Design Synthesis. specified positions called precision points zero error at precision points small error between points - optimization

KINEMATICS OF RIGID BODIES

KINEMTICS OF RIGID ODIES Introduction In rigid body kinemtics, e use the reltionships governing the displcement, velocity nd ccelertion, but must lso ccount for the rottionl motion of the body. Description

Miscellaneous Problems. pinned to the ground

Miscellneous Problems Problem. Use the mobilit formul to determine the number of degrees of freedom for this sstem. pinned to the ground pinned to the ground Problem. For this mechnism: () Define vectors

P 1 (x 1, y 1 ) is given by,.

MA00 Clculus nd Bsic Liner Alger I Chpter Coordinte Geometr nd Conic Sections Review In the rectngulr/crtesin coordintes sstem, we descrie the loction of points using coordintes. P (, ) P(, ) O The distnce

Simple Harmonic Motion I Sem

Simple Hrmonic Motion I Sem Sllus: Differentil eqution of liner SHM. Energ of prticle, potentil energ nd kinetic energ (derivtion), Composition of two rectngulr SHM s hving sme periods, Lissjous figures.

FORM FIVE ADDITIONAL MATHEMATIC NOTE. ar 3 = (1) ar 5 = = (2) (2) (1) a = T 8 = 81

FORM FIVE ADDITIONAL MATHEMATIC NOTE CHAPTER : PROGRESSION Arithmetic Progression T n = + (n ) d S n = n [ + (n )d] = n [ + Tn ] S = T = T = S S Emple : The th term of n A.P. is 86 nd the sum of the first

Mathematics. Area under Curve.

Mthemtics Are under Curve www.testprepkrt.com Tle of Content 1. Introduction.. Procedure of Curve Sketching. 3. Sketching of Some common Curves. 4. Are of Bounded Regions. 5. Sign convention for finding

Things to Memorize: A Partial List. January 27, 2017

Things to Memorize: A Prtil List Jnury 27, 2017 Chpter 2 Vectors - Bsic Fcts A vector hs mgnitude (lso clled size/length/norm) nd direction. It does not hve fixed position, so the sme vector cn e moved

CONIC SECTIONS. Chapter 11

CONIC SECTIONS Chpter. Overview.. Sections of cone Let l e fied verticl line nd m e nother line intersecting it t fied point V nd inclined to it t n ngle α (Fig..). Fig.. Suppose we rotte the line m round

H (2a, a) (u 2a) 2 (E) Show that u v 4a. Explain why this implies that u v 4a, with equality if and only u a if u v 2a.

Chpter Review 89 IGURE ol hord GH of the prol 4. G u v H (, ) (A) Use the distne formul to show tht u. (B) Show tht G nd H lie on the line m, where m ( )/( ). (C) Solve m for nd sustitute in 4, otining

The Islamic University of Gaza Faculty of Engineering Civil Engineering Department. Numerical Analysis ECIV Chapter 11

The Islmic University of Gz Fculty of Engineering Civil Engineering Deprtment Numericl Anlysis ECIV 6 Chpter Specil Mtrices nd Guss-Siedel Associte Prof Mzen Abultyef Civil Engineering Deprtment, The Islmic

NORMALS. a y a y. Therefore, the slope of the normal is. a y1. b x1. b x. a b. x y a b. x y

LOCUS 50 Section - 4 NORMALS Consider n ellipse. We need to find the eqution of the norml to this ellipse t given point P on it. In generl, we lso need to find wht condition must e stisfied if m c is to

8.6 The Hyperbola. and F 2. is a constant. P F 2. P =k The two fixed points, F 1. , are called the foci of the hyperbola. The line segments F 1

8. The Hperol Some ships nvigte using rdio nvigtion sstem clled LORAN, which is n cronm for LOng RAnge Nvigtion. A ship receives rdio signls from pirs of trnsmitting sttions tht send signls t the sme time.

