STATICS. CENTROIDS OF MASSES, AREAS, LENGTHS, AND VOLUMES The following formulas are for discrete masses, areas, lengths, and volumes: r c

148 CIVIL ENGINEERING

STRUTUR NYSS fluee es fo Bems d Tusses fluee le sows te vto of effet (eto, se d momet ems, foe tuss) used movg ut lod oss te stutue. fluee le s used to deteme te posto of movele set of lods tt uses te

Baltimore County ARML Team Formula Sheet, v2.1 (08 Apr 2008) By Raymond Cheong. Difference of squares Difference of cubes Sum of cubes.

Bltimoe Couty ARML Tem Fomul Seet, v. (08 Ap 008) By Rymo Ceog POLYNOMIALS Ftoig Diffeee of sques Diffeee of ues Sum of ues Ay itege O iteges ( )( ) 3 3 ( )( ) 3 3 ( )( ) ( )(... ) ( )(... ) Biomil expsio

The formulae in this booklet have been arranged according to the unit in which they are first

Fomule Booklet Fomule Booklet The fomule ths ooklet hve ee ge og to the ut whh the e fst toue. Thus te sttg ut m e eque to use the fomule tht wee toue peeg ut e.g. tes sttg C mght e epete to use fomule

Properties and Formulas

Popeties nd Fomuls Cpte 1 Ode of Opetions 1. Pefom ny opetion(s) inside gouping symols. 2. Simplify powes. 3. Multiply nd divide in ode fom left to igt. 4. Add nd sutt in ode fom left to igt. Identity

MECHANICS OF MATERIALS

MEHNS OF MTERS UNX STRESS-STRN Stess-Sti ue fo Mild Steel Te slope of te lie potio of te ue equls te modulus of elstiit. DEFNTONS Egieeig Sti ε / o, wee ε egieeig sti (uits pe uit) STRESS, S ge i legt

Area. Ⅱ Rectangles. Ⅲ Parallelograms A. Ⅳ Triangles. ABCD=a 2 The area of a square of side a is a 2

Ⅰ Sques e Letue: iu ng Mtemtis dution oundtion Pesident Wen-Hsien SUN Ⅱ Retngles = Te e of sque of side is Ⅲ Pllelogms = Te e of etngle of sides nd is = Te e of pllelogm is te podut of te lengt of one

ALGEBRA. ( ) is a point on the line ( ) + ( ) = + ( ) + + ) + ( Distance Formula The distance d between two points x, y

ALGEBRA Popeties of Asoute Vue Fo e umes : 0, 0 + + Tige Iequity Popeties of Itege Epoets Ris Assume tt m e positive iteges, tt e oegtive, tt eomitos e ozeo. See Appeies B D fo gps fute isussio. + ( )

Advanced Higher Maths: Formulae

: Fomule Gee (G): Fomule you bsolutely must memoise i ode to pss Advced Highe mths. Remembe you get o fomul sheet t ll i the em! Ambe (A): You do t hve to memoise these fomule, s it is possible to deive

Advanced Higher Maths: Formulae

Advced Highe Mths: Fomule Advced Highe Mthemtics Gee (G): Fomule you solutely must memoise i ode to pss Advced Highe mths. Rememe you get o fomul sheet t ll i the em! Ame (A): You do t hve to memoise these

Chapter 6 Perturbation theory

Ct 6 Ptutio to 6. Ti-iddt odgt tutio to i o tutio sst is giv to fid solutios of λ ' ; : iltoi of si stt : igvlus of : otool igfutios of ; δ ii Rlig-Södig tutio to ' λ..6. ; : gl iltoi ': tutio λ : sll

EXPONENTS AND LOGARITHMS

978--07-6- Mthemtis Stdrd Level for IB Diplom Eerpt EXPONENTS AND LOGARITHMS WHAT YOU NEED TO KNOW The rules of epoets: m = m+ m = m ( m ) = m m m = = () = The reltioship etwee epoets d rithms: = g where

10.3 The Quadratic Formula

. Te Qudti Fomul We mentioned in te lst setion tt ompleting te sque n e used to solve ny qudti eqution. So we n use it to solve 0. We poeed s follows 0 0 Te lst line of tis we ll te qudti fomul. Te Qudti

SULIT 3472/2. Rumus-rumus berikut boleh membantu anda menjawab soalan. Simbol-simbol yang diberi adalah yang biasa digunakan.

