College Board is a noforprofi membership associaion whose mission is o connec sudens o college success and
More informationUnit 2. Unit 2: Rhythms in Mexican Music. Find Our Second Neighborhood (5 minutes) Preparation
Uni 2 Prparaion Uni 2: Rhyhms in Mxican Music Find Our Scond Nighborhood (5 minus) Th Conducor now aks us on a journy from Morningsid Highs, Manhaan, o Eas Harlm, Manhaan, o m our nx singr, Clso. Hav sudns
More informationEDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 67  FURTHER ELECTRICAL PRINCIPLES NQF LEVEL 3 OUTCOME 2 TUTORIAL 1  TRANSIENTS
EDEXEL NAIONAL ERIFIAE/DIPLOMA UNI 67  FURHER ELERIAL PRINIPLE NQF LEEL 3 OUOME 2 UORIAL 1  RANIEN Uni conen 2 Undersand he ransien behaviour of resisorcapacior (R) and resisorinducor (RL) D circuis
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 informationChabot College Physics Lab RC Circuits Scott Hildreth
Chabo College Physics Lab Circuis Sco Hildreh Goals: Coninue o advance your undersanding of circuis, measuring resisances, currens, and volages across muliple componens. Exend your skills in making breadboard
More informationSection 7.1 Angles and Their Measure
Secion 7.1 Angles and Their Measure Greek Leers Commonly Used in Trigonomery Quadran II Quadran III Quadran I Quadran IV α = alpha β = bea θ = hea δ = dela ω = omega γ = gamma DEGREES The angle formed
More information1 HALFLIFE EQUATIONS
R.L. Hanna Page HALFLIFE EQUATIONS The basic equaion ; he saring poin ; : wrien for ime: x / where fracion of original maerial and / number of halflives, and / log / o calculae he age (# ears): age (halflife)
More informationChapter 2: Principles of steadystate converter analysis
Chaper 2 Principles of SeadySae Converer Analysis 2.1. Inroducion 2.2. Inducor volsecond balance, capacior charge balance, and he small ripple approximaion 2.3. Boos converer example 2.4. Cuk converer
More informationTerm Structure of Interest Rates: The Theories
Handou 03 Econ 333 Abdul Munasb Trm Srucur of Inrs Ras: Th Thors Trm Srucur Facs Lookng a Fgur, w obsrv wo rm srucur facs Fac : Inrs ras for dffrn maurs nd o mov oghr ovr m Fac : Ylds on shorrm bond mor
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 informationwww.akcp.com Virtual Sensors
www.akcp.cm Irduci: Virual Ssrs Virual ssrs ca b a vry pwrful l i yur mirig sysm. O h scuriyprb yu ca hav up 80 f hs virual ssrs ad hy allw fr a muliud f applicais. Igrai wih MODBUS wrks wih h scuriyprb
More informationCapacitors and inductors
Capaciors and inducors We coninue wih our analysis of linear circuis by inroducing wo new passive and linear elemens: he capacior and he inducor. All he mehods developed so far for he analysis of linear
More informationHFCC Math Lab Intermediate Algebra  13 SOLVING RATETIMEDISTANCE PROBLEMS
HFCC Mah Lab Inemeiae Algeba  3 SOLVING RATETIMEDISTANCE PROBLEMS The vaiables involve in a moion poblem ae isance (), ae (), an ime (). These vaiables ae elae by he equaion, which can be solve fo any
More information[ ] These are the motor parameters that are needed: Motor voltage constant. J total (lbinsec^2)
MEASURING MOOR PARAMEERS Fil: Motor paramtrs hs ar th motor paramtrs that ar ndd: Motor voltag constant (voltssc/rad Motor torqu constant (lbin/amp Motor rsistanc R a (ohms Motor inductanc L a (Hnris
More informationMOTION ALONG A STRAIGHT LINE
Chaper 2: MOTION ALONG A STRAIGHT LINE 1 A paricle moes along he ais from i o f Of he following alues of he iniial and final coordinaes, which resuls in he displacemen wih he larges magniude? A i =4m,
More informationSteps for D.C Analysis of MOSFET Circuits
10/22/2004 Seps for DC Analysis of MOSFET Circuis.doc 1/7 Seps for D.C Analysis of MOSFET Circuis To analyze MOSFET circui wih D.C. sources, we mus follow hese five seps: 1. ASSUME an operaing mode 2.