ES.182A Topic 32 Notes Jeremy Orloff

ES.8A Topic 3 Notes Jerem Orloff 3 Polr coordintes nd double integrls 3. Polr Coordintes (, ) = (r cos(θ), r sin(θ)) r θ Stndrd,, r, θ tringle Polr coordintes re just stndrd trigonometric reltions. In

DYNAMICS. Kinematics of Rigid Bodies VECTOR MECHANICS FOR ENGINEERS: Tenth Edition CHAPTER

Tenth E CHTER 15 VECTOR MECHNICS FOR ENGINEERS: YNMICS Ferdinnd. eer E. Russell Johnston, Jr. hillip J. Cornwell Lecture Notes: rin. Self Cliforni olytechnic Stte Uniersity Kinemtics of Rigid odies 013

A curve which touches each member of a given family of curves is called envelope of that family.

ENVELOPE A curve which touches ech memer of given fmil of curves is clle enveloe of tht fmil. Proceure to fin enveloe for the given fmil of curves: Cse : Enveloe of one rmeter fmil of curves Let us consier

Some Methods in the Calculus of Variations

CHAPTER 6 Some Methods in the Clculus of Vritions 6-. If we use the vried function ( α, ) α sin( ) + () Then d α cos ( ) () d Thus, the totl length of the pth is d S + d d α cos ( ) + α cos ( ) d Setting

Here we consider the matrix transformation for a square matrix from a geometric point of view.

Section. he Mgnifiction Fctor In Section.5 we iscusse the mtri trnsformtion etermine mtri A. For n m n mtri A the function f(c) = Ac provies corresponence etween vectors in R n n R m. Here we consier the

FINALTERM EXAMINATION 9 (Session - ) Clculus & Anlyticl Geometry-I Question No: ( Mrs: ) - Plese choose one f ( x) x According to Power-Rule of differentition, if d [ x n ] n x n n x n n x + ( n ) x n+

Materials Analysis MATSCI 162/172 Laboratory Exercise No. 1 Crystal Structure Determination Pattern Indexing

Mterils Anlysis MATSCI 16/17 Lbortory Exercise No. 1 Crystl Structure Determintion Pttern Inexing Objectives: To inex the x-ry iffrction pttern, ientify the Brvis lttice, n clculte the precise lttice prmeters.

ME 141. Lecture 10: Kinetics of particles: Newton s 2 nd Law

ME 141 Engineering Mechnics Lecture 10: Kinetics of prticles: Newton s nd Lw Ahmd Shhedi Shkil Lecturer, Dept. of Mechnicl Engg, BUET E-mil: sshkil@me.buet.c.bd, shkil6791@gmil.com Website: techer.buet.c.bd/sshkil

Polynomials and Division Theory

Higher Checklist (Unit ) Higher Checklist (Unit ) Polynomils nd Division Theory Skill Achieved? Know tht polynomil (expression) is of the form: n x + n x n + n x n + + n x + x + 0 where the i R re the

Network Analysis and Synthesis. Chapter 5 Two port networks

Network Anlsis nd Snthesis hpter 5 Two port networks . ntroduction A one port network is completel specified when the voltge current reltionship t the terminls of the port is given. A generl two port on

( β ) touches the x-axis if = 1

Generl Certificte of Eduction (dv. Level) Emintion, ugust Comined Mthemtics I - Prt B Model nswers. () Let f k k, where k is rel constnt. i. Epress f in the form( ) Find the turning point of f without

Eigen Values and Eigen Vectors of a given matrix

Engineering Mthemtics 0 SUBJECT NAME SUBJECT CODE MATERIAL NAME MATERIAL CODE : Engineering Mthemtics I : 80/MA : Prolem Mteril : JM08AM00 (Scn the ove QR code for the direct downlod of this mteril) Nme

x ) dx dx x sec x over the interval (, ).

