-The x-intercept of a line is the point where a line crosses the x-axis. Its coordinates are (#,0). -The y-intercept of a line is the point where a line crosses the y-axis. Its coordinates are (0,#). 1- Find the x-intercept by letting y=0. 2- Find the y-intercept by letting x=0. 3- Plot the intercepts and graph the line. (If the x and y intercepts are both 0, use a table to find the second point.) Ex: x-int: 5x-3y=-30 y=0 5x-3(0)=-30 5x=-30 –– –– 5 5 x= -6 (-6,0) y-int: x=0 ...
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more about freely falling objects. Unfortunately, his timing devices were not precise enough to allow him to study free fall directly. Therefore, he decided to limit the acceleration by using fluids, inclined planes, and pendulums. In this lab exercise, you will see how the acceleration of a rolling ball or cart depends on the ramp angle. Then, you will use your data to extrapolate to the acceleration on a vertical “ramp;” that is, the acceleration of a ball in free fall. If the angle of an incline...
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Graphs and Function What is the relation between the graphs and function and how was it applied in the real world? Graphs are frequently used in national magazines and newspaper to present information about things such as the world’s busiest airports (O’Hare in China is first, Heathrow in London is sixth), about the advertising-dollar receivers in the United States (newspaper are first, radio is fourth) and about NCAA men’s golf team title winner (Yael is first, Houston is second). The...
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LAB # 1 Graph Matching Principles of Physics I Laboratory Breanna Wilhite Introduction In this lab motion will be represented by graphs that plots distance and velocity vs. time. A motion detector will be used to measure the time it takes for a high frequency sound pulse to travel from the detector to an object and back. By using this method sound can determine the distance to the object, or its position. This device will determine in what direction the woman in the video was walking and...
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Straight Line Equations and Inequalities A: Linear Equations - Straight lines Please remember that when you are drawing graphs you should always label your axes and that y is always shown on the vertical axis. A linear equation between two variables x and y can be represented by y = a + bx where “a” and “b” are any two constants. For example, suppose we wish to plot the straight line If x = -2, say, then y = 3 + 2(-2) = 3 - 4 = -1 If x= -2 -1 -1 1 0 3 1 5 2 7 As you can see, we have plotted the...
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History: The Cartesian coordinate system is named after René Descartes(1596-1650), the noted French mathematician and philosopher, who was among the first to describe its properties. However, historical evidence shows that Pierre de Fermat (1601-1665), also a French mathematician and scholar, did more to develop the Cartesian system than did Descartes. The development of the Cartesian coordinate system enabled the development of perspective and projective geometry. It would later play an intrinsic...
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spend on goods X and Y. The market prices of these two goods are Px = $15 and Py = $5. a. Draw the budget constraint. i.e provide a carefully labeled diagram b. What is the market rate of substitution? Give an interpretation. c. Illustrate the consumer’s opportunity set in part a) above. d. Show how the consumer’s opportunity set changes if income increases by $300. e. Does the increase of income by $300 in part d) above alter the market rate of substitution between goods X and Y? Answer: a...
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Project Stat. Math 5389 Graph Analysis# 1Spring , 2012Noemi Bores | Identifying Misleading Graphs Graphs are pictorial representations of numbers. Therefore, at the least, we should expect that the representation of the numbers be proportional to the numbers themselves. Unfortunately, this is not always the case. In some cases this occurs because the graph designer wants to give the impression of better performance than is actually the case. In other cases, the designer might not have any...
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TASK 1 Consider the following equation: MRSXY < PX/PY where MRS = marginal rate of substitution x and y are two goods P = price < = is less than {draw:frame} The graph above shown us the indifference curve budget line diagram which explaining the equation MRSXY < P X / PY. There are two ways to measure the consumer preferences or what the consumer wants. The first one is by trying to put a ‘value’ on the satisfaction a consumer obtains from consuming...
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Finding the tangent line to the graph of a function at a single point can be extremely useful when interpreting the information that the function represents. So first to describe what a tangent line is: A tangent line of a function at one point shows the direction that the function is going at that point (Fig.1). Theoretically the tangent line is only touching the curve of the function at one single point, or the point of tangency. To find the equation of the tangent line, certain bits of information...