SULT 347/ Rumus-umus eikut oleh memtu d mejw sol. Simol-simol yg diei dlh yg is diguk. LGER. 4c x 5. log m log m log 9. T d. m m m 6. log = log m log 0. S d m m 3. 7. log m log m. S, m m logc 4. 8. log.

BINOMIAL THEOREM SOLUTION. 1. (D) n. = (C 0 + C 1 x +C 2 x C n x n ) (1+ x+ x 2 +.)

BINOMIAL THEOREM SOLUTION. (D) ( + + +... + ) (+ + +.) The coefficiet of + + + +... + fo. Moeove coefficiet of is + + + +... + if >. So. (B)... e!!!! The equied coefficiet coefficiet of i e -.!...!. (A),

PhysicsAndMathsTutor.com

PhysicsAMthsTuto.com . M 6 0 7 0 Leve lk 6 () Show tht 7 is eigevlue of the mti M fi the othe two eigevlues of M. (5) () Fi eigevecto coespoig to the eigevlue 7. *M545A068* (4) Questio cotiue Leve lk *M545A078*

1. Viscosities: μ = ρν. 2. Newton s viscosity law: 3. Infinitesimal surface force df. 4. Moment about the point o, dm

3- Fluid Mecnics Clss Emple 3: Newton s Viscosit Lw nd Se Stess 3- Fluid Mecnics Clss Emple 3: Newton s Viscosit Lw nd Se Stess Motition Gien elocit field o ppoimted elocit field, we wnt to be ble to estimte

GEOMETRY. Rectangle Circle Triangle Parallelogram Trapezoid. 1 A = lh A= h b+ Rectangular Prism Sphere Rectangular Pyramid.

ALGEBA Popeties of Asote Ve Fo e mes :, + + Tige Ieqit Popeties of Itege Epoets is Assme tt m e positive iteges, tt e oegtive, tt eomitos e ozeo. See Appeies B D fo gps fte isssio. + ( ) m m m m m m m

SPH3UW Unit 7.5 Snell s Law Page 1 of Total Internal Reflection occurs when the incoming refraction angle is

SPH3UW Uit 7.5 Sell s Lw Pge 1 of 7 Notes Physis Tool ox Refrtio is the hge i diretio of wve due to hge i its speed. This is most ommoly see whe wve psses from oe medium to other. Idex of refrtio lso lled

The Area of a Triangle

The e of Tingle tkhlid June 1, 015 1 Intodution In this tile we will e disussing the vious methods used fo detemining the e of tingle. Let [X] denote the e of X. Using se nd Height To stt off, the simplest

Raytracing: Intersections. Backward Tracing. Basic Ray Casting Method. Basic Ray Casting Method. Basic Ray Casting Method. Basic Ray Casting Method

Rtig: Itesetios Bkwd Tig COC 4328/5327 ott A. Kig Bsi R Cstig iels i see hoot fom the ee though the iel. Fid losest -ojet itesetio. Get olo t itesetio Bsi R Cstig iels i see hoot fom the ee though the

Properties of Addition and Multiplication. For Addition Name of Property For Multiplication

Nottio d Sols Tpes of Nues Ntul Nues (Coutig Nues): N = {,, 3, 4, 5, 6,...} Wole Nues: W = { 0,,, 3, 4, 5, 6,...} Iteges: Z = {..., 4, 3,,, 0,,, 3, 4,...} Rtiol Nues: tiol ue is ue tt e witte i te fo of

1. The 0.1 kg particle has a speed v = 10 m/s as it passes the 30 position shown. The coefficient of kinetic friction between the particle and the

1. The 0.1 kg pticle h peed v = 10 m/ it pe the 30 poitio how. The coefficiet of kietic fictio betwee the pticle d the veticl ple tck i m k = 0.0. Detemie the mgitude of the totl foce exeted by the tck

PhysicsAndMathsTutor.com

PhsicsAMthsTuto.com 6. The hpeol H hs equtio, whee e costts. The lie L hs equtio m c, whee m c e costts. Leve lk () Give tht L H meet, show tht the -cooites of the poits of itesectio e the oots of the

GEOMETRY Properties of lines

www.sscexmtuto.com GEOMETRY Popeties of lines Intesecting Lines nd ngles If two lines intesect t point, ten opposite ngles e clled veticl ngles nd tey ve te sme mesue. Pependicul Lines n ngle tt mesues

Plane Kinetics of Rigid Bodies 동역학 및 응용

Ple Kietics of igid odies 동역학 및 응용 EQUTONS O PLNE OTON esultt of the pplied etel foces : esultt foce (pss though ss cete) + ouple oets of the etel foces gul otio z ouple : sste of foces with esultt oet