Curve on 6 For -, () Evlute the integrl, n (b) check your nswer by ifferentiting. ( ). ( ). ( ).. 6. sin cos 7. sec csccot 8. sec (sec tn ) 9. sin csc. Evlute the integrl sin by multiplying the numertor

Dynamics and control of mechanical systems. Content

Dynmics nd control of mechnicl systems Dte Dy 1 (01/08) Dy (03/08) Dy 3 (05/08) Dy 4 (07/08) Dy 5 (09/08) Dy 6 (11/08) Content Review of the bsics of mechnics. Kinemtics of rigid bodies plne motion of

Area Under the Torque vs. RPM Curve: Average Power

Are Uner the orque vs. RM Curve: Averge ower Wht is torque? Some Bsics Consier wrench on nut, the torque bout the nut is Force, F F θ r rf sinθ orque, If F is t right ngle to moment rm r then rf How oes

Lecture 8 Wrap-up Part1, Matlab

Lecture 8 Wrp-up Prt1, Mtlb Homework Polic Plese stple our homework (ou will lose 10% credit if not stpled or secured) Submit ll problems in order. This mens to plce ever item relting to problem 3 (our

sec x over the interval (, ). x ) dx dx x 14. Use a graphing utility to generate some representative integral curves of the function Curve on 5

Curve on Clcultor eperience Fin n ownlo (or type in) progrm on your clcultor tht will fin the re uner curve using given number of rectngles. Mke sure tht the progrm fins LRAM, RRAM, n MRAM. (You nee to

KINEMATICS OF RIGID BODIES

KINEMTICS OF RIGI OIES Introduction In rigid body kinemtics, e use the reltionships governing the displcement, velocity nd ccelertion, but must lso ccount for the rottionl motion of the body. escription

Review: Velocity: v( t) r '( t) speed = v( t) Initial speed v, initial height h, launching angle : 1 Projectile motion: r( ) j v r

13.3 Arc Length Review: curve in spce: r t f t i g t j h t k Tngent vector: r '( t ) f ' t i g ' t j h' t k Tngent line t t t : s r( t ) sr '( t ) Velocity: v( t) r '( t) speed = v( t) Accelertion ( t)

Calculus AB. For a function f(x), the derivative would be f '(

lculus AB Derivtive Formuls Derivtive Nottion: For function f(), the derivtive would e f '( ) Leiniz's Nottion: For the derivtive of y in terms of, we write d For the second derivtive using Leiniz's Nottion:

Equations of Motion. Figure 1.1.1: a differential element under the action of surface and body forces

Equtions of Motion In Prt I, lnce of forces nd moments cting on n component ws enforced in order to ensure tht the component ws in equilirium. Here, llownce is mde for stresses which vr continuousl throughout

MCH T 111 Handout Triangle Review Page 1 of 3

Hnout Tringle Review Pge of 3 In the stuy of sttis, it is importnt tht you e le to solve lgeri equtions n tringle prolems using trigonometry. The following is review of trigonometry sis. Right Tringle:

Chapter 6 Techniques of Integration

MA Techniques of Integrtion Asst.Prof.Dr.Suprnee Liswdi Chpter 6 Techniques of Integrtion Recll: Some importnt integrls tht we hve lernt so fr. Tle of Integrls n+ n d = + C n + e d = e + C ( n ) d = ln

PROPERTIES OF AREAS In general, and for an irregular shape, the definition of the centroid at position ( x, y) is given by

PROPERTES OF RES Centroid The concept of the centroid is prol lred fmilir to ou For plne shpe with n ovious geometric centre, (rectngle, circle) the centroid is t the centre f n re hs n is of smmetr, the

Thomas Whitham Sixth Form

Thoms Whithm Sith Form Pure Mthemtics Unit C Alger Trigonometry Geometry Clculus Vectors Trigonometry Compound ngle formule sin sin cos cos Pge A B sin Acos B cos Asin B A B sin Acos B cos Asin B A B cos

Homework Assignment 6 Solution Set

Homework Assignment 6 Solution Set PHYCS 440 Mrch, 004 Prolem (Griffiths 4.6 One wy to find the energy is to find the E nd D fields everywhere nd then integrte the energy density for those fields. We know

SECTION A STUDENT MATERIAL. Part 1. What and Why.?

