PHY 222 Lab 8 MOTION OF ELECTRONS IN ELECTRIC AND MAGNETIC FIELDS

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "PHY 222 Lab 8 MOTION OF ELECTRONS IN ELECTRIC AND MAGNETIC FIELDS"

Transcription

1 PHY 222 Lb 8 MOTION OF ELECTRONS IN ELECTRIC AND MAGNETIC FIELDS Nme: Prtners: INTRODUCTION Before coming to lb, plese red this pcket nd do the prelb on pge 13 of this hndout. From previous experiments, ou re fmilir with the concepts of electric nd mgnetic fields. The most importnt formule relted to this topic describe the forces electric nd mgnetic fields exert on electric chrges. In fct, these formule re used to define fields themselves. Electrons crr one unit of negtive elementr chrge. Since n electric or mgnetic field exerts force on electrons, it ffects their motion. In spite of the fct tht electric fields re everwhere round us, in everd life we do not directl observe the motion of electrons. However, such observtions re possible with device clled cthode-r tube (CRT), which is just technicl nme for tube which ws present in erl T sets nd computer monitors, some of which re still in use. PURPOSE Exmine reltionship for electric nd mgnetic forces exerted on moving electric chrges. PRE-LAB ASSIGNMENTS A. Redings: In n electric field E, n electron experiences force F e E where e is the electric chrge of the electron. (1) In mgnetic field B, the electron is subject to force F ev B (2) where v is the velocit of the electron. A force cuses ccelertion ccording to the reltion F m (3) where m is the mss of the electron. Note from (1) nd (2) tht the electric field ccelertes n electron in the direction prllel to the electric field, while the mgnetic field ccelertes n electron in the direction perpendiculr to both the mgnetic field nd the velocit of the electron. P g e 1

2 Figure 1. Cthode-r tube. A cthode-r tube (Fig. 1) is vcuum tube in which electrons re emitted t one end from hot piece of metl (the cthode) nd then ccelerted b strong electric field creted in the electron gun. The trvel cross the tube, where the re lso subject to being deflected b electric fields creted between two pirs of prllel pltes. Electrons eventull hit the opposite end of the tube. This end is covered with fluorescent mteril, nd serves s screen. Electrons tht strike the screen cuse the fluorescent mteril to glow, nd thus the bem of electrons is visible s spot on the screen. The ctul position of the spot depends on the deflecting field inside the tube. Since electrons in the tube move t high speeds, their motion m be lso ffected b mgnetic fields. B observing the position of the bright spot on the screen, we cn mesure the deflection of electrons b electric nd mgnetic fields. Let us nle the motion of electrons in the tube. The electrons re ccelerted to velocit v in the electron gun. If the ccelerting electric potentil is we cn estimte v from the conservtion of energ, since the increse of the kinetic energ of the electron equls the chnge of potentil energ in the electrosttic field, e. Neglecting the initil speed of the electron, we hve: 1 2 mv 2 e (4) ELECTRIC DEFLECTION The electrons move with the constnt velocit v until the rech the deflecting pltes. Let us ssume tht the deflecting electric field is verticl. If the potentil difference between the pltes is, the electric field in between the pltes is pproximtel uniform nd hs mgnitude of: E (5) d where d is the plte seprtion (see Fig. 2). This electric field will ccelerte electrons in verticl directions with which cn be obtined from formule (1), (3) nd (5): P g e 2

3 F e E e (6) m m d m Thus, electrons cquire verticl component of velocit v t, where t is the time spent in the deflecting region. If the length of the pltes is l, we cn obtin t from: t l v. Therefore, v e l (7) d mv Figure 2. Deflection of electron bem in the tube. The quntit mesured in the experiment is the verticl bem displcement D on the screen (see Fig. 2). Electrons trvel with constnt velocit between the pltes nd the screen. If t is the time in which electrons trvel from the deflecting pltes to the screen, then D v t. The time t cn be found from t L v, where L is the horiontl distnce from the deflecting pltes to the screen. Combining these two equtions D Lv v, nd using Eq. (7) we obtin 2 D e l L ( d mv ). Since from Eq. (4) 2 e ( mv ) 1 (2 ), we get ll 1 D d2 (8) This formul tells us tht the verticl displcement of the bem should be directl proportionl to the deflection voltge (nd lso to the deflecting electric field E ) nd inversel proportionl to the ccelerting voltge. You will verif this sttement in the experiment. MAGNETIC DEFLECTION The CRT used in the Lb does not contin n electromgnets; therefore, the mgnetic field B will be creted b externl coils. The mgnetic field will be pproximtel uniform, horiontl nd perpendiculr to the electron flight direction. The mgnetic force cting on electrons will be, therefore, directed long the verticl xis F evb (from Eq. (2)). Even though it is not rigorousl correct, we cn ssume tht the mgnetic field cts on electrons long the distnce l nd tht the trvel distnce L to the screen. Thus, v l v F l ( mv ) el B m. Following the sme steps s in the previous section, it cn be shown tht l L D e 1 2 m (9) The verticl displcement of the bem should be directl proportionl to the deflecting B P g e 3

4 mgnetic field B nd inversel proportionl to the squre root of the ccelerting voltge. Agin, ou will verif this reltion in the experiment. In this experiment, ou will not know B in bsolute units but ou will monitor the vlue of B b mesuring the voltge cross the coils coil. This voltge is directl proportionl to the current in the coils which, in turn, is directl proportionl to the strength of the mgnetic field creted b the coils. LABORATORY ASSIGNMENTS Cution High oltge The cthode-r tube is under voltge of 500, which m be dngerous to our life. Do not touch the connections on the rer end of the cthode-r tube. The power suppl wiring should be done b the instructor. Do not chnge n connection except those to the btter, the 30 power suppl, the voltmeter, the deflecting pltes nd the electromgnet. Mterils Needed: Figure 3. Regulted Power Suppl for the CRT. Cthode-r tube Regulted power suppl for the tube 4.5 Btter 0-30 Power Suppl Experiment A: Electron motion in n electric field smll permnent mgnets (B) Two solenoids (B) Compss Cbles LoggerPro (optionl) P g e 4

5 Procedures Figure 4. Drwing of experimentl pprtus. A-1. The pprtus should be wired up b our instructor before ou come to the lbortor. You m check connections ginst Fig. 4. Leve the 30 power suppl nd voltmeter off nd disconnected for now. Check tht the 4.5 btter is connected to the sstem (see Fig. 4). Turn the regulted power suppl from the OFF to the STANDBY position nd leve it t this position for one minute. You should see red glow ner the rer end of the cthode-r tube. A-2. Turn the regulted power suppl to the ON position. The totl ccelerting voltge is the sum of two voltges, the C voltge (controlled b the left knob) nd the B+ voltge (controlled b the right knob); see Fig. 3. The voltmeter displing the C or B+ voltge is plced on the left of the power suppl, nd hs two rnges: for B+ (the upper scle) nd for C (the lower scle). The rnge switch for the meter is t the center of the power suppl. Set this switch to the position on the right. P g e 5

6 r the B control knob on the power suppl nd observe the voltge chnge on the dul-rnge voltmeter. Set the B+ voltge to pproximtel 350. Set the switch to the position on the left nd using the left knob, vr the C voltge. Set the C voltge to the vlue tht gives mximll shrp spot on the screen (pprox. 125 ). Record the vlue of (i.e. sum of B+ nd C voltges) in the tble in Report Sheet III 1. In the bsence of deflection voltge, the bem spot should be ner the center of the screen. Its position cn be chnged b creful djustment of the position of smll mgnet plced on top of the tube (do not chnge the mgnet s position unless necessr). If ou cnnot get shrp spot, or cnnot get it ner the center, sk the instructor for help. A-3. Connect the 30 power suppl to the verticl deflection pltes. Importnt: The B+ output on the regulted power suppl must be connected (in ddition to its CRT connection) to the negtive output of the 30 power suppl for ll experiments. Filure to mke this connection m result in big increse in the bem spot sie. Leve the horiontl deflection pltes nd the coils unconnected. Connect lso the digitl voltmeter to red the deflection voltge (note tht Fig. 5 shows the voltmeter connected to the coils, which will be the cse in experiment B). Using the knob on the 30 power suppl, vr the deflection voltge nd observe the motion of the bem cross the screen. If the bem moves digonll ou must hve connected both verticl nd horiontl deflection pltes to the power suppl disconnect the horiontl pltes. If the bem moves horiontll swp the 30 power suppl connection to the other deflection plte leds. The spot will move from ero onl in one direction (e.g. in +Y direction). To deflect the spot in the opposite direction (e.g. in Y direction), chnge the polrit of the connection to the 30 power suppl. A-4. In this step, ou will mesure nd plot the displcement D versus the pplied deflection voltge for two different settings of the ccelerting voltge. Becuse the mesurements of the deflecting voltge cn be mde much more precisel thn the position on the screen, ou should mesure the deflection voltges corresponding to few definite positions of the spot, for instnce when the center of the spot crosses the division mrks on the screen. For ech mesurement mke point on the grph included in Report Sheet III 1. Mesure deflective potentil t lest three division mrks down nd t lest three division mrks up of the center. Cover the lrgest rnge of bem deflections llowed b the division mrks nd the voltge rnge. Plot the dt s the re tken without tbulting them, except for the lrgest deflections up ( D ) nd down ( D d ). Record D nd for these extreme deflections in the tble in Report u P g e 6

7 Sheet III 1 next to the vlue of for this set of mesurements. Reduce the vlue of the voltge B+ b pproximtel 100 nd djust the voltge C to obtin shrp spot. Record the new vlue of. Repet the previous mesurements of D versus the deflection voltge, recording them on the sme grph. Also put coordintes of the lrgest devitions into the tble together with the new vlue of. If the theor discussed bove is correct, ou should obtin two different stright lines, ech corresponding to different vlue of the ccelerting voltge. Clculte the slopes of those lines from the dt in our tble: Slope D D u d u d From Eq. (8) the slope of the dependence of D is equl to l L ( d 2) 1, thus it should be inversel proportionl to. erif this expecttion b clculting the product of nd of the mesured slope (store our result in the 6 th column in the tble). These products should be independent of if Eq. (8) is right. Assuming d 02, L 5, l 1 clculte the slopes predicted b Eq. (8) nd compre them with wht ou ctull mesured (Report Sheet III 1). Experiment B: Electron motion in mgnetic field Procedures Figure 5. Connection of the power suppl to the coils. P g e 7

8 B-1. The two coils should be positioned nd wired s shown in the Fig. 4. Switch off the 30 power suppl, disconnect it from the deflective pltes nd connect it to the coils. There should still be connection between the B+ output of the regulted power suppl nd the negtive output of the 30 power suppl. Fig 5 shows the simple connection of power suppl to the solenoid coil. Turn the voltge setting to bout 3. You cn red the voltge on the power suppl. Use smll compss to check the direction of the mgnetic field produced b ech coils. Tp the compss since needle cn sometimes get stuck. Mke sure, tht the polrit of the two electromgnets is the sme. You should observe verticl deflection of the spot cused b the mgnetic field. Mesure nd plot, on the grph provided on Report Sheet III 2, the deflection D versus the voltge drop cross the coils (which is proportionl to the mgnetic field). Use the method suggested in A-4 to obtin the dt points. Switch the ~3 power suppl connection to reverse the current flow in the coils. The spot should now be deflected in the opposite direction. Mke mesurements of D versus the voltge drop lso for this configurtion. As in experiment A, chnge the B+ voltge b 100, djust C nd repet the mesurements for the second vlue of the ccelerting voltge. For ech vlue of the ccelerting voltge (sum of B+ nd C voltges) clculte the slope. Store our results in the tble. For the 6 th column in the tble, clculte the product of nd of the mesured slope. These products should be independent of if Eq. (9) is right. Do our results confirm the expected dependence on? B-2. (Absolutel Mndtor) Switch off the power suppl. Disconnect one led from the btter. Reduce the B+ nd C voltges to ero. Switch off the big power suppl. Show our tble to the instructor before turning in our report. P g e 8

9 REPORT SHEET III 1 Dte Nme Instructor Prtner(s) A-4 Use the grph pper" below to mke grphs displing the displcement D versus the deflection voltge (with the deflection voltge on the x-xis) for the two different vlues of the ccelerting voltge. Optionl: crete our grph in LoggerPro insted. Tr to drw stright line through ech set of our mesurements (use ruler). Is the reltion between D nd liner (circle nswer)? es no Deflection up D u u D d Deflection down Slope Mesured Expected d Slope Slope () (in) () (in) () (in/) (in) (in/) Do our results confirm the expected dependence on (circle nswer)? es no Do the expected slopes roughl gree with the observtions? es no P g e 9

10 REPORT SHEET III 2 Dte Nme Instructor Prtner(s) B-1 Below mke grph showing D versus the voltge through the coils. Tr to drw stright line through ech set of our mesurements (use ruler). Is the reltion between D nd coil liner (circle nswer)? es no Deflection up Deflection down D u D u d d Mesured Slope Slope () (in) () (in) () (in/) (in ) Do our results roughl confirm the expected dependence on? es no P g e 10

11 Nme Dte Instructor Exercise 1. PRE LAB EXERCISES Electrons in cthode-r tube re ccelerted long the length of the tube (in the -direction) b potentil difference = 300 olts. Wht is the speed of electrons in m/s when the hit the screen? (c = m/s; electron mss m = kg cn lso be expressed s m = eolts/c 2 ). Accelertion of n electron Exercise 2. In ddition to the ccelerting voltge bove, electrons re lso subject to deflection voltge 30. Wht will be the verticl deflection on the screen D, if the deflecting pltes of length l 1 re seprted b distnce d 02, nd the distnce from the pltes to the screen is L 5. Hint: Use Eq. (8). P g e 11

Graphs on Logarithmic and Semilogarithmic Paper

Graphs on Logarithmic and Semilogarithmic Paper 0CH_PHClter_TMSETE_ 3//00 :3 PM Pge Grphs on Logrithmic nd Semilogrithmic Pper OBJECTIVES When ou hve completed this chpter, ou should be ble to: Mke grphs on logrithmic nd semilogrithmic pper. Grph empiricl

More information

Experiment 6: Friction

Experiment 6: Friction Experiment 6: Friction In previous lbs we studied Newton s lws in n idel setting, tht is, one where friction nd ir resistnce were ignored. However, from our everydy experience with motion, we know tht

More information

Answer, Key Homework 8 David McIntyre 1

Answer, Key Homework 8 David McIntyre 1 Answer, Key Homework 8 Dvid McIntyre 1 This print-out should hve 17 questions, check tht it is complete. Multiple-choice questions my continue on the net column or pge: find ll choices before mking your

More information

r 2 F ds W = r 1 qe ds = q

r 2 F ds W = r 1 qe ds = q Chpter 4 The Electric Potentil 4.1 The Importnt Stuff 4.1.1 Electricl Potentil Energy A chrge q moving in constnt electric field E experiences force F = qe from tht field. Also, s we know from our study

More information

1. 1 m/s m/s m/s. 5. None of these m/s m/s m/s m/s correct m/s

1. 1 m/s m/s m/s. 5. None of these m/s m/s m/s m/s correct m/s Crete ssignment, 99552, Homework 5, Sep 15 t 10:11 m 1 This print-out should he 30 questions. Multiple-choice questions my continue on the next column or pge find ll choices before nswering. The due time

More information

Week 11 - Inductance

Week 11 - Inductance Week - Inductnce November 6, 202 Exercise.: Discussion Questions ) A trnsformer consists bsiclly of two coils in close proximity but not in electricl contct. A current in one coil mgneticlly induces n

More information

Use Geometry Expressions to create a more complex locus of points. Find evidence for equivalence using Geometry Expressions.

Use Geometry Expressions to create a more complex locus of points. Find evidence for equivalence using Geometry Expressions. Lerning Objectives Loci nd Conics Lesson 3: The Ellipse Level: Preclculus Time required: 120 minutes In this lesson, students will generlize their knowledge of the circle to the ellipse. The prmetric nd

More information

Cypress Creek High School IB Physics SL/AP Physics B 2012 2013 MP2 Test 1 Newton s Laws. Name: SOLUTIONS Date: Period:

Cypress Creek High School IB Physics SL/AP Physics B 2012 2013 MP2 Test 1 Newton s Laws. Name: SOLUTIONS Date: Period: Nme: SOLUTIONS Dte: Period: Directions: Solve ny 5 problems. You my ttempt dditionl problems for extr credit. 1. Two blocks re sliding to the right cross horizontl surfce, s the drwing shows. In Cse A

More information

AP QUIZ #2 GRAPHING MOTION 1) POSITION TIME GRAPHS DISPLACEMENT Each graph below shows the position of an object as a function of time.

AP QUIZ #2 GRAPHING MOTION 1) POSITION TIME GRAPHS DISPLACEMENT Each graph below shows the position of an object as a function of time. AP QUIZ # GRAPHING MOTION ) POSITION TIME GRAPHS DISPLAEMENT Ech grph below shows the position of n object s function of time. A, B,, D, Rnk these grphs on the gretest mgnitude displcement during the time

More information

1. 0 m/s m/s m/s m/s

1. 0 m/s m/s m/s m/s Version PREVIEW Kine Grphs PRACTICE burke (1111) 1 This print-out should he 30 questions. Multiple-choice questions m continue on the next column or pge find ll choices before nswering. Distnce Time Grph

More information

Net Change and Displacement

Net Change and Displacement mth 11, pplictions motion: velocity nd net chnge 1 Net Chnge nd Displcement We hve seen tht the definite integrl f (x) dx mesures the net re under the curve y f (x) on the intervl [, b] Any prt of the

More information

14.2. The Mean Value and the Root-Mean-Square Value. Introduction. Prerequisites. Learning Outcomes

14.2. The Mean Value and the Root-Mean-Square Value. Introduction. Prerequisites. Learning Outcomes he Men Vlue nd the Root-Men-Squre Vlue 4. Introduction Currents nd voltges often vry with time nd engineers my wish to know the men vlue of such current or voltge over some prticulr time intervl. he men

More information

Polynomial Functions. Polynomial functions in one variable can be written in expanded form as ( )

Polynomial Functions. Polynomial functions in one variable can be written in expanded form as ( ) Polynomil Functions Polynomil functions in one vrible cn be written in expnded form s n n 1 n 2 2 f x = x + x + x + + x + x+ n n 1 n 2 2 1 0 Exmples of polynomils in expnded form re nd 3 8 7 4 = 5 4 +

More information

Unit 6: Exponents and Radicals

Unit 6: Exponents and Radicals Eponents nd Rdicls -: The Rel Numer Sstem Unit : Eponents nd Rdicls Pure Mth 0 Notes Nturl Numers (N): - counting numers. {,,,,, } Whole Numers (W): - counting numers with 0. {0,,,,,, } Integers (I): -

More information

Double Integrals over General Regions

Double Integrals over General Regions Double Integrls over Generl egions. Let be the region in the plne bounded b the lines, x, nd x. Evlute the double integrl x dx d. Solution. We cn either slice the region verticll or horizontll. ( x x Slicing

More information

Electric Circuits. Simple Electric Cell. Electric Current

Electric Circuits. Simple Electric Cell. Electric Current Electric Circuits Count Alessndro olt (745-87) Georg Simon Ohm (787-854) Chrles Augustin de Coulomb (736 806) André Mrie AMPÈRE (775-836) Crbon Electrode () Simple Electric Cell wire Zn Zn Zn Zn Sulfuric

More information

Module 2. Analysis of Statically Indeterminate Structures by the Matrix Force Method. Version 2 CE IIT, Kharagpur

Module 2. Analysis of Statically Indeterminate Structures by the Matrix Force Method. Version 2 CE IIT, Kharagpur Module Anlysis of Stticlly Indeterminte Structures by the Mtrix Force Method Version CE IIT, Khrgpur esson 9 The Force Method of Anlysis: Bems (Continued) Version CE IIT, Khrgpur Instructionl Objectives

More information

SCHOOL OF ENGINEERING & BUILT ENVIRONMENT. Mathematics. Basic Algebra

SCHOOL OF ENGINEERING & BUILT ENVIRONMENT. Mathematics. Basic Algebra SCHOOL OF ENGINEERING & BUILT ENVIRONMENT Mthemtics Bsic Alger. Opertions nd Epressions. Common Mistkes. Division of Algeric Epressions. Eponentil Functions nd Logrithms. Opertions nd their Inverses. Mnipulting

More information

Chapter G - Problems

Chapter G - Problems Chpter G - Problems Blinn College - Physics 2426 - Terry Honn Problem G.1 A plne flies horizonlly t speed of 280 mês in position where the erth's mgnetic field hs mgnitude 6.0µ10-5 T nd is directed t n

More information

Mathematics. Vectors. hsn.uk.net. Higher. Contents. Vectors 128 HSN23100

Mathematics. Vectors. hsn.uk.net. Higher. Contents. Vectors 128 HSN23100 hsn.uk.net Higher Mthemtics UNIT 3 OUTCOME 1 Vectors Contents Vectors 18 1 Vectors nd Sclrs 18 Components 18 3 Mgnitude 130 4 Equl Vectors 131 5 Addition nd Subtrction of Vectors 13 6 Multipliction by

More information

PHYS1231 Higher Physics 1B Solutions Tutorial 2

PHYS1231 Higher Physics 1B Solutions Tutorial 2 PHYS3 Higher Physics Solutions Tutoril sic info: lthough the term voltge is use every y, in physics it is mesure of firly bstrct quntity clle Electric Potentil. It s importnt to istinguish electric potentil

More information

2 DIODE CLIPPING and CLAMPING CIRCUITS

2 DIODE CLIPPING and CLAMPING CIRCUITS 2 DIODE CLIPPING nd CLAMPING CIRCUITS 2.1 Ojectives Understnding the operting principle of diode clipping circuit Understnding the operting principle of clmping circuit Understnding the wveform chnge of

More information

Sirindhorn International Institute of Technology Thammasat University at Rangsit

Sirindhorn International Institute of Technology Thammasat University at Rangsit Sirindhorn Interntionl Institute of Technology Thmmst University t Rngsit School of Informtion, Computer nd Communiction Technology COURSE : ECS 204 Bsic Electricl Engineering L INSTRUCTOR : Asst. Prof.

More information

The Velocity Factor of an Insulated Two-Wire Transmission Line

The Velocity Factor of an Insulated Two-Wire Transmission Line The Velocity Fctor of n Insulted Two-Wire Trnsmission Line Problem Kirk T. McDonld Joseph Henry Lbortories, Princeton University, Princeton, NJ 08544 Mrch 7, 008 Estimte the velocity fctor F = v/c nd the

More information

Math 135 Circles and Completing the Square Examples

Math 135 Circles and Completing the Square Examples Mth 135 Circles nd Completing the Squre Exmples A perfect squre is number such tht = b 2 for some rel number b. Some exmples of perfect squres re 4 = 2 2, 16 = 4 2, 169 = 13 2. We wish to hve method for

More information

Answer, Key Homework 10 David McIntyre 1

Answer, Key Homework 10 David McIntyre 1 Answer, Key Homework 10 Dvid McIntyre 1 This print-out should hve 22 questions, check tht it is complete. Multiple-choice questions my continue on the next column or pge: find ll choices efore mking your

More information

Section 7-4 Translation of Axes

Section 7-4 Translation of Axes 62 7 ADDITIONAL TOPICS IN ANALYTIC GEOMETRY Section 7-4 Trnsltion of Aes Trnsltion of Aes Stndrd Equtions of Trnslted Conics Grphing Equtions of the Form A 2 C 2 D E F 0 Finding Equtions of Conics In the

More information

5.2. LINE INTEGRALS 265. Let us quickly review the kind of integrals we have studied so far before we introduce a new one.

5.2. LINE INTEGRALS 265. Let us quickly review the kind of integrals we have studied so far before we introduce a new one. 5.2. LINE INTEGRALS 265 5.2 Line Integrls 5.2.1 Introduction Let us quickly review the kind of integrls we hve studied so fr before we introduce new one. 1. Definite integrl. Given continuous rel-vlued

More information

AAPT UNITED STATES PHYSICS TEAM AIP 2010

AAPT UNITED STATES PHYSICS TEAM AIP 2010 2010 F = m Exm 1 AAPT UNITED STATES PHYSICS TEAM AIP 2010 Enti non multiplicnd sunt preter necessittem 2010 F = m Contest 25 QUESTIONS - 75 MINUTES INSTRUCTIONS DO NOT OPEN THIS TEST UNTIL YOU ARE TOLD

More information

Applications to Physics and Engineering

Applications to Physics and Engineering Section 7.5 Applictions to Physics nd Engineering Applictions to Physics nd Engineering Work The term work is used in everydy lnguge to men the totl mount of effort required to perform tsk. In physics

More information

Mathematics Higher Level

Mathematics Higher Level Mthemtics Higher Level Higher Mthemtics Exmintion Section : The Exmintion Mthemtics Higher Level. Structure of the exmintion pper The Higher Mthemtics Exmintion is divided into two ppers s detiled below:

More information

Phys 207. Announcements. Hwk3 is posted on course website Quizzes & answers will be posted on course website Formula sheets.

Phys 207. Announcements. Hwk3 is posted on course website Quizzes & answers will be posted on course website Formula sheets. Phys 07 Announcements Hwk3 is posted on course website Quizzes & nswers will be posted on course website ormul sheets Newton s 3 lws Tody s Agend How nd why do objects move? Dynmics 1 Dynmics Isc Newton

More information

Helicopter Theme and Variations

Helicopter Theme and Variations Helicopter Theme nd Vritions Or, Some Experimentl Designs Employing Pper Helicopters Some possible explntory vribles re: Who drops the helicopter The length of the rotor bldes The height from which the

More information

Physics 43 Homework Set 9 Chapter 40 Key

Physics 43 Homework Set 9 Chapter 40 Key Physics 43 Homework Set 9 Chpter 4 Key. The wve function for n electron tht is confined to x nm is. Find the normliztion constnt. b. Wht is the probbility of finding the electron in. nm-wide region t x

More information

Version 001 CIRCUITS holland (1290) 1

Version 001 CIRCUITS holland (1290) 1 Version CRCUTS hollnd (9) This print-out should hve questions Multiple-choice questions my continue on the next column or pge find ll choices efore nswering AP M 99 MC points The power dissipted in wire

More information

Treatment Spring Late Summer Fall 0.10 5.56 3.85 0.61 6.97 3.01 1.91 3.01 2.13 2.99 5.33 2.50 1.06 3.53 6.10 Mean = 1.33 Mean = 4.88 Mean = 3.

Treatment Spring Late Summer Fall 0.10 5.56 3.85 0.61 6.97 3.01 1.91 3.01 2.13 2.99 5.33 2.50 1.06 3.53 6.10 Mean = 1.33 Mean = 4.88 Mean = 3. The nlysis of vrince (ANOVA) Although the t-test is one of the most commonly used sttisticl hypothesis tests, it hs limittions. The mjor limittion is tht the t-test cn be used to compre the mens of only

More information

Or more simply put, when adding or subtracting quantities, their uncertainties add.

Or more simply put, when adding or subtracting quantities, their uncertainties add. Propgtion of Uncertint through Mthemticl Opertions Since the untit of interest in n eperiment is rrel otined mesuring tht untit directl, we must understnd how error propgtes when mthemticl opertions re

More information

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics. W02D3_0 Group Problem: Pulleys and Ropes Constraint Conditions

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics. W02D3_0 Group Problem: Pulleys and Ropes Constraint Conditions MSSCHUSES INSIUE OF ECHNOLOGY Deprtment of hysics 8.0 W02D3_0 Group roblem: ulleys nd Ropes Constrint Conditions Consider the rrngement of pulleys nd blocks shown in the figure. he pulleys re ssumed mssless

More information

Einstein. Mechanics. In Grade 10 we investigated kinematics, or movement described in terms of velocity, acceleration, displacement, and so on.

Einstein. Mechanics. In Grade 10 we investigated kinematics, or movement described in terms of velocity, acceleration, displacement, and so on. Cmbridge University Press 978-0-521-68359-3 - Study nd Mster Physicl Sciences Grde 11 Lerner s Book Krin Kelder More informtion MODULE 1 Einstein Mechnics motion force Glileo Newton decelerte moment of

More information

Diffraction and Interference of Light

Diffraction and Interference of Light rev 12/2016 Diffrction nd Interference of Light Equipment Qty Items Prt Number 1 Light Sensor CI-6504 1 Rotry Motion Sensor CI-6538 1 Single Slit Set OS-8523 1 Multiple Slit Set OS-8523 1 Liner Trnsltor

More information

Theory of Forces. Forces and Motion

Theory of Forces. Forces and Motion his eek extbook -- Red Chpter 4, 5 Competent roblem Solver - Chpter 4 re-lb Computer Quiz ht s on the next Quiz? Check out smple quiz on web by hurs. ht you missed on first quiz Kinemtics - Everything

More information

not to be republished NCERT POLYNOMIALS CHAPTER 2 (A) Main Concepts and Results (B) Multiple Choice Questions

not to be republished NCERT POLYNOMIALS CHAPTER 2 (A) Main Concepts and Results (B) Multiple Choice Questions POLYNOMIALS (A) Min Concepts nd Results Geometricl mening of zeroes of polynomil: The zeroes of polynomil p(x) re precisely the x-coordintes of the points where the grph of y = p(x) intersects the x-xis.

More information

Solutions to Section 1

Solutions to Section 1 Solutions to Section Exercise. Show tht nd. This follows from the fct tht mx{, } nd mx{, } Exercise. Show tht = { if 0 if < 0 Tht is, the bsolute vlue function is piecewise defined function. Grph this

More information

Newton s Three Laws. d dt F = If the mass is constant, this relationship becomes the familiar form of Newton s Second Law: dv dt

Newton s Three Laws. d dt F = If the mass is constant, this relationship becomes the familiar form of Newton s Second Law: dv dt Newton s Three Lws For couple centuries before Einstein, Newton s Lws were the bsic principles of Physics. These lws re still vlid nd they re the bsis for much engineering nlysis tody. Forml sttements

More information

Answer, Key Homework 4 David McIntyre Mar 25,

Answer, Key Homework 4 David McIntyre Mar 25, Answer, Key Homework 4 Dvid McIntyre 45123 Mr 25, 2004 1 his print-out should hve 18 questions. Multiple-choice questions my continue on the next column or pe find ll choices before mkin your selection.

More information

Lesson 10. Parametric Curves

Lesson 10. Parametric Curves Return to List of Lessons Lesson 10. Prmetric Curves (A) Prmetric Curves If curve fils the Verticl Line Test, it cn t be expressed by function. In this cse you will encounter problem if you try to find

More information

Section 2.3. Motion Along a Curve. The Calculus of Functions of Several Variables

Section 2.3. Motion Along a Curve. The Calculus of Functions of Several Variables The Clculus of Functions of Severl Vribles Section 2.3 Motion Along Curve Velocity ccelertion Consider prticle moving in spce so tht its position t time t is given by x(t. We think of x(t s moving long

More information

LECTURE #05. Learning Objective. To describe the geometry in and around a unit cell in terms of directions and planes.

LECTURE #05. Learning Objective. To describe the geometry in and around a unit cell in terms of directions and planes. LECTURE #05 Chpter 3: Lttice Positions, Directions nd Plnes Lerning Objective To describe the geometr in nd round unit cell in terms of directions nd plnes. 1 Relevnt Reding for this Lecture... Pges 64-83.

More information

PROBLEMS 13 - APPLICATIONS OF DERIVATIVES Page 1

PROBLEMS 13 - APPLICATIONS OF DERIVATIVES Page 1 PROBLEMS - APPLICATIONS OF DERIVATIVES Pge ( ) Wter seeps out of conicl filter t the constnt rte of 5 cc / sec. When the height of wter level in the cone is 5 cm, find the rte t which the height decreses.

More information

Rate and Activation Energy of the Iodination of Acetone

Rate and Activation Energy of the Iodination of Acetone nd Activtion Energ of the Iodintion of Acetone rl N. eer Dte of Eperiment: //00 Florence F. Ls (prtner) Abstrct: The rte, rte lw nd ctivtion energ of the iodintion of cetone re detered b observing the

More information

Mechanics Cycle 1 Chapter 5. Chapter 5

Mechanics Cycle 1 Chapter 5. Chapter 5 Chpter 5 Contct orces: ree Body Digrms nd Idel Ropes Pushes nd Pulls in 1D, nd Newton s Second Lw Neglecting riction ree Body Digrms Tension Along Idel Ropes (i.e., Mssless Ropes) Newton s Third Lw Bodies

More information

N Mean SD Mean SD Shelf # Shelf # Shelf #

N Mean SD Mean SD Shelf # Shelf # Shelf # NOV xercises smple of 0 different types of cerels ws tken from ech of three grocery store shelves (1,, nd, counting from the floor). summry of the sugr content (grms per serving) nd dietry fiber (grms

More information

Example 27.1 Draw a Venn diagram to show the relationship between counting numbers, whole numbers, integers, and rational numbers.

Example 27.1 Draw a Venn diagram to show the relationship between counting numbers, whole numbers, integers, and rational numbers. 2 Rtionl Numbers Integers such s 5 were importnt when solving the eqution x+5 = 0. In similr wy, frctions re importnt for solving equtions like 2x = 1. Wht bout equtions like 2x + 1 = 0? Equtions of this

More information

Math 22B Solutions Homework 1 Spring 2008

Math 22B Solutions Homework 1 Spring 2008 Mth 22B Solutions Homework 1 Spring 2008 Section 1.1 22. A sphericl rindrop evportes t rte proportionl to its surfce re. Write differentil eqution for the volume of the rindrop s function of time. Solution

More information

Chapter 6 Solving equations

Chapter 6 Solving equations Chpter 6 Solving equtions Defining n eqution 6.1 Up to now we hve looked minly t epressions. An epression is n incomplete sttement nd hs no equl sign. Now we wnt to look t equtions. An eqution hs n = sign

More information

4. DC MOTORS. Understand the basic principles of operation of a DC motor. Understand the operation and basic characteristics of simple DC motors.

4. DC MOTORS. Understand the basic principles of operation of a DC motor. Understand the operation and basic characteristics of simple DC motors. 4. DC MOTORS Almost every mechnicl movement tht we see round us is ccomplished by n electric motor. Electric mchines re mens o converting energy. Motors tke electricl energy nd produce mechnicl energy.

More information

www.mathsbox.org.uk e.g. f(x) = x domain x 0 (cannot find the square root of negative values)

www.mathsbox.org.uk e.g. f(x) = x domain x 0 (cannot find the square root of negative values) www.mthsbo.org.uk CORE SUMMARY NOTES Functions A function is rule which genertes ectl ONE OUTPUT for EVERY INPUT. To be defined full the function hs RULE tells ou how to clculte the output from the input

More information

PROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY

PROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY MAT 0630 INTERNET RESOURCES, REVIEW OF CONCEPTS AND COMMON MISTAKES PROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY Contents 1. ACT Compss Prctice Tests 1 2. Common Mistkes 2 3. Distributive

More information

A5682: Introduction to Cosmology Course Notes. 4. Cosmic Dynamics: The Friedmann Equation. = GM s R 2 s(t).

A5682: Introduction to Cosmology Course Notes. 4. Cosmic Dynamics: The Friedmann Equation. = GM s R 2 s(t). 4. Cosmic Dynmics: The Friedmnn Eqution Reding: Chpter 4 Newtonin Derivtion of the Friedmnn Eqution Consider n isolted sphere of rdius R s nd mss M s, in uniform, isotropic expnsion (Hubble flow). The

More information

Pythagoras theorem and trigonometry (2)

Pythagoras theorem and trigonometry (2) HPTR 10 Pythgors theorem nd trigonometry (2) 31 HPTR Liner equtions In hpter 19, Pythgors theorem nd trigonometry were used to find the lengths of sides nd the sizes of ngles in right-ngled tringles. These

More information

Version 001 Summer Review #03 tubman (IBII20142015) 1

Version 001 Summer Review #03 tubman (IBII20142015) 1 Version 001 Summer Reiew #03 tubmn (IBII20142015) 1 This print-out should he 35 questions. Multiple-choice questions my continue on the next column or pge find ll choices before nswering. Concept 20 P03

More information

An Off-Center Coaxial Cable

An Off-Center Coaxial Cable 1 Problem An Off-Center Coxil Cble Kirk T. McDonld Joseph Henry Lbortories, Princeton University, Princeton, NJ 08544 Nov. 21, 1999 A coxil trnsmission line hs inner conductor of rdius nd outer conductor

More information

Review Problems for the Final of Math 121, Fall 2014

Review Problems for the Final of Math 121, Fall 2014 Review Problems for the Finl of Mth, Fll The following is collection of vrious types of smple problems covering sections.,.5, nd.7 6.6 of the text which constitute only prt of the common Mth Finl. Since

More information

Lecture 3 Gaussian Probability Distribution

Lecture 3 Gaussian Probability Distribution Lecture 3 Gussin Probbility Distribution Introduction l Gussin probbility distribution is perhps the most used distribution in ll of science. u lso clled bell shped curve or norml distribution l Unlike

More information

Econ 4721 Money and Banking Problem Set 2 Answer Key

Econ 4721 Money and Banking Problem Set 2 Answer Key Econ 472 Money nd Bnking Problem Set 2 Answer Key Problem (35 points) Consider n overlpping genertions model in which consumers live for two periods. The number of people born in ech genertion grows in

More information

Projectile Motion CHAPTER 1

Projectile Motion CHAPTER 1 CHAPTER 1 PHYSICS ESSENTIALS STAGE 2 Projectile Motion Subject Outline In the bsence of ir resistnce nd moing under the ction of constnt grittionl force, projectile hs constnt ccelertion in the direction

More information

1. In the Bohr model, compare the magnitudes of the electron s kinetic and potential energies in orbit. What does this imply?

1. In the Bohr model, compare the magnitudes of the electron s kinetic and potential energies in orbit. What does this imply? Assignment 3: Bohr s model nd lser fundmentls 1. In the Bohr model, compre the mgnitudes of the electron s kinetic nd potentil energies in orit. Wht does this imply? When n electron moves in n orit, the

More information

Example A rectangular box without lid is to be made from a square cardboard of sides 18 cm by cutting equal squares from each corner and then folding

Example A rectangular box without lid is to be made from a square cardboard of sides 18 cm by cutting equal squares from each corner and then folding 1 Exmple A rectngulr box without lid is to be mde from squre crdbord of sides 18 cm by cutting equl squres from ech corner nd then folding up the sides. 1 Exmple A rectngulr box without lid is to be mde

More information

1479 INDUCTIVE PROXIMITY SENSORS

1479 INDUCTIVE PROXIMITY SENSORS 179 INDUCTIVE PROXIMITY SENSORS INTRODUCTION Principles of opertion A proximity sensor detects the pproch of n object without mking contct. There re three types of proximity sensors: 1) High-frequency

More information

, and the number of electrons is -19. e e 1.60 10 C. The negatively charged electrons move in the direction opposite to the conventional current flow.

, and the number of electrons is -19. e e 1.60 10 C. The negatively charged electrons move in the direction opposite to the conventional current flow. Prolem 1. f current of 80.0 ma exists in metl wire, how mny electrons flow pst given cross section of the wire in 10.0 min? Sketch the directions of the current nd the electrons motion. Solution: The chrge

More information

Factoring Polynomials

Factoring Polynomials Fctoring Polynomils Some definitions (not necessrily ll for secondry school mthemtics): A polynomil is the sum of one or more terms, in which ech term consists of product of constnt nd one or more vribles

More information

Plotting and Graphing

Plotting and Graphing Plotting nd Grphing Much of the dt nd informtion used by engineers is presented in the form of grphs. The vlues to be plotted cn come from theoreticl or empiricl (observed) reltionships, or from mesured

More information

Integration by Substitution

Integration by Substitution Integrtion by Substitution Dr. Philippe B. Lvl Kennesw Stte University August, 8 Abstrct This hndout contins mteril on very importnt integrtion method clled integrtion by substitution. Substitution is

More information

Vectors 2. 1. Recap of vectors

Vectors 2. 1. Recap of vectors Vectors 2. Recp of vectors Vectors re directed line segments - they cn be represented in component form or by direction nd mgnitude. We cn use trigonometry nd Pythgors theorem to switch between the forms

More information

Module Summary Sheets. C3, Methods for Advanced Mathematics (Version B reference to new book) Topic 2: Natural Logarithms and Exponentials

Module Summary Sheets. C3, Methods for Advanced Mathematics (Version B reference to new book) Topic 2: Natural Logarithms and Exponentials MEI Mthemtics in Ection nd Instry Topic : Proof MEI Structured Mthemtics Mole Summry Sheets C, Methods for Anced Mthemtics (Version B reference to new book) Topic : Nturl Logrithms nd Eponentils Topic

More information

Sect 8.3 Triangles and Hexagons

Sect 8.3 Triangles and Hexagons 13 Objective 1: Sect 8.3 Tringles nd Hexgons Understnding nd Clssifying Different Types of Polygons. A Polygon is closed two-dimensionl geometric figure consisting of t lest three line segments for its

More information

t 3 t 4 Part A: Multiple Choice Canadian Association of Physicists 1999 Prize Exam

t 3 t 4 Part A: Multiple Choice Canadian Association of Physicists 1999 Prize Exam Cndin Assocition of Physicists 1999 Prize Exm This is three hour exm. Ntionl rnking nd prizes will be bsed on student s performnce on both sections A nd B of the exm. However, performnce on the multiple

More information

Rational Functions. Rational functions are the ratio of two polynomial functions. Qx bx b x bx b. x x x. ( x) ( ) ( ) ( ) and

Rational Functions. Rational functions are the ratio of two polynomial functions. Qx bx b x bx b. x x x. ( x) ( ) ( ) ( ) and Rtionl Functions Rtionl unctions re the rtio o two polynomil unctions. They cn be written in expnded orm s ( ( P x x + x + + x+ Qx bx b x bx b n n 1 n n 1 1 0 m m 1 m + m 1 + + m + 0 Exmples o rtionl unctions

More information

Homework #6: Answers. a. If both goods are produced, what must be their prices?

Homework #6: Answers. a. If both goods are produced, what must be their prices? Text questions, hpter 7, problems 1-2. Homework #6: Answers 1. Suppose there is only one technique tht cn be used in clothing production. To produce one unit of clothing requires four lbor-hours nd one

More information

MATH 150 HOMEWORK 4 SOLUTIONS

MATH 150 HOMEWORK 4 SOLUTIONS MATH 150 HOMEWORK 4 SOLUTIONS Section 1.8 Show tht the product of two of the numbers 65 1000 8 2001 + 3 177, 79 1212 9 2399 + 2 2001, nd 24 4493 5 8192 + 7 1777 is nonnegtive. Is your proof constructive

More information

CONIC SECTIONS. Chapter 11

CONIC SECTIONS. Chapter 11 CONIC SECTIONS Chpter 11 11.1 Overview 11.1.1 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. 11.1). Fig. 11.1 Suppose we

More information

10.5 Graphing Quadratic Functions

10.5 Graphing Quadratic Functions 0.5 Grphing Qudrtic Functions Now tht we cn solve qudrtic equtions, we wnt to lern how to grph the function ssocited with the qudrtic eqution. We cll this the qudrtic function. Grphs of Qudrtic Functions

More information

Volumes of solids of revolution

Volumes of solids of revolution Volumes of solids of revolution We sometimes need to clculte the volume of solid which cn be obtined by rotting curve bout the x-xis. There is strightforwrd technique which enbles this to be done, using

More information

LINEAR TRANSFORMATIONS AND THEIR REPRESENTING MATRICES

LINEAR TRANSFORMATIONS AND THEIR REPRESENTING MATRICES LINEAR TRANSFORMATIONS AND THEIR REPRESENTING MATRICES DAVID WEBB CONTENTS Liner trnsformtions 2 The representing mtrix of liner trnsformtion 3 3 An ppliction: reflections in the plne 6 4 The lgebr of

More information

Variable Dry Run (for Python)

Variable Dry Run (for Python) Vrile Dr Run (for Pthon) Age group: Ailities ssumed: Time: Size of group: Focus Vriles Assignment Sequencing Progrmming 7 dult Ver simple progrmming, sic understnding of ssignment nd vriles 20-50 minutes

More information

P.3 Polynomials and Factoring. P.3 an 1. Polynomial STUDY TIP. Example 1 Writing Polynomials in Standard Form. What you should learn

P.3 Polynomials and Factoring. P.3 an 1. Polynomial STUDY TIP. Example 1 Writing Polynomials in Standard Form. What you should learn 33337_0P03.qp 2/27/06 24 9:3 AM Chpter P Pge 24 Prerequisites P.3 Polynomils nd Fctoring Wht you should lern Polynomils An lgeric epression is collection of vriles nd rel numers. The most common type of

More information

Scalar and Vector Quantities. A scalar is a quantity having only magnitude (and possibly phase). LECTURE 2a: VECTOR ANALYSIS Vector Algebra

Scalar and Vector Quantities. A scalar is a quantity having only magnitude (and possibly phase). LECTURE 2a: VECTOR ANALYSIS Vector Algebra Sclr nd Vector Quntities : VECTO NLYSIS Vector lgebr sclr is quntit hving onl mgnitude (nd possibl phse). Emples: voltge, current, chrge, energ, temperture vector is quntit hving direction in ddition to

More information

Section 5-4 Trigonometric Functions

Section 5-4 Trigonometric Functions 5- Trigonometric Functions Section 5- Trigonometric Functions Definition of the Trigonometric Functions Clcultor Evlution of Trigonometric Functions Definition of the Trigonometric Functions Alternte Form

More information

Basic Analysis of Autarky and Free Trade Models

Basic Analysis of Autarky and Free Trade Models Bsic Anlysis of Autrky nd Free Trde Models AUTARKY Autrky condition in prticulr commodity mrket refers to sitution in which country does not engge in ny trde in tht commodity with other countries. Consequently

More information

1. Find the zeros Find roots. Set function = 0, factor or use quadratic equation if quadratic, graph to find zeros on calculator

1. Find the zeros Find roots. Set function = 0, factor or use quadratic equation if quadratic, graph to find zeros on calculator AP Clculus Finl Review Sheet When you see the words. This is wht you think of doing. Find the zeros Find roots. Set function =, fctor or use qudrtic eqution if qudrtic, grph to find zeros on clcultor.

More information

Operations with Polynomials

Operations with Polynomials 38 Chpter P Prerequisites P.4 Opertions with Polynomils Wht you should lern: Write polynomils in stndrd form nd identify the leding coefficients nd degrees of polynomils Add nd subtrct polynomils Multiply

More information

EQUATIONS OF LINES AND PLANES

EQUATIONS OF LINES AND PLANES EQUATIONS OF LINES AND PLANES MATH 195, SECTION 59 (VIPUL NAIK) Corresponding mteril in the ook: Section 12.5. Wht students should definitely get: Prmetric eqution of line given in point-direction nd twopoint

More information

SOLUTIONS TO CONCEPTS CHAPTER 5

SOLUTIONS TO CONCEPTS CHAPTER 5 1. m k S 10m Let, ccelertion, Initil velocity u 0. S ut + 1/ t 10 ½ ( ) 10 5 m/s orce: m 5 10N (ns) 40000. u 40 km/hr 11.11 m/s. 3600 m 000 k ; v 0 ; s 4m v u ccelertion s SOLUIONS O CONCEPS CHPE 5 0 11.11

More information

6.2 Volumes of Revolution: The Disk Method

6.2 Volumes of Revolution: The Disk Method mth ppliction: volumes of revolution, prt ii Volumes of Revolution: The Disk Method One of the simplest pplictions of integrtion (Theorem ) nd the ccumultion process is to determine so-clled volumes of

More information

On the Meaning of Regression Coefficients for Categorical and Continuous Variables: Model I and Model II; Effect Coding and Dummy Coding

On the Meaning of Regression Coefficients for Categorical and Continuous Variables: Model I and Model II; Effect Coding and Dummy Coding Dt_nlysisclm On the Mening of Regression for tegoricl nd ontinuous Vribles: I nd II; Effect oding nd Dummy oding R Grdner Deprtment of Psychology This describes the simple cse where there is one ctegoricl

More information

Lecture 15 - Curve Fitting Techniques

Lecture 15 - Curve Fitting Techniques Lecture 15 - Curve Fitting Techniques Topics curve fitting motivtion liner regression Curve fitting - motivtion For root finding, we used given function to identify where it crossed zero where does fx

More information

1 Numerical Solution to Quadratic Equations

1 Numerical Solution to Quadratic Equations cs42: introduction to numericl nlysis 09/4/0 Lecture 2: Introduction Prt II nd Solving Equtions Instructor: Professor Amos Ron Scribes: Yunpeng Li, Mrk Cowlishw Numericl Solution to Qudrtic Equtions Recll

More information

9 CONTINUOUS DISTRIBUTIONS

9 CONTINUOUS DISTRIBUTIONS 9 CONTINUOUS DISTIBUTIONS A rndom vrible whose vlue my fll nywhere in rnge of vlues is continuous rndom vrible nd will be ssocited with some continuous distribution. Continuous distributions re to discrete

More information

Picture Match Words. Strobe pictures. Stopping distance. Following. Safety

Picture Match Words. Strobe pictures. Stopping distance. Following. Safety Tuesdy: Picture Mtch + Spelling Pyrmid Homework [the hndout for it is two pges down] Mterils: 1 bord + 1 set of words per 2 students (totl: 12 of ech) Routine: () once the Pictionry is completed; pirs

More information