Addendum. Addendum. Vector Review. Department of Computer Science and Engineering 1-1

Addedum Addedum Vetor Review Deprtmet of Computer Siee d Egieerig - Coordite Systems Right hded oordite system Addedum y z Deprtmet of Computer Siee d Egieerig - -3 Deprtmet of Computer Siee d Egieerig

G8-11 Congruence Rules

G8-11 ogruee Rules If two polgos re ogruet, ou ple the oe o top of the other so tht the th etl. The verties tht th re lled orrespodig verties. The gles tht th re lled orrespodig gles. The sides tht th

MAHESH TUTORIALS SUBJECT : Maths(012) First Preliminary Exam Model Answer Paper

SET - GSE tch : 0th Std. Eg. Medium MHESH TUTILS SUJET : Mths(0) First Prelimiry Exm Model swer Pper PRT -.. () like does ot exist s biomil surd. () 4.. 6. 7. 8. 9. 0... 4 (c) touches () - d () -4 7 (c)

CH 19 SOLVING FORMULAS

1 CH 19 SOLVING FORMULAS INTRODUCTION S olvig equtios suh s 2 + 7 20 is oviousl the orerstoe of lger. But i siee, usiess, d omputers it is lso eessr to solve equtios tht might hve vriet of letters i them.

z line a) Draw the single phase equivalent circuit. b) Calculate I BC.

ECE 2260 F 08 HW 7 prob 4 solutio EX: V gyb' b' b B V gyc' c' c C = 101 0 V = 1 + j0.2 Ω V gyb' = 101 120 V = 6 + j0. Ω V gyc' = 101 +120 V z LΔ = 9 j1.5 Ω ) Drw the sigle phse equivlet circuit. b) Clculte

Section 11.5 Notes Page Partial Fraction Decomposition. . You will get: +. Therefore we come to the following: x x

Setio Notes Pge Prtil Frtio Deompositio Suppose we were sked to write the followig s sigle frtio: We would eed to get ommo deomitors: You will get: Distributig o top will give you: 8 This simplifies to:

Fig. 1. I a. V ag I c. I n. V cg. Z n Z Y. I b. V bg

ymmetricl Compoets equece impedces Although the followig focuses o lods, the results pply eqully well to lies, or lies d lods. Red these otes together with sectios.6 d.9 of text. Cosider the -coected lced

2002 Quarter 1 Math 172 Final Exam. Review

00 Qute Mth 7 Fil Exm. Review Sectio.. Sets Repesettio of Sets:. Listig the elemets. Set-uilde Nottio Checkig fo Memeship (, ) Compiso of Sets: Equlity (=, ), Susets (, ) Uio ( ) d Itesectio ( ) of Sets

Reference. Reference. Properties of Equality. Properties of Segment and Angle Congruence. Other Properties. Triangle Inequalities

Refeene opeties opeties of qulity ddition opety of qulity If =, ten + = +. Multiplition opety of qulity If =, ten =, 0. Reflexive opety of qulity = Tnsitive opety of qulity If = nd =, ten =. Suttion opety

Mathematical Induction (selected questions)

Mtheticl Iductio (selected questios). () Let P() e the propositio : For P(), L.H.S. R.H.S., P() is true. Assue P() is true for soe turl uer, tht is, () For P( ),, y () By the Priciple of Mtheticl Iductio,

PhysicsAndMathsTutor.com

PhysicsAdMthsTuto.com PhysicsAdMthsTuto.com Jue 009 7. () Sketch the gph of y, whee >, showig the coodites of the poits whee the gph meets the es. () Leve lk () Solve, >. (c) Fid the set of vlues of fo

AIEEE CBSE ENG A function f from the set of natural numbers to integers defined by

AIEEE CBSE ENG. A futio f from the set of turl umers to itegers defied y, whe is odd f (), whe is eve is (A) oe oe ut ot oto (B) oto ut ot oe oe (C) oe oe d oto oth (D) either oe oe or oto. Let z d z e

Thomas J. Osler Mathematics Department Rowan University Glassboro NJ Introduction

Ot 0 006 Euler s little summtio formul d speil vlues of te zet futio Toms J Osler temtis Deprtmet Row Uiversity Glssboro J 0608 Osler@rowedu Itrodutio I tis ote we preset elemetry metod of determiig vlues