SECTION A STUDENT MATERIAL Prt Wht nd Wh.? Student Mteril Prt Prolem n > 0 n > 0 Is the onverse true? Prolem If n is even then n is even. If n is even then n is even. Wht nd Wh? Eploring Pure Mths Are

Set 6 Paper 2. Set 6 Paper 2. 1 Pearson Education Asia Limited 2017

Set 6 Pper Set 6 Pper. C. C. A. D. B 6. D 7. D 8. A 9. D 0. A. B. B. A. B. B 6. B 7. D 8. C 9. D 0. D. A. A. B. B. C 6. C 7. A 8. B 9. A 0. A. C. D. B. B. B 6. A 7. D 8. A 9. C 0. C. C. D. C. C. D Section

CBSE-XII-2015 EXAMINATION. Section A. 1. Find the sum of the order and the degree of the following differential equation : = 0

CBSE-XII- EXMINTION MTHEMTICS Pper & Solution Time : Hrs. M. Mrks : Generl Instruction : (i) ll questions re compulsory. There re questions in ll. (ii) This question pper hs three sections : Section, Section

SOLVING SYSTEMS OF EQUATIONS, ITERATIVE METHODS

ELM Numericl Anlysis Dr Muhrrem Mercimek SOLVING SYSTEMS OF EQUATIONS, ITERATIVE METHODS ELM Numericl Anlysis Some of the contents re dopted from Lurene V. Fusett, Applied Numericl Anlysis using MATLAB.

MATHEMATICS PAPER IA. Note: This question paper consists of three sections A,B and C. SECTION A VERY SHORT ANSWER TYPE QUESTIONS.

MATHEMATICS PAPER IA TIME : hrs Mx. Mrks.75 Note: This question pper consists of three sections A,B nd C. SECTION A VERY SHORT ANSWER TYPE QUESTIONS. 0X =0. If A = {,, 0,, } nd f : A B is surjection defined

1 nonlinear.mcd Find solution root to nonlinear algebraic equation f(x)=0. Instructor: Nam Sun Wang

nonlinermc Fin solution root to nonliner lgebric eqution ()= Instructor: Nm Sun Wng Bckgroun In science n engineering, we oten encounter lgebric equtions where we wnt to in root(s) tht stisies given eqution

R(3, 8) P( 3, 0) Q( 2, 2) S(5, 3) Q(2, 32) P(0, 8) Higher Mathematics Objective Test Practice Book. 1 The diagram shows a sketch of part of

Higher Mthemtics Ojective Test Prctice ook The digrm shows sketch of prt of the grph of f ( ). The digrm shows sketch of the cuic f ( ). R(, 8) f ( ) f ( ) P(, ) Q(, ) S(, ) Wht re the domin nd rnge of

10 Vector Integral Calculus

Vector Integrl lculus Vector integrl clculus extends integrls s known from clculus to integrls over curves ("line integrls"), surfces ("surfce integrls") nd solids ("volume integrls"). These integrls hve

22.615, MHD Theory of Fusion Systems Prof. Freidberg Lecture 7: The First Order Grad Shafranov Equation. dp 1 dp

First Order Eqution.65, MHD Theory of Fusion Systems Prof. Freiderg Lecture 7: The First Order Grd Shfrnov Eqution The first order Grd Shfrnov eqution is given y d p d dp d + μr + R B B = μr r cos + cos

Math 211A Homework. Edward Burkard. = tan (2x + z)

Mth A Homework Ewr Burkr Eercises 5-C Eercise 8 Show tht the utonomous system: 5 Plne Autonomous Systems = e sin 3y + sin cos + e z, y = sin ( + 3y, z = tn ( + z hs n unstble criticl point t = y = z =

u t = k 2 u x 2 (1) a n sin nπx sin 2 L e k(nπ/l) t f(x) = sin nπx f(x) sin nπx dx (6) 2 L f(x 0 ) sin nπx 0 2 L sin nπx 0 nπx

Chpter 9: Green s functions for time-independent problems Introductory emples One-dimensionl het eqution Consider the one-dimensionl het eqution with boundry conditions nd initil condition We lredy know

4. Classical lamination theory

O POSI TES GROUP U I V ERSIT Y OF T W ET E omposites orse 8-9 Uniersit o Tente Eng. & Tech. 4. 4. lssicl lmintion theor - Lrent Wrnet & Remo ermn. 4. lssicl lmintion theor 4.. Introction hpter n ocse on

