Question 3: How do you find the relative extrema of a function?

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Question 3: How do you find the relative extrema of a function?"

Transcription

1 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 th rlativ trma of a function. At a rlativ trma, a function changs from incrasing to dcrasing or dcrasing to incrasing. Th numbr lins in th prvious qustion allow us to s ths changs by obsrving changs in th sign of th drivativ of a function. Whn th drivativ of a function changs from positiv to ngativ, w know th function changs from incrasing to dcrasing. As long as th function is dfind at th critical valu whr th chang occurs, th critical point must b a rlativ maimum. If th drivativ of a function changs from ngativ to positiv, w know th function changs from dcrasing to incrasing. In this cas, th critical point is a rlativ minimum as long as th function is dfind thr. If th drivativ dos not chang sign at a critical valu, thr is no rlativ trma at th corrsponding critical point. Th First Drivativ Tst summarizs ths obsrvations and hlps us to locat rlativ trma on a function. 0

2 First Drivativ Tst Lt f b a non-constant function that is dfind at a critical valu c. If f changs from positiv to ngativ at c, thn a rlativ maimum occurs at th critical point c, f( c ). If f changs from ngativ to positiv at c, thn a rlativ minimum occurs at th critical point c, f( c ). If f dos not chang sign at trma at th corrsponding critical point. c, thn thr is no rlativ Eampl 6 Find th Rlativ Etrma of a Function Find th location of th rlativ trma of th function f 3 ( ) Solution Th first drivativ tst rquirs us to construct a numbr lin for th drivativ so that w can idntify whr th graph is incrasing and dcrasing. Using th ruls for drivativs, th first drivativ of th function f ( ) is d d d d f d d d d 3 ( ) So th drivativ is ( ) 4 8. f Us Sum / Diffrnc Rul and th Product with a Constant Rul. Us th Powr Rul for Drivativs and th fact that th drivativ of a constant is zro

3 W nd to us this drivativ to find th critical valus. St th drivativ, ( ) 4 8, qual to zro to find thos valus. f St th drivativ qual to zro Factor th gratst common factor from ach trm Factor th trinomial To find whr th product is qual to zro, st ach factor qual to zro and solv for th variabl In gnral, critical valus may also com from valus whr th drivativ is undfind. Sinc f ( ) is a polynomial, it is dfind vrywhr so th drivativ is dfind vrywhr. Although this drivativ could b factord to find th critical valus, most quadratic drivativs ar not factorabl. In this cas, th quadratic quation yilding th critical valus can b solvd using th quadratic formula. This stratgy would yild th sam critical valus as factoring: , a b c Idntify a, b, and c for th quadratic b b 4ac formula and put a in th valus Simplify th numrator and dnominator To find th critical valus with mor complicatd drivativs, w may nd to solv th quation using a graph. Th solution to th quation

4 4 8 0 can also b found by locating th intrcpts on th drivativ f ( ). = 0 = 0 3 f( ) 6 3 Lik factoring or th quadratic formula, th critical valus ar locatd at and 3. All thr stratgis yild th sam critical valus. Kp in mind that a graph will giv approimat valus whil factoring or th quadratic formula yild act valus. If th drivativ is not factorabl, linar, or quadratic, anothr mthod will nd to b usd to dtrmin whr th drivativ is qual to zro. Evn though a graph of th drivativ only givs an stimat of th critical valus, it may b th only way to find th critical valus if th drivativ is complicatd. With th critical valus in hand, labl thm on a numbr lin so that w ar abl to apply th first drivativ tst. If w slct a tst point in ach intrval and dtrmin th sign of ach factor, w can complt th numbr lin and track th sign of th drivativ. 3

5 (+)(-)(-) = + = 0 (+)(+)(-) = - = 0 (+)(+)(+) = + incrasing dcrasing 3 incrasing f( ) 6 3 f ( ) Whn a continuous function changs from incrasing to dcrasing, w hav a rlativ maimum at th critical valu. Whn a continuous function changs from dcrasing to incrasing, w hav a rlativ minimum at th critical valu. In this cas, th rlativ maimum is locatd at and th rlativ minimum is locatd at 3. To find th ordrd pairs for th rlativ trma, w nd to substitut th critical valus into th original function f( ) to find th corrsponding y valus: 3 Rlativ Maimum: f Rlativ Minimum: f Th rlativ maimum is locatd at locatd at 3,. 37 4, and th rlativ minimum is 4

6 Eampl 7 Find th Rlativ Maimum Find th location of th rlativ maimum of th function g ( ) Solution Th drivativ of gis ( ) found with th uotint Rul for Drivativs with u v u v Put ths prssions into th uotint Rul: g( ) Th uotint Rul is d u vu uv d v v To mak it asir to find th critical valus, simplify th drivativ. Factor from th numrator Rduc th common factor in th numrator and dnominator Now w can find th critical valus by dtrmining whr this fraction is qual to zro or undfind. Any fraction is qual to zro whr th numrator is qual to zro. In this cas, this is whr 0 or. Fractions ar undfind whr th dnominator is qual to zro. Th dnominator for this fraction is and is always positiv so thr ar no valus whr th fraction is undfind. 5