Parametric Methods. Autoregressive (AR) Moving Average (MA) Autoregressive - Moving Average (ARMA) LO-2.5, P-13.3 to 13.4 (skip

Pmeti Methods Autoegessive AR) Movig Avege MA) Autoegessive - Movig Avege ARMA) LO-.5, P-3.3 to 3.4 si 3.4.3 3.4.5) / Time Seies Modes Time Seies DT Rdom Sig / Motivtio fo Time Seies Modes Re the esut

CH 20 SOLVING FORMULAS

CH 20 SOLVING FORMULAS 179 Itrodutio S olvig equtios suh s 2 + 7 20 is oviousl the orerstoe of lger. But i siee, usiess, d omputers it is lso eessr to solve equtios tht might hve vriet of letters i them.

Dynamics of Marine Biological Resources * * * REVIEW OF SOME MATHEMATICS * * *

Dmis o Mrie Biologil Resores A FUNCTION * * * REVIEW OF SOME MATHEMATICS * * * z () z g(,) A tio is rle or orml whih estlishes reltioshi etwee deedet vrile (z) d oe or more ideedet vriles (,) sh tht there

NATIONAL SENIOR CERTIFICATE NASIONALE SENIOR SERTIFIKAAT GRADE 12/GRAAD 12

NAIONAL ENIOR CERIFICAE NAIONALE ENIOR ERIFIKAA GRADE /GRAAD MAHEMAIC P/WIKUNDE V NOVEMBER 7 MARKING GUIDELINE/NAIENRIGLYNE MARK/PUNE: 5 is memodum cosists o pges. Hiedie memodum best uit bldsye. Copyigt

Generating Function for

Itetiol Joul of Ltest Tehology i Egieeig, Mgemet & Applied Siee (IJLTEMAS) Volume VI, Issue VIIIS, August 207 ISSN 2278-2540 Geetig Futio fo G spt D. K. Humeddy #, K. Jkmm * # Deptmet of Memtis, Hidu College,

ECE 102 Engineering Computation

ECE Egieerig Computtio Phillip Wog Mth Review Vetor Bsis Mtri Bsis System of Lier Equtios Summtio Symol is the symol for summtio. Emple: N k N... 9 k k k k k the, If e e e f e f k Vetor Bsis A vetor is

Auchmuty High School Mathematics Department Sequences & Series Notes Teacher Version

equeces ad eies Auchmuty High chool Mathematics Depatmet equeces & eies Notes Teache Vesio A sequece takes the fom,,7,0,, while 7 0 is a seies. Thee ae two types of sequece/seies aithmetic ad geometic.

SOLUTIONS ( ) ( )! ( ) ( ) ( ) ( )! ( ) ( ) ( ) ( ) n r. r ( Pascal s equation ). n 1. Stepanov Dalpiaz

STAT UIU Pctice Poblems # SOLUTIONS Stepov Dlpiz The followig e umbe of pctice poblems tht my be helpful fo completig the homewo, d will liely be vey useful fo studyig fo ems...-.-.- Pove (show) tht. (

STUDY PACKAGE. Subject : Mathematics Topic : DETERMINANTS & MATRICES Available Online :

o/u opkj Hkh# tu] ugh vkjehks dke] oi s[k NksM+s qj e/;e eu dj ';kea iq#"k lg ldyi dj] lgs oi vusd] ^uk^ u NksM+s /;s; dks] j?kqj jk[ks VsdAA jp% ekuo /kez iz.ksk l~q# Jh j.knksm+klth egkjkt STUDY PAKAGE

PLANCESS RANK ACCELERATOR

PLANCESS RANK ACCELERATOR MATHEMATICS FOR JEE MAIN & ADVANCED Sequeces d Seies 000questios with topic wise execises 000 polems of IIT-JEE & AIEEE exms of lst yes Levels of Execises ctegoized ito JEE Mi

The formulae in this booklet have been arranged according to the unit in which they are first

Fomule Booklet Fomule Booklet The fomule ths ooklet hve ee ge ccog to the ut whch the e fst touce. Thus cte sttg ut m e eque to use the fomule tht wee touce peceg ut e.g. ctes sttg C mght e epecte to use

MATHEMATICIA GENERALLI

MATHEMATICIA GENERALLI (y Mhmmed Abbs) Lgithmi Reltis lgb ) lg lg ) b b) lg lg lg m lg m d) lg m. lg m lg m e) lg lg m lg g) lg lg h) f) lg lg f ( ) f ( ). Eetil Reltis ). lge. lge.... lge...!! b) e......