Measurement of Transmission Loss of Materials Using a Standing Wave Tube

urue University urue e-us ulictions of the Ry W. Herrick Lortories School of Mechnicl Engineering -6 Mesurement of rnsmission Loss of Mterils Using Stning Wve ue J Sturt Bolton urue University, olton@purue.eu

Section 2.3. Matrix Inverses

Mtri lger Mtri nverses Setion.. Mtri nverses hree si opertions on mtries, ition, multiplition, n sutrtion, re nlogues for mtries of the sme opertions for numers. n this setion we introue the mtri nlogue

EULER-LAGRANGE EQUATIONS. Contents. 2. Variational formulation 2 3. Constrained systems and d Alembert principle Legendre transform 6

EULER-LAGRANGE EQUATIONS EUGENE LERMAN Contents 1. Clssicl system of N prticles in R 3 1 2. Vritionl formultion 2 3. Constrine systems n Alembert principle. 4 4. Legenre trnsform 6 1. Clssicl system of

3. Vectors. Vectors: quantities which indicate both magnitude and direction. Examples: displacemement, velocity, acceleration

Rutgers University Deprtment of Physics & Astronomy 01:750:271 Honors Physics I Lecture 3 Pge 1 of 57 3. Vectors Vectors: quntities which indicte both mgnitude nd direction. Exmples: displcemement, velocity,

Physics 207 Lecture 7

Phsics 07 Lecture 7 Agend: Phsics 07, Lecture 7, Sept. 6 hpter 6: Motion in (nd 3) dimensions, Dnmics II Recll instntneous velocit nd ccelertion hpter 6 (Dnmics II) Motion in two (or three dimensions)

Exploring parametric representation with the TI-84 Plus CE graphing calculator

Exploring prmetric representtion with the TI-84 Plus CE grphing clcultor Richrd Prr Executive Director Rice University School Mthemtics Project rprr@rice.edu Alice Fisher Director of Director of Technology

Navigation Mathematics: Angular and Linear Velocity EE 570: Location and Navigation

Lecture Nvigtion Mthemtics: Angulr n Liner Velocity EE 57: Loction n Nvigtion Lecture Notes Upte on Februry, 26 Kevin Weewr n Aly El-Osery, Electricl Engineering Dept., New Mexico Tech In collbortion with

ITERATIVE SOLUTION REFINEMENT

Numericl nlysis f ngineers Germn Jdnin University ITRTIV SOLUTION RFINMNT Numericl solution of systems of liner lgeric equtions using direct methods such s Mtri Inverse, Guss limintion, Guss-Jdn limintion,

When e = 0 we obtain the case of a circle.

3.4 Conic sections Circles belong to specil clss of cures clle conic sections. Other such cures re the ellipse, prbol, n hyperbol. We will briefly escribe the stnr conics. These re chosen to he simple

, MATHS H.O.D.: SUHAG R.KARIYA, BHOPAL, CONIC SECTION PART 8 OF

DOWNLOAD FREE FROM www.tekoclsses.com, PH.: 0 903 903 7779, 98930 5888 Some questions (Assertion Reson tpe) re given elow. Ech question contins Sttement (Assertion) nd Sttement (Reson). Ech question hs

in a uniform magnetic flux density B = Boa z. (a) Show that the electron moves in a circular path. (b) Find the radius r o

6. THE TATC MAGNETC FELD 6- LOENTZ FOCE EQUATON Lorent force eqution F = Fe + Fm = q ( E + v B ) Exmple 6- An electron hs n initil velocity vo = vo y in uniform mgnetic flux density B = Bo. () how tht

u( t) + K 2 ( ) = 1 t > 0 Analyzing Damped Oscillations Problem (Meador, example 2-18, pp 44-48): Determine the equation of the following graph.

nlyzing Dmped Oscilltions Prolem (Medor, exmple 2-18, pp 44-48): Determine the eqution of the following grph. The eqution is ssumed to e of the following form f ( t) = K 1 u( t) + K 2 e!"t sin (#t + $

Review Exercises for Chapter 2

60_00R.q //0 :5 PM Pge 58 58 CHAPTER Differentition In Eercises, fin the erivtive of the function b using the efinition of the erivtive.. f. f. f. f In Eercises 5 n 6, escribe the -vlues t which ifferentible.