More informationMEASUREMENT AND ASSESSMENT OF IMPACT SOUND IN THE SAME ROOM. Hans G. Jonasson
MEASUREMENT AND ASSESSMENT OF IMPACT SOUND IN THE SAME ROOM Hans G. Jonasson SP Tchnical Rsarch Institut of Swdn Box 857, SE501 15 Borås, Swdn hans.jonasson@sp.s ABSTRACT Drum sound, that is th walking
More informationHouse Price Index (HPI)
House Price Index (HPI) The price index of second hand houses in Colombia (HPI), regisers annually and quarerly he evoluion of prices of his ype of dwelling. The calculaion is based on he repeaed sales
More informationConceptually calculating what a 110 OTM call option should be worth if the present price of the stock is 100...
Normal (Gaussian) Disribuion Probabiliy De ensiy 0.5 0. 0.5 0. 0.05 0. 0.9 0.8 0.7 0.6? 0.5 0.4 0.3 0. 0. 0 3.6 5. 6.8 8.4 0.6 3. 4.8 6.4 8 The BlackScholes Shl Ml Moel... pricing opions an calculaing
More informationChapter 2 Problems. 3600s = 25m / s d = s t = 25m / s 0.5s = 12.5m. Δx = x(4) x(0) =12m 0m =12m
Chaper 2 Problems 2.1 During a hard sneeze, your eyes migh shu for 0.5s. If you are driving a car a 90km/h during such a sneeze, how far does he car move during ha ime s = 90km 1000m h 1km 1h 3600s = 25m
More informationHSS Hollow. Structural Sections DIMENSIONS AND SECTION PROPERTIES HSS: TECHNICAL BROCHURE
HSS Hollow Srucural Secions DIMENSIONS AND SETION PROPERTIES HSS: TEHNIAL BROHURE 01 Seel Tube Insiue 516 Waukegan Road, Suie 17 Glenview, IL 6005 TEL: 87.61.1701 FA: 87.660.7981 Technical Brochure: Dimensions
More informationTransient Analysis of First Order RC and RL circuits
Transien Analysis of Firs Order and iruis The irui shown on Figure 1 wih he swih open is haraerized by a pariular operaing ondiion. Sine he swih is open, no urren flows in he irui (i=0) and v=0. The volage
More informationDETERMINISTIC INVENTORY MODEL FOR ITEMS WITH TIME VARYING DEMAND, WEIBULL DISTRIBUTION DETERIORATION AND SHORTAGES KUNSHAN WU
Yugoslav Journal of Operaions Research 2 (22), Number, 67 DEERMINISIC INVENORY MODEL FOR IEMS WIH IME VARYING DEMAND, WEIBULL DISRIBUION DEERIORAION AND SHORAGES KUNSHAN WU Deparmen of Bussines Adminisraion
More informationGraduate Macro Theory II: Notes on Neoclassical Growth Model
Graduae Macro Theory II: Noes on Neoclassical Growh Model Eric Sims Universiy of Nore Dame Spring 2011 1 Basic Neoclassical Growh Model The economy is populaed by a large number of infiniely lived agens.
