✎ ✍ 5.2 ✌ Cramer’s Rule Introduction Cramer’s rule is a method 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
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Keyboard shortcuts Keyboard shortcuts are combinations of two or more keys that‚ when pressed‚ can be used to perform a task that would typically require a mouse or other pointing device. Keyboard shortcuts can make it easier to interact with your computer‚ saving you time and effort as you work with Windows and other programs. Most programs also provide accelerator keys that can make it easier to work with menus and other commands. Check the menus of programs for accelerator keys. If a letter
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Procedural Programming vs Object Oriented Programming When writing code for a program it is very important to make sure that you use the best language for what the client needs. Prior to making a decision on what language to use‚ a programmer needs to decide which method he or she wants to use. The two most common methods used by coders in the field today are procedural and object oriented programming (OOP). Making the decision to use an incorrect option could run cause problems during the maintenance
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Exercise 4.32 [Assessment 2(16): You must have this exercise signed off by your class supervisor] On paper‚ write a method called sum with a while loop that adds up all numbers between two numbers a and b‚ inclusive‚ and returns the sum as its result. The values for a and b can be passed to the sum method as parameters. For instance: sum(1‚ 5) would return the value 15 (i.e.‚ 1 + 2 + 3 + 4 + 5). What happens if the value of the second parameter is less than the value of the first? public
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CHAPTER 8 Linear Programming Applications Teaching Suggestions Teaching Suggestion 8.1: Importance of Formulating Large LP Problems. Since computers are used to solve virtually all business LP problems‚ the most important thing a student can do is to get experience in formulating a wide variety of problems. This chapter provides such a variety. Teaching Suggestion 8.2: Note on Production Scheduling Problems. The Greenberg Motor example in this chapter is largest large
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Herpes-Simplex: Type 2 Herpes is a name that is used to describe several types of skin eruptions that are characterized by formation of blisters. The term embraces primarily two distinct disorders‚ herpes simplex and herpes zoster‚ both caused by viruses. Together‚ these "herpes" viruses are estimated to cause more human illnesses than any other group of viruses. Two types of herpes simplex are known. The first causes cold sores or fever blisters‚ which is an eruption of blisters that often
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should contribute at most 25% of the total calories intake that will result from the diet plan. The vegetable food type should provide at least 30% of the minimum daily requirements for vitamins. Provide a linear programming formulation for the above case. (No need to solve the problem.) Element | Milk | Chicken | Bread | Vegetables | Calories (X1) | 160 | 25% * 210 | 120 | 150 | Carbohydrates (X2) | 110 | 130 | 110 | 120 | Protein (X3) | 90 | 190 | 90 | 130 | Vitamins (X4) | 50 |
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the deposits”? Or would the “problem posing” style of teaching be the most effective‚ where by “responding to the essence of consciousness—intentionally—rejects communiqués and embodies communications. It epitomizes the special characteristic of consciousness”. Through my own experiences as well as intensive research‚ the “problem posing” style of teaching has proven to the most effective application of fundamental attainment. There are many advantages of “problem posing” style to education
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Executive Summary: Marketing Strategy Optimization: Using linear programming to establish an optimal marketing mixture. Drew M. Stapleton‚ Joe B. Hanna and Dan Markussen‚ American Business Review 2(21)-pg 54-62 June 2003 In recent times marketing strategy is playing a vital role in a firm success. It optimizes the marketing resources and can improve the revenue generation and market share. Since the global market place is increasing‚ companies find optimizing the marketing effort even more
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GENETIC PROGRAMMING: AN INTRODUCTION AND SURVEY OF APPLICATIONS M.J. Willis*‚ H.G Hiden*‚ P. Marenbach+‚ B. McKay* and G.A. Montague* * Symbolic Optimisation Research Group (SORG) Dept. of Chemical and Process Engineering University of Newcastle upon Tyne NE1 7RU‚ UK + Institute of Control Engineering Darmstadt University of Technology Landgraf-Georg-Strasse 4 D-64283 Darmstadt‚ Germany {Mark.Willis‚ H.G.Hiden‚ Ben.McKay‚ Gary.Montague} @ncl.ac.uk http://lorien.ncl.ac.uk/sorg mali@rt.e-technik
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