WORKSHOP 7 PARASOLID SOLID EXAMPLE
|
|
|
- Audrey Greer
- 5 years ago
- Views:
Transcription
1 WORKSHOP 7 PARASOLID SOLID EXAMPLE WS7-1
2 WS7-2
3 Workshop Ojetives Lern some of the steps tht n e use to rete B-rep soli, i.e. extrue surfe, shell, n ege len. Then, rete the finite element moel. Anlyze the moel, n postproess the results from its nlysis. Prolem Desription Disply the eforme shpe of the moel using she rener. Also, isply the von Mises stress fringe. Tension fitting mteril: Aluminum with E = 10 x 10 6 psi n ν = 0.3 Totl lo on tension fitting = 5000 lf Softwre Version MSC.Ptrn 2005r2 MSC.Nstrn 2005r2 WS7-3
4 Key Conepts n Steps: Dtse: rete new tse with Anlysis Coe = MSC.Nstrn n Anlysis Type = Struturl Geometry: rete B-rep soli y extruing rete surfe, then o vrious things like shell n ege len Elements: mesh the geometri soli with soli Tet10 elements Los/BCs: onstrin the three holes t ottom of soli, n pply Totl Lo to the lrge hole t the k of the fitting Mterils: speify n isotropi mteril for Aluminum Properties: rete 3D soli property Anlysis: Solution Type = Nstrn Liner Stti, Solution Sequene = 101, Metho = Full Run Anlysis: ess nlysis results y tthing the XDB file to tse Results: plot moel eformtion n von Mises stress results WS7-4
5 Step 1. Crete New Dtse for Tension Fitting Crete new tse lle tension_fitting... File / New.. Enter tension_fitting s the file nme.. Clik OK.. Choose Bse on Moel for Tolerne. e. Choose MSC Nstrn n Struturl for Anlysis Coe n Type. f. Clik OK. f e WS7-5
6 Step 2. Crete Surfe Crete the Geometry for the tension fitting.. Geometry : Crete / Surfe / XYZ.. Enter <5 2 0>for Vetor Coorintes List.. Enter [0 0 0] for Origin Coorintes List.. Clik Apply. WS7-6
7 Step 2. Crete Surfe (Cont.) Copy points t opposite orners.. Clik inrese Point Size ion to show ll points enlrge.. Geometry : Trnsform / Point / Trnslte.. Enter < > for Trnsltion Vetor.. Selet top-left orner n lik Apply. e. Enter < > for Trnsltion Vetor. f. Selet ottom-right orner n lik Apply. f e f WS7-7
8 Step 2. Crete Surfe (Cont.) Crete urve y onneting the two trnslte points n rek the surfe with the urve.. Geometry: Crete/Curve/ Point.. Clik on one of the two points from trnsltion s the strting point n the other s the ening point. WS7-8
9 Step 2. Crete Surfe (Cont.) e Brek the surfe n elete the upper portion of the originl surfe.. Geometry : Eit / Surfe / Brek.. Turn Auto Exeute off.. Selet the retngulr surfe for the Surfe List n the slope urve for the Brek Curve List.. Clik Apply n Yes when messge ox ppers. e. Clik the Refresh Grphis ion. WS7-9
10 Step 2. Crete Surfe (Cont.) Delete the upper surfe (ove the rek urve).. Geometry : Delete / Surfe.. Clik on the tringulr surfe for the Surfe List.. Clik Apply. WS7-10
11 Step 3. Extrue the Surfe to Crete Soli f e Crete Prsoli soli y extruing the surfe in the Z- iretion.. Geometry : Crete / Soli / Extrue.. Mke sure TetMeshle soli ion is selete.. Enter <0 0 2> for the Trnsltion Vetor.. Selet Surfe 2 in the Surfe List Box. e. Clik Iso1 view. f. Clik the Smooth-she ion. WS7-11
12 Step 4. Crete Shell Soli Eit the soli using the shell metho to rete shelle soli.. Geometry : Eit / Soli / Shell. Enter 0.25 for Thikness. Turn off Auto Exeute.. Clik on Soli Fe List n hol own the shift utton n selet the top, slope, n front fes of the soli.. Clik Apply. WS7-12
13 Step 5. Crete Fillets Crete the fillets on the inner eges of the soli.. Geometry : Eit / Soli /Ege Blen.. Mke sure tht the onstnt rius ion is selete.. Enter 0.25 for Constnt Rius.. Mke sure Ege(s) of Soli ion is selete. e. Turn Auto Exeute Off. f. Clik on Soli Ege List n use the shift-lik tehnique n selet the 5 eges on the insie of thesoli. g. Clik Apply. It my e neessry to rotte the ojet in orer to see the inner eges more esily. This n e one y using the mile mouse utton. f e g f WS7-13
14 Step 6. Crete Holes for the Tension Fitting Crete the holes for the tension fitting yreting primitive solis tht pss through the soli, then sutrting them.. Geometry : Crete / Soli / Primitive.. Selet the yliner ion.. Enter 2.0 for the Height n 0.25 for the rius.. Enter [ ] for the Bse Center Point List n Coor 0.1 for the Axis List. e. Clik Apply. f. Geometry : Eit / Soli /Boolen. g. Selet Sutrt ion. h. Selet the tension fitting for the Trget Soli. i. Selet the yliner for the Sutrting Soli List. e h i g f WS7-14