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d-t & v-t Graphs Graphing the motion of objects gives us a way to interpret the motion that would otherwise be difficult. ● Graphs will also allow you to show a large amount of information in a compact way. Essentially you need to be able to sketch and interpret two main kinds of graphs in kinematics: 1. Displacement – Time Graphs ● Sometimes called d-t graphs, or position – time graphs. 2. Velocity – Time Graphs ● Sometimes called v-t graphs. Displacement - Time (d-t) Graphs This type of...
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correctly rather than a limited number. For example, the candidate who writes: The number of cases of X disease started at 50 in 1965 and then went up to 200 in 1970 and then went up to 500 in 1980 and then went down to zero in 1990. will lose marks for being repetitive. You should therefore practise writing reports using a wide variety of terms to describe the different movements in the graphs and different structures to vary your writing. Describing trends Trends are changes or movements....
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How to Make Really Nice Graphs Using Microsoft Excel 2011 Data Entry: Enter your data into Excel in column form such as the following: Horizontal Variable Name x1 x2 x3 x4 x5 x6 Uncertainties ∆x1 ∆x2 ∆x3 ∆x4 ∆x5 ∆x6 Vertical Variable Name y1 y2 y3 y4 y5 y6 Uncertainties ∆y1 ∆y2 ∆y3 ∆y4 ∆y5 ∆y6 For example, if you are measuring the length of a spring under the application of a force, the table might look like this: Position (m) ∆Position (m) 0.595 0.612 0.631 0.649 0.667 0.686 0.001 0.001 0...
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finally, answer the questions below. Table 2: Water quality vs. fish population Dissolved Oxygen (ppm) 0 2 4 6 8 10 12 14 16 18 Number of Fish Observed 0 1 3 10 12 13 15 10 12 13 1. Based on the information in Table 2, what patterns do you observe? Based on the information in Table 2, the patterns that I observe is that wherever there are fish, there is dissolved oxygen. The more fish there are, the more dissolved oxygen there is. Since fish are living organisms that...
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V. Adamchik 1 Graph Theory Victor Adamchik Fall of 2005 Plan 1. Basic Vocabulary 2. Regular graph 3. Connectivity 4. Representing Graphs Introduction A.Aho and J.Ulman acknowledge that “Fundamentally, computer science is a science of abstraction.” Computer scientists must create abstractions of real-world problems that can be represented and manipulated in a computer. Sometimes the process of abstraction is simple. For example, we use a logic to design a computer circuits. Another example - scheduling...
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FUNCTIONS AND THEIR GRAPHS 4.1 Definition of Function A function from one set X to another set Y is a rule that assigns each element in X to one element in Y. 4.1.1 Notation If f denotes a function from X to Y, we write 4.1.2 Domain and range X is known as the domain of f and Y the range of f. (Note that domain and range are sets.) 4.1.3 Object and image If and , then x and y are known respectively as the objects and images of f. We can write , , . We can represent a function in...
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Questions 1. What patterns do you observe based on the information in Table 4? As the Dissolved oxygen increases so does the number of fish that are observed, until the ppm gets up to 14 then the number of fish is not steadily increasing, as it was before. 2. Develop a hypothesis relating to the amount of dissolved oxygen measured in the water sample and the number of fish observed in the body of water? You cannot have too much oxygen compared to the number of fish. 3. What would your...
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SCIENCE HISTOGRAM(BAR GRAPH): Definition: It is a chart that uses either horizontal or vertical bars to show comparisons among categories. One axis of the chart shows the specific categories being compared and the other axis represents a discrete value. DESCRIPTION: This is a way to show class progress but in chunks of time. It shows No. Of students or percent of students on Y axis and the Number they got correct on the X- axis. Each Bar on the graph represents how many times a score...
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A p p e n d i x GRAPHS IN ECONOMICS Key Concepts Graphing Data Graphs represent quantity as a distance on a line. On a graph, the horizontal scale line is the x-axis, the vertical scale line is the y-axis, and the intersection of the two scale lines is the origin. The three main types of economic graphs are: ♦ Time-series graphs demonstrate the relationship between time, measured on the x-axis, and other variable(s), measured on the y-axis. Time-series graphs show the variable’s level, direction...
