Centroids Method of Composite Areas
|
|
|
- Ursula Dickerson
- 5 years ago
- Views:
Transcription
1 Cetrods Method of Composte reas small boy swallowed some cos ad was take to a hosptal. Whe hs gradmother telephoed to ask how he was a urse sad 'No chage yet'. Cetrods Prevously, we developed a geeral formulato for fdg the cetrod for a seres of areas 2 Cetrods by Composte reas Moday, November 2, 202
2 Cetrods was the dstace from the y-as to the local cetrod of the area 3 Cetrods by Composte reas Moday, November 2, 202 Cetrods If we ca break up a shape to a seres of smaller shapes that have predefed local cetrod locatos, we ca use ths formula to locate the cetrod of the composte shape 4 Cetrods by Composte reas Moday, November 2, 202 2
3 Cetrod by Composte Bodes There s a table the back cover of your book that gves you the locato of local cetrods for a select group of shapes The pot labeled C s the locato of the cetrod of that shape. 5 Cetrods by Composte reas Moday, November 2, 202 Cetrod by Composte Bodes Please ote that these are local cetrods, they are gve referece to the ad y aes as show the table. 6 Cetrods by Composte reas Moday, November 2, 202 3
4 Cetrod by Composte Bodes For eample, the cetrod locato of the semcrcular area has the y-as through the ceter of the area ad the -as at the bottom of the area The -cetrod would be located at 0 ad the y-cetrod would be located at 4r 3π 7 Cetrods by Composte reas Moday, November 2, 202 Cetrod by Composte Bodes If we wated the cetrod wth respect to aother as, say alog the top of the semcrcle ad alog the left edge, the values the table could t be used eactly y C 8 Cetrods by Composte reas Moday, November 2, 202 4
5 Cetrod by Composte Bodes The table would gve you the dstace of C above the base of the semcrcle, but that s t the dstace from the cetrod to the -as 9 Cetrods by Composte reas Moday, November 2, 202 Cetrod by Composte Bodes y 4r/3π C 0 Cetrods by Composte reas Moday, November 2, 202 5
6 Cetrod by Composte Bodes Sce the radus of the semcrcle, ths case the dstace to the y-cetrod would be 4 y r r 3π Cetrods by Composte reas Moday, November 2, 202 Cetrod by Composte Bodes y 4r y r 3π 4r/3π C 2 Cetrods by Composte reas Moday, November 2, 202 6
7 Cetrod by Composte Bodes By the same logc, the dstace to the - cetrod would be r 3 Cetrods by Composte reas Moday, November 2, 202 Cetrod by Composte Bodes y r r-(4r/3π) 4r/3π C 4 Cetrods by Composte reas Moday, November 2, 202 7
8 Eample Lets start wth a eample problem ad see how ths develops 3 5 Cetrods by Composte reas Moday, November 2, 202 Eample We wat to locate both the ad y cetrods 3 6 Cetrods by Composte reas Moday, November 2, 202 8
9 Eample There s t much of a chace of developg a fucto that s easy to tegrate ths case 3 7 Cetrods by Composte reas Moday, November 2, 202 Eample We ca break ths fgure up to a seres of shapes ad fd the locato of the local cetrod of each 3 8 Cetrods by Composte reas Moday, November 2, 202 9
10 Eample There are multple ways to do ths as log as you are cosstet 3 9 Cetrods by Composte reas Moday, November 2, 202 Eample Frst, we ca develop a rectagle o the left sde of the dagram, we wll label that as area, 3 20 Cetrods by Composte reas Moday, November 2, 202 0
11 Eample secod rectagle wll be placed the bottom of the fgure, we wll label t Cetrods by Composte reas Moday, November 2, 202 Eample rght tragle wll complete the upper rght sde of the fgure, label t Cetrods by Composte reas Moday, November 2, 202
12 Eample Fally, we wll develop a egatve area to remove the quarter crcle the lower left had corer, label t Cetrods by Composte reas Moday, November 2, 202 Eample We wll beg to buld a table so that keepg up wth thgs wll be easer The frst colum wll be the areas ID rea ( 2 ) Cetrods by Composte reas 3 Moday, November 2, 202 2
13 Eample Now we wll calculate the dstace to the local cetrods from the y-as (we are calculatg a -cetrod) ID rea ( 2 ) () Cetrods by Composte reas 3 Moday, November 2, 202 Eample To calculate the top term the epresso we eed to multply the etres the last two colums by oe aother ID rea *rea ( 2 ) () ( 3 ) Cetrods by Composte reas 3 Moday, November 2, 202 3
