Aaron Griffin Math 4091A March 17‚ 2015 The Cartesian Coordinate System Linear inequalities (statements such as “4≤X+10<18”) can be represented graphically along a number line. In similar manner‚ a linear equation in two variables (this being the form ax+by=c) can also be represented graphically‚ using two axes; the x axis‚ the horizontal plane‚ and the y axis‚ the vertical plane. There are memory tricks with which to distinguish the x from the y axis and remember their horizontal and vertical
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Linear Programming History of linear programming goes back as far as 1940s. Main motivation for the need of linear programming goes back to the war time when they needed ways to solve many complex planning problems. The simplex method which is used to solve linear programming was developed by George B. Dantzig‚ in 1947. Dantzig‚ was one in who did a lot of work on linear programming‚ he was reconzied by several honours. Dantzig’s discovery was through his personal contribution‚ during WWII when Dantzig
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Chapter I Introduction to control systems 1 EE352: Lecture 01: Introduction to linear control systems Definition 1 (Control system). an interconnection of subsystems and processes forming a configuration that will lead to the desired output‚ given a specified input. Desired output Reference input Control system plant reference input Actual output system response controlled variable The control system manipulates the input of the process to get the desired response
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To solve a system of equations by addition or subtraction (or elimination)‚ you must eliminate one of the variables so that you could solve for one of the variables. First‚ in this equation‚ you must look for a way to eliminate a variable (line the equations up vertically and look to see if there are any numbers that are equal to each other). If there is lets say a –2y on the top equation and a –2y on the bottom equation you could subtract them and they would eliminate themselves by equaling zero
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The Maxwell equations Introduction:- One of Newton’s great achievements was to show that all of the phenomena of classical mechanics can be deduced as consequences of three basic‚ fundamental laws‚ namely Newton’s laws of motion. It was likewise one of Maxwell’s great achievements to show that all of the phenomena of classical electricity and magnetism – all of the phenomena discovered by Oersted‚ Ampère‚ Henry‚ Faraday and others whose names are commemorated in several electrical
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329 Quadratic Equations Chapter-15 Quadratic Equations Important Definitions and Related Concepts 1. Quadratic Equation If p(x) is a quadratic polynomial‚ then p(x) = 0 is called a quadratic equation. The general formula of a quadratic equation is ax 2 + bx + c = 0; where a‚ b‚ c are real numbers and a 0. For example‚ x2 – 6x + 4 = 0 is a quadratic equation. 2. Roots of a Quadratic Equation Let p(x) = 0 be a quadratic equation‚ then the values of x satisfying p(x) = 0 are called its roots or
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Linear Technology Linear Technology is a technology company that focuses on the different elements of semiconductors. The company mostly focuses on analog products within the semiconductor portion of the electronic industry. Linear Technology was unique in their payout policy in the sense that they started with announcing dividends and then continued onto repurchasing. Linear started dividends to gain the respect of investors as well as show that buying shares in the company of Linear was less
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TO: Board of Directors‚ Linear Technologies FROM: Mr. Paul Coghlan CFO‚ Linear Technologies RE: Dividend Policy Summary: Based on the financials to date and the forward looking capital investments required Linear should increase their dividend payout by $0.01 per share. Entering the fourth quarter of 2003 the market seems to show continued signs of improvement. The company has shown steady growth and revenues are forecasted to exceed 2002’s by 19%. The forecast shows net income coming in
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Linear-Regression Analysis Introduction Whitner Autoplex located in Raytown‚ Missouri‚ is one of the AutoUSA dealerships. Whitner Autoplex includes Pontiac‚ GMC‚ and Buick franchises as well as a BMW store. Using data found on the AutoUSA website‚ Team D will use Linear Regression Analysis to determine whether the purchase price of a vehicle purchased from Whitner Autoplex increases as the age of the consumer purchasing the vehicle increases. The data set provided information about the purchasing
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The development of linear programming has been ranked among the most important scientific advances of the mid 20th century. Its impact since the 1950’s has been extraordinary. Today it is a standard tool used by some companies (around 56%) of even moderate size. Linear programming uses a mathematical model to describe the problem of concern. Linear programming involves the planning of activities to obtain an optimal result‚ i.e.‚ a result that reaches the specified goal best (according to the mathematical
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