Page 21 GRAPHING OBJECTIVES:
|
|
- Virgil Smith
- 5 years ago
- Views:
Transcription
1 Page 21 GRAPHING OBJECTIVES: 1. To learn how to present data in graphical form manually (paper-and-pencil) and using computer software. 2. To learn how to interpret graphical data by, a. determining the slope and intercept of a straight-line graph b. interpolating and extrapolating from graphical data. INTRODUCTION: In many scientific experiments the value of one measurable property is deliberately varied and the resultant change in a second property is then measured. The general nature of the relationship between the two variables is often more apparent when it is presented pictorially as a graph, rather than as a table of numerical data. A properly drawn graph also allows predictions to be made about what would have been observed under conditions other than those used in the experiment, and it can be used to identify data points involving significant experimental error. There are certain general principles to remember when presenting data in graphical form. 1. Label the axes of the graph. Identify both the quantity being measured and its units. Generally, the independent variable, the quantity whose value you control, is plotted along the horizontal axis (also called the abscissa or x-axis). The dependent variable, whose value changes as a result of the change in the independent variable, is plotted along the vertical axis (also called the ordinate or y-axis). 2. Choose an appropriate and convenient scale. Generally, the graph should use as much of the available space, e.g., graph paper, as possible. Look at the range of values of each variable. The scale on each axis should start below the minimum data value for the corresponding variable and should extend beyond the maximum data value for that variable. It is generally NOT necessary, and may be undesirable, for the scale on either axis to start at a value of zero. The numerical scale should be indicated along each axis. Each grid space on an axis should represent the same value range. 3. Locate data points by a small dot with a circle drawn around it or at the center of a cross or X (the circle or cross is termed a point protector ). Use of a large dot makes it difficult to determine the actual coordinates of the data point and small dots without point protectors are difficult to see. 4. To emphasize the pattern in the data, draw a smooth line which best fits the data points. Do not simply draw straight lines from one data point to the next. In general chemistry, the relation between the variables will most often be linear and the graph will be a straight line, but other relationships are possible. When drawing the line that best fits the data, it should pass close to all of the data points, but may, in fact, not pass through any individual data point. 5. Choose a descriptive title for your graph. Generally, the title will indicate the use to which the graph will be put (e.g., the title of the graph which you will draw in the Density exercise might be Determination of the Density of a Solid ) or the variables being plotted (e.g., Mass vs. Volume for an Unknown Solid ). In the latter case, the dependent variable (y-axis) should be listed first.
2 Page 22 GRAPH The data below will be used to illustrate two different methods of creating a graph: plotting the graph on graph paper and using a computer with specialized software (we will use a program called Logger Pro). The following data were obtained when the volume of a gas was measured as the temperature was changed. Temperature ( C) Volume (mm 3 ) Manual Graphing (using graph paper): Using the graph paper found on page 28, plot the data in the table above. First, choose an appropriate scale and label the axes. Temperature is the independent variable and volume the dependent variable. In order to plot all of the data points the temperature scale must run from below -78 C to above 97 C (a minimum range of 175 C) and the volume scale from below 165 mm 3 to above 301 mm 3 (a minimum range of 136 mm 3 ). To represent these data it is not necessary for either scale to begin at zero. In the example figure below the graph paper has 5 large units along the horizontal axis. Starting at -100 C and allowing each large unit to represent 50 C will spread our temperature scale over most of this axis. It will also make plotting temperatures relatively convenient, since each small unit will represent 10 C. Similar considerations suggest starting the volume scale at 125 mm 3 and allowing each large block along the vertical axis to represent 50 mm 3, thus making each small division equal to 10 mm 3. Volume of a Gas as a Function of Temperature: Determination of Slope 325 X Volume (mm³) Y Temperature ( C)
3 GRAPH Page 23 After plotting the data points, notice that they lie, more or less in a straight line, so use a ruler to draw the straight line which best fits the data. Adjust the ruler so the edge passes near as many of the data points as possible with roughly as many points above the line as there are points below the line A straight line can be represented by an equation of the form Y = Ax + B, where A is the slope of the graph and B its intercept on the y-axis, i.e., the value of y when x = 0. The slope is defined as the change in the dependent variable (y) divided by the change in the independent variable (x). To find the slope, choose two points on the best fit straight line; for example, points 1 and 2 on the sample graph on page 22. The selected points should be as far apart as possible and should not be measured data points. Subtracting the y-value (in this case the volume) of point 1 from that of point 2 gives y = ( ) mm 3 = 93 mm 3. Now subtracting the x-value (in this case temperature) of point 1 from that of point 2 gives x = [68 ( 53)] C = 121 C. Note that the subtraction must always be done in the order