Answer, Key Homework 10 David McIntyre 1


 Randell Owen
 2 years ago
 Views:
Transcription
1 Answer, Key Homework 10 Dvid McIntyre 1 This printout should hve 22 questions, check tht it is complete. Multiplechoice questions my continue on the next column or pge: find ll choices efore mking your selection. The due time is Centrl time. Chpter 26 prolems. 001 (prt 1 of 1) 0 points A prllelplte cpcitor is chrged y connecting it to ttery. If the ttery is disconnected nd the seprtion etween the pltes is incresed, wht will hppen to the chrge on the cpcitor nd the electric potentil cross it? 1. The chrge increses nd the electric potentil decreses. 2. The chrge decreses nd the electric potentil increses. 3. The chrge nd the electric potentil increse. 4. The chrge decreses nd the electric potentil remins fixed. 5. The chrge nd the electric potentil decrese. 6. The chrge remins fixed nd the electric potentil increses. correct 7. The chrge nd the electric potentil remin fixed. 8. The chrge increses nd the electric potentil remins fixed. 9. The chrge remins fixed nd the electric potentil decreses. Chrge is conserved, so it must remin constnt since it is stuck on the pltes. With the ttery disconnected, Q is fixed. C ɛ A d A lrger d mkes the frction smller, so C is smller. Thus the new potentil V Q C is lrger. 002 (prt 1 of 2) 5 points Given: A cpcitor network is shown elow. 14 µf 20 µf 7 µf 116 V Find the equivlent cpcitnce C etween points nd for the group of cpcitors. Correct nswer: µf. Given : C 1 14 µf, C 2 20 µf, C 3 7 µf, E B 116 V. C 1 C 2 C 3 E B nd The cpcitors C 1 nd C 2 re in series, so ( 1 C s + 1 ) 1 C 1 C 2 C 1 C 2. C s is prllel with C 3, so C C s + C 3 C 1 C 2 + C 3 (14 µf) (20 µf) 14 µf + 20 µf + 7 µf µf + 7 µf µf.
2 Answer, Key Homework 10 Dvid McIntyre (prt 2 of 2) 5 points Wht chrge is stored on the 7 µf cpcitor on the lower portin of the prllel circuit? Correct nswer: 812 µc. Since C s nd C 3 re prllel, the sme potentil E B V is cross oth, so q 3 C 3 V (7 µf) (116 V) 812 µc. 004 (prt 1 of 2) 5 points Four cpcitors re connected s shown in the figure. c 97 V 21 µf 68 µf d 35 µf 84 µf Find the cpcitnce etween points nd. Correct nswer: µf. A good rule of thum is to eliminte junctions connected y zero cpcitnce. C 1 C 4 C 2 C 3 The definition of cpcitnce is C Q V. The series connection of C 2 nd C 3 gives the equivlent cpcitnce 1 C C 2 C 3 C 2 C 3 C 2 + C 3 (35 µf) (68 µf) 35 µf + 68 µf µf. The totl cpcitnce C etween nd cn e otined y clculting the cpcitnce in the prllel comintion of the cpcitors C 1, C 4, nd C 23 ; i.e., C C 1 + C 4 + C µf + 84 µf µf µf. Given : C 1 21 µf, C 2 35 µf, C 3 68 µf, C 4 84 µf, E 97 V. C 1 c nd 005 (prt 2 of 2) 5 points Wht is the chrge on the 35 µf uppercentered cpcitor? Correct nswer: µc. The voltges cross C 2 nd C 3, respectively, (the voltge etween nd ) re V V V, nd we hve E B C 3 d C 2 C 4 Q 23 Q 3 Q 2 V C 23 (97 V) ( µf) µc. 006 (prt 1 of 2) 0 points
3 Answer, Key Homework 10 Dvid McIntyre 3 Two cpcitors of 21 µf nd 4.1 µf re connected prllel nd chrged with 131 V power supply. Clculte the totl energy stored in the two cpcitors. Correct nswer: J V 4.78 µf 5.6 µf 13.8 µf U C V 2 2 C prllel. Ech cpcitor hs voltge V, so U 1 2 ( ) V 2 Wht is effective cpcitnce C entire cpcitor network? Correct nswer: µf. Given: of the 1 (21 µf µf) (131 V) J. 007 (prt 2 of 2) 0 points Wht potentil difference would e required cross the sme two cpcitors connected in series in order for the comintion to store the sme energy s in the first prt? Correct nswer: V. When in series the equivlent cpcitnce is E B C µf, C µf, C µf, E B 17.1 V. nd C 1 C 2 C 3 C series C 1 C 2 (21 µf) (4.1 µf) 21 µf µf µf. Since U C eq V 2, we hve 2 V 2 U C eq 2 ( J) µf 106 µf 1 F V. 008 (prt 1 of 7) 2 points Given: A cpcitor network is shown in the following figure. C 1 nd C 2 re in series with ech other, nd they re together re prllel with C 3. So C C 1 C 2 + C 3 (4.78 µf) (5.6 µf) µf 4.78 µf µf µf. 009 (prt 2 of 7) 2 points Wht is the voltge cross the 5.6 µf upper righthnd cpcitor? Correct nswer: V. Since C 1 nd C 2 re in series they crry the sme chrge C 1 V 1 C 2 V 2,
4 Answer, Key Homework 10 Dvid McIntyre 4 nd their voltges dd up to V, voltge of the ttery V 1 + V 2 V C 2 V 2 + V 2 V C 1 C 2 V 2 + C 1 V 2 V C 1 V 2 V C 1 (17.1 V)(4.78 µf) 4.78 µf µf V. 010 (prt 3 of 7) 2 points If dielectric of constnt 4.18 is inserted in the 5.6 µf top righthnd cpcitor (when the ttery is connected), wht is the electric potentil cross the 4.78 µf top lefthnd cpcitor? Correct nswer: V. Given : κ When the dielectric is inserted, the cpcitnce formerly C 2 ecomes C 2 κ C 2, nd the new voltge cross C 1 is V 1 V C 2 C 1 + C 2 κ V C 2 C 1 + κ C 2 (4.18)(17.1 V)(5.6 µf) 4.78 µf + (4.18)(5.6 µf) V. 011 (prt 4 of 7) 1 points If the ttery is disconnected nd then the dielectric is removed, wht is the chrge on 4.78 µf top lefthnd cpcitor? Correct nswer: µc. Immeditely efore the ttery ws disconnected the chrges on the cpcitors hd een Q 3 C 3 V (13.8 µf)(17.1 V) µc Q 1 Q 2 C 12V ( µf)(17.1 V) µc. When we remove the dielectric, the sum of the chrges stys the sme, nd the voltges on C 3 nd on C 12 (where C 12 is the equivlent cpcitnce of C 1 nd C 2 in series) re equl to ech other Therefore Q 1 + Q 3 Q 1 + Q 3 Q 1 Q 3. C 12 C 3 Q 1 Q 1 + Q C 3 C µc µc 13.8 µf µf µc. 012 (prt 5 of 7) 1 points Wht is now the voltge drop cross the 5.6 µf top righthnd cpcitor? Correct nswer: V. V 2 Q 2 C 2 Q 1 C µc 5.6 µf V. 013 (prt 6 of 7) 1 points Wht ws the energy stored in the system
5 Answer, Key Homework 10 Dvid McIntyre 5 efore the dielectric ws removed? Correct nswer: J. The totl cpcitnce of the system efore the dielectric ws removed hd een C C 12 + C µf µf µf so the energy stored in the system ws U 1 2 C V µj J. 014 (prt 7 of 7) 1 points Wht is the energy stored in the system fter the dielectric ws removed? Correct nswer: J. Since the ttery is disconnected, the totl chrge is conserved: Q Q C V ( µf)(17.1 V) µc. Therefore, the energy stored is U Q 2 2 C µj J. 015 (prt 1 of 1) 0 points A sheet of mic is inserted etween the pltes of n isolted chrged prllelplte cpcitor. Which of the following sttements is true? 1. The potentil difference cross the cpcitor decreses. correct 2. The energy of the cpcitor does not chnge. 3. The cpcitnce decreses. 4. The chrge on the cpcitor pltes decreses. 5. The electric field etween the cpcitor pltes increses. Since the cpcitor is isolted, the chrge on the cpcitor pltes remins the sme. On the other hnd, the cpcitnce is incresed y introducing dielectric. Therefore, from V Q, the potentil difference cross the C cpcitor is decresed. 016 (prt 1 of 1) 0 points A prllel plte cpcitor is ttched to ttery which mintins constnt potentil difference of V etween the pltes. While the ttery is still connected, glss sl is inserted so s to just fill the spce etween the cpcitor pltes. V The stored energy will 1. remin the sme. 2. increse. correct 3. decrese. The energy stored in the cpcitor is given y U V Q2 2 κc κ C 2 V 2 Without the glss, the stored energy is U C V 2 After inserting the glss, it ecomes U 1 2 κ C V 2
6 Answer, Key Homework 10 Dvid McIntyre 6 Since κ > 1, the stored energy will increse. 017 (prt 1 of 6) 2 points A prllelplte cpcitor hs plte re of 105 cm 2 nd plte seprtion of 2.25 mm. A potentil difference of 5.87 V is pplied cross the pltes with only ir etween the pltes. The ttery is then disconnected, nd piece of glss (κ 8.53) is inserted to completely fill the spce etween the pltes. Wht is the cpcitnce efore the dielectric is inserted? Correct nswer: F. Given : ɛ C 2 /N m 2, A 105 cm 2, nd d 2.25 mm. The cpcitnce efore the dielectric is inserted is C 1 ɛ 0 A ( d C 2 /N m 2) (105 cm 2 ) (2.25 mm) F. 018 (prt 2 of 6) 2 points Wht is the cpcitnce fter the dielectric is inserted? Correct nswer: F. Given : κ The cpcitnce fter the dielectric is inserted is C 2 κ ɛ 0 A d (8.53) (ɛ 0) (105 cm 2 ) (2.25 mm) F. Wht is the chrge on the pltes efore the dielectric is inserted? Correct nswer: C. Given : V 5.87 V. The chrge on the pltes efore the dielectric is inserted is given y Q 1 C 1 V ( F) (5.87 V) C. 020 (prt 4 of 6) 2 points Wht is the chrge on the pltes fter the dielectric is inserted? Correct nswer: C. The chrge on the pltes doesn t chnge fter the dielectric is inserted, so it is given y Q 2 Q C. 021 (prt 5 of 6) 1 points Wht is the potentil difference cross the pltes efore the dielectric is inserted? Correct nswer: 5.87 V. The potentil difference cross the pltes efore the dielectric is inserted is given y V 1 V 5.87 V. 022 (prt 6 of 6) 1 points Wht is the potentil difference cross the pltes fter the dielectric is inserted? Correct nswer: V. The potentil difference cross the pltes fter the dielectric is inserted is given y V 2 V κ 5.87 V V. 019 (prt 3 of 6) 2 points
Version 001 CIRCUITS holland (1290) 1
Version CRCUTS hollnd (9) This printout should hve questions Multiplechoice 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 informationENGR HOMEWORK6SOLUTIONS
ENGR 215 HOMEWORK6SOLUTIONS 1. Exercise 26.5 2. Exercise 26.6 3. Exercise 26.31 4. Exercise 26.32 5. Exercise 26.36 6. Exercise 26.4 7. Exercise 26.43 8. Exercise 26.54 9. Prolem 26.64 1. Prolem 26.67
More informationAnswer, Key Homework 8 David McIntyre 1
Answer, Key Homework 8 Dvid McIntyre 1 This printout should hve 17 questions, check tht it is complete. Multiplechoice questions my continue on the net column or pge: find ll choices before mking your
More informationWeek 4  Capacitors and Capacitance
Week 4  Cpcitors nd Cpcitnce Sheldon, you don t give your mother enough credit. She s wrm, she s loving, she doesn t glue electrodes to your hed to mesure your brin wves while potty trining. Leonrd Hofstdter
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.
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 information2 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 informationWeek 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 informationPHYS1231 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 informationSirindhorn 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 information5.2 The Definite Integral
5.2 THE DEFINITE INTEGRAL 5.2 The Definite Integrl In the previous section, we sw how to pproximte totl chnge given the rte of chnge. In this section we see how to mke the pproximtion more ccurte. Suppose
More informationPSI AP Physics 2 Electric Potential and Capacitors Multiple Choice Questions. Multiple Choice Questions
PSI AP Phyic 2 Electric Potentil nd Cpcitor Multiple Choice Quetion Multiple Choice Quetion. A metl wire connect two chrged conducting phere. Sphere h greter rdiu thn phere 2. Which of the following ttement
More informationElectric Circuits. Simple Electric Cell. Electric Current
Electric Circuits Count Alessndro olt (74587) Georg Simon Ohm (787854) Chrles Augustin de Coulomb (736 806) André Mrie AMPÈRE (775836) Crbon Electrode () Simple Electric Cell wire Zn Zn Zn Zn Sulfuric
More informationNumerical Solutions of Linear Systems of Equations
EE 6 Clss Notes Numericl Solutions of Liner Systems of Equtions Liner Dependence nd Independence An eqution in set of equtions is linerly independent if it cnnot e generted y ny liner comintion of the
More informationChapter 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 6.0µ105 T nd is directed t n
More informationGRADE 7 ADAPTED NJDOE ASSESSMENT. Assessed Standards: 7.NS.1 7.NS.2 7.NS.3. (To be administered after NPS Grade 7 Scope and Sequence Units 1&2)
ADAPTED NJDOE ASSESSMENT GRADE 7 (To e dministered fter NPS Grde 7 Scope nd Sequence Units &2) Assessed Stndrds: 7.NS. 7.NS.2 7.NS.3 The Newrk Pulic Schools  Office of Mthemtics 203 Nme Period Dte Grde
More information1. 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 printout should he 30 questions. Multiplechoice questions my continue on the next column or pge find ll choices before nswering. The due time
More informationCapacitance and Dielectrics
2.2 This is the Nerest One He 803 P U Z Z L E R Mny electronic components crry wrning lel like this one. Wht is there insie these evices tht mkes them so ngerous? Why wouln t you e sfe if you unplugge
More information2 If a branch is prime, no other factors
Chpter 2 Multiples, nd primes 59 Find the prime of 50 by drwing fctor tree. b Write 50 s product of its prime. 1 Find fctor pir of the given 50 number nd begin the fctor tree (50 = 5 10). 5 10 2 If brnch
More information11. PYTHAGORAS THEOREM
11. PYTHAGORAS THEOREM 111 Along the Nile 2 112 Proofs of Pythgors theorem 3 113 Finding sides nd ngles 5 114 Semiirles 7 115 Surds 8 116 Chlking hndll ourt 9 117 Pythgors prolems 10 118 Designing
More informationChapter 28. Direct Current Circuits
858 CHAPTER 28 Direct Current Circuits Chpter 28 Direct Current Circuits CHAPTER OUTLNE 28.1 Electromotive Force 28.2 Resistors in Series nd Prllel 28.3 Kirchhoff s Rules 28.4 RC Circuits 28.5 Electricl
More informationFactoring 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 informationr 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 informationPolynomial 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 informationLet us recall some facts you have learnt in previous grades under the topic Area.
6 Are By studying this lesson you will be ble to find the res of sectors of circles, solve problems relted to the res of compound plne figures contining sectors of circles. Ares of plne figures Let us
More informationFirm Objectives. The Theory of the Firm II. Cost Minimization Mathematical Approach. First order conditions. Cost Minimization Graphical Approach
Pro. Jy Bhttchry Spring 200 The Theory o the Firm II st lecture we covered: production unctions Tody: Cost minimiztion Firm s supply under cost minimiztion Short vs. long run cost curves Firm Ojectives
More informationProblem Set 2 Solutions
University of Cliforni, Berkeley Spring 2012 EE 42/100 Prof. A. Niknej Prolem Set 2 Solutions Plese note tht these re merely suggeste solutions. Mny of these prolems n e pprohe in ifferent wys. 1. In prolems
More information1. 0 m/s m/s m/s m/s
Version PREVIEW Kine Grphs PRACTICE burke (1111) 1 This printout should he 30 questions. Multiplechoice questions m continue on the next column or pge find ll choices before nswering. Distnce Time Grph
More informationBinary Representation of Numbers Autar Kaw
Binry Representtion of Numbers Autr Kw After reding this chpter, you should be ble to: 1. convert bse rel number to its binry representtion,. convert binry number to n equivlent bse number. In everydy
More informationThe Velocity Factor of an Insulated TwoWire Transmission Line
The Velocity Fctor of n Insulted TwoWire 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 informationVersion 001 Summer Review #03 tubman (IBII20142015) 1
Version 001 Summer Reiew #03 tubmn (IBII20142015) 1 This printout should he 35 questions. Multiplechoice questions my continue on the next column or pge find ll choices before nswering. Concept 20 P03
More informationP.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 informationName: Lab Partner: Section:
Chpter 4 Newton s 2 nd Lw Nme: Lb Prtner: Section: 4.1 Purpose In this experiment, Newton s 2 nd lw will be investigted. 4.2 Introduction How does n object chnge its motion when force is pplied? A force
More informationPHYS 110A  HW #7 Solutions by David Pace Any referenced equations are from Griffiths
PHYS 110A  HW #7 Solutions by Dvid Pce Any referenced equtions re from Griffiths [1.] Problem 4.11 from Griffiths A cylinder of length L nd rdius hs permnent polriztion prllel to its xis. Find the bound
More information4.0 5Minute Review: Rational Functions
mth 130 dy 4: working with limits 1 40 5Minute Review: Rtionl Functions DEFINITION A rtionl function 1 is function of the form y = r(x) = p(x) q(x), 1 Here the term rtionl mens rtio s in the rtio of two
More informationQuadratic Equations  1
Alger Module A60 Qudrtic Equtions  1 Copyright This puliction The Northern Alert Institute of Technology 00. All Rights Reserved. LAST REVISED Novemer, 008 Qudrtic Equtions  1 Sttement of Prerequisite
More informationTwo hours UNIVERSITY OF MANCHESTER SCHOOL OF COMPUTER SCIENCE. Date: Friday 16 th May 2008. Time: 14:00 16:00
COMP20212 Two hours UNIVERSITY OF MANCHESTER SCHOOL OF COMPUTER SCIENCE Digitl Design Techniques Dte: Fridy 16 th My 2008 Time: 14:00 16:00 Plese nswer ny THREE Questions from the FOUR questions provided
More informationStrong acids and bases
Monoprotic AcidBse Equiliri (CH ) ϒ Chpter monoprotic cids A monoprotic cid cn donte one proton. This chpter includes uffers; wy to fi the ph. ϒ Chpter 11 polyprotic cids A polyprotic cid cn donte multiple
More informationChapter 9: Quadratic Equations
Chpter 9: Qudrtic Equtions QUADRATIC EQUATIONS DEFINITION + + c = 0,, c re constnts (generlly integers) ROOTS Synonyms: Solutions or Zeros Cn hve 0, 1, or rel roots Consider the grph of qudrtic equtions.
More informationSAT PHYSICS SUBJECT TEST 1
SAT PHYSICS SUBJECT TEST TEST Your responses to the Physics Subject Test questions should be filled in on Test of your nswer sheet (t the bck of the book). PHYSICS SUBJECT TEST 75 Questions Time limit
More informationhas the desired form. On the other hand, its product with z is 1. So the inverse x
First homework ssignment p. 5 Exercise. Verify tht the set of complex numers of the form x + y 2, where x nd y re rtionl, is sufield of the field of complex numers. Solution: Evidently, this set contins
More informationCHAPTEROPENING QUESTION
This cell phone hs n ttchment tht mesures person s lood sugr level, nd plots it over period of dys. All electronic devices contin circuits tht re dc, t lest in prt. The circuit digrm elow shows possile
More informationPhysics 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. nmwide region t x
More informationCapacitance and Dielectrics. Q26.3 The parallelconnected capacitors store more energy, since they have higher equivalent capacitance.
6 pcitnce n Dielectrics HAPTER OUTLNE 6 Deinition o pcitnce 6 lculting pcitnce 6 omintions o pcitors 64 Energy Store in hrge pcitor 65 pcitors with Dielectrics 66 Electric Dipole in n Electric iel 67 An
More informationAssuming all values are initially zero, what are the values of A and B after executing this Verilog code inside an always block? C=1; A <= C; B = C;
B26 Appendix B The Bsics of Logic Design Check Yourself ALU n [Arthritic Logic Unit or (rre) Arithmetic Logic Unit] A rndomnumer genertor supplied s stndrd with ll computer systems Stn KellyBootle,
More information4 Geometry: Shapes. 4.1 Circumference and area of a circle. FM Functional Maths AU (AO2) Assessing Understanding PS (AO3) Problem Solving HOMEWORK 4A
Geometry: Shpes. Circumference nd re of circle HOMEWORK D C 3 5 6 7 8 9 0 3 U Find the circumference of ech of the following circles, round off your nswers to dp. Dimeter 3 cm Rdius c Rdius 8 m d Dimeter
More information1.2 c. = or 58.7% Similarly weight fraction of Se is. = or 41.3%
1. c Consider the semiconducting IIVI compound cdmium selenide,. Given the tomic msses of nd, find the weight frctions of nd in the compound nd grms of nd needed to mke 100 grms of. The tomic mss of nd
More informationDouble 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 informationBasic Math Review. Numbers. Important Properties. Absolute Value PROPERTIES OF ADDITION NATURAL NUMBERS {1, 2, 3, 4, 5, }
ƒ Bsic Mth Review Numers NATURAL NUMBERS {1,, 3, 4, 5, } WHOLE NUMBERS {0, 1,, 3, 4, } INTEGERS {, 3,, 1, 0, 1,, } The Numer Line 5 4 3 1 0 1 3 4 5 Negtive integers Positive integers RATIONAL NUMBERS All
More informationSimple Electric Circuits
Simple Eletri Ciruits Gol: To uild nd oserve the opertion of simple eletri iruits nd to lern mesurement methods for eletri urrent nd voltge using mmeters nd voltmeters. L Preprtion Eletri hrges move through
More informationCONIC 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 informationPROBLEMS 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 information1 of 7 9/14/15, 10:27 AM
Stuent: Dte: Instructor: Doug Ensle Course: MAT117 1 Applie Sttistics  Ensle Assignment: Online 6  Section 3.2 1 of 7 9/14/15, 1:27 AM 1. 2 of 7 9/14/15, 1:27 AM The t on the right shows the percent
More informationVariable 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 2050 minutes
More informationMultiplication and Division  Left to Right. Addition and Subtraction  Left to Right.
Order of Opertions r of Opertions Alger P lese Prenthesis  Do ll grouped opertions first. E cuse Eponents  Second M D er Multipliction nd Division  Left to Right. A unt S hniqu Addition nd Sutrction
More informationHomework #6 Chapter 7 Homework Acids and Bases
Homework #6 Chpter 7 Homework Acids nd Bses 18. ) H O(l) H 3O (q) OH (q) H 3 O OH Or H O(l) H (q) OH (q) H OH ) HCN(q) H O(l) H 3O (q) CN (q) H 3 O HCN CN Or HCN(q) H (q) CN (q) H CN HCN c) NH 3(q) H O(l)
More informationPhysics 2102 Lecture 2. Physics 2102
Physics 10 Jonthn Dowling Physics 10 Lecture Electric Fields ChrlesAugustin de Coulomb (17361806) Jnury 17, 07 Version: 1/17/07 Wht re we going to lern? A rod mp Electric chrge Electric force on other
More informationv T R x m Version PREVIEW Practice 7 carroll (11108) 1
Version PEVIEW Prctice 7 crroll (08) his printout should he 5 questions. Multiplechoice questions y continue on the next colun or pge find ll choices before nswering. Atwood Mchine 05 00 0.0 points A
More informationOr 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 informationIn the following there are presented four different kinds of simulation games for a given Büchi automaton A = :
Simultion Gmes Motivtion There re t lest two distinct purposes for which it is useful to compute simultion reltionships etween the sttes of utomt. Firstly, with the use of simultion reltions it is possile
More informationt 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 informationHomework 3 Solutions
CS 341: Foundtions of Computer Science II Prof. Mrvin Nkym Homework 3 Solutions 1. Give NFAs with the specified numer of sttes recognizing ech of the following lnguges. In ll cses, the lphet is Σ = {,1}.
More informationThe R here might represent the resistance of the flashlight bulb. Here, V=IR1, or I = V*(1/R1)
191 (SJP, Phys 2020, F 01) Electricl Circuits: Mny rel world electronic devices re just collections of wires, resistors, cpcitors, nd btteries, forming circuits tht do something (flshlights, tosters,
More informationSolutions 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 informationAluminium 3 Section Loft Ladder
Instlltion nd User Instructions Aluminium Section Loft Ldder Model No. LT0 IMPORTANT: DO NOT use the loft ldder until fully instlled. Before instlltion crefully red ll of the sfety, instlltion nd user
More informationTests for One Poisson Mean
Chpter 412 Tests for One Poisson Men Introduction The Poisson probbility lw gives the probbility distribution of the number of events occurring in specified intervl of time or spce. The Poisson distribution
More informationRational Expressions
C H A P T E R Rtionl Epressions nformtion is everywhere in the newsppers nd mgzines we red, the televisions we wtch, nd the computers we use. And I now people re tlking bout the Informtion Superhighwy,
More informationnot 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 xcoordintes of the points where the grph of y = p(x) intersects the xxis.
More informationOperations 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 informationPHY 222 Lab 8 MOTION OF ELECTRONS IN ELECTRIC AND MAGNETIC FIELDS
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,
More informationThe remaining two sides of the right triangle are called the legs of the right triangle.
10 MODULE 6. RADICAL EXPRESSIONS 6 Pythgoren Theorem The Pythgoren Theorem An ngle tht mesures 90 degrees is lled right ngle. If one of the ngles of tringle is right ngle, then the tringle is lled right
More informationCHAPTER 9: Moments of Inertia
HPTER 9: Moments of nerti! Moment of nerti of res! Second Moment, or Moment of nerti, of n re! Prllelis Theorem! Rdius of Grtion of n re! Determintion of the Moment of nerti of n re ntegrtion! Moments
More informationEQUATIONS 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 pointdirection nd twopoint
More information. At first sight a! b seems an unwieldy formula but use of the following mnemonic will possibly help. a 1 a 2 a 3 a 1 a 2
7 CHAPTER THREE. Cross Product Given two vectors = (,, nd = (,, in R, the cross product of nd written! is defined to e: " = (!,!,! Note! clled cross is VECTOR (unlike which is sclr. Exmple (,, " (4,5,6
More informationChapter 5: Elasticity. measures how strongly people respond to changes in prices and changes in income.
Chpter 5: Elsticity Elsticity responsiveness mesures how strongly people respond to chnges in prices nd chnges in income. Exmples of questions tht elsticity helps nswer Wht hppens to ttendnce t your museum
More informationMath 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 informationECO 201: ELEMENTS OF MICROECONOMICS
ECO 0: ELEENTS OF ICROECONOICS The Theor of Consumer ehviour SALE QUESTIONS AND ANSWERS ) Dorcs level 00 student of Ketsco, clls her prent to send her mone to u ilo which cost $ ech nd ooks which cost
More informationHomework Assignment 1 Solutions
Dept. of Mth. Sci., WPI MA 1034 Anlysis 4 Bogdn Doytchinov, Term D01 Homework Assignment 1 Solutions 1. Find n eqution of sphere tht hs center t the point (5, 3, 6) nd touches the yzplne. Solution. The
More informationSolutions for the problems about Calculation of ph in the case of monoprotic acids and bases. 1. What is the ph of a 0.1 M acetic acid solution?
Solutions for the prolems out Clcultion of ph in the cse of monoprotic cids nd ses 1. Wht is the ph of 0.1 M cetic cid solution? Acetic cid is wek cid with = 1.86 5 nd in this cse c wek cid >>>, tht is
More informationAnswer, Key Homework 4 David McIntyre Mar 25,
Answer, Key Homework 4 Dvid McIntyre 45123 Mr 25, 2004 1 his printout should hve 18 questions. Multiplechoice questions my continue on the next column or pe find ll choices before mkin your selection.
More informationUnit 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 informationReasoning to Solve Equations and Inequalities
Lesson4 Resoning to Solve Equtions nd Inequlities In erlier work in this unit, you modeled situtions with severl vriles nd equtions. For exmple, suppose you were given usiness plns for concert showing
More informationSurface Area and Volume
Surfce Are nd Volume Student Book  Series J Mthletics Instnt Workooks Copyright Surfce re nd volume Student Book  Series J Contents Topics Topic  Surfce re of right prism Topic 2  Surfce re of right
More informationVectors and dyadics. Chapter 2. Summary. 2.1 Examples of scalars, vectors, and dyadics
Chpter 2 Vectors nd dydics Summry Circ 1900 A.D., J. Willird Gis proposed the ide of vectors nd their higherdimensionl counterprts dydics, tridics, ndpolydics. Vectors descrie threedimensionl spce nd
More informationNQF Level: 2 US No: 7480
NQF Level: 2 US No: 7480 Assessment Guide Primry Agriculture Rtionl nd irrtionl numers nd numer systems Assessor:.......................................... Workplce / Compny:.................................
More informationScalar 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 informationUse 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 information1. 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 informationNet 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 informationMath 314, Homework Assignment 1. 1. Prove that two nonvertical lines are perpendicular if and only if the product of their slopes is 1.
Mth 4, Homework Assignment. Prove tht two nonverticl lines re perpendiculr if nd only if the product of their slopes is. Proof. Let l nd l e nonverticl lines in R of slopes m nd m, respectively. Suppose
More informationLines and Angles. 2. Straight line is a continuous set of points going on forever in both directions:
Lines nd Angles 1. Point shows position. A 2. Stright line is continuous set of points going on forever in oth directions: 3. Ry is line with one endpoint. The other goes on forever. G 4. Line segment
More informationExponentiation: Theorems, Proofs, Problems Pre/Calculus 11, Veritas Prep.
Exponentition: Theorems, Proofs, Problems Pre/Clculus, Verits Prep. Our Exponentition Theorems Theorem A: n+m = n m Theorem B: ( n ) m = nm Theorem C: (b) n = n b n ( ) n n Theorem D: = b b n Theorem E:
More informationMerCarb 2 bbl Carburetor
TO: SERVICE MANAGER TECHNICIANS PARTS MANAGER No. 978 Revised June 1999. Informtion underlined is new. MerCr 2 l Cruretor 8 Point Cruretor Check List To ensure tht the cruretor is the cuse of the engine
More informationSquare Roots Teacher Notes
Henri Picciotto Squre Roots Techer Notes This unit is intended to help students develop n understnding of squre roots from visul / geometric point of view, nd lso to develop their numer sense round this
More informationBasic Research in Computer Science BRICS RS0213 Brodal et al.: Solving the String Statistics Problem in Time O(n log n)
BRICS Bsic Reserch in Computer Science BRICS RS0213 Brodl et l.: Solving the String Sttistics Prolem in Time O(n log n) Solving the String Sttistics Prolem in Time O(n log n) Gerth Stølting Brodl Rune
More informationBasic 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 informationUniform convergence and its consequences
Uniform convergence nd its consequences The following issue is centrl in mthemtics: On some domin D, we hve sequence of functions {f n }. This mens tht we relly hve n uncountble set of ordinry sequences,
More informationExperiment 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 informationAcidBase Equilibria. 18.1 AcidBase Definitions
AcidBse Equiliri Acids shrp, sour tste; Bses sopy, itter tste Neutrliztion (proton trnsfer) rections cid se slt wter (or other products) Proton (H ) strongly hydrted in wter H(H O) n Hydronium ion H O
More informationLectures 8 and 9 1 Rectangular waveguides
1 Lectures 8 nd 9 1 Rectngulr wveguides y b x z Consider rectngulr wveguide with 0 < x b. There re two types of wves in hollow wveguide with only one conductor; Trnsverse electric wves
More information