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1. PIE CHART This pie chart shows Mark’s monthly budget. The highest designation of his budget will go to his foods with 45% of his total allowance. Next is for lodging with 30% followed by the projects and fare which will have 10%. The least designation for his budget will be for his savings which has 5% only. 2. BAR GRAPH The bar graph shows the yearly tourist count for the provinces of region V. the province of Albay got the highest number of tourist with 450 000. It is followed by the...
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DESCRIBING GRAPHS AND CHARTS The function of a line graph is to describe a TREND pictorially. You therefore should try and describe the trend in it. If there are many lines in the graph(s), then just generally describe the trend. If there is only one or two, then use more detail. So, describe the movement of the line(s) of the graph giving numerical detail at the important points of the line. To describe the movement, there is some language which will always be useful. Below is a list of language...
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questions using what you've learned from this lesson. Write your responses in the space provided, and turn the assignment in to your instructor. 1. What is the slope of the line in the graph below? Show your work. Answer: To find out the slope, you must first take two separate points on the graph, such as (-5,-1) and (0,1). Then, it’s a simple matter to use the equation [pic] to find the slope: [pic]= [pic] 2. What is the slope of the line represented...
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------------------------------------------------- ------------------------------------------------- Speed Speed is defined as a measure of the distance an object travels in a given length of time. The average speed of an object can be determined from the equation below: Thus, if a car travels 100 meters in 5 seconds its average speed can be calculated as; Average speed = 100/5 = 20 meters per second Average speed is used to give the speed of an object over a given interval of time, if...
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Security Market Line In Markowitz Portfolio Theory, a line on a chart representing the capital asset pricing model. The security market line plots risk versus expected return of the market. The security market line is a useful tool in determining whether a given security is undervalued and/or a market outperform. If a security plots the security market line, it indicates a higher expected return for a given level of risk than the market as a whole. security market line A line used to illustrate...
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How to write a lab report Let’s take as an example a free-fall experiment. You drop a small steel ball from various heights and use an electronic timer to measure how long it takes the ball to hit the ground. From this you calculate the final speed of the ball using v = 2x/t. You believe that the ball will have a constant acceleration of “g,” 9.8 m/s2. This will be seen if you graph velocity vs. time and get a straight line with a slope of 9.8. You end up with a table of data giving distances...
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1) Effect of Increase of Non-Labour Income in Desired Working Hours Assuming that the individual has zero non-labour income and faces the income budget line of JZ, the individual would choose point A as the ‘optimal’ utility-maximizing point as it is the highest attainable indifference curve(tangent to the income budget line or MRS = |w/p|). At this point A, the individual will work Ls1 hours, enjoy La leisure hours and enjoy an income of Ca. Assuming the individual has attained a source of non-labour...
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Carlos. At what time of day will she overtake him? | Rate | Time | Distance | Carlos | 12 | n | 12n | Denise | 36 | n - 1 | 36n - 36 | Note: Denise travels one hour less than Carlos. When Denise catches up, Carlos and Denise will have travelled equal distances. 12n = 36n - 36 -24n = -36 n = 1.5 Answer: Denise overtakes Carlos at 11:30 A.M. 2. It takes a plane 40 min. longer to fly from Boston to Los Angeles at 525 mph than it does to return at 600 mph. How far apart are...
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How to Analyze the Regression Analysis Output from Excel In a simple regression model, we are trying to determine if a variable Y is linearly dependent on variable X. That is, whenever X changes, Y also changes linearly. A linear relationship is a straight line relationship. In the form of an equation, this relationship can be expressed as Y = α + βX + e In this equation, Y is the dependent variable, and X is the independent variable. α is the intercept of the regression line, and β is the...
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GRAPH OF LINEAR FUNCTIONS Teacher’s Guide Description This Teacher Support Material is designed to provide students with hands on activity relative to teaching linear functions. Rationale It has been observed that students find difficulty in graphing linear functions because students cannot relate previous knowledge of linear equations in their Intermediate Algebra to linear functions in Advance Algebra. This TSM is designed to help students graph linear function effectively. ...
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How to Work with Dummy Independent Variables Chapter 8 is devoted to dummy (independent) variables. This How To answers common questions on working with and interpreting dummy variables. Questions: 1) How to include dummy variables in a regression? 2) How to interpret a coefficient on a dummy variable? 3) How to test hypotheses with dummy variables and interaction terms? 4) How to create a double-log functional form with dummy variables? 5) How to interpret a coefficient...