Project 3: Using Identities to Rewrite Expressions

MAT 5 Projet 3: Usig Idetities to Rewrite Expressios Wldis I lger, equtios tht desrie properties or ptters re ofte lled idetities. Idetities desrie expressio e repled with equl or equivlet expressio tht

BITSAT MATHEMATICS PAPER. If log 0.0( ) log 0.( ) the elogs to the itervl (, ] () (, ] [,+ ). The poit of itersectio of the lie joiig the poits i j k d i+ j+ k with the ple through the poits i+ j k, i

CHAPTER 7 Applications of Integration

CHAPTER 7 Applitions of Integtion Setion 7. Ae of Region Between Two Cuves.......... Setion 7. Volume: The Disk Method................. Setion 7. Volume: The Shell Method................ Setion 7. A Length

1/16/2013. Overview. 05-Three Phase Analysis Text: Three Phase. Three-Phase Voltages. Benefits of Three-Phase Systems.

oltge () 1/16/21 Overview 5Three Phse Alysis Text: 2.4 2.7 ECEGR 451 Power Systems ThreePhse Soures Delt d Y Coetios ThreePhse Lods ThreePhse Power ThreePhse Alysis PerPhse Alysis Dr. Louie 2 ThreePhse

Chapter 21: Electric Charge and Electric Field

Chpte 1: Electic Chge nd Electic Field Electic Chge Ancient Gees ~ 600 BC Sttic electicit: electic chge vi fiction (see lso fig 1.1) (Attempted) pith bll demonsttion: inds of popeties objects with sme

Equations from the Millennium Theory of Inertia and Gravity. Copyright 2004 Joseph A. Rybczyk

Equtions fo the illenniu heoy of Ineti nd vity Copyight 004 Joseph A. Rybzyk ollowing is oplete list of ll of the equtions used o deived in the illenniu heoy of Ineti nd vity. o ese of efeene the equtions

334 MATHS SERIES DSE MATHS PREVIEW VERSION B SAMPLE TEST & FULL SOLUTION

MATHS SERIES DSE MATHS PREVIEW VERSION B SAMPLE TEST & FULL SOLUTION TEST SAMPLE TEST III - P APER Questio Distributio INSTRUCTIONS:. Attempt ALL questios.. Uless otherwise specified, ll worig must be

8.1 Arc Length. What is the length of a curve? How can we approximate it? We could do it following the pattern we ve used before

8.1 Arc Legth Wht is the legth of curve? How c we pproximte it? We could do it followig the ptter we ve used efore Use sequece of icresigly short segmets to pproximte the curve: As the segmets get smller

AP Calculus AB AP Review

AP Clulus AB Chpters. Re limit vlues from grphsleft-h Limits Right H Limits Uerst tht f() vlues eist ut tht the limit t oes ot hve to.. Be le to ietify lel isotiuities from grphs. Do t forget out the 3-step

PROGRESSION AND SERIES

INTRODUCTION PROGRESSION AND SERIES A gemet of umbes {,,,,, } ccodig to some well defied ule o set of ules is clled sequece Moe pecisely, we my defie sequece s fuctio whose domi is some subset of set of

x a y n + b = 1 0<b a, n > 0 (1.1) x 1 - a y = b 0<b a, n > 0 (1.1') b n sin 2 + cos 2 = 1 x n = = cos 2 6 Superellipse (Lamé curve)

6 Supeellipse (Lmé cuve) 6. Equtios of supeellipse A supeellipse (hoizotlly log) is epessed s follows. Implicit Equtio y + b 0 0 (.) Eplicit Equtio y b - 0 0 (.') Whe 3, b, the supeellipses fo

Static Surface Forces. Forces on Plane Areas: Horizontal surfaces. Forces on Plane Areas. Hydrostatic Forces on Plane Surfaces

Hdrostti ores on Plne Surfes Stti Surfe ores ores on lne res ores on urved surfes Buont fore Stbilit of floting nd submerged bodies ores on Plne res Two tes of roblems Horizontl surfes (ressure is ) onstnt

MATHEMATICS II PUC VECTOR ALGEBRA QUESTIONS & ANSWER

MATHEMATICS II PUC VECTOR ALGEBRA QUESTIONS & ANSWER I One M Queston Fnd the unt veto n the deton of Let ˆ ˆ 9 Let & If Ae the vetos & equl? But vetos e not equl sne the oespondng omponents e dstnt e detons

