| | |Assignment title | | | | |Simultaneous Equation | | |Programme (e.g.: APDMS) |HND CSD | |
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between two points using Pythagoras’ theorem. The midpoint is the average (mean) of the coordinates. The gradient = Parallel lines have the same gradient. The gradients of perpendicular lines have a product of -1. Straight Lines: Equation of a straight line is y = mx + c‚ where m = gradient‚ c = y-intercept. The equation of a line‚ if we know one point and the gradient is found using: (y - y1) = m(x - x1) (If given two points‚ find the gradient first‚ and then use the formula.) Two lines
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Applications: Graphing Simultaneous 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
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What is the DuPont equation‚ and how does it capture the nature of expense control‚ efficiency of asset management‚ and financial leverage (or debt) of a firm? If you were the CFO of your firm (or a hypothetical firm)‚ what variable would you concentrate your efforts on and why? The DuPont equation is a method of measurement that was started by the DuPont Corporation in the 1920s. In this method of measurement the assets are measured at their gross book value rather than at their net book value which
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construction as of May 31. During May the following transactions occurred: 1-May Smith received $10‚000 as an inheritance and used it to buy stock in the company. 7-May Smith paid his accounts payable balance. 15-May Smith replaced some windows for a client and received $5‚000 cash for his services 17-May Smith collected $1‚200 from a customer for a job performed in April
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for solving linear simultaneous equations. It makes use of determinants and so a knowledge of these is necessary before proceeding. 1. Cramer’s Rule - two equations If we are given a pair of simultaneous equations a1 x + b1 y = d1 a2 x + b2 y = d2 then x‚ and y can be found from d1 b1 d2 b2 a1 b1 a2 b2 a1 d1 a2 d2 a1 b 1 a2 b 2 x= y= Example Solve the equations 3x + 4y = −14 −2x − 3y = 11 Solution Using Cramer’s rule we can write the solution as the ratio of two determinants. −14 4
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6 Systems Represented by Differential and Difference Equations Recommended Problems P6.1 Suppose that y 1(t) and y 2(t) both satisfy the homogeneous linear constant-coeffi cient differential equation (LCCDE) dy(t) + ay(t) = 0 dt Show that y 3 (t) = ayi(t) + 3y2 (t)‚ where a and # are any two constants‚ is also a solution to the homogeneous LCCDE. P6.2 In this problem‚ we consider the homogeneous LCCDE d 2yt + 3 dy(t) + 2y(t) = 0 dt 2 dt (P6.2-1) (a) Assume that a solution to
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2014/9/16 Linear Equations Ad Options Ads by Vidx Linear Equations A linear equation is an equation for a straight line These are all linear equations: y = 2x+1 5x = 6+3y y/2 = 3 x Let us look more closely at one example: Example: y = 2x+1 is a linear equation: The graph of y = 2x+1 is a straight line When x increases‚ y increases twice as fast‚ hence 2x When x is 0‚ y is already 1. Hence +1 is also needed So: y = 2x + 1 Here are some example values: http://www.mathsisfun.com/algebra/linear-equations
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Balancing Equations Balancing equations is a fundamental skill in Chemistry. Solving a system of linear equations is a fundamental skill in Algebra. Remarkably‚ these two field specialties are intrinsically and inherently linked. 2 + O2 ----> H2OA. This is not a difficult task and can easily be accomplished using some basic problem solving skills. In fact‚ what follows is a chemistry text’s explanation of the situation: Taken from: Chemistry Wilberham‚ Staley‚ Simpson‚ Matta Addison Wesley
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DIFFERENTIAL EQUATIONS: A SIMPLIFIED APPROACH‚ 2nd Edition DIFFERENTIAL EQUATIONS PRIMER By: AUSTRIA‚ Gian Paulo A. ECE / 3‚ Mapúa Institute of Technology NOTE: THIS PRIMER IS SUBJECT TO COPYRIGHT. IT CANNOT BE REPRODUCED WITHOUT PRIOR PERMISSION FROM THE AUTHOR. DEFINITIONS / TERMINOLOGIES A differential equation is an equation which involves derivatives and is mathematical models which can be used to approximate real-world problems. It is a specialized area of differential calculus but it involves
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