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submit this assignment to your teacher by the due date for full credit. (8 points) |Score | | | 1. Name three different kinds of graphs that are often used to plot information and discuss the value of each. Answer: Three types of graphs are line graph, histogram or bar graph, and pie chart graph. The line graph is used to describe how an object moves explaining relationship between time and distance traveled. A histogram or bar graph is used...
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Aaleah Brown Mr. Gunderson Honors English 3, Period 4 08 November 2013 The Walk “I have passed by the watchman on his beat and dropped my eyes, unwilling to explain” (II. 5-6). Depression causes a person to distance themselves from the world. It also causes them to not want to associate themselves with people. In the poem, “Acquainted with the Night,” by Robert Frost, a persona seems to be walking aimlessly alone at night in the rain. The persona passes a watchman whom he refuses to associate...
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Slope Gaby Ruiz Table of Contents I. Introduction – Big Idea II. Clinical interview 2 analysis III. Rationale for your instructional design: IV. Part 1 – Pre-Assessment Sub-Part 1 – Quantitative Analysis of Pre-Assessments Sub-Part 2 – Qualitative Analysis of Pre-Assessments V. Forming Our Lesson VI. The Lesson VII. Post-assessment analysis Sub-Part 1 – Quantitative Analysis of Post Assessments Sub-Part 2 – Qualitative Analysis of Post Assessments VIII. Conclusion IX. References X. Appendix...
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Walk the Line Release Date: 11/18/05 Running Length: 134 mins Rating: PG-13 (Profanity, drugs) Cast: Joaquin Phoenix, Reese Witherspoon, Ginnifer Goodwin, Robert Patrick, Dallas Roberts, Dan John Miller, Larry Bagby, Shelby Lynne Director: James Mangold Producers: James Keach, Cathy Konrad Screenplay: Gill Dennis & James Mangold Cinematography: Phedon Papamichael Music: Johnny Cash, T Bone Burnett Studio: 20th Century Fox Theatre: Empire Theatres Date: 12/12/05 Time: 7:15 P.M. ...
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Tree definitions If you already know what a binary tree is, but not a general tree, then pay close attention, because binary trees are not just the special case of general trees with degree two. I use the definition of a tree from the textbook, but bear in mind that other definitions are possible. Definition. A tree consists of a (possible empty) set of nodes. If it is not empty, it consists of a distinguished node r called the root and zero or more non-empty subtrees T1, T2, …, Tk such that there...
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Cartesian Coordinate System -A Cartesian coordinate system specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length. Cartesian coordinate system is a way of locating objects in either two- or three-dimensional space by specifying their X(horizontal) position, Y (vertical) position and Z (through) position. It is used in graphics and in positioning text...
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making this poem an enjoyable reading. “Silver” is a poem that demonstrates the coming of night time, and what everything becomes when the moon goes up. These affects are shown through imagery. Throughout the poem Walter de la Mare uses many sound devices such as the assonance of the "s" to exemplify the mood and give it a mysterious and deep feeling. He also uses things such as allusion of the moon which is very similar the story about King Midas who turned everything into gold, in this poem the...
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the difference between the two lines on your graph made in Step 6. Explain why the lines are different. Referring to graph on the right the difference between the two lines is that one line is at a faster speed than the other in the same amount of time. While one is steeper the other one is not as steep. 2. How would the graph change if you walked toward the Motion Detector rather than away from it? Test your answer using the Motion Detector. Since the graph is going in a positive direction...
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ALL CBSE STUFF Class XI Chapter 10 – Straight Lines Maths Exercise 10.1 Question 1: Draw a quadrilateral in the Cartesian plane, whose vertices are (–4, 5), (0, 7), (5, –5) and (–4, –2). Also, find its area. 14 Answer Let ABCD be the given quadrilateral with vertices A (–4, 5), B (0, 7), C (5, –5), and D (– 4, –2). Then, by plotting A, B, C, and D on the Cartesian plane and joining AB, BC, CD, and DA, SU M IT © 20 the given quadrilateral can be drawn as To find the area of quadrilateral...
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value of one variable, y, given the value of another variable, x. The term simple linear regression refers to the use of one independent variable, x, to predict one dependent variable, y. The regression line is usually plotted on a graph, with the horizontal axis representing x (the independent or predictor variable) and the vertical axis representing the y (the dependent or predicted variable) (see Figure 27-1). The value represented by the letter a is referred to as the y intercept or the point...