Chapter 23. Geometric Optics

Cpter 23 Geometric Optic Ligt Wt i ligt? Wve or prticle? ot Geometric optic: ligt trvel i trigt-lie pt clled ry Ti i true if typicl ditce re muc lrger t te wvelegt Geometric Optic 2 Wt it i out eome ddreed

One of the common descriptions of curvilinear motion uses path variables, which are measurements made along the tangent t and normal n to the path of

Oe of he commo descipios of cuilie moio uses ph ibles, which e mesuemes mde log he ge d oml o he ph of he picles. d e wo ohogol xes cosideed sepely fo eey is of moio. These coodies poide ul descipio fo

Two or more points can be used to describe a rigid body. This will eliminate the need to define rotational coordinates for the body!

OINTCOORDINATE FORMULATION Two or more poits ca be used to describe a rigid body. This will elimiate the eed to defie rotatioal coordiates for the body i z r i i, j r j j rimary oits: The coordiates of

Mathematical Reflections, Issue 5, INEQUALITIES ON RATIOS OF RADII OF TANGENT CIRCLES. Y.N. Aliyev

themtil efletions, Issue 5, 015 INEQULITIES ON TIOS OF DII OF TNGENT ILES YN liev stt Some inequlities involving tios of dii of intenll tngent iles whih inteset the given line in fied points e studied

ELECTROSTATICS. 4πε0. E dr. The electric field is along the direction where the potential decreases at the maximum rate. 5. Electric Potential Energy:

LCTROSTATICS. Quntiztion of Chge: Any chged body, big o smll, hs totl chge which is n integl multile of e, i.e. = ± ne, whee n is n intege hving vlues,, etc, e is the chge of electon which is eul to.6

PhysicsAndMathsTutor.com

PhysicsAdMthsTuto.com PhysicsAdMthsTuto.com Jue 009 3. Fid the geel solutio of the diffeetil equtio blk d si y ycos si si, d givig you swe i the fom y = f(). (8) 6 *M3544A068* PhysicsAdMthsTuto.com Jue

Definition Integral. over[ ab, ] the sum of the form. 2. Definite Integral

Defiite Itegrl Defiitio Itegrl. Riem Sum Let f e futio efie over the lose itervl with = < < < = e ritrr prtitio i suitervl. We lle the Riem Sum of the futio f over[, ] the sum of the form ( ξ ) S = f Δ

Homework: Study 6.2 #1, 3, 5, 7, 11, 15, 55, 57

Gols: 1. Undestnd volume s the sum of the es of n infinite nume of sufces. 2. Be le to identify: the ounded egion the efeence ectngle the sufce tht esults fom evolution of the ectngle ound n xis o foms

Easy Steps to build a part number... Tri-Start Series III CF P

ulti-l i Oti iul ( oto) ow to O ol os sy ts to uil t u... i-tt is 1. 2 3 4. 5. 6. oto y til iis ll tyl ll iz- st t ott y & y/ ywy ositio 50 9 0 17-08 ol ulti-l i oti otos o us wit ulti-o sil o tii o y

AP Calculus BC Formulas, Definitions, Concepts & Theorems to Know

P Clls BC Formls, Deiitios, Coepts & Theorems to Kow Deiitio o e : solte Vle: i 0 i 0 e lim Deiitio o Derivtive: h lim h0 h ltertive orm o De o Derivtive: lim Deiitio o Cotiity: is otios t i oly i lim

Semiconductors materials

Semicoductos mteils Elemetl: Goup IV, Si, Ge Biy compouds: III-V (GAs,GSb, ISb, IP,...) IV-VI (PbS, PbSe, PbTe,...) II-VI (CdSe, CdTe,...) Tey d Qutey compouds: G x Al -x As, G x Al -x As y P -y III IV

Assessment Center Elementary Algebra Study Guide for the ACCUPLACER (CPT)

Assessmet Ceter Elemetr Alger Stud Guide for the ACCUPLACER (CPT) The followig smple questios re similr to the formt d cotet of questios o the Accuplcer Elemetr Alger test. Reviewig these smples will give

ME260W Mid-Term Exam Instructor: Xinyu Huang Date: Mar

ME60W Mid-Term Exam Istrutor: Xiyu Huag Date: Mar-03-005 Name: Grade: /00 Problem. A atilever beam is to be used as a sale. The bedig momet M at the gage loatio is P*L ad the strais o the top ad the bottom

( ) 2 3 ( ) I. Order of operations II. Scientific Notation. Simplify. Write answers in scientific notation. III.

