ENGG250 MATERIALS ASSIGNMENT 1 20 marks DUE: 20 MARCH 2015 These are the sort of questions you can expect in the Class Test on 23 March. Completing this assignment should therefore be considered part of your preparation for the Class Test. (The Class Test will cover more material than the assignment). When you have completed the questions‚ make an electronic file from your answers (you can put together an electronic file‚ or scan your handwritten copy – as long as it is legible). Create a cover
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. Student Exploration: Graphing Skills Vocabulary: bar graph‚ line graph‚ negative relationship‚ pie chart‚ positive relationship‚ scale‚ scatter plot‚ variable Prior Knowledge Questions (Do these BEFORE using the Gizmo.) 1. Four kinds of graphs are shown in this Gizmo. Circle the kinds you have seen before. [pic] [pic] [pic] [pic] Bar graph Line graph Pie chart Scatter plot 2. Where have you seen graphs used? Graphs are used everywhere.
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Homogeneous Coordinates and Matrix Representation Homogeneous Coordinates Homogenous coordinates utilize a mathematical trick to embed three-dimensional coordinates and transformations into a four-dimensional matrix format. As a result‚ inversions or combinations of linear transformations are simplified to inversion or multiplication of the corresponding matrices. Homogenous coordinates also make it possible to define perspective transformations. Homogenous coordinates allow each point
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Convex Optimization Solutions Manual Stephen Boyd Lieven Vandenberghe January 4‚ 2006 Chapter 2 Convex sets Exercises Exercises Definition of convexity 2.1 Let C ⊆ Rn be a convex set‚ with x1 ‚ . . . ‚ xk ∈ C‚ and let θ1 ‚ . . . ‚ θk ∈ R satisfy θi ≥ 0‚ θ1 + · · · + θk = 1. Show that θ1 x1 + · · · + θk xk ∈ C. (The definition of convexity is that this holds for k = 2; you must show it for arbitrary k.) Hint. Use induction on k. Solution. This is readily shown by induction from
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The production possibilities (PP) curve is a graphical medium of highlighting the central problem of ’what to produce’. To decide what to produce and in what quantities‚ it is first necessary to know what is obtainable. The PP curve shows the options that are obtainable‚ or simply the production possibilities. What is obtainable is based on the following assumptions: 1. The resources available are fixed. 2. The technology remains unchanged. 3. The resources are fully employed. 4. The resources
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The Vector equation of a plane To find the vector equation of a plane a point on the plane and two different direction vectors are required. The equation is defined as: where a is the point on the plane and b and c are the vectors. This equation can then be written as: The Cartesian equation of a plane The cartesian equation of the plane is easier to use. The equation is defined as: One of the advantages to writing the equation in cartesian form is that we can easily find the normal
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Buried Treasure MAT 221 Instructor Date Buried Treasure In this essay of Buried Treasure we will use many different ways to attempt to factor down three expressions problems. Our first problem from our reading talks about Ahmed and Vanessa‚ Ahmed has half of a treasure map‚ which indicates that the treasure is buried in the desert 2x + 6 paces from Castle Rock. The other half of the map is in Vanessa possession and her half indicates that to find the treasure‚ one must
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C1 MOCK PAPER 1. Solve the inequality . (3) 2. Find . (4) 3. Find the value of (a) ‚ (b) ‚ (c) . (1) (2) (1) 4. A sequence is defined by ‚ where k is a constant. (a) Write down an expression for a2 in terms of k. (1) (b) Find a3 in terms of k‚ simplifying your answer. (2) Given that a3 = 13‚ (c) find the value of k. (2) 5. (a) Show that eliminating y from the equations 2x + y = 8‚ 3x2 + xy = 1 produces the equation x2 + 8x - 1 =
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Symbol of peace Content Name page no. 1. Introduction 2. Subject 3. Object 4. Design &sculpture- Form (Sarmin Sultana -1020861) Color
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Problem 705 Determine the centroid of the shaded area shown in Fig. P-705‚ which is bounded by the x-axis‚ the line x = a and the parabola y2 = kx. Solution 705 HideClick here to show or hide the solution At (a‚ b) Thus‚ → equation of parabola Differential area Area of parabola by integration Location of centroid from the y-axis (x-intercept of centroid) answer Location of centroid from the x-axis (y-intercept
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