7 To apply th first drivativ tst, labl a numbr lin with this critical valu and tst th first drivativ on ithr sid of th critical valu: incrasing = 0 dcrasing f( ) Sinc this function is continuous and th drivativ changs from incrasing to dcrasing at, th critical point is a rlativ maimum. Th y valu for th rlativ maimum coms from th function g ( ) and is g(). Th ordrd pair for th rlativ maimum is,. Eampl 8 Find th Minimum Avrag Cost Th total daily cost to produc units of a product is givn by th function C dollars Th avrag cost function C is found by dividing th total daily cost function C by th quantity. a. Find th avrag cost function C. C. Substitut th total daily cost function into th numrator of this fraction to yild Solution Th avrag cost function is dfind by C 6

8 C b. Find th quantity that yilds th minimum avrag cost. Solution Th minimum avrag cost is found by locating th rlativ minimum of th avrag cost function. To us th first drivativ tst to find this rlativ minimum, w nd to tak th drivativ of C using th uotint Rul for Drivativs. Th numrator, dnominator and thir drivativs ar u v u0.000 v Th drivativ of th avrag cost function is C vu uv v Sinc w nd to us th drivativ to find th critical valus, w simplify th drivativ as much as possibl: C Simplify th numrator by carrying out th multiplication and subtraction Combin lik trms Any fraction is qual to zro whn th numrator is qual to zro and undfind whr th dnominator is qual to zro. 7

9 St th numrator qual to St th dnominator qual to Sinc quantitis producd must b positiv, only 447 is a rasonabl critical valu for this function. Th numbr lin for this function only includs positiv quantitis. Tsting on ithr sid of th critical numbrs yilds th bhavior of C. 0 dcrasing = incrasing C Sinc th function dcrass on th lft sid of th critical valu and incrass on th right sid of th critical valu, th quantity at approimatly 447 units is a rlativ minimum. Th minimum avrag cost is obtaind from C and is calculatd as 8

10 C Sinc th total daily cost is in dollars and w ar dividing by th numbr of units to gt th avrag cost, th units on th avrag cost ar dollars pr unit. This mans that a production lvl of about 447 units givs th lowst avrag cost of 4.47 dollars pr unit. Figur 6 - Th rlativ minimum for th avrag cost function. 9

AP Calculus AB 2008 Scoring Guidelines

AP Calculus AB 2008 Scoring Guidelines AP Calculus AB 8 Scoring Guidlins Th Collg Board: Conncting Studnts to Collg Succss Th Collg Board is a not-for-profit mmbrship association whos mission is to connct studnts to collg succss and opportunity.

More information

QUANTITATIVE METHODS CLASSES WEEK SEVEN

QUANTITATIVE 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 information

Mathematics. Mathematics 3. hsn.uk.net. Higher HSN23000

Mathematics. 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 information

Econ 371: Answer Key for Problem Set 1 (Chapter 12-13)

Econ 371: Answer Key for Problem Set 1 (Chapter 12-13) con 37: Answr Ky for Problm St (Chaptr 2-3) 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 information

ME 612 Metal Forming and Theory of Plasticity. 6. Strain

ME 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 information

EFFECT OF GEOMETRICAL PARAMETERS ON HEAT TRANSFER PERFORMACE OF RECTANGULAR CIRCUMFERENTIAL FINS

EFFECT OF GEOMETRICAL PARAMETERS ON HEAT TRANSFER PERFORMACE OF RECTANGULAR CIRCUMFERENTIAL FINS 25 Vol. 3 () January-March, pp.37-5/tripathi EFFECT OF GEOMETRICAL PARAMETERS ON HEAT TRANSFER PERFORMACE OF RECTANGULAR CIRCUMFERENTIAL FINS *Shilpa Tripathi Dpartmnt of Chmical Enginring, Indor Institut

More information

Parallel and Distributed Programming. Performance Metrics

Parallel 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 information

Category 7: Employee Commuting

Category 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 information

CPU. Rasterization. Per Vertex Operations & Primitive Assembly. Polynomial Evaluator. Frame Buffer. Per Fragment. Display List.

CPU. 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 information

Current and Resistance

Current and Resistance Chaptr 6 Currnt and Rsistanc 6.1 Elctric Currnt...6-6.1.1 Currnt Dnsity...6-6. Ohm s Law...6-4 6.3 Elctrical Enrgy and Powr...6-7 6.4 Summary...6-8 6.5 Solvd Problms...6-9 6.5.1 Rsistivity of a Cabl...6-9

More information

Projections - 3D Viewing. Overview Lecture 4. Projection - 3D viewing. Projections. Projections Parallel Perspective

Projections - 3D Viewing. Overview Lecture 4. Projection - 3D viewing. Projections. Projections Parallel Perspective Ovrviw Lctur 4 Projctions - 3D Viwing Projctions Paralll Prspctiv 3D Viw Volum 3D Viwing Transformation Camra Modl - Assignmnt 2 OFF fils 3D mor compl than 2D On mor dimnsion Displa dvic still 2D Analog

