1.1 SOLUTIONS Notes: The key exercises are 7 (or 11 or 12)‚ 19–22‚ and 25. For brevity‚ the symbols R1‚ R2‚…‚ stand for row 1 (or equation 1)‚ row 2 (or equation 2)‚ and so on. Additional notes are at the end of the section. 1. x1 + 5 x2 = 7 −2 x1 − 7 x2 = −5 1 −2 5 −7 7 −5 x1 + 5 x2 = 7 Replace R2 by R2 + (2)R1 and obtain: 3x2 = 9 x1 + 5 x2 = 7 x2 = 3 x1 1 0 1 0 1 0 5 3 5 1 0 1 7 9 7 3 −8 3 Scale R2 by 1/3: Replace R1 by R1
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Module 1 Energy Methods in Structural Analysis Version 2 CE IIT‚ Kharagpur Lesson 2 Principle of Superposition‚ Strain Energy Version 2 CE IIT‚ Kharagpur Instructional Objectives After reading this lesson‚ the student will be able to 1. State and use principle of superposition. 2. Explain strain energy concept. 3. Differentiate between elastic and inelastic strain energy and state units of strain energy. 4. Derive an expression for strain energy stored in one-dimensional structure under
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give you some advises for your separation.The way to say goodbye that less hurt to ex. When the couple’s relationship cannot develop or even trend to be worse‚ saying goodbye is only way to solve problem. U can be shy when express your love‚ but u can not hesitate when say in goodbye.‚ If u don’t want to continue this relationship any more‚ you have to say goodbye‚ but sometime saying goodbye in wrong way will make your relationship worse so that the question how to say goodbye without hurting
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MA1506 LECTURE NOTES CHAPTER 1 DIFFERENTIAL EQUATIONS 1.1 Introduction A differential equation is an equation that contains one or more derivatives of a differentiable function. [In this chapter we deal only with ordinary DEs‚ NOT partial DEs.] The order of a d.e. is the order of the equation’s highest order derivative; and a d.e. is linear if it can be put in the form any (n)(x)+an−1y (n−1)(x)+· · ·+a1y (1)(x)+a0y(x) = F‚ 1 where ai‚ 0 ≤ i ≤ n‚ and F are all functions of x. For example
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Sustainable supply chain management across the UK private sector Helen Walker Cardiff Business School‚ Cardiff University‚ Cardiff‚ UK‚ and Neil Jones Alliance Boots‚ Nottingham‚ UK Abstract Purpose – Increasingly‚ private sector companies are aiming to buy and supply products and services in a sustainable way‚ termed “sustainable supply chain management” (sustainable SCM)‚ using purchasing and supply to reduce negative impacts on the environment‚ economy and society. There is often a gap
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at the keyboard‚ I see that "U" and "I" are always together.:) Dont hide up feelings for someone special...... bcoz 1 day wen u realize to express ur feelings 2 them dat special1 may be special to sumone else. I Know that you know that i know what you dont think i know but i know that you know that i know what you know that i know that you dont think i know but i know! "Trouble is not a trouble‚trouble wont trouble you‚if u trouble a trouble‚trouble will trouble u double trouble ’’The sixth
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εr=1 * The charges of the conductors: * Conductor c1: 1C= q * Conductor c2: -1C= -q * Conductor c3: 1C= q * Conductor c4: -1C= -q * The boundary has U=0 The table with elements of the geometry: Object | Contained elements/labels | Observations | Vacuum block | Border linesAir block | On the border lines U=0 | Auxiliary block | Lines that form the auxiliary square with margin 8 cm | The lines have no property‚ only to serve in controlling the mesh | | | | Capacitor
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Utility Maximization Steps MPP 801 Fall‚ 2007 The MRS and the Cobb-Douglas Consider a two-good world‚ x and y. Our consumer‚ Skippy‚ wishes to maximize utility‚ denoted U (x‚ y). Her problem is then to Maximize: U = U (x‚ y) subject to the constraint B = p x x + py y Unless there is a Corner Solution‚ the solution will occur where the highest indifference curve is tangent to the budget constraint. Equivalent to that is the statement: The Marginal Rate of Substitution equals the price ratio‚ or px
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Кубанска ракетна криза је један од критичних момената хладног рата‚ који је свет довео на ивицу нуклеарног уништења. Сукоб је настао када је 1962. године СССР инсталирао нуклеарне ракете на Куби‚ што су Сједињене америчке државе прогласиле за претњу својој безбедности и повреду интересне сфере. Криза је ескалирала крајем октобра 1962. године блокадом Кубе од стране САД. После вишедневног натезања и „игре живаца”‚ у којој су главни актери били Џон Ф. Кенеди‚ Никита С. Хрушчов и Фидел Кастро‚ Совјетски
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