Assessmet Ceter Elemetry Alger Study Guide for the ACCUPLACER (CPT) The followig smple questios re similr to the formt d otet of questios o the Aupler Elemetry Alger test. Reviewig these smples will give

Appendix A Examples for Labs 1, 2, 3 1. FACTORING POLYNOMIALS

Appedi A Emples for Ls,,. FACTORING POLYNOMIALS Tere re m stdrd metods of fctorig tt ou ve lered i previous courses. You will uild o tese fctorig metods i our preclculus course to ele ou to fctor epressios

The evaluation of P, and T from these formulae indeed requires that the energy E be expressed as a function of the quantities N, V and S.

d dq, dq d d d, d d d d, e evlutio of, d from tese formule ideed requires tt te eerg be epressed s fuctio of te qutities, d. f (,,) is sould, i priciple, be possible oce is kow s fuctio of, d. f (,, )

A Dynamical Quasi-Boolean System

ULETNUL Uestăţ Petol Gze Ploeşt Vol LX No / - 9 Se Mtetă - otă - Fză l Qs-oole Sste Gel Mose Petole-Gs Uest o Ploest ots etet est 39 Ploest 68 o el: ose@-loesto stt Ths e oes the esto o ol theoetl oet:

We show that every analytic function can be expanded into a power series, called the Taylor series of the function.

10 Lectue 8 We show tht evey lytic fuctio c be expded ito powe seies, clled the Tylo seies of the fuctio. Tylo s Theoem: Let f be lytic i domi D & D. The, f(z) c be expessed s the powe seies f( z) b (

UNIT V: Z-TRANSFORMS AND DIFFERENCE EQUATIONS. Dr. V. Valliammal Department of Applied Mathematics Sri Venkateswara College of Engineering

UNIT V: -TRANSFORMS AND DIFFERENCE EQUATIONS D. V. Vllimml Deptmet of Applied Mthemtics Si Vektesw College of Egieeig TOPICS:. -Tsfoms Elemet popeties.. Ivese -Tsfom usig ptil fctios d esidues. Covolutio

M3P14 EXAMPLE SHEET 1 SOLUTIONS

M3P14 EXAMPLE SHEET 1 SOLUTIONS 1. Show tht for, b, d itegers, we hve (d, db) = d(, b). Sice (, b) divides both d b, d(, b) divides both d d db, d hece divides (d, db). O the other hd, there exist m d

2. Elementary Linear Algebra Problems

. Eleety e lge Pole. BS: B e lge Suoute (Pog pge wth PCK) Su of veto opoet:. Coputto y f- poe: () () () (3) N 3 4 5 3 6 4 7 8 Full y tee Depth te tep log()n Veto updte the f- poe wth N : ) ( ) ( ) ( )

MA 1201 Engineering Mathematics MO/2017 Tutorial Sheet No. 2

BIRLA INSTITUTE OF TECHNOLOGY, MESRA, RANCHI DEPARTMENT OF MATHEMATICS MA Egieeig Matheatis MO/7 Tutoia Sheet No. Modue IV:. Defie Beta futio ad Gaa futio.. Pove that,,,. Pove that, d. Pove that. & whee

Taylor Polynomials. The Tangent Line. (a, f (a)) and has the same slope as the curve y = f (x) at that point. It is the best

Tylor Polyomils Let f () = e d let p() = 1 + + 1 + 1 6 3 Without usig clcultor, evlute f (1) d p(1) Ok, I m still witig With little effort it is possible to evlute p(1) = 1 + 1 + 1 (144) + 6 1 (178) =

Dynamically Equivalent Systems. Dynamically Equivalent Systems. Dynamically Equivalent Systems. ME 201 Mechanics of Machines

ME 0 Mechnics of Mchines 8//006 Dynmicy Equivent Systems Ex: Connecting od G Dynmicy Equivent Systems. If the mss of the connecting od m G m m B m m m. Moment out cente of gvity shoud e zeo m G m B Theefoe;

HIGHER SCHOOL CERTIFICATE EXAMINATION MATHEMATICS 4 UNIT (ADDITIONAL) Time allowed Three hours (Plus 5 minutes reading time)

HIGHER SCHOOL CERTIFICATE EXAMINATION 998 MATHEMATICS 4 UNIT (ADDITIONAL) Time llowed Three hours (Plus 5 miutes redig time) DIRECTIONS TO CANDIDATES Attempt ALL questios ALL questios re of equl vlue All