MATHEMATICS PAPER IIB COORDINATE GEOMETRY AND CALCULUS. Note: This question paper consists of three sections A,B and C. SECTION A

MATHEMATICS PAPER IIB COORDINATE GEOMETRY AND CALCULUS. TIME : 3hrs M. Mrks.75 Note: This question pper consists of three sections A,B nd C. SECTION A VERY SHORT ANSWER TYPE QUESTIONS. X = ) Find the eqution

On the Design of 2-DOF Robot Grippers

On the esign of -OF Root Grippers ION SIMIONSU, ION ION eprtment of Mechnism n Mchine Theory POLITHNI University of uchrest Spliul Inepenentei no., sector 6, uchrest ROMNI strct: - The gripper constitutes

Problem Solving 7: Faraday s Law Solution

MASSACHUSETTS NSTTUTE OF TECHNOLOGY Deprtment of Physics: 8.02 Prolem Solving 7: Frdy s Lw Solution Ojectives 1. To explore prticulr sitution tht cn led to chnging mgnetic flux through the open surfce

CET MATHEMATICS 2013

CET MATHEMATICS VERSION CODE: C. If sin is the cute ngle between the curves + nd + 8 t (, ), then () () () Ans: () Slope of first curve m ; slope of second curve m - therefore ngle is o A sin o (). The

Section 1.3 Triangles

Se 1.3 Tringles 21 Setion 1.3 Tringles LELING TRINGLE The line segments tht form tringle re lled the sides of the tringle. Eh pir of sides forms n ngle, lled n interior ngle, nd eh tringle hs three interior

Topics Covered AP Calculus AB

Topics Covered AP Clculus AB ) Elementry Functions ) Properties of Functions i) A function f is defined s set of ll ordered pirs (, y), such tht for ech element, there corresponds ectly one element y.

2A1A Vector Algebra and Calculus I

Vector Algebr nd Clculus I (23) 2AA 2AA Vector Algebr nd Clculus I Bugs/queries to sjrob@robots.ox.c.uk Michelms 23. The tetrhedron in the figure hs vertices A, B, C, D t positions, b, c, d, respectively.

TIME VARYING MAGNETIC FIELDS AND MAXWELL S EQUATIONS

TIME VARYING MAGNETIC FIED AND MAXWE EQUATION Introuction Electrosttic fiels re usull prouce b sttic electric chrges wheres mgnetosttic fiels re ue to motion of electric chrges with uniform velocit (irect

10.2 The Ellipse and the Hyperbola

CHAPTER 0 Conic Sections Solve. 97. Two surveors need to find the distnce cross lke. The plce reference pole t point A in the digrm. Point B is meters est nd meter north of the reference point A. Point

Extension of the Villarceau-Section to Surfaces of Revolution with a Generating Conic

Journl for Geometry n Grphics Volume 6 (2002), No. 2, 121 132. Extension of the Villrceu-Section to Surfces of Revolution with Generting Conic Anton Hirsch Fchereich uingenieurwesen, FG Sthlu, Drstellungstechnik

Sketch graphs of conic sections and write equations related to conic sections

Achievement Stndrd 909 Sketch grphs of conic sections nd write equtions relted to conic sections Clculus.5 Eternll ssessed credits Sketching Conics the Circle nd the Ellipse Grphs of the conic sections

x dx does exist, what does the answer look like? What does the answer to

Review Guie or MAT Finl Em Prt II. Mony Decemer th 8:.m. 9:5.m. (or the 8:3.m. clss) :.m. :5.m. (or the :3.m. clss) Prt is worth 5% o your Finl Em gre. NO CALCULATORS re llowe on this portion o the Finl