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send their best athletes to compete and see who the best of the best is when it comes to sports. The Olympics date back to Ancient Greece where their basic events included track and field, which are like men’s high jump which is the topic of this report. In this problem we are looking at the data collected from the gold medalists in the men’s high jump in from the years 1932-1980, excluding the years 1940 and 1944 where the Olympics were not held due to World War II. Below is the data for the gold...
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Case Analysis “X-Opoly, Inc.” 1 Summary The text deals with the topic of developing and producing a board game, called X-Opoly. The game is similar to the famous game ‘’Monopoly’’. It was the idea of two students. Their business has grown rapidly. This year they are expecting that they will sell 50,000 units. Over next 5 years the sales will grow 25 percent annually. The order of the game has to be differentiated in ordering a new game and ordering a game, which was already produced...
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/35 How Does Temperature Affect Respiration Rates of Fish? Google the web site www.biologycorner.com/ and in the upper left corner search for “goldfish lab”. Select the fish temperature lab. Use the simulator to gather data. Contact 4 classmates and get their data. (or run the simulation 5 times yourself) Complete the table. Complete a graph using the average respiration rate vs time. Answer the questions. ** no additional report is needed** Introduction: In this lab you will...
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Graphing Practice Name ___RaeAnne Phillips________________________________ Date __________ ▪ Save this file as a WORD document with a new name (LastNameGraph1) ▪ Use Create a Graph (http://nces.ed.gov/nceskids/graphing/) to graph the following data sets. ▪ Copy and paste the graphs AFTER each data set. ▪ Answer the questions AFTER each graph. ▪ Save Frequently! ▪ Email me (mruthenberg@findlaycityschools.org) the finished document. 1. Baby chickens, like all baby birds, require a constant...
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Risk Assessment ` Table of Results Line of Best Fit Graph Error Bars Graph Gradients Graph Analysis • Error Bars Analysis Evaluation • Improvement Assessment • Improved Experiment. • Reliability References Introduction: For this data analysis project, I conducted and experiment to investigate how the concentration of an acid affects the rate of the reaction. I have set up the experiment’s equipment...
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# What is price? The answer depends upon whether the concept is viewed from the market place or from the stand point of costs. Consumers view price as a monetary expression of the value for dimensions of quality or features benefits for a given products or services. This relationships can be expressed as follows: Price = Quality Value In other words , Price is the payment for quality as interpreted by the valuation of the marketplace. From a psychological...
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HOW TO TALK ABOUT A VISUAL AID ------------------------------------------------- Choosing the right visual aid A flow chart is a diagram showing the progress of material through the steps of a manufacturing process or the succession of operations in a complex activity | A pie chart displays the size of each part as a percentage of a whole | A (vertical or horizontal) bar chart is used to compare unlike items | | | | A line chart depicts changes over a period of time, showing data...
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Making PowerPoint Charts and Graphs clear I found this link to some before and after slides. One thing one needs to be careful of is to make sure that the information that one chooses to portray on a chart or graph or table is clear to the audience. The first 5 or 6 slides here are examples of slides that were at first unclear, followed by the "cleaner-looking" and clearer revisions of those slides. Hope it helps. http://www.slideshare.net/garr/sample-slides-by-garr-reynolds Funny and Helpful...
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expression that says this? A. B. C. D. E. 4. If f is a continuous and differentiable function, then approximate the value of . A. 4.5 B. 4 C. 2 D. 1/2 E. 1/4 5. . Over the open interval (0, 0.7], at what value of x is the tangent line to f horizontal? A. 0.390 B. 0.555 C. 0.368 D. 0.567 D. 0.195 6. At which x-value over the interval (0, 2] does the graph of f have a relative ...
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as showing knowledge of the incident concerned, depending on the particular task it may be helpful if candidates demonstrate some awareness of what has led up to it. Their identification with the character might also be conditioned by their awareness of what happens to the character later in the novel/play (if that is appropriate to the task), though this will probably not be referred to specifically. Through their responses, candidates are expected to demonstrate detailed knowledge of the text and...