More informationA Universal Pricing Framework for Guaranteed Minimum Benefits in Variable Annuities *
A Universal Pricing Framework for Guaraneed Minimum Benefis in Variable Annuiies * Daniel Bauer Deparmen of Risk Managemen and Insurance, Georgia Sae Universiy 35 Broad Sree, Alana, GA 333, USA Phone:
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 informationCHAPTER 13. CHEMICAL KINETICS
CHAPTR 3. CHMICAL KINTICS Kineics  Sudy of facors ha affec how fas a reacion occurs and he sepbysep processes involved in chemical reacions. Facors ha Affec Reacion Rae A. Concenraion of reacans  higher
More informationEXTERNAL DEBT, GROWTH AND SUSTAINABILITY. Abstract. Introduction
ETERNAL EBT, GROWTH AN SUSTAINABILIT Absrac Robro Frnkl * Th papr prsns a odl inndd o dfin and discuss h susainabili of rnal dbs in rgn arks. Th firs susainabili condiion is h isnc of a aiu in h dboupu
More informationDiagnostic Examination
Diagnosic Examinaion TOPIC XV: ENGINEERING ECONOMICS TIME LIMIT: 45 MINUTES 1. Approximaely how many years will i ake o double an invesmen a a 6% effecive annual rae? (A) 10 yr (B) 12 yr (C) 15 yr (D)
More informationMortality Variance of the Present Value (PV) of Future Annuity Payments
Morali Variance of he Presen Value (PV) of Fuure Annui Pamens Frank Y. Kang, Ph.D. Research Anals a Frank Russell Compan Absrac The variance of he presen value of fuure annui pamens plas an imporan role
More information4. International Parity Conditions
4. Inernaional ariy ondiions 4.1 urchasing ower ariy he urchasing ower ariy ( heory is one of he early heories of exchange rae deerminaion. his heory is based on he concep ha he demand for a counry's currency
More informationFollow links Class Use and other Permissions. For more information, send to:
COPYRIGHT NOTICE: David A. Kendrick, P. Ruben Mercado, and Hans M. Amman: Compuaional Economics is published by Princeon Universiy Press and copyrighed, 2006, by Princeon Universiy Press. All righs reserved.
More informationPRESSURE BUILDUP. Figure 1: Schematic of an ideal buildup test
Tom Aage Jelmer NTNU Dearmen of Peroleum Engineering and Alied Geohysics PRESSURE BUILDUP I is difficul o kee he rae consan in a roducing well. This is no an issue in a buildu es since he well is closed.
More informationRC Circuit and Time Constant
ircui and Time onsan 8M Objec: Apparaus: To invesigae he volages across he resisor and capacior in a resisorcapacior circui ( circui) as he capacior charges and discharges. We also wish o deermine he
More informationSTUDY ON THE GRAVIMETRIC MEASUREMENT OF THE SWELLING BEHAVIORS OF POLYMER FILMS
452 Rev. Adv. Maer. Sci. 33 (2013) 452458 J. Liu, X.J. Zheng and K.Y. Tang STUDY ON THE GRAVIMETRIC MEASUREMENT OF THE SWELLING BEHAVIORS OF POLYMER FILMS J. Liu, X. J. Zheng and K. Y. Tang College of
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 informationCHAPTER FIVE. Solutions for Section 5.1
CHAPTER FIVE 5. SOLUTIONS 87 Soluions for Secion 5.. (a) The velociy is 3 miles/hour for he firs hours, 4 miles/hour for he ne / hour, and miles/hour for he las 4 hours. The enire rip lass + / + 4 = 6.5
More informationUsing RCtime to Measure Resistance
Basic Express Applicaion Noe Using RCime o Measure Resisance Inroducion One common use for I/O pins is o measure he analog value of a variable resisance. Alhough a builin ADC (Analog o Digial Converer)
More informationReturn Calculation of U.S. Treasury Constant Maturity Indices
Reurn Calculaion of US Treasur Consan Mauri Indices Morningsar Mehodolog Paper Sepeber 30 008 008 Morningsar Inc All righs reserved The inforaion in his docuen is he proper of Morningsar Inc Reproducion
More informationI. Basic Concepts (Ch. 14)
(Ch. 14) A. Real vs. Financial Asses (Ch 1.2) Real asses (buildings, machinery, ec.) appear on he asse side of he balance shee. Financial asses (bonds, socks) appear on boh sides of he balance shee. Creaing
More informationSecond Order Linear Differential Equations
Second Order Linear Differenial Equaions Second order linear equaions wih consan coefficiens; Fundamenal soluions; Wronskian; Exisence and Uniqueness of soluions; he characerisic equaion; soluions of homogeneous
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 informationNASDAQ100 Futures Index SM Methodology
NASDAQ100 Fuures Index SM Mehodology Index Descripion The NASDAQ100 Fuures Index (The Fuures Index ) is designed o rack he performance of a hypoheical porfolio holding he CME NASDAQ100 Emini Index
More information