SUPPLEMENTARY NOTES ON THE CONNECTION FORMULAE FOR THE SEMICLASSICAL APPROXIMATION

Physics 8.06 Apr, 2008 SUPPLEMENTARY NOTES ON THE CONNECTION FORMULAE FOR THE SEMICLASSICAL APPROXIMATION c R. L. Jffe 2002 The WKB connection formuls llow one to continue semiclssicl solutions from n

Method of Localisation and Controlled Ejection of Swarms of Likely Charged Particles

Method of Loclistion nd Controlled Ejection of Swrms of Likely Chrged Prticles I. N. Tukev July 3, 17 Astrct This work considers Coulom forces cting on chrged point prticle locted etween the two coxil,

THREE-DIMENSIONAL KINEMATICS OF RIGID BODIES

THREE-DIMENSIONAL KINEMATICS OF RIGID BODIES 1. TRANSLATION Figure shows rigid body trnslting in three-dimensionl spce. Any two points in the body, such s A nd B, will move long prllel stright lines if

MATH1013 Tutorial 12. Indefinite Integrals

MATH Tutoril Indefinite Integrls The indefinite integrl f() d is to look for fmily of functions F () + C, where C is n rbitrry constnt, with the sme derivtive f(). Tble of Indefinite Integrls cf() d c

APPENDIX. Precalculus Review D.1. Real Numbers and the Real Number Line

APPENDIX D Preclculus Review APPENDIX D.1 Rel Numers n the Rel Numer Line Rel Numers n the Rel Numer Line Orer n Inequlities Asolute Vlue n Distnce Rel Numers n the Rel Numer Line Rel numers cn e represente

( ) Same as above but m = f x = f x - symmetric to y-axis. find where f ( x) Relative: Find where f ( x) x a + lim exists ( lim f exists.

AP Clculus Finl Review Sheet solutions When you see the words This is wht you think of doing Find the zeros Set function =, fctor or use qudrtic eqution if qudrtic, grph to find zeros on clcultor Find

PROBLEM deceleration of the cable attached at B is 2.5 m/s, while that + ] ( )( ) = 2.5 2α. a = rad/s. a 3.25 m/s. = 3.

PROLEM 15.105 A 5-m steel bem is lowered by mens of two cbles unwinding t the sme speed from overhed crnes. As the bem pproches the ground, the crne opertors pply brkes to slow the unwinding motion. At

k ) and directrix x = h p is A focal chord is a line segment which passes through the focus of a parabola and has endpoints on the parabola.

Stndrd Eqution of Prol with vertex ( h, k ) nd directrix y = k p is ( x h) p ( y k ) = 4. Verticl xis of symmetry Stndrd Eqution of Prol with vertex ( h, k ) nd directrix x = h p is ( y k ) p( x h) = 4.

First, we will find the components of the force of gravity: Perpendicular Forces (using away from the ramp as positive) ma F

1.. In Clss or Homework Eercise 1. An 18.0 kg bo is relesed on 33.0 o incline nd ccelertes t 0.300 m/s. Wht is the coeicient o riction? m 18.0kg 33.0? 0 0.300 m / s irst, we will ind the components o the

In-Class Problems 2 and 3: Projectile Motion Solutions. In-Class Problem 2: Throwing a Stone Down a Hill

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Deprtment of Physics Physics 8T Fll Term 4 In-Clss Problems nd 3: Projectile Motion Solutions We would like ech group to pply the problem solving strtegy with the

Version 001 HW#6 - Circular & Rotational Motion arts (00223) 1

Version 001 HW#6 - Circulr & ottionl Motion rts (00223) 1 This print-out should hve 14 questions. Multiple-choice questions my continue on the next column or pge find ll choices before nswering. Circling

3.4 Conic sections. In polar coordinates (r, θ) conics are parameterized as. Next we consider the objects resulting from

3.4 Conic sections Net we consier the objects resulting from + by + cy + + ey + f 0. Such type of cures re clle conics, becuse they rise from ifferent slices through cone In polr coorintes r, θ) conics

KINETICS OF RIGID BODIES PROBLEMS

KINETICS OF RIID ODIES PROLEMS PROLEMS 1. The 6 kg frme C nd the 4 kg uniform slender br of length l slide with negligible friction long the fied horizontl br under the ction of the 80 N force. Clculte

at its center, then the measure of this angle in radians (abbreviated rad) is the length of the arc that subtends the angle.

Notes 6 ngle Mesure Definition of Rdin If circle of rdius is drwn with the vertex of n ngle Mesure: t its center, then the mesure of this ngle in rdins (revited rd) is the length of the rc tht sutends

Fundamental Theorem of Calculus

Fundmentl Theorem of Clculus Recll tht if f is nonnegtive nd continuous on [, ], then the re under its grph etween nd is the definite integrl A= f() d Now, for in the intervl [, ], let A() e the re under

JEE Advnced Mths Assignment Onl One Correct Answer Tpe. The locus of the orthocenter of the tringle formed the lines (+P) P + P(+P) = 0, (+q) q+q(+q) = 0 nd = 0, where p q, is () hperol prol n ellipse

Lesson 8.1 Graphing Parametric Equations

Lesson 8.1 Grphing Prmetric Equtions 1. rete tle for ech pir of prmetric equtions with the given vlues of t.. x t 5. x t 3 c. x t 1 y t 1 y t 3 y t t t {, 1, 0, 1, } t {4,, 0,, 4} t {4, 0,, 4, 8}. Find

Numbers and indices. 1.1 Fractions. GCSE C Example 1. Handy hint. Key point

GCSE C Emple 7 Work out 9 Give your nswer in its simplest form Numers n inies Reiprote mens invert or turn upsie own The reiprol of is 9 9 Mke sure you only invert the frtion you re iviing y 7 You multiply

1 ELEMENTARY ALGEBRA and GEOMETRY READINESS DIAGNOSTIC TEST PRACTICE

ELEMENTARY ALGEBRA nd GEOMETRY READINESS DIAGNOSTIC TEST PRACTICE Directions: Study the exmples, work the prolems, then check your nswers t the end of ech topic. If you don t get the nswer given, check

Section - 2 MORE PROPERTIES

LOCUS Section - MORE PROPERTES n section -, we delt with some sic properties tht definite integrls stisf. This section continues with the development of some more properties tht re not so trivil, nd, when

Plane curvilinear motion is the motion of a particle along a curved path which lies in a single plane.

Plne curiliner motion is the motion of prticle long cured pth which lies in single plne. Before the description of plne curiliner motion in n specific set of coordintes, we will use ector nlsis to describe

KENDRIYA VIDYALAYA IIT KANPUR HOME ASSIGNMENTS FOR SUMMER VACATIONS CLASS - XII MATHEMATICS (Relations and Functions & Binary Operations)

KENDRIYA VIDYALAYA IIT KANPUR HOME ASSIGNMENTS FOR SUMMER VACATIONS 6-7 CLASS - XII MATHEMATICS (Reltions nd Funtions & Binry Opertions) For Slow Lerners: - A Reltion is sid to e Reflexive if.. every A

MATHEMATICS PART A. 1. ABC is a triangle, right angled at A. The resultant of the forces acting along AB, AC

FIITJEE Solutions to AIEEE MATHEMATICS PART A. ABC is tringle, right ngled t A. The resultnt of the forces cting long AB, AC with mgnitudes AB nd respectively is the force long AD, where D is the AC foot

2. VECTORS AND MATRICES IN 3 DIMENSIONS

2 VECTORS AND MATRICES IN 3 DIMENSIONS 21 Extending the Theory of 2-dimensionl Vectors x A point in 3-dimensionl spce cn e represented y column vector of the form y z z-xis y-xis z x y x-xis Most of the

Chapter 36. a λ 2 2. (minima-dark fringes) Diffraction and the Wave Theory of Light. Diffraction by a Single Slit: Locating the Minima, Cont'd

Chpter 36 Diffrction In Chpter 35, we sw how light bes pssing through ifferent slits cn interfere with ech other n how be fter pssing through single slit flres-iffrcts- in Young's experient. Diffrction