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Physics Lab Report Distance Time Walking Relationship Experimentation For Mr.Williams SPH3U1-02 Sept.13/10 Written by: Dong Chang, Gloria Chan, Sanjay Tanirige, and Waleed Shehzad Image credits Distance Time Walking Relationship Experimentation Purpose The purpose of this experiment is to determine the amount of time in seconds that it takes to walk a distance of 84 metres on the running track. In addition, the person that is the most reliable to perform this test will have to be determined...
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SATURATION LINE OF WATER/STEAM INTRODUCTION When water is heated to steam, they are in thermal contact, are said to be saturated. The water is called saturated because it cannot absorb more energy without changing into steam, and the steam is called saturated vapor because it cannot absorb any more energy unless temperature increase and it becomes superheated. AIM: The aim of this laboratory is to find a mathematical model for the saturation curve for water/steam. APPARATUS The apparatus...
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How do we know that Climate Change exists and what causes it? Climate change as many know it, has been a big issue around the world. There are anthropogenic and natural causes which are responsible for this cause but individually they contribute a small amount but are a huge factor as a whole. One of the main problems about the climate change is global warming. What is global warming? It is the increase in the mean temperature of the Earth’s atmosphere. It is said that the temperature has been...
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Equations − − − − Relating linear graphs and simultaneous equations Analysing graphs Practical applications of linear graphs Writing algebraic equations Jane Stratton Objectives: • Use linear graphs to solve simultaneous equations • Use graphs of linear equations to solve a range of problems • Translate worded problems into graphical and algebraic form Finding the Solution to an Equation from a graph • Finding solutions to an equation when we have a graph is easy, we just need to find the coordinates...
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gives values of distance and time for a child travelling along a straight track competing in an egg and spoon race. Time (seconds) |0 |5 |10 |15 |20 |25 | |Distance (metres) |0 |8 |20 |20 |24 |40 | | a Copy the graph axes below on to graph paper. Plot a graph of distance against time for the child. [pic] (3) b Name the dependent variable shown on the graph. (1) c What type of variable is this? (1) d Use your graph to estimate the distance travelled in...
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Answer: x = 5, x = -2 (x+5)(x+2) = 0 x = -5 x = -2 b) [pic] Answer: x = 0, x = 2 3x(x-2) = 0 x = 0 x = 2 2) If [pic], find: a) f(2) Answer: f(2) = -3 [pic] b) f(-3) Answer: f(-3) = 42 [pic] 3) Solve [pic] using the quadratic formula. Answer: x = -1/2, x = 2 [pic] 4) Use the graph of [pic] to answer the following: [pic] a) Without solving the equation, or factoring, determine the solution(s) to the equation [pic] using only the graph. Answer: x = -1, x...
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Introduction Hypothesis To what extent do the dunes at camber show the characteristics typical of this depositional landform? To start my geography GCSE controlled assessment I have gone to Camber sands beach to record a variety of characteristics from the dunes in order to answer my hypothesis, shown above. There were a few key concepts and processes we used in our investigation they were Coastal deposition, Sand Dunes, Psammosere and Plant Succession. These four concepts above all fit in with...
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Today’s lecture will be spent entirely in the computer lab. At the end of lab, submit this worksheet. Part 1: Weather (3) 1. Open the following link: http://climate.weatheroffice.gc.ca/climateData/canada_e.html 2. Click “customized search” button 3. Search by station name a. Enter “Hamilton” in the text field b. Years: 2006 to 2011 4. Click “Search” 5. For “Hamilton A” station, select ‘daily’ in the “data interval drop-down box. 6. Click “Go” You now have access...
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How Do Hypotonic, Hypertonic, and Isotonic Solutions Affect the Water Movement of a Cell? Michael Halverson Valhalla High School El Cajon, California Research Host: Kim E. Barrett, Ph.D. University of California, San Diego 1997 Grade Level: High School How Do Hypotonic, Hypertonic, and Isotonic Solutions Affect the Water Movement of a Cell? Purpose: The purpose of this activity is to teach students about osmosis and the effects of hypotonic, hypertonic, and isotonic solutions on animal...
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the units. Download and name this file as LastnameFirstnameMat116SGE. Post to the Assignments Section. Use a math editor (Equation Editor or MathType) to write all math text to insure proper formatting of work and answers. |# | |Show your Work using a math editor and state Final Answer |- pts |+ pts | |1 |Suppose you are at the gas station filling your tank with gas. The function C(g) represents the cost C of filling up ...
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