15 Step 6. Crete Holes for the Tension Fitting (Cont.) Crete the points where the three ottom holes will e ple y trnslting n existing point n, then trnslting gin.. Clik wirefrme ion.. Geometry : Trnsform /Point / Trnslte.. Enter < > for Trnsltion Vetor.. Selet point t se ege of fillet. e. Apply f. Enter < > for Trnsltion Vetor. g. Selet trnslte point. h. Apply i. Enter < > for Trnsltion Vetor. j. Enter 2 for repet ount. k. Selet trnslte point. l. Apply k g j e WS7-15
16 Step 6. Crete Holes for the Tension Fitting (Cont.) Crete yliners using points s se enters n then rete holes y sutrting them from the soli.. Clik Smooth she ion.. Geometry : Crete / Soli / Primitive.. Selet yliner ion.. Enter -1.0 for Height List n for Rius List. e. Use the shift-lik tehnique to selet the three trnslte points for Bse Center Point List. f. Enter Coor 0.2 for xis list n lik Apply. g. Geometry : Eit / Soli /Boolen. h. Selet sutrt ion. i. Selet tension fitting (Soli 1) s Trget Soli. j. Shift-lik ll three yliners for Sutrting Soli List. k. Clik Apply. f e WS7-16 j e k i j h g It my e neessry to rotte the ojet severl times in orer to selet the yliners with ese
17 Step 7. Crete Cyliner to Imprint Tension Fitting k Crete point in the enter of the lrge hole in orer to rete the yliner to imprint onto the soli.. Clik wirefrme ion.. Geometry : Crete / Point / ArCenter.. Selet the lrger hole ege.. Apply e. Geometry : Crete / Soli / Primitive. f. Selet yliner ion. g. Enter 1.0 for Height List n for Rius List. h. Clik on point in the enter of the lrge hole. i. Enter Coor 0.1 for Axis List. j. Clik Apply. k. Selet Smooth She ion. h g f h e WS7-17 i j
18 Step 8. Imprint the Soli Use the yliner to imprint the soli n then elete the yliner, resulting in the finishe soli.. Geometry : Eit / Soli / Imprint.. Selet the tension fitting for the Soli List (A).. Selet the yliner for the Soli to Imprint List (B). WS7-18 The soli my seem unhnge, ut the imprint on the soli will not e visile until the yliner hs een elete.
19 Step 9. Delete the Cyliner Delete the yliner n mke sure imprint metho ws omplete.. Geometry : Delete / Soli. Selet the yliner for Soli List.. Clik Apply. Ege e to soli. WS7-19
20 Step 10. TetMesh the Complete Soli Crete the TetMesh for the tension fitting.. Elements : Crete / Mesh / Soli.. Mke sure Tet, TetMesh, n Tet10 re ll selete.. Clik on Input List n selet the soli.. Remove hek for Automti Clultion n enter 0.25 for Glol Ege Length. e. Clik Apply. WS7-20 e
21 Step 11. Crete Los n Constrints Crete the los n onstrints for the moel.. Clik Smooth She ion. Los/BCs : Crete / Totl Lo / Element Uniform.. Enter Fore s the New Set Nme.. Clik Input Dt e. Enter < > for the Lo n lik OK. f. Clik Selet Applition Region g. Selet the vertil soli fe rete y imprinting t the lrger hole, then lik A. h. Clik OK i. Clik Apply. i f WS7-21 e g h g Illustrte here is the esire pplition region.
22 Step 11. Crete Los n Constrints (Cont.) WS7-22
23 Step 11. Crete Los n Constrints (Cont.) Crete the onstrints t the se holes.. Los/BCs : Crete / Displement / Nol.. Enter Fixe s New Set Nme.. Clik Input Dt. Enter <0 0 0> for Trnsltion only, n lik OK. e. Clik Selet Applition Region. f. Clik on Selet Geometry Entities. g. Selet Surfe or Fe ion h. Shift-lik the ylinril fes of the three holes t the se, n Clik A. i. Clik OK. j. Clik Apply. g h f e j WS7-23 h Illustrte here is the pplition region for one of the three holes. i
24 Step 11. Crete Los n Constrints (Cont.) WS7-24
25 Step 12. Crete Mteril Properties Crete the mteril properties for the moel.. Mterils : Crete / Isotropi / Mnul Input. Enter Aluminum for Mteril Nme.. Clik Input Properties. Enter 10E6 for Elsti Moulus n 0.3 for Poisson Rtio. e. Clik OK f. Clik Apply. f WS7-25 e
26 Step 13. Crete 3D Element Properties Crete the 3D element properties for the tension fitting.. Properties : Crete / 3D / Soli.. Enter 3D_tets for Property Set Nme.. Clik Input Properties. Clik Mt Prop Nme ion. Selet Aluminum from Selet Mteril. e. Clik OK f. For Applition Region, selet entire soli y rgging ox roun it n lik A. g. Clik Apply. f e g WS7-26
27 Step 14. Chek the Lo Cse Chek the lo se Defult to mke sure tht the lo n onstrint Are selete.. Lo Cses : Moify. Clik on the lo se nme Defult.. Chek to see tht oth the lo n onstrints re ssigne.. Clik Cnel. WS7-27
28 Step 15. Run the Anlysis Run the Anlysis with MSC.Nstrn.. Anlysis : Anlyze / Entire Moel / Full Run.. Clik Trnsltion Prmeters.... Mke sure XDB n Print is selete.. Clik OK. e. Clik Solution Type f. Mke sure LINEAR STATIC is selete. g. Clik OK. h. Clik Apply. f e h WS7-28 g
29 Step 16. Aess the Results Atth the XDB file n ess the results.. Anlysis : Aess Results / Atth XDB / Result Entities.. Clik Selet Results File. Selet tension_fitting.x n lik OK.. Clik Apply. WS7-29
30 Step 17. Disply Results Crete eformtion plot. Results : Crete / Deformtion.. Selet SC1: DEFAULT, A1:Stti Suse uner Selet Result Cse(s). Selet Displements, Trnsitionl from Selet Deformtion Result.. Clik Apply. WS7-30
31 Step 17. Disply Results (Cont.) Erse the geometry n o not show the uneforme moel, so tht only the eforme moel is shown.. Disply : Plot/Erse. Clik Erse uner Geometry.. Clik OK.. Clik Disply Attriutes. e. Remove hek from Show Uneforme. f. For the Rener Style, hoose She. g. Clik Apply. e f WS7-31 g
32 Step 17. Disply Results (Cont.) WS7-32
33 Step 17. Disply Results (Cont.) Plot the von Mises stress for the moel.. Results : Crete / Fringe.. Selet Stress Tensor from Selet Fringe Result.. Selet Disply Attriutes, then set Disply to Element Eges. Clik Apply. It my lso e helpful to hnge the view severl times in orer to get etter visuliztion of the eformtions. This n e one either y holing own the mile utton on the mouse, or using the view ions. WS7-33
34 WS7-34
WORKSHOP 1 Composite Wing
WORKSHOP 1 Composite Wing WS1-1 WS1-2 Workshop Ojetives Beome fmilir with the si steps in doing omposites nlysis Softwre Version Ptrn 2011 MD Nstrn 2011.1 Required File: omposite_wing.d WS1-3 Prolem Desription
MSC Studentenwettbewerb. Wintersemester 2012/13. Nastran - Patran
MSC Stuntnwttwr Wintrsmstr 2012/13 Nstrn - Ptrn Aufg Wi groß ist i mximl Vrshiung? Softwr Vrsion Ptrn 2011 MSC/MD Nstrn 2011 Fils Rquir strut.xmt 3 TUTORIAL Prolm Dsription A lning gr strut hs n sign for
WORKSHOP 6 BRIDGE TRUSS
WORKSHOP 6 BRIDGE TRUSS WS6-2 Workshop Ojtivs Lrn to msh lin gomtry to gnrt CBAR lmnts Bom fmilir with stting up th CBAR orinttion vtor n stion proprtis Lrn to st up multipl lo ss Lrn to viw th iffrnt
for all x in [a,b], then the area of the region bounded by the graphs of f and g and the vertical lines x = a and x = b is b [ ( ) ( )] A= f x g x dx
![for all x in [a,b], then the area of the region bounded by the graphs of f and g and the vertical lines x = a and x = b is b [ ( ) ( )] A= f x g x dx](/thumbs/74/70408252.jpg "for all x in [a,b], then the area of the region bounded by the graphs of f and g and the vertical lines x = a and x = b is b [ ( ) ( )] A= f x g x dx")
Applitions of Integrtion Are of Region Between Two Curves Ojetive: Fin the re of region etween two urves using integrtion. Fin the re of region etween interseting urves using integrtion. Desrie integrtion
GM1 Consolidation Worksheet
Cmridge Essentils Mthemtis Core 8 GM1 Consolidtion Worksheet GM1 Consolidtion Worksheet 1 Clulte the size of eh ngle mrked y letter. Give resons for your nswers. or exmple, ngles on stright line dd up
SIMPLE NONLINEAR GRAPHS
S i m p l e N o n l i n e r G r p h s SIMPLE NONLINEAR GRAPHS www.mthletis.om.u Simple SIMPLE Nonliner NONLINEAR Grphs GRAPHS Liner equtions hve the form = m+ where the power of (n ) is lws. The re lle
Solids of Revolution
Solis of Revolution Solis of revolution re rete tking n re n revolving it roun n is of rottion. There re two methos to etermine the volume of the soli of revolution: the isk metho n the shell metho. Disk
Plotting Ordered Pairs Using Integers
SAMPLE Plotting Ordered Pirs Using Integers Ple two elsti nds on geoord to form oordinte xes shown on the right to help you solve these prolems.. Wht letter of the lphet does eh set of pirs nme?. (, )
Counting Paths Between Vertices. Isomorphism of Graphs. Isomorphism of Graphs. Isomorphism of Graphs. Isomorphism of Graphs. Isomorphism of Graphs
Isomorphism of Grphs Definition The simple grphs G 1 = (V 1, E 1 ) n G = (V, E ) re isomorphi if there is ijetion (n oneto-one n onto funtion) f from V 1 to V with the property tht n re jent in G 1 if
First compression (0-6.3 GPa) First decompression ( GPa) Second compression ( GPa) Second decompression (35.
0.9 First ompression (0-6.3 GP) First deompression (6.3-2.7 GP) Seond ompression (2.7-35.5 GP) Seond deompression (35.5-0 GP) V/V 0 0.7 0.5 0 5 10 15 20 25 30 35 P (GP) Supplementry Figure 1 Compression
MATH 122, Final Exam
MATH, Finl Exm Winter Nme: Setion: You must show ll of your work on the exm pper, legily n in etil, to reeive reit. A formul sheet is tthe.. (7 pts eh) Evlute the following integrls. () 3x + x x Solution.
I1 = I2 I1 = I2 + I3 I1 + I2 = I3 + I4 I 3
2 The Prllel Circuit Electric Circuits: Figure 2- elow show ttery nd multiple resistors rrnged in prllel. Ech resistor receives portion of the current from the ttery sed on its resistnce. The split is
22: Union Find. CS 473u - Algorithms - Spring April 14, We want to maintain a collection of sets, under the operations of:
22: Union Fin CS 473u - Algorithms - Spring 2005 April 14, 2005 1 Union-Fin We wnt to mintin olletion of sets, uner the opertions of: 1. MkeSet(x) - rete set tht ontins the single element x. 2. Fin(x)
PYTHAGORAS THEOREM WHAT S IN CHAPTER 1? IN THIS CHAPTER YOU WILL:
PYTHAGORAS THEOREM 1 WHAT S IN CHAPTER 1? 1 01 Squres, squre roots nd surds 1 02 Pythgors theorem 1 03 Finding the hypotenuse 1 04 Finding shorter side 1 05 Mixed prolems 1 06 Testing for right-ngled tringles
Intermediate Math Circles Wednesday 17 October 2012 Geometry II: Side Lengths
Intermedite Mth Cirles Wednesdy 17 Otoer 01 Geometry II: Side Lengths Lst week we disussed vrious ngle properties. As we progressed through the evening, we proved mny results. This week, we will look t
Factorising FACTORISING.
Ftorising FACTORISING www.mthletis.om.u Ftorising FACTORISING Ftorising is the opposite of expning. It is the proess of putting expressions into rkets rther thn expning them out. In this setion you will
Eigenvectors and Eigenvalues
MTB 050 1 ORIGIN 1 Eigenvets n Eigenvlues This wksheet esries the lger use to lulte "prinipl" "hrteristi" iretions lle Eigenvets n the "prinipl" "hrteristi" vlues lle Eigenvlues ssoite with these iretions.
ANALYSIS AND MODELLING OF RAINFALL EVENTS
Proeedings of the 14 th Interntionl Conferene on Environmentl Siene nd Tehnology Athens, Greee, 3-5 Septemer 215 ANALYSIS AND MODELLING OF RAINFALL EVENTS IOANNIDIS K., KARAGRIGORIOU A. nd LEKKAS D.F.
Linear Algebra Introduction
Introdution Wht is Liner Alger out? Liner Alger is rnh of mthemtis whih emerged yers k nd ws one of the pioneer rnhes of mthemtis Though, initilly it strted with solving of the simple liner eqution x +
Forces on curved surfaces Buoyant force Stability of floating and submerged bodies
Stti Surfe ores Stti Surfe ores 8m wter hinge? 4 m ores on plne res ores on urved surfes Buont fore Stbilit of floting nd submerged bodies ores on Plne res Two tpes of problems Horizontl surfes (pressure
Activities. 4.1 Pythagoras' Theorem 4.2 Spirals 4.3 Clinometers 4.4 Radar 4.5 Posting Parcels 4.6 Interlocking Pipes 4.7 Sine Rule Notes and Solutions
MEP: Demonstrtion Projet UNIT 4: Trigonometry UNIT 4 Trigonometry tivities tivities 4. Pythgors' Theorem 4.2 Spirls 4.3 linometers 4.4 Rdr 4.5 Posting Prels 4.6 Interloking Pipes 4.7 Sine Rule Notes nd
Numbers and indices. 1.1 Fractions. GCSE C Example 1. Handy hint. Key point
GCSE C Emple 7 Work out 9 Give your nswer in its simplest form Numers n inies Reiprote mens invert or turn upsie own The reiprol of is 9 9 Mke sure you only invert the frtion you re iviing y 7 You multiply
Comparing the Pre-image and Image of a Dilation
hpter Summry Key Terms Postultes nd Theorems similr tringles (.1) inluded ngle (.2) inluded side (.2) geometri men (.) indiret mesurement (.6) ngle-ngle Similrity Theorem (.2) Side-Side-Side Similrity
1 This diagram represents the energy change that occurs when a d electron in a transition metal ion is excited by visible light.
1 This igrm represents the energy hnge tht ours when eletron in trnsition metl ion is exite y visile light. Give the eqution tht reltes the energy hnge ΔE to the Plnk onstnt, h, n the frequeny, v, of the
CSE 332. Sorting. Data Abstractions. CSE 332: Data Abstractions. QuickSort Cutoff 1. Where We Are 2. Bounding The MAXIMUM Problem 4
Am Blnk Leture 13 Winter 2016 CSE 332 CSE 332: Dt Astrtions Sorting Dt Astrtions QuikSort Cutoff 1 Where We Are 2 For smll n, the reursion is wste. The onstnts on quik/merge sort re higher thn the ones
Algebra 2 Semester 1 Practice Final
Alger 2 Semester Prtie Finl Multiple Choie Ientify the hoie tht est ompletes the sttement or nswers the question. To whih set of numers oes the numer elong?. 2 5 integers rtionl numers irrtionl numers
Part I: Study the theorem statement.
Nme 1 Nme 2 Nme 3 A STUDY OF PYTHAGORAS THEOREM Instrutions: Together in groups of 2 or 3, fill out the following worksheet. You my lift nswers from the reding, or nswer on your own. Turn in one pket for
Now we must transform the original model so we can use the new parameters. = S max. Recruits
MODEL FOR VARIABLE RECRUITMENT (ontinue) Alterntive Prmeteriztions of the pwner-reruit Moels We n write ny moel in numerous ifferent ut equivlent forms. Uner ertin irumstnes it is onvenient to work with
ES-TA-3..1 Six- and Ten-Input E-Stop Safety Modules with DeviceNet
Emergeny Stop Sfety Moules Moel Seletion ES-TA-3..1 Six- n Ten-Input E-Stop Sfety Moules with DevieNet Sfety Moules s up to ten normlly lose emergeny stop swith iruits for ontt filure or wiring fult Diverse-reunnt
The Stirling Engine: The Heat Engine
Memoril University of Newfounln Deprtment of Physis n Physil Oenogrphy Physis 2053 Lortory he Stirling Engine: he Het Engine Do not ttempt to operte the engine without supervision. Introution Het engines
Instructions. An 8.5 x 11 Cheat Sheet may also be used as an aid for this test. MUST be original handwriting.
ID: B CSE 2021 Computer Orgniztion Midterm Test (Fll 2009) Instrutions This is losed ook, 80 minutes exm. The MIPS referene sheet my e used s n id for this test. An 8.5 x 11 Chet Sheet my lso e used s
Momentum and Energy Review
Momentum n Energy Review Nme: Dte: 1. A 0.0600-kilogrm ll trveling t 60.0 meters per seon hits onrete wll. Wht spee must 0.0100-kilogrm ullet hve in orer to hit the wll with the sme mgnitue of momentum
6.5 Improper integrals
Eerpt from "Clulus" 3 AoPS In. www.rtofprolemsolving.om 6.5. IMPROPER INTEGRALS 6.5 Improper integrls As we ve seen, we use the definite integrl R f to ompute the re of the region under the grph of y =
C REVISED PER ECR DEC2015 T.S E.T $ D/C MATING CONNECTOR PART NUMBER WEIGHT. (g)
THIS RWING IS UNPULISHE. OPYRIGHT 00 Y RELESE FOR PULITION LL RIGHTS RESERVE. 00 ISIONS P LTR ESRIPTION TE WN PV 0.7 ISE PER ER0800 E0 T.S E.T 0.7 MTERIL HOUSING:POLYESTER OF GLSS FILLE THERMO PLSTI(UL9V0),
The DOACROSS statement
The DOACROSS sttement Is prllel loop similr to DOALL, ut it llows prouer-onsumer type of synhroniztion. Synhroniztion is llowe from lower to higher itertions sine it is ssume tht lower itertions re selete
Generalization of 2-Corner Frequency Source Models Used in SMSIM
Generliztion o 2-Corner Frequeny Soure Models Used in SMSIM Dvid M. Boore 26 Mrh 213, orreted Figure 1 nd 2 legends on 5 April 213, dditionl smll orretions on 29 My 213 Mny o the soure spetr models ville
Project 6: Minigoals Towards Simplifying and Rewriting Expressions
MAT 51 Wldis Projet 6: Minigols Towrds Simplifying nd Rewriting Expressions The distriutive property nd like terms You hve proly lerned in previous lsses out dding like terms ut one prolem with the wy
Designing Information Devices and Systems I Anant Sahai, Ali Niknejad. This homework is due October 19, 2015, at Noon.
EECS 16A Designing Informtion Devices nd Systems I Fll 2015 Annt Shi, Ali Niknejd Homework 7 This homework is due Octoer 19, 2015, t Noon. 1. Circuits with cpcitors nd resistors () Find the voltges cross
Reference : Croft & Davison, Chapter 12, Blocks 1,2. A matrix ti is a rectangular array or block of numbers usually enclosed in brackets.
I MATRIX ALGEBRA INTRODUCTION TO MATRICES Referene : Croft & Dvison, Chpter, Blos, A mtri ti is retngulr rr or lo of numers usull enlosed in rets. A m n mtri hs m rows nd n olumns. Mtri Alger Pge If the
Similar Right Triangles
Geometry V1.noteook Ferury 09, 2012 Similr Right Tringles Cn I identify similr tringles in right tringle with the ltitude? Cn I identify the proportions in right tringles? Cn I use the geometri mens theorems
Section 6: Area, Volume, and Average Value
Chpter The Integrl Applied Clculus Section 6: Are, Volume, nd Averge Vlue Are We hve lredy used integrls to find the re etween the grph of function nd the horizontl xis. Integrls cn lso e used to find
2 Calculate the size of each angle marked by a letter in these triangles.
Cmridge Essentils Mthemtics Support 8 GM1.1 GM1.1 1 Clculte the size of ech ngle mrked y letter. c 2 Clculte the size of ech ngle mrked y letter in these tringles. c d 3 Clculte the size of ech ngle mrked
Tutorial Worksheet. 1. Find all solutions to the linear system by following the given steps. x + 2y + 3z = 2 2x + 3y + z = 4.
Mth 5 Tutoril Week 1 - Jnury 1 1 Nme Setion Tutoril Worksheet 1. Find ll solutions to the liner system by following the given steps x + y + z = x + y + z = 4. y + z = Step 1. Write down the rgumented mtrix
A Lower Bound for the Length of a Partial Transversal in a Latin Square, Revised Version
A Lower Bound for the Length of Prtil Trnsversl in Ltin Squre, Revised Version Pooy Htmi nd Peter W. Shor Deprtment of Mthemtil Sienes, Shrif University of Tehnology, P.O.Bo 11365-9415, Tehrn, Irn Deprtment
50 AMC Lectures Problem Book 2 (36) Substitution Method
0 AMC Letures Prolem Book Sustitution Metho PROBLEMS Prolem : Solve for rel : 9 + 99 + 9 = Prolem : Solve for rel : 0 9 8 8 Prolem : Show tht if 8 Prolem : Show tht + + if rel numers,, n stisf + + = Prolem
10. AREAS BETWEEN CURVES
. AREAS BETWEEN CURVES.. Ares etween curves So res ove the x-xis re positive nd res elow re negtive, right? Wrong! We lied! Well, when you first lern out integrtion it s convenient fiction tht s true in
THE PYTHAGOREAN THEOREM
THE PYTHAGOREAN THEOREM The Pythgoren Theorem is one of the most well-known nd widely used theorems in mthemtis. We will first look t n informl investigtion of the Pythgoren Theorem, nd then pply this
CARLETON UNIVERSITY. 1.0 Problems and Most Solutions, Sect B, 2005
RLETON UNIVERSIT eprtment of Eletronis ELE 2607 Swithing iruits erury 28, 05; 0 pm.0 Prolems n Most Solutions, Set, 2005 Jn. 2, #8 n #0; Simplify, Prove Prolem. #8 Simplify + + + Reue to four letters (literls).
CS 491G Combinatorial Optimization Lecture Notes
CS 491G Comintoril Optimiztion Leture Notes Dvi Owen July 30, August 1 1 Mthings Figure 1: two possile mthings in simple grph. Definition 1 Given grph G = V, E, mthing is olletion of eges M suh tht e i,
CHEM1611 Answers to Problem Sheet 9
CEM1611 Answers to Prolem Sheet 9 1. Tutomers re struturl isomers whih re relte y migrtion of hyrogen tom n the exhnge of single on n jent oule on. Compoun Tutomer 2 2 2 2 2 2 2 2 2 2 2 2. () Whih pir
KINEMATICS OF RIGID BODIES
KINEMTICS OF RIGID ODIES Introduction In rigid body kinemtics, e use the reltionships governing the displcement, velocity nd ccelertion, but must lso ccount for the rottionl motion of the body. Description
Designing Information Devices and Systems I Fall 2016 Babak Ayazifar, Vladimir Stojanovic Homework 6. This homework is due October 11, 2016, at Noon.
EECS 16A Designing Informtion Devices nd Systems I Fll 2016 Bk Ayzifr, Vldimir Stojnovic Homework 6 This homework is due Octoer 11, 2016, t Noon. 1. Homework process nd study group Who else did you work
Electronic Circuits I Revision after midterm
Eletroni Ciruits I Revision fter miterm Dr. Ahme ElShfee, ACU : Fll 2018, Eletroni Ciruits I -1 / 14 - MCQ1 # Question If the frequeny of the input voltge in Figure 2 36 is inrese, the output voltge will
1 PYTHAGORAS THEOREM 1. Given a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
1 PYTHAGORAS THEOREM 1 1 Pythgors Theorem In this setion we will present geometri proof of the fmous theorem of Pythgors. Given right ngled tringle, the squre of the hypotenuse is equl to the sum of the
MATH 1080: Calculus of One Variable II Spring 2018 Textbook: Single Variable Calculus: Early Transcendentals, 7e, by James Stewart.
MATH 1080: Clulus of One Vrile II Spring 2018 Textook: Single Vrile Clulus: Erly Trnsenentls, 7e, y Jmes Stewrt Unit 2 Skill Set Importnt: Stuents shoul expet test questions tht require synthesis of these
If we have a function f(x) which is well-defined for some a x b, its integral over those two values is defined as
Y. D. Chong (26) MH28: Complex Methos for the Sciences 2. Integrls If we hve function f(x) which is well-efine for some x, its integrl over those two vlues is efine s N ( ) f(x) = lim x f(x n ) where x
I 3 2 = I I 4 = 2A
ECE 210 Eletril Ciruit Anlysis University of llinois t Chigo 2.13 We re ske to use KCL to fin urrents 1 4. The key point in pplying KCL in this prolem is to strt with noe where only one of the urrents
Year 10 Maths. Semester One Revision Booklet.
Yer 0 Mths. Semester One Revision Booklet. Nme YEAR 0 MATHEMATICS REVISION BOOKLET AND STUDY SUGGESTIONS NAME: READ through ALL of this vie prior to strting your revision. It is essentil informtion. Chpters
Sketchpad Lab Make An Equatorial Sundial Face Plate
Make n Equatorial Sundial Face Plate ate Per ssign# The following instructions will produce a faceplate for an Equatorial Sundial In a new sketch, construct ircle of a fairly large diameter. onstruct radius.
2. VECTORS AND MATRICES IN 3 DIMENSIONS
2 VECTORS AND MATRICES IN 3 DIMENSIONS 21 Extending the Theory of 2-dimensionl Vectors x A point in 3-dimensionl spce cn e represented y column vector of the form y z z-xis y-xis z x y x-xis Most of the
Alpha Algorithm: Limitations
Proess Mining: Dt Siene in Ation Alph Algorithm: Limittions prof.dr.ir. Wil vn der Alst www.proessmining.org Let L e n event log over T. α(l) is defined s follows. 1. T L = { t T σ L t σ}, 2. T I = { t
Lecture Solution of a System of Linear Equation
ChE Lecture Notes, Dept. of Chemicl Engineering, Univ. of TN, Knoville - D. Keffer, 5/9/98 (updted /) Lecture 8- - Solution of System of Liner Eqution 8. Why is it importnt to e le to solve system of liner
Explain shortly the meaning of the following eight words in relation to shells structures.
Delft University of Technology Fculty of Civil Engineering nd Geosciences Structurl Mechnics Section Write your nme nd study number t the top right-hnd of your work. Exm CIE4143 Shell Anlysis Tuesdy 15
Intermediate Math Circles Wednesday, November 14, 2018 Finite Automata II. Nickolas Rollick a b b. a b 4
Intermedite Mth Circles Wednesdy, Novemer 14, 2018 Finite Automt II Nickols Rollick nrollick@uwterloo.c Regulr Lnguges Lst time, we were introduced to the ide of DFA (deterministic finite utomton), one
ILLUSTRATING THE EXTENSION OF A SPECIAL PROPERTY OF CUBIC POLYNOMIALS TO NTH DEGREE POLYNOMIALS
ILLUSTRATING THE EXTENSION OF A SPECIAL PROPERTY OF CUBIC POLYNOMIALS TO NTH DEGREE POLYNOMIALS Dvid Miller West Virgini University P.O. BOX 6310 30 Armstrong Hll Morgntown, WV 6506 millerd@mth.wvu.edu
Solutions to Problem Set #1
CSE 233 Spring, 2016 Solutions to Prolem Set #1 1. The movie tse onsists of the following two reltions movie: title, iretor, tor sheule: theter, title The first reltion provies titles, iretors, n tors
Section 4: Integration ECO4112F 2011
Reding: Ching Chpter Section : Integrtion ECOF Note: These notes do not fully cover the mteril in Ching, ut re ment to supplement your reding in Ching. Thus fr the optimistion you hve covered hs een sttic
Instructions to students: Use your Text Book and attempt these questions.
Instrutions to students: Use your Text Book nd ttempt these questions. Due Dte: 16-09-2018 Unit 2 Chpter 8 Test Slrs nd vetors Totl mrks 50 Nme: Clss: Dte: Setion A Selet the est nswer for eh question.
Edexcel Level 3 Advanced GCE in Mathematics (9MA0) Two-year Scheme of Work
Eexel Level 3 Avne GCE in Mthemtis (9MA0) Two-yer Sheme of Work Stuents stuying A Level Mthemtis will tke 3 ppers t the en of Yer 13 s inite elow. All stuents will stuy Pure, Sttistis n Mehnis. A level
12.4 Similarity in Right Triangles
Nme lss Dte 12.4 Similrit in Right Tringles Essentil Question: How does the ltitude to the hpotenuse of right tringle help ou use similr right tringles to solve prolems? Eplore Identifing Similrit in Right
Lesson 2.1 Inductive Reasoning
Lesson 2.1 Inutive Resoning Nme Perio Dte For Eerises 1 7, use inutive resoning to fin the net two terms in eh sequene. 1. 4, 8, 12, 16,, 2. 400, 200, 100, 50, 25,, 3. 1 8, 2 7, 1 2, 4, 5, 4. 5, 3, 2,
Using the Printable Sticker Function. Using the Edit Screen. Computer. Tablet. ScanNCutCanvas
SnNCutCnvs Using th Printl Stikr Funtion On-o--kin stikrs n sily rt y using your inkjt printr n th Dirt Cut untion o th SnNCut mhin. For inormtion on si oprtions o th SnNCutCnvs, rr to th Hlp. To viw th
AP Calculus BC Review Applications of Integration (Chapter 6) noting that one common instance of a force is weight
AP Clculus BC Review Applictions of Integrtion (Chpter Things to Know n Be Able to Do Fin the re between two curves by integrting with respect to x or y Fin volumes by pproximtions with cross sections:
( ) as a fraction. Determine location of the highest
AB/ Clulus Exm Review Sheet Solutions A Prelulus Type prolems A1 A A3 A4 A5 A6 A7 This is wht you think of doing Find the zeros of f( x) Set funtion equl to Ftor or use qudrti eqution if qudrti Grph to
] dx (3) = [15x] 2 0
![] dx (3) = [15x] 2 0](/thumbs/80/81916477.jpg "] dx (3) = [15x] 2 0")
Leture 6. Double Integrls nd Volume on etngle Welome to Cl IV!!!! These notes re designed to be redble nd desribe the w I will eplin the mteril in lss. Hopefull the re thorough, but it s good ide to hve
2.4 Linear Inequalities and Interval Notation
.4 Liner Inequlities nd Intervl Nottion We wnt to solve equtions tht hve n inequlity symol insted of n equl sign. There re four inequlity symols tht we will look t: Less thn , Less thn or
Linear Systems with Constant Coefficients
Liner Systems with Constnt Coefficients 4-3-05 Here is system of n differentil equtions in n unknowns: x x + + n x n, x x + + n x n, x n n x + + nn x n This is constnt coefficient liner homogeneous system
Calculus - Activity 1 Rate of change of a function at a point.
Nme: Clss: p 77 Mths Helper Plus Resource Set. Copright 00 Bruce A. Vughn, Techers Choice Softwre Clculus - Activit Rte of chnge of function t point. ) Strt Mths Helper Plus, then lod the file: Clculus
K 7. Quadratic Equations. 1. Rewrite these polynomials in the form ax 2 + bx + c = 0. Identify the values of a, b and c:
Qudrti Equtions The Null Ftor Lw Let's sy there re two numers nd. If # = then = or = (or oth re ) This mens tht if the produt of two epressions is zero, then t lest one of the epressions must e equl to
Green s Theorem. (2x e y ) da. (2x e y ) dx dy. x 2 xe y. (1 e y ) dy. y=1. = y e y. y=0. = 2 e
Green s Theorem. Let be the boundry of the unit squre, y, oriented ounterlokwise, nd let F be the vetor field F, y e y +, 2 y. Find F d r. Solution. Let s write P, y e y + nd Q, y 2 y, so tht F P, Q. Let
SIDESWAY MAGNIFICATION FACTORS FOR STEEL MOMENT FRAMES WITH VARIOUS TYPES OF COLUMN BASES
Advned Steel Constrution Vol., No., pp. 7-88 () 7 SIDESWAY MAGNIFICATION FACTORS FOR STEEL MOMENT FRAMES WIT VARIOUS TYPES OF COLUMN BASES J. ent sio Assoite Professor, Deprtment of Civil nd Environmentl
Lesson 2: The Pythagorean Theorem and Similar Triangles. A Brief Review of the Pythagorean Theorem.
27 Lesson 2: The Pythgoren Theorem nd Similr Tringles A Brief Review of the Pythgoren Theorem. Rell tht n ngle whih mesures 90º is lled right ngle. If one of the ngles of tringle is right ngle, then we
1B40 Practical Skills
B40 Prcticl Skills Comining uncertinties from severl quntities error propgtion We usully encounter situtions where the result of n experiment is given in terms of two (or more) quntities. We then need
x dx does exist, what does the answer look like? What does the answer to
Review Guie or MAT Finl Em Prt II. Mony Decemer th 8:.m. 9:5.m. (or the 8:3.m. clss) :.m. :5.m. (or the :3.m. clss) Prt is worth 5% o your Finl Em gre. NO CALCULATORS re llowe on this portion o the Finl
Applied. Grade 9 Assessment of Mathematics. Multiple-Choice Items. Winter 2005
Applie Gre 9 Assessment of Mthemtis Multiple-Choie Items Winter 2005 Plese note: The formt of these ooklets is slightly ifferent from tht use for the ssessment. The items themselves remin the sme. . Multiple-Choie
MATH 144: Business Calculus Final Review
MATH 144: Business Clculus Finl Review 1 Skills 1. Clculte severl limits. 2. Find verticl nd horizontl symptotes for given rtionl function. 3. Clculte derivtive by definition. 4. Clculte severl derivtives
Algorithms & Data Structures Homework 8 HS 18 Exercise Class (Room & TA): Submitted by: Peer Feedback by: Points:
Eidgenössishe Tehnishe Hohshule Zürih Eole polytehnique fédérle de Zurih Politenio federle di Zurigo Federl Institute of Tehnology t Zurih Deprtement of Computer Siene. Novemer 0 Mrkus Püshel, Dvid Steurer
Test , 8.2, 8.4 (density only), 8.5 (work only), 9.1, 9.2 and 9.3 related test 1 material and material from prior classes
Test 2 8., 8.2, 8.4 (density only), 8.5 (work only), 9., 9.2 nd 9.3 relted test mteril nd mteril from prior clsses Locl to Globl Perspectives Anlyze smll pieces to understnd the big picture. Exmples: numericl
Designing Information Devices and Systems I Spring 2018 Homework 7
EECS 16A Designing Informtion Devices nd Systems I Spring 2018 omework 7 This homework is due Mrch 12, 2018, t 23:59. Self-grdes re due Mrch 15, 2018, t 23:59. Sumission Formt Your homework sumission should
CS 360 Exam 2 Fall 2014 Name
CS 360 Exm 2 Fll 2014 Nme 1. The lsses shown elow efine singly-linke list n stk. Write three ifferent O(n)-time versions of the reverse_print metho s speifie elow. Eh version of the metho shoul output
CIT 596 Theory of Computation 1. Graphs and Digraphs
CIT 596 Theory of Computtion 1 A grph G = (V (G), E(G)) onsists of two finite sets: V (G), the vertex set of the grph, often enote y just V, whih is nonempty set of elements lle verties, n E(G), the ege
Arrow s Impossibility Theorem
Rep Voting Prdoxes Properties Arrow s Theorem Arrow s Impossiility Theorem Leture 12 Arrow s Impossiility Theorem Leture 12, Slide 1 Rep Voting Prdoxes Properties Arrow s Theorem Leture Overview 1 Rep
Equivalent fractions have the same value but they have different denominators. This means they have been divided into a different number of parts.
Frtions equivlent frtions Equivlent frtions hve the sme vlue ut they hve ifferent enomintors. This mens they hve een ivie into ifferent numer of prts. Use the wll to fin the equivlent frtions: Wht frtions
CS 311 Homework 3 due 16:30, Thursday, 14 th October 2010
CS 311 Homework 3 due 16:30, Thursdy, 14 th Octoer 2010 Homework must e sumitted on pper, in clss. Question 1. [15 pts.; 5 pts. ech] Drw stte digrms for NFAs recognizing the following lnguges:. L = {w
Algebra Readiness PLACEMENT 1 Fraction Basics 2 Percent Basics 3. Algebra Basics 9. CRS Algebra 1
Algebr Rediness PLACEMENT Frction Bsics Percent Bsics Algebr Bsics CRS Algebr CRS - Algebr Comprehensive Pre-Post Assessment CRS - Algebr Comprehensive Midterm Assessment Algebr Bsics CRS - Algebr Quik-Piks
Chapter 4: Techniques of Circuit Analysis. Chapter 4: Techniques of Circuit Analysis
Chpter 4: Techniques of Circuit Anlysis Terminology Node-Voltge Method Introduction Dependent Sources Specil Cses Mesh-Current Method Introduction Dependent Sources Specil Cses Comprison of Methods Source
1.3 SCALARS AND VECTORS
Bridge Course Phy I PUC 24 1.3 SCLRS ND VECTORS Introdution: Physis is the study of nturl phenomen. The study of ny nturl phenomenon involves mesurements. For exmple, the distne etween the plnet erth nd
13: Diffusion in 2 Energy Groups
3: Diffusion in Energy Groups B. Rouben McMster University Course EP 4D3/6D3 Nucler Rector Anlysis (Rector Physics) 5 Sept.-Dec. 5 September Contents We study the diffusion eqution in two energy groups
Lesson 2.1 Inductive Reasoning
Lesson 2.1 Inutive Resoning Nme Perio Dte For Eerises 1 7, use inutive resoning to fin the net two terms in eh sequene. 1. 4, 8, 12, 16,, 2. 400, 200, 100, 50, 25,, 3. 1 8, 2 7, 1 2, 4, 5, 4. 5, 3, 2,
Duality # Second iteration for HW problem. Recall our LP example problem we have been working on, in equality form, is given below.
Dulity #. Second itertion for HW problem Recll our LP emple problem we hve been working on, in equlity form, is given below.,,,, 8 m F which, when written in slightly different form, is 8 F Recll tht we