14 Eample If we sum the secod colum, we have the bottom term the dvso, the total area ID rea *rea ( 2 ) () ( 3 ) Cetrods by Composte reas 3 Moday, November 2, 202 Eample d f we sum the fourth colum, we have the top term, the area momet ID rea *rea ( 2 ) () ( 3 ) Cetrods by Composte reas 3 Moday, November 2, 202 4
15 Eample Dvdg the sum of the area momets by the total area we calculate the -cetrod ID rea *rea ( 2 ) () ( 3 ) bar Cetrods by Composte reas 3 Moday, November 2, 202 Eample You ca always remember whch to dvde by f you look at the fal uts, remember that a cetrod s a dstace ID rea *rea ( 2 ) () ( 3 ) bar Cetrods by Composte reas 3 Moday, November 2, 202 5
16 Eample We ca do the same process wth the y cetrod ID rea *rea ( 2 ) () ( 3 ) bar y y 3 Cetrods by Composte reas 3 Moday, November 2, 202 Eample Notce that the bottom term does t chage, the area of the fgure has t chaged ID rea *rea ( 2 ) () ( 3 ) bar y y 32 Cetrods by Composte reas 3 Moday, November 2, 202 6
17 Eample We oly eed to add a colum of y s ID rea *rea y ( 2 ) () ( 3 ) () bar.954 y y Cetrods by Composte reas Moday, 3 November 2, 202 Eample Calculate the area momets about the - as ID rea *rea y y *rea ( 2 ) () ( 3 ) () ( 3 ) bar.954 y y Cetrods by Composte reas Moday, 3 November 2, 202 7
18 Eample Sum the area momets ID rea *rea y y *rea ( 2 ) () ( 3 ) () ( 3 ) bar.954 y y Cetrods by Composte reas Moday, 3 November 2, 202 Eample d make the dvso of the area momets by the total area ID rea *rea y y *rea ( 2 ) () ( 3 ) () ( 3 ) bar.954 y bar y y Cetrods by Composte reas Moday, 3 November 2, 202 8
19 Eample Problem 9-60 Problem Cetrods by Composte reas Moday, November 2, 202 Eample Problem Cetrods by Composte reas Moday, November 2, 202 9
20 Homework Problem 9-64 Problem 9-65 Problem Cetrods by Composte reas Moday, November 2,
Mechanics of Materials CIVL 3322 / MECH 3322
Mechacs of Materals CVL / MECH Cetrods ad Momet of erta Calculatos Cetrods = A = = = A = = Cetrod ad Momet of erta Calculatos z= z A = = Parallel As Theorem f ou kow the momet of erta about a cetrodal
Centroids & Moments of Inertia of Beam Sections
RCH 614 Note Set 8 S017ab Cetrods & Momets of erta of Beam Sectos Notato: b C d d d Fz h c Jo L O Q Q = ame for area = ame for a (base) wdth = desgato for chael secto = ame for cetrod = calculus smbol
Centers of Gravity - Centroids
RCH Note Set 9. S205ab Ceters of Gravt - Cetrods Notato: C Fz L O Q Q t tw = ame for area = desgato for chael secto = ame for cetrod = force compoet the z drecto = ame for legth = ame for referece org
Mu Sequences/Series Solutions National Convention 2014
Mu Sequeces/Seres Solutos Natoal Coveto 04 C 6 E A 6C A 6 B B 7 A D 7 D C 7 A B 8 A B 8 A C 8 E 4 B 9 B 4 E 9 B 4 C 9 E C 0 A A 0 D B 0 C C Usg basc propertes of arthmetc sequeces, we fd a ad bm m We eed
CHAPTER 4 RADICAL EXPRESSIONS
6 CHAPTER RADICAL EXPRESSIONS. The th Root of a Real Number A real umber a s called the th root of a real umber b f Thus, for example: s a square root of sce. s also a square root of sce ( ). s a cube
Multiple Regression. More than 2 variables! Grade on Final. Multiple Regression 11/21/2012. Exam 2 Grades. Exam 2 Re-grades
STAT 101 Dr. Kar Lock Morga 11/20/12 Exam 2 Grades Multple Regresso SECTIONS 9.2, 10.1, 10.2 Multple explaatory varables (10.1) Parttog varablty R 2, ANOVA (9.2) Codtos resdual plot (10.2) Trasformatos
1 Onto functions and bijections Applications to Counting
1 Oto fuctos ad bectos Applcatos to Coutg Now we move o to a ew topc. Defto 1.1 (Surecto. A fucto f : A B s sad to be surectve or oto f for each b B there s some a A so that f(a B. What are examples of
( ) 2 2. Multi-Layer Refraction Problem Rafael Espericueta, Bakersfield College, November, 2006
Mult-Layer Refracto Problem Rafael Espercueta, Bakersfeld College, November, 006 Lght travels at dfferet speeds through dfferet meda, but refracts at layer boudares order to traverse the least-tme path.
Taylor s Series and Interpolation. Interpolation & Curve-fitting. CIS Interpolation. Basic Scenario. Taylor Series interpolates at a specific
CIS 54 - Iterpolato Roger Crawfs Basc Scearo We are able to prod some fucto, but do ot kow what t really s. Ths gves us a lst of data pots: [x,f ] f(x) f f + x x + August 2, 25 OSU/CIS 54 3 Taylor s Seres
Lecture 9: Tolerant Testing
Lecture 9: Tolerat Testg Dael Kae Scrbe: Sakeerth Rao Aprl 4, 07 Abstract I ths lecture we prove a quas lear lower boud o the umber of samples eeded to do tolerat testg for L dstace. Tolerat Testg We have
PTAS for Bin-Packing
CS 663: Patter Matchg Algorthms Scrbe: Che Jag /9/00. Itroducto PTAS for B-Packg The B-Packg problem s NP-hard. If we use approxmato algorthms, the B-Packg problem could be solved polyomal tme. For example,
Introduction to local (nonparametric) density estimation. methods
Itroducto to local (oparametrc) desty estmato methods A slecture by Yu Lu for ECE 66 Sprg 014 1. Itroducto Ths slecture troduces two local desty estmato methods whch are Parze desty estmato ad k-earest
( ) ( ) A number of the form x+iy, where x & y are integers and i = 1 is called a complex number.
A umber of the form y, where & y are tegers ad s called a comple umber. Dfferet Forms )Cartesa Form y )Polar Form ( cos s ) r or r cs )Epoetal Form r e Demover s Theorem If s ay teger the cos s cos s If
Machine Learning. Topic 4: Measuring Distance
Mache Learg Topc 4: Measurg Dstace Bra Pardo Mache Learg: EECS 349 Fall 2009 Wh measure dstace? Clusterg requres dstace measures. Local methods requre a measure of localt Search eges requre a measure of
Lecture Notes Types of economic variables
Lecture Notes 3 1. Types of ecoomc varables () Cotuous varable takes o a cotuum the sample space, such as all pots o a le or all real umbers Example: GDP, Polluto cocetrato, etc. () Dscrete varables fte
CHAPTER 5 INTEGRATION
CHAPTER 5 INTEGRATION 5.1 AREA AND ESTIMATING WITH FINITE SUMS 1. fax x Sce f s creasg o Ò!ß Ó, we use left edpots to ota lower sums ad rght edpots to ota upper sums.! )!! ( (!ˆ 4 4 4Š ˆ ˆ ˆ 4 4 )! (a)
Discrete Mathematics and Probability Theory Fall 2016 Seshia and Walrand DIS 10b
CS 70 Dscrete Mathematcs ad Probablty Theory Fall 206 Sesha ad Walrad DIS 0b. Wll I Get My Package? Seaky delvery guy of some compay s out delverg packages to customers. Not oly does he had a radom package
Test Paper-II. 1. If sin θ + cos θ = m and sec θ + cosec θ = n, then (a) 2n = m (n 2 1) (b) 2m = n (m 2 1) (c) 2n = m (m 2 1) (d) none of these
Test Paer-II. If s θ + cos θ = m ad sec θ + cosec θ =, the = m ( ) m = (m ) = m (m ). If a ABC, cos A = s B, the t s C a osceles tragle a eulateral tragle a rght agled tragle. If cos B = cos ( A+ C), the
2006 Jamie Trahan, Autar Kaw, Kevin Martin University of South Florida United States of America
SOLUTION OF SYSTEMS OF SIMULTANEOUS LINEAR EQUATIONS Gauss-Sedel Method 006 Jame Traha, Autar Kaw, Kev Mart Uversty of South Florda Uted States of Amerca kaw@eg.usf.edu Itroducto Ths worksheet demostrates
Outline. Point Pattern Analysis Part I. Revisit IRP/CSR
Pot Patter Aalyss Part I Outle Revst IRP/CSR, frst- ad secod order effects What s pot patter aalyss (PPA)? Desty-based pot patter measures Dstace-based pot patter measures Revst IRP/CSR Equal probablty:
Midterm Exam 1, section 1 (Solution) Thursday, February hour, 15 minutes
coometrcs, CON Sa Fracsco State Uversty Mchael Bar Sprg 5 Mdterm am, secto Soluto Thursday, February 6 hour, 5 mutes Name: Istructos. Ths s closed book, closed otes eam.. No calculators of ay kd are allowed..
Laboratory I.10 It All Adds Up
Laboratory I. It All Adds Up Goals The studet wll work wth Rema sums ad evaluate them usg Derve. The studet wll see applcatos of tegrals as accumulatos of chages. The studet wll revew curve fttg sklls.
Econometric Methods. Review of Estimation
Ecoometrc Methods Revew of Estmato Estmatg the populato mea Radom samplg Pot ad terval estmators Lear estmators Ubased estmators Lear Ubased Estmators (LUEs) Effcecy (mmum varace) ad Best Lear Ubased Estmators
3D Geometry for Computer Graphics. Lesson 2: PCA & SVD
3D Geometry for Computer Graphcs Lesso 2: PCA & SVD Last week - egedecomposto We wat to lear how the matrx A works: A 2 Last week - egedecomposto If we look at arbtrary vectors, t does t tell us much.
DATE: 21 September, 1999 TO: Jim Russell FROM: Peter Tkacik RE: Analysis of wide ply tube winding as compared to Konva Kore CC: Larry McMillan
M E M O R A N D U M DATE: 1 September, 1999 TO: Jm Russell FROM: Peter Tkack RE: Aalyss of wde ply tube wdg as compared to Kova Kore CC: Larry McMlla The goal of ths report s to aalyze the spral tube wdg
PGE 310: Formulation and Solution in Geosystems Engineering. Dr. Balhoff. Interpolation
PGE 30: Formulato ad Soluto Geosystems Egeerg Dr. Balhoff Iterpolato Numercal Methods wth MATLAB, Recktewald, Chapter 0 ad Numercal Methods for Egeers, Chapra ad Caale, 5 th Ed., Part Fve, Chapter 8 ad
MEASURES OF DISPERSION
MEASURES OF DISPERSION Measure of Cetral Tedecy: Measures of Cetral Tedecy ad Dsperso ) Mathematcal Average: a) Arthmetc mea (A.M.) b) Geometrc mea (G.M.) c) Harmoc mea (H.M.) ) Averages of Posto: a) Meda
2SLS Estimates ECON In this case, begin with the assumption that E[ i
SLS Estmates ECON 3033 Bll Evas Fall 05 Two-Stage Least Squares (SLS Cosder a stadard lear bvarate regresso model y 0 x. I ths case, beg wth the assumto that E[ x] 0 whch meas that OLS estmates of wll
Descriptive Statistics
Page Techcal Math II Descrptve Statstcs Descrptve Statstcs Descrptve statstcs s the body of methods used to represet ad summarze sets of data. A descrpto of how a set of measuremets (for eample, people
Assignment 5/MATH 247/Winter Due: Friday, February 19 in class (!) (answers will be posted right after class)
Assgmet 5/MATH 7/Wter 00 Due: Frday, February 9 class (!) (aswers wll be posted rght after class) As usual, there are peces of text, before the questos [], [], themselves. Recall: For the quadratc form
, so the next 5 terms are 31, 4, 37, 12, and The constant is π. Ptolemy used a 360-gon to approximate π as
. The umber chose was, guessg as e tes dgt ad as e oes dgt each ears hal a pot.. The best way to do s s rough brute orce o a computer. The rst two are 6867 ad 68. The rd s + 7 + 6 867767.. The eve term
hp calculators HP 30S Statistics Averages and Standard Deviations Average and Standard Deviation Practice Finding Averages and Standard Deviations
HP 30S Statstcs Averages ad Stadard Devatos Average ad Stadard Devato Practce Fdg Averages ad Stadard Devatos HP 30S Statstcs Averages ad Stadard Devatos Average ad stadard devato The HP 30S provdes several
Computational Geometry
Problem efto omputatoal eometry hapter 6 Pot Locato Preprocess a plaar map S. ve a query pot p, report the face of S cotag p. oal: O()-sze data structure that eables O(log ) query tme. pplcato: Whch state
The z-transform. LTI System description. Prof. Siripong Potisuk
The -Trsform Prof. Srpog Potsuk LTI System descrpto Prevous bss fucto: ut smple or DT mpulse The put sequece s represeted s ler combto of shfted DT mpulses. The respose s gve by covoluto sum of the put
Midterm Exam 1, section 2 (Solution) Thursday, February hour, 15 minutes
coometrcs, CON Sa Fracsco State Uverst Mchael Bar Sprg 5 Mdterm xam, secto Soluto Thursda, Februar 6 hour, 5 mutes Name: Istructos. Ths s closed book, closed otes exam.. No calculators of a kd are allowed..
The conformations of linear polymers
The coformatos of lear polymers Marc R. Roussel Departmet of Chemstry ad Bochemstry Uversty of Lethbrdge February 19, 9 Polymer scece s a rch source of problems appled statstcs ad statstcal mechacs. I
02/15/04 INTERESTING FINITE AND INFINITE PRODUCTS FROM SIMPLE ALGEBRAIC IDENTITIES
0/5/04 ITERESTIG FIITE AD IFIITE PRODUCTS FROM SIMPLE ALGEBRAIC IDETITIES Thomas J Osler Mathematcs Departmet Rowa Uversty Glassboro J 0808 Osler@rowaedu Itroducto The dfferece of two squares, y = + y
Simple Linear Regression
Statstcal Methods I (EST 75) Page 139 Smple Lear Regresso Smple regresso applcatos are used to ft a model descrbg a lear relatoshp betwee two varables. The aspects of least squares regresso ad correlato
EECE 301 Signals & Systems
EECE 01 Sgals & Systems Prof. Mark Fowler Note Set #9 Computg D-T Covoluto Readg Assgmet: Secto. of Kame ad Heck 1/ Course Flow Dagram The arrows here show coceptual flow betwee deas. Note the parallel
Minimizing spherical aberrations Exploiting the existence of conjugate points in spherical lenses
Mmzg sphecal abeatos Explotg the exstece of cojugate pots sphecal leses Let s ecall that whe usg asphecal leses, abeato fee magg occus oly fo a couple of, so called, cojugate pots ( ad the fgue below)
We have already referred to a certain reaction, which takes place at high temperature after rich combustion.
ME 41 Day 13 Topcs Chemcal Equlbrum - Theory Chemcal Equlbrum Example #1 Equlbrum Costats Chemcal Equlbrum Example #2 Chemcal Equlbrum of Hot Bured Gas 1. Chemcal Equlbrum We have already referred to a
means the first term, a2 means the term, etc. Infinite Sequences: follow the same pattern forever.
9.4 Sequeces ad Seres Pre Calculus 9.4 SEQUENCES AND SERIES Learg Targets:. Wrte the terms of a explctly defed sequece.. Wrte the terms of a recursvely defed sequece. 3. Determe whether a sequece s arthmetc,
Statistics: Unlocking the Power of Data Lock 5
STAT 0 Dr. Kar Lock Morga Exam 2 Grades: I- Class Multple Regresso SECTIONS 9.2, 0., 0.2 Multple explaatory varables (0.) Parttog varablty R 2, ANOVA (9.2) Codtos resdual plot (0.2) Exam 2 Re- grades Re-
Integral Equation Methods. Jacob White. Thanks to Deepak Ramaswamy, Michal Rewienski, Xin Wang and Karen Veroy
Itroducto to Smulato - Lecture 22 Itegral Equato ethods Jacob Whte Thaks to Deepak Ramaswamy, chal Rewesk, X Wag ad Kare Veroy Outle Itegral Equato ethods Exteror versus teror problems Start wth usg pot
Unsupervised Learning and Other Neural Networks
CSE 53 Soft Computg NOT PART OF THE FINAL Usupervsed Learg ad Other Neural Networs Itroducto Mture Destes ad Idetfablty ML Estmates Applcato to Normal Mtures Other Neural Networs Itroducto Prevously, all
MA 524 Homework 6 Solutions
MA 524 Homework 6 Solutos. Sce S(, s the umber of ways to partto [] to k oempty blocks, ad c(, s the umber of ways to partto to k oempty blocks ad also the arrage each block to a cycle, we must have S(,
Multiple Choice Test. Chapter Adequacy of Models for Regression
Multple Choce Test Chapter 06.0 Adequac of Models for Regresso. For a lear regresso model to be cosdered adequate, the percetage of scaled resduals that eed to be the rage [-,] s greater tha or equal to
Evaluating Polynomials
Uverst of Nebraska - Lcol DgtalCommos@Uverst of Nebraska - Lcol MAT Exam Expostor Papers Math the Mddle Isttute Partershp 7-7 Evaluatg Polomals Thomas J. Harrgto Uverst of Nebraska-Lcol Follow ths ad addtoal
ROOT-LOCUS ANALYSIS. Lecture 11: Root Locus Plot. Consider a general feedback control system with a variable gain K. Y ( s ) ( ) K
ROOT-LOCUS ANALYSIS Coder a geeral feedback cotrol yte wth a varable ga. R( Y( G( + H( Root-Locu a plot of the loc of the pole of the cloed-loop trafer fucto whe oe of the yte paraeter ( vared. Root locu
Can we take the Mysticism Out of the Pearson Coefficient of Linear Correlation?
Ca we tae the Mstcsm Out of the Pearso Coeffcet of Lear Correlato? Itroducto As the ttle of ths tutoral dcates, our purpose s to egeder a clear uderstadg of the Pearso coeffcet of lear correlato studets
12.2 Estimating Model parameters Assumptions: ox and y are related according to the simple linear regression model
1. Estmatg Model parameters Assumptos: ox ad y are related accordg to the smple lear regresso model (The lear regresso model s the model that says that x ad y are related a lear fasho, but the observed
Complex Numbers and Polynomials pages (d) If A = (6, 1), then A = (1, 6). (c) If A = (3, 5), then A = ( 5, 3).
Chapter 6 Complex Numbers ad Polyomals pages 7 7... INVESTIGATION 6A 6. Gettg Started GRAPHING COMPLEX NUMBERS For You to Explore. a + + + + + + + b + + + + c + + + + + 6 + + + d + + + + + 9 + 6 8 + 6
Lecture 7. Confidence Intervals and Hypothesis Tests in the Simple CLR Model
Lecture 7. Cofdece Itervals ad Hypothess Tests the Smple CLR Model I lecture 6 we troduced the Classcal Lear Regresso (CLR) model that s the radom expermet of whch the data Y,,, K, are the outcomes. The
arxiv:math/ v1 [math.gm] 8 Dec 2005
![arxiv:math/ v1 [math.gm] 8 Dec 2005](/thumbs/94/118250722.jpg "arxiv:math/ v1 [math.gm] 8 Dec 2005")
arxv:math/05272v [math.gm] 8 Dec 2005 A GENERALIZATION OF AN INEQUALITY FROM IMO 2005 NIKOLAI NIKOLOV The preset paper was spred by the thrd problem from the IMO 2005. A specal award was gve to Yure Boreko
CHAPTER 3 POSTERIOR DISTRIBUTIONS
CHAPTER 3 POSTERIOR DISTRIBUTIONS If scece caot measure the degree of probablt volved, so much the worse for scece. The practcal ma wll stck to hs apprecatve methods utl t does, or wll accept the results
Econ 388 R. Butler 2016 rev Lecture 5 Multivariate 2 I. Partitioned Regression and Partial Regression Table 1: Projections everywhere
Eco 388 R. Butler 06 rev Lecture 5 Multvarate I. Parttoed Regresso ad Partal Regresso Table : Projectos everywhere P = ( ) ad M = I ( ) ad s a vector of oes assocated wth the costat term Sample Model Regresso
Complex Numbers Primer
Complex Numbers Prmer Before I get started o ths let me frst make t clear that ths documet s ot teded to teach you everythg there s to kow about complex umbers. That s a subject that ca (ad does) take
b. There appears to be a positive relationship between X and Y; that is, as X increases, so does Y.
.46. a. The frst varable (X) s the frst umber the par ad s plotted o the horzotal axs, whle the secod varable (Y) s the secod umber the par ad s plotted o the vertcal axs. The scatterplot s show the fgure
UNIVERSITY OF OSLO DEPARTMENT OF ECONOMICS
UNIVERSITY OF OSLO DEPARTMENT OF ECONOMICS Postpoed exam: ECON430 Statstcs Date of exam: Jauary 0, 0 Tme for exam: 09:00 a.m. :00 oo The problem set covers 5 pages Resources allowed: All wrtte ad prted
Applying the condition for equilibrium to this equilibrium, we get (1) n i i =, r G and 5 i
CHEMICAL EQUILIBRIA The Thermodyamc Equlbrum Costat Cosder a reversble reacto of the type 1 A 1 + 2 A 2 + W m A m + m+1 A m+1 + Assgg postve values to the stochometrc coeffcets o the rght had sde ad egatve
Introduction to Computer Design. Standard Forms for Boolean Functions. Sums and Products. Standard Forms for Boolean Functions (cont ) CMPT-150
CMPT- Itroducto to Computer Desg SFU Harbour Cetre Sprg 7 Lecture : Ja. 6 7 Stadard orms or boolea uctos Sum o Products Product o Sums Stadard Forms or Boolea Fuctos (cot ) It s useul to spec Boolea uctos
Lecture 07: Poles and Zeros
Lecture 07: Poles ad Zeros Defto of poles ad zeros The trasfer fucto provdes a bass for determg mportat system respose characterstcs wthout solvg the complete dfferetal equato. As defed, the trasfer fucto
Model Fitting, RANSAC. Jana Kosecka
Model Fttg, RANSAC Jaa Kosecka Fttg: Issues Prevous strateges Le detecto Hough trasform Smple parametrc model, two parameters m, b m + b Votg strateg Hard to geeralze to hgher dmesos a o + a + a 2 2 +
Loop-independent dependence: dependence exists within an iteration; i.e., if the loop is removed, the dependence still exists.
Loop-depedet vs. loop-carred depedeces [ 3.] Loop-carred depedece: depedece exsts across teratos;.e., f the loop s removed, the depedece o loger exsts. Loop-depedet depedece: depedece exsts wth a terato;.e.,
Overview of the weighting constants and the points where we evaluate the function for The Gaussian quadrature Project two
Overvew of the weghtg costats ad the pots where we evaluate the fucto for The Gaussa quadrature Project two By Ashraf Marzouk ChE 505 Fall 005 Departmet of Mechacal Egeerg Uversty of Teessee Koxvlle, TN
CP 2 Properties of polygonal plane areas
CP Propertes of polgoal plae areas Ket D. Hjelmstad Scool for Sustaale Egeerg ad te Bult Evromet Ira. Fulto Scools of Egeerg roa State Uverst Te propertes of cross sectos Cross Secto Cross Secto Logtudal
Lecture Notes Forecasting the process of estimating or predicting unknown situations
Lecture Notes. Ecoomc Forecastg. Forecastg the process of estmatg or predctg ukow stuatos Eample usuall ecoomsts predct future ecoomc varables Forecastg apples to a varet of data () tme seres data predctg
MATH 247/Winter Notes on the adjoint and on normal operators.
MATH 47/Wter 00 Notes o the adjot ad o ormal operators I these otes, V s a fte dmesoal er product space over, wth gve er * product uv, T, S, T, are lear operators o V U, W are subspaces of V Whe we say
1. Overview of basic probability
13.42 Desg Prcples for Ocea Vehcles Prof. A.H. Techet Sprg 2005 1. Overvew of basc probablty Emprcally, probablty ca be defed as the umber of favorable outcomes dvded by the total umber of outcomes, other
QR Factorization and Singular Value Decomposition COS 323
QR Factorzato ad Sgular Value Decomposto COS 33 Why Yet Aother Method? How do we solve least-squares wthout currg codto-squarg effect of ormal equatos (A T A A T b) whe A s sgular, fat, or otherwse poorly-specfed?
Third handout: On the Gini Index
Thrd hadout: O the dex Corrado, a tala statstca, proposed (, 9, 96) to measure absolute equalt va the mea dfferece whch s defed as ( / ) where refers to the total umber of dvduals socet. Assume that. The
Chapter 3 Sampling For Proportions and Percentages
Chapter 3 Samplg For Proportos ad Percetages I may stuatos, the characterstc uder study o whch the observatos are collected are qualtatve ature For example, the resposes of customers may marketg surveys
{ }{ ( )} (, ) = ( ) ( ) ( ) Chapter 14 Exercises in Sampling Theory. Exercise 1 (Simple random sampling): Solution:
Chapter 4 Exercses Samplg Theory Exercse (Smple radom samplg: Let there be two correlated radom varables X ad A sample of sze s draw from a populato by smple radom samplg wthout replacemet The observed
ENGI 3423 Simple Linear Regression Page 12-01
ENGI 343 mple Lear Regresso Page - mple Lear Regresso ometmes a expermet s set up where the expermeter has cotrol over the values of oe or more varables X ad measures the resultg values of aother varable
Beam Warming Second-Order Upwind Method
Beam Warmg Secod-Order Upwd Method Petr Valeta Jauary 6, 015 Ths documet s a part of the assessmet work for the subject 1DRP Dfferetal Equatos o Computer lectured o FNSPE CTU Prague. Abstract Ths documet
9 U-STATISTICS. Eh =(m!) 1 Eh(X (1),..., X (m ) ) i.i.d
9 U-STATISTICS Suppose,,..., are P P..d. wth CDF F. Our goal s to estmate the expectato t (P)=Eh(,,..., m ). Note that ths expectato requres more tha oe cotrast to E, E, or Eh( ). Oe example s E or P((,
8.1 Hashing Algorithms
CS787: Advaced Algorthms Scrbe: Mayak Maheshwar, Chrs Hrchs Lecturer: Shuch Chawla Topc: Hashg ad NP-Completeess Date: September 21 2007 Prevously we looked at applcatos of radomzed algorthms, ad bega
PHYS Look over. examples 2, 3, 4, 6, 7, 8,9, 10 and 11. How To Make Physics Pay PHYS Look over. Examples: 1, 4, 5, 6, 7, 8, 9, 10,
PHYS Look over Chapter 9 Sectos - Eamples:, 4, 5, 6, 7, 8, 9, 0, PHYS Look over Chapter 7 Sectos -8 8, 0 eamples, 3, 4, 6, 7, 8,9, 0 ad How To ake Phscs Pa We wll ow look at a wa of calculatg where the
ENGI 4430 Numerical Integration Page 5-01
ENGI 443 Numercal Itegrato Page 5-5. Numercal Itegrato I some o our prevous work, (most otaly the evaluato o arc legth), t has ee dcult or mpossle to d the dete tegral. Varous symolc algera ad calculus
d dt d d dt dt Also recall that by Taylor series, / 2 (enables use of sin instead of cos-see p.27 of A&F) dsin
Learzato of the Swg Equato We wll cover sectos.5.-.6 ad begg of Secto 3.3 these otes. 1. Sgle mache-fte bus case Cosder a sgle mache coected to a fte bus, as show Fg. 1 below. E y1 V=1./_ Fg. 1 The admttace
Lecture 2 - What are component and system reliability and how it can be improved?
Lecture 2 - What are compoet ad system relablty ad how t ca be mproved? Relablty s a measure of the qualty of the product over the log ru. The cocept of relablty s a exteded tme perod over whch the expected
2/20/2013. Topics. Power Flow Part 1 Text: Power Transmission. Power Transmission. Power Transmission. Power Transmission
/0/0 Topcs Power Flow Part Text: 0-0. Power Trassso Revsted Power Flow Equatos Power Flow Proble Stateet ECEGR 45 Power Systes Power Trassso Power Trassso Recall that for a short trassso le, the power
Module 7. Lecture 7: Statistical parameter estimation
Lecture 7: Statstcal parameter estmato Parameter Estmato Methods of Parameter Estmato 1) Method of Matchg Pots ) Method of Momets 3) Mamum Lkelhood method Populato Parameter Sample Parameter Ubased estmato
Lecture 2: Linear Least Squares Regression
Lecture : Lear Least Squares Regresso Dave Armstrog UW Mlwaukee February 8, 016 Is the Relatoshp Lear? lbrary(car) data(davs) d 150) Davs$weght[d]
Ideal multigrades with trigonometric coefficients
Ideal multgrades wth trgoometrc coeffcets Zarathustra Brady December 13, 010 1 The problem A (, k) multgrade s defed as a par of dstct sets of tegers such that (a 1,..., a ; b 1,..., b ) a j = =1 for all
(b) By independence, the probability that the string 1011 is received correctly is
Soluto to Problem 1.31. (a) Let A be the evet that a 0 s trasmtted. Usg the total probablty theorem, the desred probablty s P(A)(1 ɛ ( 0)+ 1 P(A) ) (1 ɛ 1)=p(1 ɛ 0)+(1 p)(1 ɛ 1). (b) By depedece, the probablty
Lecture 5: Interpolation. Polynomial interpolation Rational approximation
Lecture 5: Iterpolato olyomal terpolato Ratoal appromato Coeffcets of the polyomal Iterpolato: Sometme we kow the values of a fucto f for a fte set of pots. Yet we wat to evaluate f for other values perhaps
18.413: Error Correcting Codes Lab March 2, Lecture 8
18.413: Error Correctg Codes Lab March 2, 2004 Lecturer: Dael A. Spelma Lecture 8 8.1 Vector Spaces A set C {0, 1} s a vector space f for x all C ad y C, x + y C, where we take addto to be compoet wse
UNIT 2 SOLUTION OF ALGEBRAIC AND TRANSCENDENTAL EQUATIONS
Numercal Computg -I UNIT SOLUTION OF ALGEBRAIC AND TRANSCENDENTAL EQUATIONS Structure Page Nos..0 Itroducto 6. Objectves 7. Ital Approxmato to a Root 7. Bsecto Method 8.. Error Aalyss 9.4 Regula Fals Method
7. Joint Distributions
7. Jot Dstrbutos Chrs Pech ad Mehra Saham Ma 2017 Ofte ou wll work o problems where there are several radom varables (ofte teractg wth oe aother. We are gog to start to formall look at how those teractos
Lecture 02: Bounding tail distributions of a random variable
CSCI-B609: A Theorst s Toolkt, Fall 206 Aug 25 Lecture 02: Boudg tal dstrbutos of a radom varable Lecturer: Yua Zhou Scrbe: Yua Xe & Yua Zhou Let us cosder the ubased co flps aga. I.e. let the outcome
Arithmetic Mean and Geometric Mean
Acta Mathematca Ntresa Vol, No, p 43 48 ISSN 453-6083 Arthmetc Mea ad Geometrc Mea Mare Varga a * Peter Mchalča b a Departmet of Mathematcs, Faculty of Natural Sceces, Costate the Phlosopher Uversty Ntra,
1 Lyapunov Stability Theory
Lyapuov Stablty heory I ths secto we cosder proofs of stablty of equlbra of autoomous systems. hs s stadard theory for olear systems, ad oe of the most mportat tools the aalyss of olear systems. It may
Johns Hopkins University Department of Biostatistics Math Review for Introductory Courses
Johs Hopks Uverst Departmet of Bostatstcs Math Revew for Itroductor Courses Ratoale Bostatstcs courses wll rel o some fudametal mathematcal relatoshps, fuctos ad otato. The purpose of ths Math Revew s
Block-Based Compact Thermal Modeling of Semiconductor Integrated Circuits
Block-Based Compact hermal Modelg of Semcoductor Itegrated Crcuts Master s hess Defese Caddate: Jg Ba Commttee Members: Dr. Mg-Cheg Cheg Dr. Daqg Hou Dr. Robert Schllg July 27, 2009 Outle Itroducto Backgroud
F. Inequalities. HKAL Pure Mathematics. 進佳數學團隊 Dr. Herbert Lam 林康榮博士. [Solution] Example Basic properties
![F. Inequalities. HKAL Pure Mathematics. 進佳數學團隊 Dr. Herbert Lam 林康榮博士. [Solution] Example Basic properties](/thumbs/82/86768390.jpg "F. Inequalities. HKAL Pure Mathematics. 進佳數學團隊 Dr. Herbert Lam 林康榮博士. [Solution] Example Basic properties")
進佳數學團隊 Dr. Herbert Lam 林康榮博士 HKAL Pure Mathematcs F. Ieualtes. Basc propertes Theorem Let a, b, c be real umbers. () If a b ad b c, the a c. () If a b ad c 0, the ac bc, but f a b ad c 0, the ac bc. Theorem
Investigating Cellular Automata
Researcher: Taylor Dupuy Advsor: Aaro Wootto Semester: Fall 4 Ivestgatg Cellular Automata A Overvew of Cellular Automata: Cellular Automata are smple computer programs that geerate rows of black ad whte
STA 108 Applied Linear Models: Regression Analysis Spring Solution for Homework #1
STA 08 Appled Lear Models: Regresso Aalyss Sprg 0 Soluto for Homework #. Let Y the dollar cost per year, X the umber of vsts per year. The the mathematcal relato betwee X ad Y s: Y 300 + X. Ths s a fuctoal
Johns Hopkins University Department of Biostatistics Math Review for Introductory Courses
Johs Hopks Uverst Departmet of Bostatstcs Math Revew for Itroductor Courses Ratoale Bostatstcs courses wll rel o some fudametal mathematcal relatoshps, fuctos ad otato. The purpose of ths Math Revew s
COS 341 Discrete Mathematics. Exponential Generating Functions
COS 341 Dscrete Mathematcs Epoetal Geeratg Fuctos 1 Read the tetbook Trouble keepg pace? Optoal referece tet (Rose) has may more solved eercses ad practce problems Start early o homework assgmets Come