point 2 minus point 1. The slope is thus A = y x 3 93 mm 121 C mm 0.77 C The line crosses the y-axis (The y-axis is the vertical line corresponding to a value of zero for the independent variable, T = 0 C in our case) at 227 mm 3, which is B. The relation between our variables may now be written as V = 0.77 mm 3 C T mm 3 Following the instructions above, determine the slope and intercept of the straight line you have drawn on your graph. Show your calculations and record your results on the Homework sheet on page 27 (Item 1). The equation of the straight line that you draw will probably differ slightly from the one determined in the example. Computer (using Logger Pro) The use of a computer and graphing software can greatly facilitate the graphical presentation and analysis of experimental data. The computer can automate many of the mechanical steps of creating the graph, allowing you to focus on its interpretation. The following instructions will guide you in the use of the program Logger Pro to graph the same temperature-volume data used for the manual graph above. Start the Logger Pro program. On the left of the screen you should see a table labeled Data Set with two columns labeled X and Y and to the right you should see a blank graph grid. Manually enter the Temperature data into the X-column and the Volume data into the Y-column (data collected with the LabQuest 2 data logger can be imported into Logger Pro, see page 31 of the LabQuest 2 Data Logger exercise for directions). As you enter the data, you will begin to see it plotted on the graph. To present the graph properly, you must follow the same basic steps used in manual graphing. First, double click on the column heading X. A dialog box labeled Manual Column Options will appear. Click the Column Definition tab. In the Name box, enter: Temperature, in the Short Name box, enter: T, and in the Units box, enter: C (to enter the degree symbol, click the pull-down box to the right of the Units box and click on the degree symbol in the list that appears). Click the Options tab. In the Displayed Precision box, make sure that Decimal Places is selected, then click the blue) box and select 1 (corresponding to the precision of the collected temperature data), and click Done. Note that the X-axis is now properly labeled. Next, double click on the column heading Y. Click the Column Definition tab and enter into the Name box: Volume, into the Short Name box: V, and into the Units box: mm 3 (to enter the superscript, click the pull-down box to the right of the Units box then click on Superscript, and finally select 3 in the list that appears). Click the Options tab. Set Displayed Precision this time to 0 decimal place (corresponding to the precision of the collected volume data), change Color to Black (this makes the printed graph more legible), and click Done or OK. Now both axes are properly labeled. Next, you will need to adjust the way the data are displayed on the graph and to set the appropriate ranges for the scales on the two axes. Click anywhere in the graph to highlight it. On the menu bar, click Options, then Graph Options. Click the Graph Options tab and in the Title box enter: Volume of a Gas as a Function of Temperature. On this same tab, in the box labeled Plot Appearance, confirm that Point Symbols is checked and that Connect Points is 3
4 Page 24 GRAPH not checked. Click the Axes Options tab. You will notice that Top and Bottom values have automatically been set for the Y (Volume) axis and Left and Right values for the X (Temperature) axis. Although these values could be left as they are, reset them to the same limits used for the paper-and-pencil graph above. In the Scaling box, choose Manual and set the limits Bottom : 125 and Top : 325 for Volume, then set Left : 100 and Right : 150 for Temperature and click Done or OK. To determine the equation for the best fit line and to display it on the graph, click on the Linear Fit button on the tool bar (this button has a diagonal red line superimposed on a blue curve). The line of best fit will appear on the graph along with a box containing the equation for this line (slope and intercept) as well as two additional parameters: the Correlation and RMSE. Both of these parameters are measures of the goodness of the fit. If all the data points lie close to the calculated line, the value of the Correlation (often designated by the letter R) will be close to 1.0. The RMSE is effectively the average distance of the points above or below the line. Position the box so that data points are not obscured (click anywhere inside the box and drag it to where you want it to appear). You are now ready to print your data table and graph. On the menu bar, click on File and then on Page Setup. Check to see that the correct printer has been selected (your instructor will tell you what printer to use) and select Landscape icon as the orientation, then click OK. On the menu bar click on File again and then on Print. In the Print Options dialog box, be sure that Print Footer is checked, in the Name box fill in your name, and click OK and then click OK again or click Print. Record the value of the slope, intercept, and correlation coefficient on page 27 (Item 2). The printed graph and data table should be attached to the Homework sheet and turned in to your instructor. INTERPOLATION AND EXTRAPOLATION Consider the following questions: 1. What will be the value of V when T is 41.0 C? 2. At what temperature will V = 259 mm 3? 