Introduction to Matrix Algebra

Itrodutio to Mtri Alger George H Olso, Ph D Dotorl Progrm i Edutiol Ledership Applhi Stte Uiversit Septemer Wht is mtri? Dimesios d order of mtri A p q dimesioed mtri is p (rows) q (olums) rr of umers,

On the k-lucas Numbers of Arithmetic Indexes

Alied Mthetics 0 3 0-06 htt://d.doi.og/0.436/.0.307 Published Olie Octobe 0 (htt://www.scirp.og/oul/) O the -ucs Nubes of Aithetic Idees Segio lco Detet of Mthetics d Istitute fo Alied Micoelectoics (IUMA)

MATHEMATICS IV 2 MARKS. 5 2 = e 3, 4

MATHEMATICS IV MARKS. If + + 6 + c epesents cicle with dius 6, find the vlue of c. R 9 f c ; g, f 6 9 c 6 c c. Find the eccenticit of the hpeol Eqution of the hpeol Hee, nd + e + e 5 e 5 e. Find the distnce

Computer Aided Geometric Design

Copue Aided Geoei Design Geshon Ele, Tehnion sed on ook Cohen, Riesenfeld, & Ele Geshon Ele, Tehnion Definiion 3. The Cile Given poin C in plne nd nue R 0, he ile ih ene C nd dius R is defined s he se

Series III, TV Breakaway Fail-Safe Connectors Quick-Disconnect with an Axial Pull of Lanyard

is, wy il- otos Qui-isot wit xil ull o y ulo ss quo mol i-tt wy il- otos ovi uqul om i viomts quii istt ismt. wy il- oto mily os wi o ltil mil tus: stt ouli m stio omltly itmtl wit st tls (/20 /2) vtoy

Student Success Center Elementary Algebra Study Guide for the ACCUPLACER (CPT)

Studet Success Ceter Elemetry Algebr Study Guide for the ACCUPLACER (CPT) The followig smple questios re similr to the formt d cotet of questios o the Accuplcer Elemetry Algebr test. Reviewig these smples

STD: XI MATHEMATICS Total Marks: 90. I Choose the correct answer: ( 20 x 1 = 20 ) a) x = 1 b) x =2 c) x = 3 d) x = 0

STD: XI MATHEMATICS Totl Mks: 90 Time: ½ Hs I Choose the coect nswe: ( 0 = 0 ). The solution of is ) = b) = c) = d) = 0. Given tht the vlue of thid ode deteminnt is then the vlue of the deteminnt fomed

ENGINEERING MATHEMATICS I QUESTION BANK. Module Using the Leibnitz theorem find the nth derivative of the following : log. e x log d.

ENGINEERING MATHEMATICS I QUESTION BANK Modle Usig the Leibit theoem id the th deivtive o the ollowig : b si c e d e Show tht d d! Usig the Leibit theoem pove the ollowig : I si b the pove tht b I si show

AN ALGEBRAIC APPROACH TO M-BAND WAVELETS CONSTRUCTION

AN ALGEBRAIC APPROACH TO -BAN WAELETS CONSTRUCTION Toy L Qy S Pewe Ho Ntol Lotoy o e Peeto Pe Uety Be 8 P. R. C Att T e eet le o to ott - otool welet e. A yte of ott eto ote fo - otool flte te olto e o

[5 points] (c) Find the charge enclosed by the cylindrical surface of radius ρ 0 = 9 mm and length L = 1 m. [2

STUDENT NAME: STUDENT ID: ELEC ENG FH3: MIDTERM EXAMINATION QUESTION SHEET This emitio is TWO HOURS log. Oe double-sided cib sheet is llowed. You c use the McMste ppoved clculto Csio f99. You c tke y mteil

Lecture 2. Rational Exponents and Radicals. 36 y. b can be expressed using the. Rational Exponent, thus b. b can be expressed using the

Lecture. Rtiol Epoets d Rdicls Rtiol Epoets d Rdicls Lier Equtios d Iequlities i Oe Vrile Qudrtic Equtios Appedi A6 Nth Root - Defiitio Rtiol Epoets d Rdicls For turl umer, c e epressed usig the r is th

13.5. Torsion of a curve Tangential and Normal Components of Acceleration

13.5 osion of cuve ngentil nd oml Components of Acceletion Recll: Length of cuve '( t) Ac length function s( t) b t u du '( t) Ac length pmetiztion ( s) with '( s) 1 '( t) Unit tngent vecto '( t) Cuvtue: