1. 1 m/s m/s m/s. 5. None of these m/s m/s m/s m/s correct m/s
|
|
|
- Angelina Reeves
- 7 years ago
- Views:
Transcription
1 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 is Centrl time. Displcement s Time 04 02:02, trigonometry, multiple choice, > 1 min, fixed. 001 Consider the following grph Displcement s Time 10 displcement (m) time (s) Wht is the position t 10 s? 1. 3 m Explntion: Red the position from the grph. 002 Wht is the elocity t 10 s? 1. 1 m/s 2. Unble to determine 3. 2 m/s 4. 3 m/s 5. None of these 6. 4 m/s 7. 3 m/s 8. 2 m/s 9. 0 m/s m/s Explntion: At 10 s, the slope is Unble to determine 3. 2 m 4. 4 m 5. 2 m 6. 1 m 7. 3 m 8. None of these 9. 0 m m Kinemtics2 1 02:02, trigonometry, multiple choice, < 1 min, fixed. 003 The grph shows position s function of time for two trins running on prllel trcks. At time t = 0 (origin) the position of both trins is 0.
2 Crete ssignment, 99552, Homework 5, Sep 15 t 10:11 m 2 position A B cr g O + Which is true? t B time Which elocity grph shows the cr moing towrd the right (wy from the origin) t stedy (constnt) elocity? 1. At time t B, both trins he the sme elocity 2. Both trins speed up ll the time 3. Both trins he the sme elocity t some time before t B 4. Somewhere before time t B, both trins he the sme ccelertion 5. In the time interl from t=0 to t=t B, trin B coers more distnce thn trin A Explntion: The slope of the cure B is prllel to line A t some point t < t B. Velocity Time Grph 02:02, trigonometry, multiple choice, < 1 min, wording-rible. 004 The following 4 questions refer to toy cr which cn moe to the right or left long horizontl line. The positie direction is to the right. Choose the elocity-time grph for ech of the following questions. Assume: Friction is so smll tht it cn be ignored.
3 Crete ssignment, 99552, Homework 5, Sep 15 t 10:11 m 3 8. t 9. t 10. None of these grphs re. Explntion: Since the elocity is constnt, the grph is stright line. Since the cr is moing to the right the elocity is positie. t 005 Which elocity grph shows the cr moing towrds the right (wy from the origin) reersing direction nd then moing to the left? 8. t 9. t 10. None of these grphs re. Explntion: Since the cr reerses its direction, the elocity is positie nd then negtie.
4 Crete ssignment, 99552, Homework 5, Sep 15 t 10:11 m 4 t 006 Which elocity grph shows the cr moing towrd the left (towrd the origin) t stedy (constnt) elocity? 8. t 9. t 10. None of these grphs re. Explntion: The sme reson s Prt Which elocity grph shows the cr incresing its speed towrds the right (wy from the origin) t stedy (constnt) rte?
5 Crete ssignment, 99552, Homework 5, Sep 15 t 10:11 m 5 X s T 02:02, trigonometry, multiple choice, > 1 min, fixed. 008 A trin cr moes long long stright trck. The grph shows the position s function of time for this trin. x The grph shows tht the trin t 1. speeds up ll the time. 8. t 9. t 10. None of these grphs re. Explntion: Since the cr s speed is incresing t constnt rte, the slope of the grph is constnt. t 2. slows down ll the time. 3. speeds up prt of the time nd slows down prt of the time. 4. moes t constnt elocity. Explntion: The slope of the cure diminishes s time increses, hence the trin slows down ll the time. Velocity Reltionships 01 02:03, trigonometry, multiple choice, > 1 min, fixed. 009 Consider three position cures between time points t A nd t B. s s A = A + B, A 2 3 when is constnt. 2 s 1 B B 0 t A t B t Choose the reltionship mong quntities 1, 2, nd = 2 = 3
6 Crete ssignment, 99552, Homework 5, Sep 15 t 10:11 m < 2 < > 2 > 3 Explntion: Bsic Concepts: The erge elocity of n object is defined s follows = displcement time = s B s A t B t A. Solution: All three cures he exctly the sme chnge in position s = s B s A in exctly the sme time interl t = t B t A. Hence ll three erge elocities re equl 1 = 2 = 3. Displcement s Time 02 02:04, trigonometry, multiple choice, < 1 min, fixed. 010 Consider the displcement cure: OABC Displcement s Time x (m) O A t (s) Choose the pproprite quntity for the erge elocity OA from point O to A. 1. OA = +2 m/s 2. OA = 0 m/s B C 3. OA = + 3 m/s 4. OA = 3 m/s 5. OA = 2 m/s Explntion: Definitions: Aerge elocity: = displcement time Aerge speed: s = distnce time Instntneous elocity: = d x dt Instntneous speed: s = Solution: Note tht the displcement x is on the erticl xis nd tht time t is on the horizontl xis. The key here is to know tht elocity uses net displcement in its eqution while speed uses totl distnce treled. OA = x A x O t A t O = = +2 m/s. The lues for the erge elocity come directly from eluting the definitions. 011 Choose the pproprite quntity for the erge elocity OB for the motion from point O to point B. 1. OB = 0 m/s 2. OB = +2 m/s 3. OB = + 3 m/s 4. OB = 3 m/s 5. OB = 2 m/s Explntion:
7 Crete ssignment, 99552, Homework 5, Sep 15 t 10:11 m 7 OB = x B x O t B t O = = 0 m/s. 012 Choose the pproprite quntity for the erge speed s OB for the motion from point O to point B. 1. s OB = +2 m/s 2. s OB = 0 m/s 3. s OB = + 3 m/s 4. s OB = 3 m/s 5. s OB = 2 m/s Explntion: s OB = x A x O + x B x A t B t O = = +2 m/s. 2 0 The lues for the erge speed come directly from eluting the definitions. 013 Choose the pproprite quntity for the instntneous elocity B t point B. 1. B = 2 m/s 2. B = +2 m/s 3. B = 0 m/s 4. B = + 3 m/s 5. B = 3 m/s Explntion: The instntneous elocity t point B cn be obtined by first finding n expression for the grph describing the position of the moing object nd tking its deritie eluted t time t B. Howeer, since the grph ner B is liner, it is simpler to clculte the slope of the line oer the interl from A to B. The result ly describes the instntneous elocity t B becuse the deritie of stright line is constnt t ll points on the line nd cn be obtined for our cse by B = x B x A t B t A = 0 2 = 2 m/s Choose the pproprite quntity for the instntneous speed s B t point B. 1. s B = +2 m/s 2. s B = 2 m/s 3. s B = 0 4. s B = + 3 m/s 5. s B = 3 m/s Explntion: Instntneous speed, is simply the bsolute lue of instntneous elocity becuse speed hs mgnitude but no direction. s B = B = 2 = +2 m/s. Accelertion Time Grph 01 02:05, trigonometry, multiple choice, < 1 min, wording-rible. 015 The following 5 questions refer to toy cr which cn moe to the right or left on horizontl surfce long stright line (the + distnce xis). The positie direction is to the right. Different motions of the cr re described below. Choose the ccelertion-time grph
8 Crete ssignment, 99552, Homework 5, Sep 15 t 10:11 m 8 which corresponds to the motion of the cr described in ech sttement. g cr O + The cr moes towrd the right (wy from the origin), speeding up t stedy rte. 8. None of these grphs re. Explntion: Since the cr speeds up t stedy rte, the ccelertion is constnt. 016 The cr moes towrd the right, slowing down t stedy rte.
9 Crete ssignment, 99552, Homework 5, Sep 15 t 10:11 m 9 8. None of these grphs re. Explntion: Since the cr slows down, the ccelertion is in the opposite direction. 017 The cr moes towrds the left (towrd the origin) t constnt elocity. 8. None of these grphs re. Explntion: Since the cr moes t constnt elocity, the ccelertion is zero. 018 The cr moes towrd the left, speeding up t stedy rte.
10 Crete ssignment, 99552, Homework 5, Sep 15 t 10:11 m None of these grphs re. Explntion: The sme reson s Prt The cr moes towrd the right t constnt elocity. 8. None of these grphs re. Explntion: The sme reson s Prt 3. Accelertion s Time 01 02:05, trigonometry, numeric, > 1 min, norml. 020 Consider the plot below describing the ccelertion of prticle long stright line with n initil position of 30 m nd n initil elocity of 4 m/s.
11 Crete ssignment, 99552, Homework 5, Sep 15 t 10:11 m 11 ccelertion (m/s 2 ) time (s) Wht is the elocity t 3 s? Correct nswer: 5 m/s. Explntion: In order to use the boe grph, let x 0 = x 0,1 = 30 m, 0 = 0,1 = 4 m/s, (t 0, 0 ) = (t 0,1, 0 ) = (0 s, 0 m/s 2 ), (t 1, 1 ) = (t 0,1, 1,2 ) = (0 s, 3 m/s 2 ), (t 2, 2 ) = (t 2,3, 1,2 ) = (4 s, 3 m/s 2 ), (t 3, 3 ) = (t 2,3, 3,4 ) = (4 s, 5 m/s 2 ), (t 4, 4 ) = (t 4,5, 3,4 ) = (9 s, 5 m/s 2 ), nd (t 5, 5 ) = (t 4,5, 5 ) = (9 s, 0 m/s 2 ). Bsic Concepts: The plot shows cure of ccelertion ersus time. The chnge in elocity is the re ( 1,2 t) between the ccelertion cure nd the time xis = 0,1 + 1,2 t, where the ccelertion is constnt. Solution: With constnt ccelertion ( 1,2 = 3 m/s 2 ), = 0,1 + 1,2 t (1) = (4 m/s) + ( 3 m/s 2 ) (3 s) = 5 m/s. elocity (m/s) [ 0.1] 1 Equtions 1 nd 3 re plotted below time (s) 021 Wht is the position t 3 s? Correct nswer: 31.5 m. Explntion: Bsic Concepts: The chnge in position is the re ( 0,1 t t2 ) between the elocity cure nd the time xis x = x 0,1 + 0,1 t t2. Solution: With constnt ccelertion ( 1,2 = 3 m/s 2 ), position (m) [ 0.1] x = x 0,1 + 0,1 t ,2 t 2 (2) = ( 30 m) + (4 m/s) (3 s) ( 3 m/s2 ) (3 s) 2 = 31.5 m. Equtions 2 nd 4 re plotted below time (s) 022 Wht is the elocity t 7 s? Correct nswer: 7 m/s. Explntion:
12 Crete ssignment, 99552, Homework 5, Sep 15 t 10:11 m 12 The clcultion is done in two prts, ech with constnt ccelertion ( 1,2 = 3 m/s 2 ) nd ( 3,4 = 5 m/s 2 ). where = 0,1 + 1,2 t 2,3 + 3,4 [t t 2,3 ] (3) = (4 m/s) + ( 3 m/s 2 ) (4 s) + (5 m/s 2 ) [(7 s) (4 s)] = 7 m/s, 02:05, trigonometry, multiple choice, < 1 min, fixed. 024 Identify ll of those grphs tht represent motion t constnt speed (note the xes crefully). x ) t 2,3 = 0,1 + 1,2 t 2,3 = (4 m/s) + ( 3 m/s 2 ) (4 s) = 8 m/s. b) t 023 Wht is the position t 7 s? Correct nswer: 39.5 m. Explntion: The clcultion is done in two prts, ech with constnt ccelertion ( 1,2 = 3 m/s 2 ) nd ( 3,4 = 5 m/s 2 ). where x = x 0,1 + 0,1 t 2, ,2 t 2 2,3 (4) + 2,3 [t t 2,3 ] ,4 [t t 2,3 ] 2 = ( 30 m) + (4 m/s) (4 s) ( 3 m/s2 ) (4 s) 2 + ( 8 m/s) [(7 s) (4 s)] (5 m/s2 ) [(7 s) (4 s)] 2 = 39.5 m, x 2,3 = x 0,1 + 0,1 t 2, ,2 t 2 2,3 = ( 30 m) + (4 m/s) (4 s) ( 3 m/s2 ) (4 s) 2 = 38 m. c) t d) t e) t 1. () nd (d) 2. (), (b), nd (c) 3. () nd (c) 4. (), (b), nd (d) 5. (d) only 6. (), (b), nd (e) Grphicl Anlysis
13 Crete ssignment, 99552, Homework 5, Sep 15 t 10:11 m () only 8. (c) only t i = 0 s t f = 5 s. nd 9. (e) only 10. None of these Explntion: Bsic Concepts: = o nd = 0. Solution: ) x = k t, k > 0 is liner function of t, so it is. b) = k t, k > 0 increses t constnt rte, so it is in. c) = k t, k > 0, so it is in. d) = k, k > 0, so it is. e) = k, k > 0, so it is in. Serwy CP :05, trigonometry, numeric, > 1 min, norml. 025 Consider the plot below describing motion of n object long stright pth s shown in the figure below. elocity (m/s) time (s) Find the erge ccelertion during the time interl 0 s to 5 s. Correct nswer: 0 m/s 2. Explntion: Gien : i = 6 m/s, f = 6 m/s, g = t = f i t ( 6 m/s) ( 6 m/s) = (5 s) (0 s) = 0 m/s Find the erge ccelertion during the time interl 5 s to 15 s. Correct nswer: 1.2 m/s 2. Explntion: Gien : i = 6 m/s, f = 6 m/s, t i = 5 s nd t f = 15 s. g = (6 m/s) ( 6 m/s) (15 s) (5 s) = 1.2 m/s Find the erge ccelertion during the time interl 0 s to 20 s. Correct nswer: 0.6 m/s 2. Explntion: Gien : i = 6 m/s, f = 6 m/s, t i = 0 s nd t f = 20 s. g = (6 m/s) ( 6 m/s) (20 s) (0 s) = 0.6 m/s 2.
14 Crete ssignment, 99552, Homework 5, Sep 15 t 10:11 m Find the instntneous ccelertion t 2 s. Correct nswer: 0 m/s 2. Explntion: At t = 2 s, the slope of the tngent line is zero; therefore the ccelertion is zero. 029 Find the instntneous ccelertion t 10 s. Correct nswer: 1.2 m/s 2. Explntion: At t = 10 s, the slope of the tngent line is the sme s in Prt 2. g = (6 m/s) ( 6 m/s) (15 s) (5 s) = 1.2 m/s Find the instntneous ccelertion t 18 s. Correct nswer: 0 m/s 2. Explntion: At t = 18 s, the slope of the tngent line is zero; therefore the ccelertion is zero.
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
v T R x m Version PREVIEW Practice 7 carroll (11108) 1
Version PEVIEW Prctice 7 crroll (08) his print-out should he 5 questions. Multiple-choice questions y continue on the next colun or pge find ll choices before nswering. Atwood Mchine 05 00 0.0 points A
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
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.
PHY 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,
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
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
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
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
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
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
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
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
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
GENERALIZED QUATERNIONS SERRET-FRENET AND BISHOP FRAMES SERRET-FRENET VE BISHOP ÇATILARI
Sy 9, Arlk 0 GENERALIZED QUATERNIONS SERRET-FRENET AND BISHOP FRAMES Erhn ATA*, Ysemin KEMER, Ali ATASOY Dumlupnr Uniersity, Fculty of Science nd Arts, Deprtment of Mthemtics, KÜTAHYA, et@dpu.edu.tr ABSTRACT
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
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
9.3. The Scalar Product. Introduction. Prerequisites. Learning Outcomes
The Sclr Product 9.3 Introduction There re two kinds of multipliction involving vectors. The first is known s the sclr product or dot product. This is so-clled becuse when the sclr product of two vectors
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
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
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
AREA OF A SURFACE OF REVOLUTION
AREA OF A SURFACE OF REVOLUTION h cut r πr h A surfce of revolution is formed when curve is rotted bout line. Such surfce is the lterl boundr of solid of revolution of the tpe discussed in Sections 7.
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
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
Firm 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
4.11 Inner Product Spaces
314 CHAPTER 4 Vector Spces 9. A mtrix of the form 0 0 b c 0 d 0 0 e 0 f g 0 h 0 cnnot be invertible. 10. A mtrix of the form bc d e f ghi such tht e bd = 0 cnnot be invertible. 4.11 Inner Product Spces
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
Exponential and Logarithmic Functions
Nme Chpter Eponentil nd Logrithmic Functions Section. Eponentil Functions nd Their Grphs Objective: In this lesson ou lerned how to recognize, evlute, nd grph eponentil functions. Importnt Vocbulr Define
Integration. 148 Chapter 7 Integration
48 Chpter 7 Integrtion 7 Integrtion t ech, by supposing tht during ech tenth of second the object is going t constnt speed Since the object initilly hs speed, we gin suppose it mintins this speed, but
6 Energy Methods And The Energy of Waves MATH 22C
6 Energy Methods And The Energy of Wves MATH 22C. Conservtion of Energy We discuss the principle of conservtion of energy for ODE s, derive the energy ssocited with the hrmonic oscilltor, nd then use this
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 +
Project Recovery. . It Can Be Done
Project Recovery. It Cn Be Done IPM Conference Wshington, D.C. Nov 4-7, 200 Wlt Lipke Oklhom City Air Logistics Center Tinker AFB, OK Overview Mngement Reserve Project Sttus Indictors Performnce Correction
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
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.
addition, there are double entries for the symbols used to signify different parameters. These parameters are explained in this appendix.
APPENDIX A: The ellipse August 15, 1997 Becuse of its importnce in both pproximting the erth s shpe nd describing stellite orbits, n informl discussion of the ellipse is presented in this ppendix. The
Linear Equations in Two Variables
Liner Equtions in Two Vribles In this chpter, we ll use the geometry of lines to help us solve equtions. Liner equtions in two vribles If, b, ndr re rel numbers (nd if nd b re not both equl to 0) then
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
Reasoning 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
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
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
and thus, they are similar. If k = 3 then the Jordan form of both matrices is
Homework ssignment 11 Section 7. pp. 249-25 Exercise 1. Let N 1 nd N 2 be nilpotent mtrices over the field F. Prove tht N 1 nd N 2 re similr if nd only if they hve the sme miniml polynomil. Solution: If
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
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
Derivatives and Rates of Change
Section 2.1 Derivtives nd Rtes of Cnge 2010 Kiryl Tsiscnk Derivtives nd Rtes of Cnge Te Tngent Problem EXAMPLE: Grp te prbol y = x 2 nd te tngent line t te point P(1,1). Solution: We ve: DEFINITION: Te
Geometry 7-1 Geometric Mean and the Pythagorean Theorem
Geometry 7-1 Geometric Men nd the Pythgoren Theorem. Geometric Men 1. Def: The geometric men etween two positive numers nd is the positive numer x where: = x. x Ex 1: Find the geometric men etween the
Distributions. (corresponding to the cumulative distribution function for the discrete case).
Distributions Recll tht n integrble function f : R [,] such tht R f()d = is clled probbility density function (pdf). The distribution function for the pdf is given by F() = (corresponding to the cumultive
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
Vectors 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 higher-dimensionl counterprts dydics, tridics, ndpolydics. Vectors descrie three-dimensionl spce nd
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.
The Definite Integral
Chpter 4 The Definite Integrl 4. Determining distnce trveled from velocity Motivting Questions In this section, we strive to understnd the ides generted by the following importnt questions: If we know
Pure C4. Revision Notes
Pure C4 Revision Notes Mrch 0 Contents Core 4 Alger Prtil frctions Coordinte Geometry 5 Prmetric equtions 5 Conversion from prmetric to Crtesin form 6 Are under curve given prmetriclly 7 Sequences nd
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): -
Math 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
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
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
Orbits and Kepler s Laws
Obits nd Keple s Lws This web pge intoduces some of the bsic ides of obitl dynmics. It stts by descibing the bsic foce due to gvity, then consides the ntue nd shpe of obits. The next section consides how
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
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
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
Binary 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
Radius of the Earth - Radii Used in Geodesy James R. Clynch February 2006
dius of the Erth - dii Used in Geodesy Jmes. Clynch Februry 006 I. Erth dii Uses There is only one rdius of sphere. The erth is pproximtely sphere nd therefore, for some cses, this pproximtion is dequte.
Vector differentiation. Chapters 6, 7
Chpter 2 Vectors Courtesy NASA/JPL-Cltech Summry (see exmples in Hw 1, 2, 3) Circ 1900 A.D., J. Willird Gis invented useful comintion of mgnitude nd direction clled vectors nd their higher-dimensionl counterprts
Small Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology
SPH simulation of fluid-structure interaction problems
Diprtimento di ingegneri idrulic e mientle SPH simultion of fluid-structure interction prolems C. Antoci, M. Gllti, S. Siill Reserch project Prolem: deformtion of plte due to the ction of fluid (lrge displcement
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
Small Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology
A.7.1 Trigonometric interpretation of dot product... 324. A.7.2 Geometric interpretation of dot product... 324
A P P E N D I X A Vectors CONTENTS A.1 Scling vector................................................ 321 A.2 Unit or Direction vectors...................................... 321 A.3 Vector ddition.................................................
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
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
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
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
3 The Utility Maximization Problem
3 The Utility Mxiiztion Proble We hve now discussed how to describe preferences in ters of utility functions nd how to forulte siple budget sets. The rtionl choice ssuption, tht consuers pick the best
Vectors 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 higher-dimensionl counterprts dydics, tridics, ndpolydics. Vectors descrie three-dimensionl spce nd
Harvard College. Math 21a: Multivariable Calculus Formula and Theorem Review
Hrvrd College Mth 21: Multivrible Clculus Formul nd Theorem Review Tommy McWillim, 13 tmcwillim@college.hrvrd.edu December 15, 2009 1 Contents Tble of Contents 4 9 Vectors nd the Geometry of Spce 5 9.1
Warm-up for Differential Calculus
Summer Assignment Wrm-up for Differentil Clculus Who should complete this pcket? Students who hve completed Functions or Honors Functions nd will be tking Differentil Clculus in the fll of 015. Due Dte:
, 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
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
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
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
Rotating DC Motors Part II
Rotting Motors rt II II.1 Motor Equivlent Circuit The next step in our consiertion of motors is to evelop n equivlent circuit which cn be use to better unerstn motor opertion. The rmtures in rel motors
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
trademark and symbol guidelines FOR CORPORATE STATIONARY APPLICATIONS reviewed 01.02.2007
trdemrk nd symbol guidelines trdemrk guidelines The trdemrk Cn be plced in either of the two usul configurtions but horizontl usge is preferble. Wherever possible the trdemrk should be plced on blck bckground.
Bayesian Updating with Continuous Priors Class 13, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom
Byesin Updting with Continuous Priors Clss 3, 8.05, Spring 04 Jeremy Orloff nd Jonthn Bloom Lerning Gols. Understnd prmeterized fmily of distriutions s representing continuous rnge of hypotheses for the
Review guide for the final exam in Math 233
Review guide for the finl exm in Mth 33 1 Bsic mteril. This review includes the reminder of the mteril for mth 33. The finl exm will be cumultive exm with mny of the problems coming from the mteril covered
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
One Minute To Learn Programming: Finite Automata
Gret Theoreticl Ides In Computer Science Steven Rudich CS 15-251 Spring 2005 Lecture 9 Fe 8 2005 Crnegie Mellon University One Minute To Lern Progrmming: Finite Automt Let me tech you progrmming lnguge
Uplift Capacity of K-Series Open Web Steel Joist Seats. Florida, Gainesville, FL 32611; email: psgreen@ce.ufl.edu
Uplift Cpcity of K-Series Open Web Steel Joist Sets Perry S. Green, Ph.D, M.ASCE 1 nd Thoms Sputo, Ph.D., P.E., M.ASCE 2 1 Assistnt Professor, Deprtment of Civil nd Costl Engineering, University of Florid,
Rotational Equilibrium: A Question of Balance
Prt of the IEEE Techer In-Service Progrm - Lesson Focus Demonstrte the concept of rottionl equilirium. Lesson Synopsis The Rottionl Equilirium ctivity encourges students to explore the sic concepts of
CURVES ANDRÉ NEVES. that is, the curve α has finite length. v = p q p q. a i.e., the curve of smallest length connecting p to q is a straight line.
CURVES ANDRÉ NEVES 1. Problems (1) (Ex 1 of 1.3 of Do Crmo) Show tht the tngent line to the curve α(t) (3t, 3t 2, 2t 3 ) mkes constnt ngle with the line z x, y. (2) (Ex 6 of 1.3 of Do Crmo) Let α(t) (e
Project 6 Aircraft static stability and control
Project 6 Aircrft sttic stbility nd control The min objective of the project No. 6 is to compute the chrcteristics of the ircrft sttic stbility nd control chrcteristics in the pitch nd roll chnnel. The
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
SINCLAIR COMMUNITY COLLEGE DAYTON, OHIO DEPARTMENT SYLLABUS FOR COURSE IN MAT 1470 - COLLEGE ALGEBRA (4 SEMESTER HOURS)
SINCLAIR COMMUNITY COLLEGE DAYTON, OHIO DEPARTMENT SYLLABUS FOR COURSE IN MAT 470 - COLLEGE ALGEBRA (4 SEMESTER HOURS). COURSE DESCRIPTION: Polynomil, rdicl, rtionl, exponentil, nd logrithmic functions
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
Two 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
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
Lecture 5. Inner Product
Lecture 5 Inner Product Let us strt with the following problem. Given point P R nd line L R, how cn we find the point on the line closest to P? Answer: Drw line segment from P meeting the line in right
Design Example 1 Special Moment Frame
Design Exmple 1 pecil Moment Frme OVERVIEW tructurl steel specil moment frmes (MF) re typiclly comprised of wide-flnge bems, columns, nd bem-column connections. Connections re proportioned nd detiled to
CHAPTER 11 Numerical Differentiation and Integration
CHAPTER 11 Numericl Differentition nd Integrtion Differentition nd integrtion re bsic mthemticl opertions with wide rnge of pplictions in mny res of science. It is therefore importnt to hve good methods
AP STATISTICS SUMMER MATH PACKET
AP STATISTICS SUMMER MATH PACKET This pcket is review of Algebr I, Algebr II, nd bsic probbility/counting. The problems re designed to help you review topics tht re importnt to your success in the clss.
I calculate the unemployment rate as (In Labor Force Employed)/In Labor Force
Introduction to the Prctice of Sttistics Fifth Edition Moore, McCbe Section 4.5 Homework Answers to 98, 99, 100,102, 103,105, 107, 109,110, 111, 112, 113 Working. In the lnguge of government sttistics,