3. Theoretically, at what temperature would the gas have zero volume? Each of these questions can be answered by substituting the given value of T or V into the equation of the straight line on your graph and solving for the requested variable. Before continuing, carry out the suggested calculations. Show your work and record your answers on your Homework sheet (Items 3, 4, and 5). These questions can also be answered by interpolating or extrapolating directly on a graph of the sample data provided. Interpolation refers to the process of relating values of the dependent and independent variables which lie between the data points. Extrapolation refers to the process of relating values of the dependent and independent variables which lie beyond any of the data points, i.e., before the first data point or after the last data point. Manual Graphing: To answer the first question, draw a vertical line upward at a temperature of 41 C until it intersects the line you have drawn to fit the data points. Then move horizontally to the volume axis, and read the corresponding value of the volume. Similarly, to answer the second question, draw a horizontal line across from the volume of 259 mm 3 until it intersects the line, and then draw a vertical line from this point down to the temperature axis where we find the desired temperature. Record your answers in the appropriate spaces in Items 3 and 4 on page 27. To the number of significant figures justified by the data, are these results the same as those you calculated from the equation of the best fit straight line? Because answering the third question directly from the graph would require replotting the data, instructions for answering it will be provided only for the computer graphing (one advantage of using the computer is that changes such as this can be made quickly). Computer (using Logger Pro )
5 GRAPH Page 25 With Logger Pro open and the graph of the sample data that you previously created displayed, click Analyze on the menu bar and click Interpolate on the drop-down menu. A vertical line will appear on your graph with a small circle where it crosses the line of best fit. The coordinates of the center of the circle will be displayed in a box on the graph. The position of this line can be moved by dragging the mouse. Drag the line until the Temperature in the box is 41 C. Read and record the value of Volume (Item 3, page 27). Now drag the line until the Volume is 259 mm 3. Read and record the value of Temperature (Item 4, page 27). Now you are ready to answer the third question posed above. To do so, you will need to adjust the scale on your graph. Click anywhere in the graph to make it active, then click Options on the menu bar; next click Graph Options; and finally click the Axis Options tab. In the section for the y-axis (Volume) choose Manual in the Scaling box and set the limits Bottom : 0 (you want to know the temperature when the volume is zero) and Top : 325 (i.e., leave this limit alone). In the section for the x-axis (Temperature) again choose Manual for Scaling and set Left : 300 and Right : 150, then click Done or OK. The line of best fit will automatically be extended and you can read from the scale where it intersects the x-axis or you can drag the interpolation line as described above until Volume in the box is zero. Read and record the corresponding value of Temperature (Item 5, page 27).
6 Page 26 GRAPH
7 GRAPH Page 27 Name Section HOMEWORK: 1. Follow the instructions on pages to plot the temperature-volume data in the table at the top of page 22 (use the graph paper on the next page). Be sure to label your axes. Use a straight edge/ruler to draw the straight line that you think best fits the data. In the space below, calculate the slope of straight line which you have drawn (show on the graph the two points used for this calculation). Record the value that you calculate for the slope as well as the value of the y-intercept read from the graph: Slope: Y-Intercept: 2. Follow the instructions on pages to enter the data from the table at the top of page 22 into Logger Pro and determine the equation of the line of best fit (linear regression). Record the slope, intercept, correlation Root Mean Square Error (RMSE) below (Attach the print out of your graph and data table): Slope (m): Correlation: Intercept (b): RMSE: 3. Determination of V when T is 41 : Calculated from equation of best fit line: From Graph: From Logger Pro : 4. Determination of T when V is 259 mm 3 : Calculated from equation of best fit line: From Graph: From Logger Pro : 5. Determination of T when V is zero: Calculated from equation of best fit line: From Logger Pro :
8 Page 28 GRAPH
Graphing Techniques. Figure 1. c 2011 Advanced Instructional Systems, Inc. and the University of North Carolina 1
Graphing Techniques The construction of graphs is a very important technique in experimental physics. Graphs provide a compact and efficient way of displaying the functional relationship between two experimental
More informationLaboratory 2: Graphing
Purpose It is often said that a picture is worth 1,000 words, or for scientists we might rephrase it to say that a graph is worth 1,000 words. Graphs are most often used to express data in a clear, concise
More informationAppendix C: Graphing. How do I plot data and uncertainties? Another technique that makes data analysis easier is to record all your data in a table.
Appendix C: Graphing One of the most powerful tools used for data presentation and analysis is the graph. Used properly, graphs are an important guide to understanding the results of an experiment. They
More informationAppendix 3 - Using A Spreadsheet for Data Analysis
105 Linear Regression - an Overview Appendix 3 - Using A Spreadsheet for Data Analysis Scientists often choose to seek linear relationships, because they are easiest to understand and to analyze. But,
More informationAppendix III Graphs in the Introductory Physics Laboratory
Appendix III Graphs in the Introductory Physics Laboratory 1. Introduction One of the purposes of the introductory physics laboratory is to train the student in the presentation and analysis of experimental
More informationA graph is an effective way to show a trend in data or relating two variables in an experiment.