More information

Gold versus stock investment: An econometric analysis

Gold versus stock investment: An econometric analysis Intrnational Journal of Dvlopmnt and Sustainability Onlin ISSN: 268-8662 www.isdsnt.com/ijds Volum Numbr, Jun 202, Pag -7 ISDS Articl ID: IJDS20300 Gold vrsus stock invstmnt: An conomtric analysis Martin

More information

Cloud and Big Data Summer School, Stockholm, Aug., 2015 Jeffrey D. Ullman

Cloud 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 information

Magic Message Maker Amaze your customers with this Gift of Caring communication piece

Magic 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 information

Adverse Selection and Moral Hazard in a Model With 2 States of the World

Adverse 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 information

The international Internet site of the geoviticulture MCC system Le site Internet international du système CCM géoviticole

The international Internet site of the geoviticulture MCC system Le site Internet international du système CCM géoviticole Th intrnational Intrnt sit of th goviticultur MCC systm L sit Intrnt intrnational du systèm CCM géoviticol Flávio BELLO FIALHO 1 and Jorg TONIETTO 1 1 Rsarchr, Embrapa Uva Vinho, Caixa Postal 130, 95700-000

More information

Fraud, Investments and Liability Regimes in Payment. Platforms

Fraud, Investments and Liability Regimes in Payment. Platforms Fraud, Invstmnts and Liability Rgims in Paymnt Platforms Anna Crti and Mariann Vrdir y ptmbr 25, 2011 Abstract In this papr, w discuss how fraud liability rgims impact th pric structur that is chosn by

More information

Keywords Cloud Computing, Service level agreement, cloud provider, business level policies, performance objectives.

Keywords Cloud Computing, Service level agreement, cloud provider, business level policies, performance objectives. Volum 3, Issu 6, Jun 2013 ISSN: 2277 128X Intrnational Journal of Advancd Rsarch in Computr Scinc and Softwar Enginring Rsarch Papr Availabl onlin at: wwwijarcsscom Dynamic Ranking and Slction of Cloud

More information

FACULTY SALARIES FALL 2004. NKU CUPA Data Compared To Published National Data

FACULTY 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 information

A Theoretical Model of Public Response to the Homeland Security Advisory System

A 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 information

Production Costing (Chapter 8 of W&W)

Production Costing (Chapter 8 of W&W) Production Costing (Chaptr 8 of W&W).0 Introduction Production costs rfr to th oprational costs associatd with producing lctric nrgy. Th most significant componnt of production costs ar th ful costs ncssary

More information

Problem Set 6 Solutions

Problem Set 6 Solutions 6.04/18.06J Mathmatics for Computr Scic March 15, 005 Srii Dvadas ad Eric Lhma Problm St 6 Solutios Du: Moday, March 8 at 9 PM Problm 1. Sammy th Shar is a fiacial srvic providr who offrs loas o th followig

More information

Electronic Commerce. and. Competitive First-Degree Price Discrimination

Electronic Commerce. and. Competitive First-Degree Price Discrimination Elctronic Commrc and Comptitiv First-Dgr Pric Discrimination David Ulph* and Nir Vulkan ** Fbruary 000 * ESRC Cntr for Economic arning and Social Evolution (ESE), Dpartmnt of Economics, Univrsity Collg

More information

Rural and Remote Broadband Access: Issues and Solutions in Australia

Rural and Remote Broadband Access: Issues and Solutions in Australia Rural and Rmot Broadband Accss: Issus and Solutions in Australia Dr Tony Warrn Group Managr Rgulatory Stratgy Tlstra Corp Pag 1 Tlstra in confidnc Ovrviw Australia s gographical siz and population dnsity

More information

MONEY ILLUSION IN THE STOCK MARKET: THE MODIGLIANI-COHN HYPOTHESIS*

MONEY ILLUSION IN THE STOCK MARKET: THE MODIGLIANI-COHN HYPOTHESIS* MONEY ILLUSION IN THE STOCK MARKET: THE MODIGLIANI-COHN HYPOTHESIS* RANDOLPH B. COHEN CHRISTOPHER POLK TUOMO VUOLTEENAHO Modigliani and Cohn hypothsiz that th stock markt suffrs from mony illusion, discounting

More information

the so-called KOBOS system. 1 with the exception of a very small group of the most active stocks which also trade continuously through

the so-called KOBOS system. 1 with the exception of a very small group of the most active stocks which also trade continuously through Liquidity and Information-Basd Trading on th Ordr Drivn Capital Markt: Th Cas of th Pragu tock Exchang Libor 1ÀPH³HN Cntr for Economic Rsarch and Graduat Education, Charls Univrsity and Th Economic Institut

More information

Upper Bounding the Price of Anarchy in Atomic Splittable Selfish Routing

Upper Bounding the Price of Anarchy in Atomic Splittable Selfish Routing Uppr Bounding th Pric of Anarchy in Atomic Splittabl Slfish Routing Kamyar Khodamoradi 1, Mhrdad Mahdavi, and Mohammad Ghodsi 3 1 Sharif Univrsity of Tchnology, Thran, Iran, khodamoradi@c.sharif.du Sharif

More information

WORKERS' COMPENSATION ANALYST, 1774 SENIOR WORKERS' COMPENSATION ANALYST, 1769

WORKERS' COMPENSATION ANALYST, 1774 SENIOR WORKERS' COMPENSATION ANALYST, 1769 08-16-85 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 information

Abstract. Introduction. Statistical Approach for Analyzing Cell Phone Handoff Behavior. Volume 3, Issue 1, 2009

Abstract. Introduction. Statistical Approach for Analyzing Cell Phone Handoff Behavior. Volume 3, Issue 1, 2009 Volum 3, Issu 1, 29 Statistical Approach for Analyzing Cll Phon Handoff Bhavior Shalini Saxna, Florida Atlantic Univrsity, Boca Raton, FL, shalinisaxna1@gmail.com Sad A. Rajput, Farquhar Collg of Arts

More information

TIME MANAGEMENT. 1 The Process for Effective Time Management 2 Barriers to Time Management 3 SMART Goals 4 The POWER Model e. Section 1.

TIME 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 information

Hardware Modules of the RSA Algorithm

Hardware Modules of the RSA Algorithm SERBIAN JOURNAL OF ELECTRICAL ENGINEERING Vol. 11, No. 1, Fbruary 2014, 121-131 UDC: 004.3`142:621.394.14 DOI: 10.2298/SJEE140114011S Hardwar Moduls of th RSA Algorithm Vlibor Škobić 1, Branko Dokić 1,

More information

C H A P T E R 1 Writing Reports with SAS

C 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 information

Vector Network Analyzer

Vector Network Analyzer Cours on Microwav Masurmnts Vctor Ntwork Analyzr Prof. Luca Prrgrini Dpt. of Elctrical, Computr and Biomdical Enginring Univrsity of Pavia -mail: luca.prrgrini@unipv.it wb: microwav.unipv.it Microwav Masurmnts

More information

June 2012. Enprise Rent. Enprise 1.1.6. Author: Document Version: Product: Product Version: SAP Version: 8.81.100 8.8

June 2012. Enprise Rent. Enprise 1.1.6. Author: Document Version: Product: Product Version: SAP Version: 8.81.100 8.8 Jun 22 Enpris Rnt Author: Documnt Vrsion: Product: Product Vrsion: SAP Vrsion: Enpris Enpris Rnt 88 88 Enpris Rnt 22 Enpris Solutions All rights rsrvd No parts of this work may b rproducd in any form or

More information

Category 11: Use of Sold Products

Category 11: Use of Sold Products 11 Catgory 11: Us of Sold Products Catgory dscription T his catgory includs missions from th us of goods and srvics sold by th rporting company in th rporting yar. A rporting company s scop 3 missions

More information

In the previous two chapters, we clarified what it means for a problem to be decidable or undecidable.

In 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 information

In the first years of the millennium, Americans flocked to Paris to enjoy French

In the first years of the millennium, Americans flocked to Paris to enjoy French 14 chaptr Exchang Rats and th Forign Exchang Markt: An Asst Approach 320 In th first yars of th millnnium, Amricans flockd to Paris to njoy Frnch cuisin whil shopping for dsignr clothing and othr spcialtis.

More information

union scholars program APPLICATION DEADLINE: FEBRUARY 28 YOU CAN CHANGE THE WORLD... AND EARN MONEY FOR COLLEGE AT THE SAME TIME!

union 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 information

Transistor is a semiconductor device with fast respond and accuracy. There are two types

Transistor is a semiconductor device with fast respond and accuracy. There are two types Tranitor Amplifir Prpard y: Poa Xuan Yap Thory: Tranitor i a miondutor dvi with fat rpond and auray. Thr ar two typ of tranitor, a Bipolar Juntion Tranitor and a Fild Efft Tranitor. Hr, w will looking

More information

Constraint-Based Analysis of Gene Deletion in a Metabolic Network

Constraint-Based Analysis of Gene Deletion in a Metabolic Network Constraint-Basd Analysis of Gn Dltion in a Mtabolic Ntwork Abdlhalim Larhlimi and Alxandr Bockmayr DFG-Rsarch Cntr Mathon, FB Mathmatik und Informatik, Fri Univrsität Brlin, Arnimall, 3, 14195 Brlin, Grmany

More information

1.3 Algebraic Expressions

1.3 Algebraic Expressions 1.3 Algebraic Expressions A polynomial is an expression of the form: a n x n + a n 1 x n 1 +... + a 2 x 2 + a 1 x + a 0 The numbers a 1, a 2,..., a n are called coefficients. Each of the separate parts,

More information

Cost-Volume-Profit Analysis

Cost-Volume-Profit Analysis ch03.qxd 9/7/04 4:06 PM Pag 86 CHAPTER Cost-Volum-Profit Analysis In Brif Managrs nd to stimat futur rvnus, costs, and profits to hlp thm plan and monitor oprations. Thy us cost-volum-profit (CVP) analysis

More information

AC Circuits Three-Phase Circuits

AC Circuits Three-Phase Circuits AC Circuits Thr-Phs Circuits Contnts Wht is Thr-Phs Circuit? Blnc Thr-Phs oltgs Blnc Thr-Phs Connction Powr in Blncd Systm Unblncd Thr-Phs Systms Aliction Rsidntil Wiring Sinusoidl voltg sourcs A siml

More information

Theoretical aspects of investment demand for gold

Theoretical aspects of investment demand for gold Victor Sazonov (Russia), Dmitry Nikolav (Russia) Thortical aspcts of invstmnt dmand for gold Abstract Th main objctiv of this articl is construction of a thortical modl of invstmnt in gold. Our modl is

More information

The Australian Rules Football Fixed Odds and Line Betting Markets: Econometric Tests for Efficiency and Simulated Betting Systems

The Australian Rules Football Fixed Odds and Line Betting Markets: Econometric Tests for Efficiency and Simulated Betting Systems Th Australian Ruls Football Fixd Odds and Lin Btting Markts: Economtric Tsts for Efficincy and Simulatd Btting Systms by Adi Schnytzr and Guy Winbrg a Papr to b prsntd at: Th 4 th Binnial Equin Industry

More information

METHODS FOR HANDLING TIED EVENTS IN THE COX PROPORTIONAL HAZARD MODEL

METHODS FOR HANDLING TIED EVENTS IN THE COX PROPORTIONAL HAZARD MODEL STUDIA OECONOMICA POSNANIENSIA 204, vol. 2, no. 2 (263 Jadwiga Borucka Warsaw School of Economics, Institut of Statistics and Dmography, Evnt History and Multilvl Analysis Unit jadwiga.borucka@gmail.com

More information

Noise Power Ratio (NPR) A 65-Year Old Telephone System Specification Finds New Life in Modern Wireless Applications.

Noise Power Ratio (NPR) A 65-Year Old Telephone System Specification Finds New Life in Modern Wireless Applications. TUTORIL ois Powr Ratio (PR) 65-Yar Old Tlphon Systm Spcification Finds w Lif in Modrn Wirlss pplications ITRODUTIO by Walt Kstr Th concpt of ois Powr Ratio (PR) has bn around sinc th arly days of frquncy

More information

Continuity Cloud Virtual Firewall Guide

Continuity 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 HYPER-V/VIRTUALBOX CONTINUITY

More information

Intermediate Macroeconomic Theory / Macroeconomic Analysis (ECON 3560/5040) Final Exam (Answers)

Intermediate 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 information

Section 5.0A Factoring Part 1

Section 5.0A Factoring Part 1 Section 5.0A Factoring Part 1 I. Work Together A. Multiply the following binomials into trinomials. (Write the final result in descending order, i.e., a + b + c ). ( 7)( + 5) ( + 7)( + ) ( + 7)( + 5) (

More information

The price of liquidity in constant leverage strategies. Marcos Escobar, Andreas Kiechle, Luis Seco and Rudi Zagst

The price of liquidity in constant leverage strategies. Marcos Escobar, Andreas Kiechle, Luis Seco and Rudi Zagst RACSAM Rv. R. Acad. Cin. Sri A. Mat. VO. 103 2, 2009, pp. 373 385 Matmática Aplicada / Applid Mathmatics Th pric of liquidity in constant lvrag stratgis Marcos Escobar, Andras Kichl, uis Sco and Rudi Zagst

More information

Entity-Relationship Model

Entity-Relationship Model Entity-Rlationship Modl Kuang-hua 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 information

Remember 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

Remember 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 information

Saving Through Trailer Tracking

Saving 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 information

Why An Event App... Before You Start... Try A Few Apps... Event Management Features... Generate Revenue... Vendors & Questions to Ask...

Why An Event App... Before You Start... Try A Few Apps... Event Management Features... Generate Revenue... Vendors & Questions to Ask... Mo b i l E v ntap pgui d : Ho wt op ur c ha t hb te v ntap p f o ry o ura o c i a t i o n T he nt i a l Gui d t oe v ntap p E v nt nt i a l b y Tabl of Contnt Why An Evnt App......... o Whr to Start With

More information

An Adaptive Clustering MAP Algorithm to Filter Speckle in Multilook SAR Images

An Adaptive Clustering MAP Algorithm to Filter Speckle in Multilook SAR Images An Adaptiv Clustring MAP Algorithm to Filtr Spckl in Multilook SAR Imags FÁTIMA N. S. MEDEIROS 1,3 NELSON D. A. MASCARENHAS LUCIANO DA F. COSTA 1 1 Cybrntic Vision Group IFSC -Univrsity of São Paulo Caia

More information

Logo Design/Development 1-on-1

Logo Design/Development 1-on-1 Logo Dsign/Dvlopmnt 1-on-1 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 information

Chapter 2: Privatization, Diffusion of Share Ownership, and Politics

Chapter 2: Privatization, Diffusion of Share Ownership, and Politics Chiara ratton-lavoi Chaptr Chaptr : rivatization Diusion o har wnrship an olitics. Introuction inc th 980s many national govrnmnts hav pursu privatization programs. Although th wor "privatization" ncompasss

More information

Journal of Engineering and Natural Sciences Mühendislik ve Fen Bilimleri Dergisi

Journal of Engineering and Natural Sciences Mühendislik ve Fen Bilimleri Dergisi Journal of Enginring and Natural Scincs Mühndisli v Fn Bilimlri Drgisi Sigma 4/ Invitd Rviw Par OPTIMAL DESIGN OF NONLINEAR MAGNETIC SYSTEMS USING FINITE ELEMENTS Lvnt OVACIK * Istanbul Tchnical Univrsity,

More information

The fitness value of information

The fitness value of information Oikos 119: 219230, 2010 doi: 10.1111/j.1600-0706.2009.17781.x, # 2009 Th Authors. Journal compilation # 2009 Oikos Subjct Editor: Knnth Schmidt. Accptd 1 Sptmbr 2009 Th fitnss valu of information Matina

More information

Five 5. Rational Expressions and Equations C H A P T E R

Five 5. Rational Expressions and Equations C H A P T E R Five C H A P T E R Rational Epressions and Equations. Rational Epressions and Functions. Multiplication and Division of Rational Epressions. Addition and Subtraction of Rational Epressions.4 Comple Fractions.

More information

IMES DISCUSSION PAPER SERIES

IMES DISCUSSION PAPER SERIES IMES DISCUSSIN PAPER SERIES Th Choic of Invoic Currncy in Intrnational Trad: Implications for th Intrnationalization of th Yn Hiroyuki I, Akira TANI, and Toyoichirou SHIRTA Discussion Papr No. 003-E-13

More information

Defining Retirement Success for Defined Contribution Plan Sponsors: Begin with the End in Mind

Defining Retirement Success for Defined Contribution Plan Sponsors: Begin with the End in Mind Dfining Rtirmnt Succss for Dfind Contribution Plan Sponsors: Bgin with th End in Mind David Blanchtt, CFA, CFP, AIFA Had of Rtirmnt Rsarch Morningstar Invstmnt Managmnt david.blanchtt@morningstar.com Nathan

More information

IOWA End-of-Course Assessment Programs. Released Items ALGEBRA I. Copyright 2010 by The University of Iowa.

IOWA End-of-Course Assessment Programs. Released Items ALGEBRA I. Copyright 2010 by The University of Iowa. IOWA End-of-Course Assessment Programs Released Items Copyright 2010 by The University of Iowa. ALGEBRA I 1 Sally works as a car salesperson and earns a monthly salary of $2,000. She also earns $500 for

More information

SPREAD OPTION VALUATION AND THE FAST FOURIER TRANSFORM

SPREAD OPTION VALUATION AND THE FAST FOURIER TRANSFORM RESEARCH PAPERS IN MANAGEMENT STUDIES SPREAD OPTION VALUATION AND THE FAST FOURIER TRANSFORM M.A.H. Dmpstr & S.S.G. Hong WP 26/2000 Th Judg Institut of Managmnt Trumpington Strt Cambridg CB2 1AG Ths paprs

More information

Ethanolic Extraction of Soybean Oil: Oil Solubility Equilibria and Kinetic Studies

Ethanolic Extraction of Soybean Oil: Oil Solubility Equilibria and Kinetic Studies Ethanolic Extraction of Soyban Oil: Oil Solubility Equilibria and Kintic Studis Christiann E. C. Rodrigus*, Natália M. Longo, Cibl C. Silva, Kila K.. Aracava, Bruna R. Garavazo Sparation Enginring Laboratory

More information

Combinatorial Analysis of Network Security

Combinatorial Analysis of Network Security Combinatorial Analysis of Ntwork Scurity Stvn Nol a, Brian O Brry a, Charls Hutchinson a, Sushil Jajodia a, Lynn Kuthan b, and Andy Nguyn b a Gorg Mason Univrsity Cntr for Scur Information Systms b Dfns

More information

Methods for quantitative relaxation parameter mapping: measuring T 1 and T 2

Methods for quantitative relaxation parameter mapping: measuring T 1 and T 2 thods for quantitativ rlaxation paramtr mapping: masuring T and T 2 ISR April 8 th 29 Hawaii Paul S Tofts Chair in Imaging Physics, Brighton and Sussx dical School, BN 9PX, UK : p.s.tofts@bsms.ac.uk w:

More information

Establishing Wireless Conference Calls Under Delay Constraints

Establishing Wireless Conference Calls Under Delay Constraints Establishing Wirlss Confrnc Calls Undr Dlay Constraints Aotz Bar-Noy aotz@sci.brooklyn.cuny.du Grzgorz Malwicz grg@cs.ua.du Novbr 17, 2003 Abstract A prvailing fatur of obil tlphony systs is that th cll

More information

1.3 Polynomials and Factoring

1.3 Polynomials and Factoring 1.3 Polynomials and Factoring Polynomials Constant: a number, such as 5 or 27 Variable: a letter or symbol that represents a value. Term: a constant, variable, or the product or a constant and variable.

More information

Many quantities are transduced in a displacement and then in an electric signal (pressure, temperature, acceleration). Prof. B.

Many 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 information

An Broad outline of Redundant Array of Inexpensive Disks Shaifali Shrivastava 1 Department of Computer Science and Engineering AITR, Indore

An Broad outline of Redundant Array of Inexpensive Disks Shaifali Shrivastava 1 Department of Computer Science and Engineering AITR, Indore Intrnational Journal of mrging Tchnology and dvancd nginring Wbsit: www.ijta.com (ISSN 2250-2459, Volum 2, Issu 4, pril 2012) n road outlin of Rdundant rray of Inxpnsiv isks Shaifali Shrivastava 1 partmnt

More information

1754 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 6, NO. 5, MAY 2007

1754 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 6, NO. 5, MAY 2007 1754 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 6, NO. 5, MAY 007 On th Fasibility of Distributd Bamforming in Wirlss Ntworks R. Mudumbai, Studnt Mmbr, IEEE, G. Barriac, Mmbr, IEEE, and U. Madhow,

More information

Online Price Competition within and between Heterogeneous Retailer Groups

Online Price Competition within and between Heterogeneous Retailer Groups Onlin Pric Comptition within and btwn Htrognous Rtailr Groups Cnk Kocas Dpartmnt of Markting and Supply Chain Managmnt, Michigan Stat Univrsity kocas@msu.du Abstract This study prsnts a modl of pric comptition

More information

Factoring Quadratic Trinomials

Factoring Quadratic Trinomials Factoring Quadratic Trinomials Student Probe Factor x x 3 10. Answer: x 5 x Lesson Description This lesson uses the area model of multiplication to factor quadratic trinomials. Part 1 of the lesson consists

More information

Usability Test of UCRS e-learning DVD

Usability Test of UCRS e-learning DVD Usability Tst of UCRS -Larning DVD Dcmbr 2006 Writtn by Thrsa Wilkinson Excutiv Summary Usability Tst of th UCRS -Larning DVD, Dcmbr 2006 This rport documnts th findings of a usability tst of th UCRS -Larning

More information

Sharp bounds for Sándor mean in terms of arithmetic, geometric and harmonic means

Sharp bounds for Sándor mean in terms of arithmetic, geometric and harmonic means Qian t al. Journal of Inqualitis and Applications (015) 015:1 DOI 10.1186/s1660-015-0741-1 R E S E A R C H Opn Accss Sharp bounds for Sándor man in trms of arithmtic, gomtric and harmonic mans Wi-Mao Qian

More information

Factoring Quadratic Expressions

Factoring Quadratic Expressions Factoring the trinomial ax 2 + bx + c when a = 1 A trinomial in the form x 2 + bx + c can be factored to equal (x + m)(x + n) when the product of m x n equals c and the sum of m + n equals b. (Note: the

More information

Factoring Quadratic Trinomials

Factoring Quadratic Trinomials Factoring Quadratic Trinomials Student Probe Factor Answer: Lesson Description This lesson uses the area model of multiplication to factor quadratic trinomials Part 1 of the lesson consists of circle puzzles

More information

ALGEBRA 2: 4.1 Graph Quadratic Functions in Standard Form

ALGEBRA 2: 4.1 Graph Quadratic Functions in Standard Form ALGEBRA 2: 4.1 Graph Quadratic Functions in Standard Form Goal Graph quadratic functions. VOCABULARY Quadratic function A function that can be written in the standard form y = ax 2 + bx+ c where a 0 Parabola

More information

Who uses our services? We have a growing customer base. with institutions all around the globe.

Who 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 information

Algebra 1 If you are okay with that placement then you have no further action to take Algebra 1 Portion of the Math Placement Test

Algebra 1 If you are okay with that placement then you have no further action to take Algebra 1 Portion of the Math Placement Test Dear Parents, Based on the results of the High School Placement Test (HSPT), your child should forecast to take Algebra 1 this fall. If you are okay with that placement then you have no further action

More information

International Association of Scientific Innovation and Research (IASIR) (An Association Unifying the Sciences, Engineering, and Applied Research)

International Association of Scientific Innovation and Research (IASIR) (An Association Unifying the Sciences, Engineering, and Applied Research) Intrnational Association of Scintific Innovation and Rsarch (IASIR) (An Association Unifing th Scincs, Enginring, and Applid Rsarch) ISSN (Print): 79-000 ISSN (Onlin): 79-009 Intrnational Journal of Enginring,

More information

ITIL & Service Predictability/Modeling. 2006 Plexent

ITIL & Service Predictability/Modeling. 2006 Plexent ITIL & Srvic Prdictability/Modling 1 2 Plxnt Th Company 2001 Foundd Plxnt basd on an Expandd ITIL Architctur, CMMI, ISO, and BS15000 - itdna 2003 Launchd itdna Srvic Offring 2003 John Groom, past Dirctor

More information

Probabilistic maintenance and asset management on moveable storm surge barriers

Probabilistic maintenance and asset management on moveable storm surge barriers Probabilistic maintnanc an asst managmnt on movabl storm surg barrirs Patrick Wbbrs Ministry of Transport, Public Works an Watr Managmnt Civil Enginring Division A n a l y s O n r h o u F a a l k a n s

More information

FEASIBILITY STUDY OF JUST IN TIME INVENTORY MANAGEMENT ON CONSTRUCTION PROJECT

FEASIBILITY STUDY OF JUST IN TIME INVENTORY MANAGEMENT ON CONSTRUCTION PROJECT FEASIBILITY STUDY OF JUST IN TIME INVENTORY MANAGEMENT ON CONSTRUCTION PROJECT Patil Yogndra R. 1, Patil Dhananjay S. 2 1P.G.Scholar, Dpartmnt of Civil Enginring, Rajarambapu Institut of Tchnology, Islampur,

More information

Review of Intermediate Algebra Content

Review of Intermediate Algebra Content Review of Intermediate Algebra Content Table of Contents Page Factoring GCF and Trinomials of the Form + b + c... Factoring Trinomials of the Form a + b + c... Factoring Perfect Square Trinomials... 6

More information

A.3. Polynomials and Factoring. Polynomials. What you should learn. Definition of a Polynomial in x. Why you should learn it

A.3. Polynomials and Factoring. Polynomials. What you should learn. Definition of a Polynomial in x. Why you should learn it Appendi A.3 Polynomials and Factoring A23 A.3 Polynomials and Factoring What you should learn Write polynomials in standard form. Add,subtract,and multiply polynomials. Use special products to multiply

More information

Dehumidifiers: A Major Consumer of Residential Electricity

Dehumidifiers: A Major Consumer of Residential Electricity Dhumidifirs: A Major Consumr of Rsidntial Elctricity Laurn Mattison and Dav Korn, Th Cadmus Group, Inc. ABSTRACT An stimatd 19% of U.S. homs hav dhumidifirs, and thy can account for a substantial portion

More information

Factoring Polynomials

Factoring Polynomials UNIT 11 Factoring Polynomials You can use polynomials to describe framing for art. 396 Unit 11 factoring polynomials A polynomial is an expression that has variables that represent numbers. A number can

More information

Polynomial Degree and Finite Differences

Polynomial Degree and Finite Differences CONDENSED LESSON 7.1 Polynomial Degree and Finite Differences In this lesson you will learn the terminology associated with polynomials use the finite differences method to determine the degree of a polynomial

More information

Asset set Liability Management for

Asset set Liability Management for KSD -larning and rfrnc products for th global financ profssional Highlights Library of 29 Courss Availabl Products Upcoming Products Rply Form Asst st Liability Managmnt for Insuranc Companis A comprhnsiv

More information

CHAPTER 7: FACTORING POLYNOMIALS

CHAPTER 7: FACTORING POLYNOMIALS CHAPTER 7: FACTORING POLYNOMIALS FACTOR (noun) An of two or more quantities which form a product when multiplied together. 1 can be rewritten as 3*, where 3 and are FACTORS of 1. FACTOR (verb) - To factor

More information

An International Journal of the Polish Statistical Association

An International Journal of the Polish Statistical Association STATISTICS IN TRANSITION nw sris An Intrnational Journal of th Polish Statistical Association CONTENTS From th Editor... Submission information for authors... 5 Sampling mthods and stimation CIEPIELA P.,

More information

HERO OPTIMAL PREVENTION WHEN INFORMAL PENALTIES MATTER: UNIVERSITY OF OSLO HEALTH ECONOMICS RESEARCH PROGRAMME Working paper 2007: 5

HERO OPTIMAL PREVENTION WHEN INFORMAL PENALTIES MATTER: UNIVERSITY OF OSLO HEALTH ECONOMICS RESEARCH PROGRAMME Working paper 2007: 5 OPTIMAL PREVENTION WHEN INFORMAL PENALTIES MATTER: THE CASE OF MEDICAL ERRORS Svrr Grpprud Institut of Halth Managmnt and Halth Economics, Univrsity of Oslo and Norwgian Univrsity of Lif Scincs, Aas, Norway

More information

Use a high-level conceptual data model (ER Model). Identify objects of interest (entities) and relationships between these objects

Use a high-level 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 high-lvl concptual data modl (ER Modl). Idntify objcts of intrst (ntitis) and rlationships btwn ths objcts Idntify constraints (conditions) End

More information

Fredy Vélez. Centro Tecnológico CARTIF, Valladolid, España. frevel@cartif.es

Fredy Vélez. Centro Tecnológico CARTIF, Valladolid, España. frevel@cartif.es Slcting working fluids in an organic Rankin cycl for powr gnration from low tmpratur hat sourcs Frdy Vélz Cntro Tcnológico CARTIF, Valladolid, España. frvl@cartif.s Rcivd: January 21th, d 2014. Rcivd in

More information

Planning and Managing Copper Cable Maintenance through Cost- Benefit Modeling

Planning 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, Cost-bnfit Analysis, Rliability

More information

Authenticated Encryption. Jeremy, Paul, Ken, and Mike

Authenticated Encryption. Jeremy, Paul, Ken, and Mike uthntcatd Encrypton Jrmy Paul Kn and M Objctvs Examn thr mthods of authntcatd ncrypton and dtrmn th bst soluton consdrng prformanc and scurty Basc Componnts Mssag uthntcaton Cod + Symmtrc Encrypton Both

More information

On the moments of the aggregate discounted claims with dependence introduced by a FGM copula

On the moments of the aggregate discounted claims with dependence introduced by a FGM copula On th momnts of th aggrgat discountd claims with dpndnc introducd by a FGM copula - Mathiu BARGES Univrsité Lyon, Laboratoir SAF, Univrsité Laval - Hélèn COSSETTE Ecol Actuariat, Univrsité Laval, Québc,

More information