Chem 111-Packet GRAPHING A graph is an effective way to show a trend in data or relating two variables in an experiment. Consider the following data for exercises #1 and 2 given below. Temperature, ºC
More informationMATHEMATICAL FUNCTIONS AND GRAPHS
1 MATHEMATICAL FUNCTIONS AND GRAPHS Objectives Learn how to enter formulae and create and edit graphs. Familiarize yourself with three classes of functions: linear, exponential, and power. Explore effects
More informationE. Slope-Intercept Form and Direct Variation (pp )
and Direct Variation (pp. 32 35) For any two points, there is one and only one line that contains both points. This fact can help you graph a linear equation. Many times, it will be convenient to use the
More informationExperiment G: Introduction to Graphical Representation of Data & the Use of Excel
Experiment G: Introduction to Graphical Representation of Data & the Use of Excel Scientists answer posed questions by performing experiments which provide information about a given problem. After collecting
More informationCHM 109 Excel Refresher Exercise adapted from Dr. C. Bender s exercise
CHM 109 Excel Refresher Exercise adapted from Dr. C. Bender s exercise (1 point) (Also see appendix II: Summary for making spreadsheets and graphs with Excel.) You will use spreadsheets to analyze data
More informationHonors Chemistry Summer Assignment
Honors Chemistry Summer Assignment Page 1 Honors Chemistry Summer Assignment 2014-2015 Materials needed for class: Scientific or Graphing Calculator Mrs. Dorman ldorman@ringgold.org Notebook with folder
More informationGraphing with Excel. Data Table
Graphing with Excel Copyright L. S. Quimby There are many spreadsheet programs and graphing programs that you can use to produce very nice graphs for your laboratory reports and homework papers, but Excel
More informationLab 4 Projectile Motion
b Lab 4 Projectile Motion What You Need To Know: x x v v v o ox ox v v ox at 1 t at a x FIGURE 1 Linear Motion Equations The Physics So far in lab you ve dealt with an object moving horizontally or an
More informationCHM 152 Lab 1: Plotting with Excel updated: May 2011
CHM 152 Lab 1: Plotting with Excel updated: May 2011 Introduction In this course, many of our labs will involve plotting data. While many students are nerds already quite proficient at using Excel to plot
More information2. To receive credit on any problem, you must show work that explains how you obtained your answer or you must explain how you obtained your answer.
Math 50, Spring 2006 Test 2 PRINT your name on the back of the test. Circle your class: MW @ 11 TTh @ 2:30 Directions 1. Time limit: 50 minutes. 2. To receive credit on any problem, you must show work
More informationChapter 6 Title Blocks
Chapter 6 Title Blocks In previous exercises, every drawing started by creating a number of layers. This is time consuming and unnecessary. In this exercise, we will start a drawing by defining layers
More informationScience Binder and Science Notebook. Discussions
Lane Tech H. Physics (Joseph/Machaj 2016-2017) A. Science Binder Science Binder and Science Notebook Name: Period: Unit 1: Scientific Methods - Reference Materials The binder is the storage device for
More informationPASS Sample Size Software
Chapter 945 Introduction This section describes the options that are available for the appearance of a histogram. A set of all these options can be stored as a template file which can be retrieved later.
More informationChapter 2: PRESENTING DATA GRAPHICALLY
2. Presenting Data Graphically 13 Chapter 2: PRESENTING DATA GRAPHICALLY A crowd in a little room -- Miss Woodhouse, you have the art of giving pictures in a few words. -- Emma 2.1 INTRODUCTION Draw a
More informationDrawing Bode Plots (The Last Bode Plot You Will Ever Make) Charles Nippert
Drawing Bode Plots (The Last Bode Plot You Will Ever Make) Charles Nippert This set of notes describes how to prepare a Bode plot using Mathcad. Follow these instructions to draw Bode plot for any transfer
More informationThis tutorial will lead you through step-by-step to make the plot below using Excel.
GES 131 Making Plots with Excel 1 / 6 This tutorial will lead you through step-by-step to make the plot below using Excel. Number of Non-Student Tickets vs. Student Tickets Y, Number of Non-Student Tickets
More informationGetting Started. Right click on Lateral Workplane. Left Click on New Sketch
Getting Started 1. Open up PTC Pro/Desktop by either double clicking the icon or through the Start button and in Programs. 2. Once Pro/Desktop is open select File > New > Design 3. Close the Pallet window
More informationLaboratory 1: Motion in One Dimension
Phys 131L Spring 2018 Laboratory 1: Motion in One Dimension Classical physics describes the motion of objects with the fundamental goal of tracking the position of an object as time passes. The simplest
More informationPatterns and Graphing Year 10
Patterns and Graphing Year 10 While students may be shown various different types of patterns in the classroom, they will be tested on simple ones, with each term of the pattern an equal difference from
More informationy-intercept remains constant?
1. The graph of a line that contains the points ( 1, 5) and (4, 5) is shown below. Which best represents this line if the slope is doubled and the y-intercept remains constant? F) G) H) J) 2. The graph
More informationYear 11 Graphing Notes
Year 11 Graphing Notes Terminology It is very important that students understand, and always use, the correct terms. Indeed, not understanding or using the correct terms is one of the main reasons students
More informationLab 4 Projectile Motion
b Lab 4 Projectile Motion Physics 211 Lab What You Need To Know: 1 x = x o + voxt + at o ox 2 at v = vox + at at 2 2 v 2 = vox 2 + 2aΔx ox FIGURE 1 Linear FIGURE Motion Linear Equations Motion Equations
More informationPhysics 253 Fundamental Physics Mechanic, September 9, Lab #2 Plotting with Excel: The Air Slide
1 NORTHERN ILLINOIS UNIVERSITY PHYSICS DEPARTMENT Physics 253 Fundamental Physics Mechanic, September 9, 2010 Lab #2 Plotting with Excel: The Air Slide Lab Write-up Due: Thurs., September 16, 2010 Place
More informationPASS Sample Size Software. These options specify the characteristics of the lines, labels, and tick marks along the X and Y axes.
Chapter 940 Introduction This section describes the options that are available for the appearance of a scatter plot. A set of all these options can be stored as a template file which can be retrieved later.
More informationMathematics Success Grade 8
Mathematics Success Grade 8 T429 [OBJECTIVE] The student will solve systems of equations by graphing. [PREREQUISITE SKILLS] solving equations [MATERIALS] Student pages S207 S220 Rulers [ESSENTIAL QUESTIONS]
More informationStudent Exploration: Standard Form of a Line
Name: Date: Student Exploration: Standard Form of a Line Vocabulary: slope, slope-intercept form, standard form, x-intercept, y-intercept Prior Knowledge Questions (Do these BEFORE using the Gizmo.) 1.
More informationSect Linear Equations in Two Variables
99 Concept # Sect. - Linear Equations in Two Variables Solutions to Linear Equations in Two Variables In this chapter, we will examine linear equations involving two variables. Such equations have an infinite
More informationMicroLab 500-series Getting Started
MicroLab 500-series Getting Started 2 Contents CHAPTER 1: Getting Started Connecting the Hardware....6 Installing the USB driver......6 Installing the Software.....8 Starting a new Experiment...8 CHAPTER
More information10 GRAPHING LINEAR EQUATIONS
0 GRAPHING LINEAR EQUATIONS We now expand our discussion of the single-variable equation to the linear equation in two variables, x and y. Some examples of linear equations are x+ y = 0, y = 3 x, x= 4,
More informationNCSS Statistical Software
Chapter 147 Introduction A mosaic plot is a graphical display of the cell frequencies of a contingency table in which the area of boxes of the plot are proportional to the cell frequencies of the contingency
More informationMathematics Success Grade 8
T936 Mathematics Success Grade 8 [OBJECTIVE] The student will find the line of best fit for a scatter plot, interpret the equation and y-intercept of the linear representation, and make predictions based
More informationSection 3 Correlation and Regression - Worksheet
The data are from the paper: Exploring Relationships in Body Dimensions Grete Heinz and Louis J. Peterson San José State University Roger W. Johnson and Carter J. Kerk South Dakota School of Mines and
More informationMath Labs. Activity 1: Rectangles and Rectangular Prisms Using Coordinates. Procedure
Math Labs Activity 1: Rectangles and Rectangular Prisms Using Coordinates Problem Statement Use the Cartesian coordinate system to draw rectangle ABCD. Use an x-y-z coordinate system to draw a rectangular
More informationGraphs. This tutorial will cover the curves of graphs that you are likely to encounter in physics and chemistry.
Graphs Graphs are made by graphing one variable which is allowed to change value and a second variable that changes in response to the first. The variable that is allowed to change is called the independent
More information4.4 Slope and Graphs of Linear Equations. Copyright Cengage Learning. All rights reserved.
4.4 Slope and Graphs of Linear Equations Copyright Cengage Learning. All rights reserved. 1 What You Will Learn Determine the slope of a line through two points Write linear equations in slope-intercept
More informationConstructing Line Graphs Appendix B AP Biology Investigative Lab Essentials
Constructing Line Graphs Appendix B AP Biology Investigative Lab Essentials Directions: Reading, constructing and interpreting graphs are essential skills for any Biology/Science student. We will spend
More informationStep 1: Set up the variables AB Design. Use the top cells to label the variables that will be displayed on the X and Y axes of the graph
Step 1: Set up the variables AB Design Use the top cells to label the variables that will be displayed on the X and Y axes of the graph Step 1: Set up the variables X axis for AB Design Enter X axis label
More informationUncovering a Hidden RCL Series Circuit
Purpose Uncovering a Hidden RCL Series Circuit a. To use the equipment and techniques developed in the previous experiment to uncover a hidden series RCL circuit in a box and b. To measure the values of
More informationExcel Lab 2: Plots of Data Sets
Excel Lab 2: Plots of Data Sets Excel makes it very easy for the scientist to visualize a data set. In this assignment, we learn how to produce various plots of data sets. Open a new Excel workbook, and
More informationExercise 8. The Four-Quadrant Chopper EXERCISE OBJECTIVE DISCUSSION OUTLINE DISCUSSION. The Four-Quadrant Chopper
Exercise 8 The Four-Quadrant Chopper EXERCISE OBJECTIVE When you have completed this exercise, you will be familiar with the operation of the four-quadrant chopper. DISCUSSION OUTLINE The Discussion of
More informationForensics with TI-NspireTM Technology
Forensics with TI-NspireTM Technology 2013 Texas Instruments Incorporated 1 education.ti.com Science Objectives Identify counterfeit coins based on the characteristic property of density. Model data using
More informationComputer Tools for Data Acquisition
Computer Tools for Data Acquisition Introduction to Capstone You will be using a computer to assist in taking and analyzing data throughout this course. The software, called Capstone, is made specifically
More informationPhysics 131 Lab 1: ONE-DIMENSIONAL MOTION
1 Name Date Partner(s) Physics 131 Lab 1: ONE-DIMENSIONAL MOTION OBJECTIVES To familiarize yourself with motion detector hardware. To explore how simple motions are represented on a displacement-time graph.
More information6. Multivariate EDA. ACE 492 SA - Spatial Analysis Fall 2003
1 Objectives 6. Multivariate EDA ACE 492 SA - Spatial Analysis Fall 2003 c 2003 by Luc Anselin, All Rights Reserved This lab covers some basic approaches to carry out EDA with a focus on discovering multivariate
More informationEvaluation Chapter by CADArtifex
The premium provider of learning products and solutions www.cadartifex.com EVALUATION CHAPTER 2 Drawing Sketches with SOLIDWORKS In this chapter: Invoking the Part Modeling Environment Invoking the Sketching
More informationAlgebra Success. LESSON 16: Graphing Lines in Standard Form. [OBJECTIVE] The student will graph lines described by equations in standard form.
T328 [OBJECTIVE] The student will graph lines described by equations in standard form. [MATERIALS] Student pages S125 S133 Transparencies T336, T338, T340, T342, T344 Wall-size four-quadrant grid [ESSENTIAL
More informationEngineering Fundamentals and Problem Solving, 6e
Engineering Fundamentals and Problem Solving, 6e Chapter 5 Representation of Technical Information Chapter Objectives 1. Recognize the importance of collecting, recording, plotting, and interpreting technical
More informationDetermining the Dynamic Characteristics of a Process
Exercise 5-1 Determining the Dynamic Characteristics of a Process EXERCISE OBJECTIVE In this exercise, you will determine the dynamic characteristics of a process. DISCUSSION OUTLINE The Discussion of
More informationEE 210 Lab Exercise #3 Introduction to PSPICE
EE 210 Lab Exercise #3 Introduction to PSPICE Appending 4 in your Textbook contains a short tutorial on PSPICE. Additional information, tutorials and a demo version of PSPICE can be found at the manufacturer
More informationSTAB22 section 2.4. Figure 2: Data set 2. Figure 1: Data set 1
STAB22 section 2.4 2.73 The four correlations are all 0.816, and all four regressions are ŷ = 3 + 0.5x. (b) can be answered by drawing fitted line plots in the four cases. See Figures 1, 2, 3 and 4. Figure
More informationAutoCAD LT 2012 Tutorial. Randy H. Shih Oregon Institute of Technology SDC PUBLICATIONS. Schroff Development Corporation
AutoCAD LT 2012 Tutorial Randy H. Shih Oregon Institute of Technology SDC PUBLICATIONS www.sdcpublications.com Schroff Development Corporation AutoCAD LT 2012 Tutorial 1-1 Lesson 1 Geometric Construction
More informationConstructing Line Graphs*
Appendix B Constructing Line Graphs* Suppose we are studying some chemical reaction in which a substance, A, is being used up. We begin with a large quantity (1 mg) of A, and we measure in some way how
More informationStudent Exploration: Quadratics in Factored Form
Name: Date: Student Exploration: Quadratics in Factored Form Vocabulary: factored form of a quadratic function, linear factor, parabola, polynomial, quadratic function, root of an equation, vertex of a
More informationSDC. AutoCAD LT 2007 Tutorial. Randy H. Shih. Schroff Development Corporation Oregon Institute of Technology
AutoCAD LT 2007 Tutorial Randy H. Shih Oregon Institute of Technology SDC PUBLICATIONS Schroff Development Corporation www.schroff.com www.schroff-europe.com AutoCAD LT 2007 Tutorial 1-1 Lesson 1 Geometric
More informationReference Manual SPECTRUM. Signal Processing for Experimental Chemistry Teaching and Research / University of Maryland
Reference Manual SPECTRUM Signal Processing for Experimental Chemistry Teaching and Research / University of Maryland Version 1.1, Dec, 1990. 1988, 1989 T. C. O Haver The File Menu New Generates synthetic
More informationCreo Revolve Tutorial
Creo Revolve Tutorial Setup 1. Open Creo Parametric Note: Refer back to the Creo Extrude Tutorial for references and screen shots of the Creo layout 2. Set Working Directory a. From the Model Tree navigate
More informationProducts of Linear Functions
Math Objectives Students will understand relationships between the horizontal intercepts of two linear functions and the horizontal intercepts of the quadratic function resulting from their product. Students
More informationAutoCAD Tutorial First Level. 2D Fundamentals. Randy H. Shih SDC. Better Textbooks. Lower Prices.
AutoCAD 2018 Tutorial First Level 2D Fundamentals Randy H. Shih SDC PUBLICATIONS Better Textbooks. Lower Prices. www.sdcpublications.com Powered by TCPDF (www.tcpdf.org) Visit the following websites to
More informationOHM S LAW. Ohm s Law The relationship between potential difference (V) across a resistor of resistance (R) and the current (I) passing through it is
OHM S LAW Objectives: a. To find the unknown resistance of an ohmic resistor b. To investigate the series and parallel combination of resistors c. To investigate the non-ohmic resistors Apparatus Required:
More informationHow to create a cove for cove lighting in DIALux In this tutorial you will learn how to make a cove similar to the one in the following image
How to create a cove for cove lighting in DIALux In this tutorial you will learn how to make a cove similar to the one in the following image The cove dimension will be 4 meter by 5 meter and the other
More informationRegression: Tree Rings and Measuring Things
Objectives: Measure biological data Use biological measurements to calculate means, slope and intercept Determine best linear fit of data Interpret fit using correlation Materials: Ruler (in millimeters)
More informationUsing Charts and Graphs to Display Data
Page 1 of 7 Using Charts and Graphs to Display Data Introduction A Chart is defined as a sheet of information in the form of a table, graph, or diagram. A Graph is defined as a diagram that represents
More informationEQ7 Summer Drawing Series: Block 4
EQ7 Summer Drawing Series: Block 4 www.doyoueq.com/blog Welcome to the Block 4 post for the EQ7 Summer Drawing Series! It s the last block in this drawing+sewing series and I hope you ve learned a lot
More information2.3 BUILDING THE PERFECT SQUARE
16 2.3 BUILDING THE PERFECT SQUARE A Develop Understanding Task Quadratic)Quilts Optimahasaquiltshopwhereshesellsmanycolorfulquiltblocksforpeoplewhowant tomaketheirownquilts.shehasquiltdesignsthataremadesothattheycanbesized
More informationLesson 1b Linear Equations
In the first lesson we looked at the concepts and rules of a Function. The first Function that we are going to investigate is the Linear Function. This is a good place to start because with Linear Functions,
More informationIn this section, we find equations for straight lines lying in a coordinate plane.
2.4 Lines Lines In this section, we find equations for straight lines lying in a coordinate plane. The equations will depend on how the line is inclined. So, we begin by discussing the concept of slope.
More informationMicrosoft Excel: Data Analysis & Graphing. College of Engineering Engineering Education Innovation Center
Microsoft Excel: Data Analysis & Graphing College of Engineering Engineering Education Innovation Center Objectives Use relative, absolute, and mixed cell referencing Identify the types of graphs and their
More informationAutoCAD LT 2009 Tutorial
AutoCAD LT 2009 Tutorial Randy H. Shih Oregon Institute of Technology SDC PUBLICATIONS Schroff Development Corporation www.schroff.com Better Textbooks. Lower Prices. AutoCAD LT 2009 Tutorial 1-1 Lesson
More informationYear 10 Practical Assessment Skills Lesson 1 Results tables and Graph Skills
Year 10 Practical Assessment Skills Lesson 1 Results tables and Graph Skills Aim: to be able to present results and draw appropriate types of graphs Must: identify mistakes in data recording Should: be
More informationMath 1023 College Algebra Worksheet 1 Name: Prof. Paul Bailey September 22, 2004
Math 1023 College Algebra Worksheet 1 Name: Prof. Paul Bailey September 22, 2004 Every vertical line can be expressed by a unique equation of the form x = c, where c is a constant. Such lines have undefined
More information4: EXPERIMENTS WITH SOUND PULSES
4: EXPERIMENTS WITH SOUND PULSES Sound waves propagate (travel) through air at a velocity of approximately 340 m/s (1115 ft/sec). As a sound wave travels away from a small source of sound such as a vibrating
More informationAppendix B: Autocad Booklet YR 9 REFERENCE BOOKLET ORTHOGRAPHIC PROJECTION
Appendix B: Autocad Booklet YR 9 REFERENCE BOOKLET ORTHOGRAPHIC PROJECTION To load Autocad: AUTOCAD 2000 S DRAWING SCREEN Click the start button Click on Programs Click on technology Click Autocad 2000
More informationSample Lesson Plan for Standard 5.MD.B.2: Creating Line Plots. An Introduction to Line Plots Using Whole Numbers
Sample Lesson Plan for Standard 5.MD.B.2: Creating Line Plots An Introduction to Line Plots Using Whole Numbers Grade Level Expectations For this standard, fifth grade students are expected to create line
More informationMoving Man Introduction Motion in 1 Direction
Moving Man Introduction Motion in 1 Direction Go to http://www.colorado.edu/physics/phet and Click on Play with Sims On the left hand side, click physics, and find The Moving Man simulation (they re listed
More informationExcel Tool: Plots of Data Sets
Excel Tool: Plots of Data Sets Excel makes it very easy for the scientist to visualize a data set. In this assignment, we learn how to produce various plots of data sets. Open a new Excel workbook, and
More informationHomework 4: Understanding Graphs [based on the Chauffe & Jefferies (2007)]
3 September 2008 MAR 110 HW4 -Graphs 1 Homework 4: Understanding Graphs [based on the Chauffe & Jefferies (2007)] The term "datum" refers to one unit of information. The plural of datum is "data." In science
More informationwith MultiMedia CD Randy H. Shih Jack Zecher SDC PUBLICATIONS Schroff Development Corporation
with MultiMedia CD Randy H. Shih Jack Zecher SDC PUBLICATIONS Schroff Development Corporation WWW.SCHROFF.COM Lesson 1 Geometric Construction Basics AutoCAD LT 2002 Tutorial 1-1 1-2 AutoCAD LT 2002 Tutorial
More informationConstructing a Wedge Die
1-(800) 877-2745 www.ashlar-vellum.com Using Graphite TM Copyright 2008 Ashlar Incorporated. All rights reserved. C6CAWD0809. Ashlar-Vellum Graphite This exercise introduces the third dimension. Discover
More informationUnderstanding Projection Systems
Understanding Projection Systems A Point: A point has no dimensions, a theoretical location that has neither length, width nor height. A point shows an exact location in space. It is important to understand
More informationAlgebra I Notes Unit Seven: Writing Linear Equations
Sllabus Objective.6 The student will be able to write the equation of a linear function given two points, a point and the slope, table of values, or a graphical representation. Slope-Intercept Form of
More informationAnsoft Designer Tutorial ECE 584 October, 2004
Ansoft Designer Tutorial ECE 584 October, 2004 This tutorial will serve as an introduction to the Ansoft Designer Microwave CAD package by stepping through a simple design problem. Please note that there
More informationUsing Google SketchUp
Using Google SketchUp Opening sketchup 1. From the program menu click on the SketchUp 8 folder and select 3. From the Template Selection select Architectural Design Millimeters. 2. The Welcome to SketchUp
More informationTO PLOT OR NOT TO PLOT?
Graphic Examples This document provides examples of a number of graphs that might be used in understanding or presenting data. Comments with each example are intended to help you understand why the data
More informationExperiment 8: An AC Circuit
Experiment 8: An AC Circuit PART ONE: AC Voltages. Set up this circuit. Use R = 500 Ω, L = 5.0 mh and C =.01 μf. A signal generator built into the interface provides the emf to run the circuit from Output
More informationVolume of Revolution Investigation
Student Investigation S2 Volume of Revolution Investigation Student Worksheet Name: Setting up your Page In order to take full advantage of Autograph s unique 3D world, we first need to set up our page
More informationExcel Manual X Axis Label Below Chart 2010 >>>CLICK HERE<<<
Excel Manual X Axis Label Below Chart 2010 When the X-axis is crowded with labels one way to solve the problem is to split the labels for to use two rows of labels enter the two rows of X-axis labels as
More informationTennessee Senior Bridge Mathematics
A Correlation of to the Mathematics Standards Approved July 30, 2010 Bid Category 13-130-10 A Correlation of, to the Mathematics Standards Mathematics Standards I. Ways of Looking: Revisiting Concepts
More informationGraphs of linear equations will be perfectly straight lines. Why would we say that A and B are not both zero?
College algebra Linear Functions : Definition, Horizontal and Vertical Lines, Slope, Rate of Change, Slopeintercept Form, Point-slope Form, Parallel and Perpendicular Lines, Linear Regression (sections.3
More informationChemistry 401 Laboratory Manual Introduction
Chemistry 401 Laboratory Manual Introduction You are responsible to read and prepare a pre-lab write-up before each week s experiment. The items required in the pre-lab write-up are specified in the Before
More informationLearning Guide. ASR Automated Systems Research Inc. # Douglas Crescent, Langley, BC. V3A 4B6. Fax:
Learning Guide ASR Automated Systems Research Inc. #1 20461 Douglas Crescent, Langley, BC. V3A 4B6 Toll free: 1-800-818-2051 e-mail: support@asrsoft.com Fax: 604-539-1334 www.asrsoft.com Copyright 1991-2013
More informationChapter 9 Linear equations/graphing. 1) Be able to graph points on coordinate plane 2) Determine the quadrant for a point on coordinate plane
Chapter 9 Linear equations/graphing 1) Be able to graph points on coordinate plane 2) Determine the quadrant for a point on coordinate plane Rectangular Coordinate System Quadrant II (-,+) y-axis Quadrant
More informationUsing Curves and Histograms
Written by Jonathan Sachs Copyright 1996-2003 Digital Light & Color Introduction Although many of the operations, tools, and terms used in digital image manipulation have direct equivalents in conventional
More information6.1 Slope of a Line Name: Date: Goal: Determine the slope of a line segment and a line.
6.1 Slope of a Line Name: Date: Goal: Determine the slope of a line segment and a line. Toolkit: - Rate of change - Simplifying fractions Main Ideas: Definitions Rise: the vertical distance between two
More informationEXPLORING POLAR COORDINATES WITH THE GEOMETER S SKETCHPAD
EXPLORING POLAR COORDINATES WITH THE GEOMETER S SKETCHPAD Barbara K. D Ambrosia Carl R. Spitznagel John Carroll University Department of Mathematics and Computer Science Cleveland, OH 44118 bdambrosia@jcu.edu
More informationUnit 5: Moving Straight Ahead
Unit 5: Moving Straight Ahead Investigation 4 Exploring Slope: Connecting Rates and Ratios I can demonstrate understanding that linear relationships are relationships represented by the slope of the line
More information