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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QUADRATIC EQUATIONS Quadratic equations Any equation of the form ax2 + bx + c=0‚ where a‚b‚c are real numbers‚ a 0 is a quadratic equation. For example‚ 2x2 -3x+1=0 is quadratic equation in variable x. SOLVING A QUADRATIC EQUATION 1.Factorisation A real number a is said to be a root of the quadratic equation ax2 + bx + c=0‚ if aa2+ba+c=0. If we can factorise ax2 + bx + c=0‚ a 0‚ into a product of linear factors‚ then the roots of the quadratic equation ax2 + bx + c=0 can be found
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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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questions one by one Image462.gif Which mixture will enable the fastest reaction to take place between solid calcium carbonate (marble chips) and dilute hydrochloric acid? [rr-13] YES concentrated acid‚ high temperature‚ small chips ? high temperature‚ small chips‚ dilute acid ? large chips‚ concentrated acid‚ low temperature ? low temperature‚ small chips‚ dilute acid Image50.gifImage51.gifImage52.gifSodium thiosulphate solution reacts with hydrochloric acid to form sodium chloride‚ sulphur
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L7: Memory Basics and Timing Acknowledgements: Materials in this lecture are courtesy of the following sources and are used with permission. Nathan Ickes Rex Min Yun Wu J. Rabaey‚ A. Chandrakasan‚ B. Nikolic. Digital Integrated Circuits: A Design Perspective. Prentice Hall/Pearson‚ 2003. L7: 6.111 Spring 2006 Introductory Digital Systems Laboratory 1 Memory Classification & Metrics Read-Write Memory Random Access Non-Random Access SRAM FIFO DRAM Non-Volatile
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THE ACCOUNTING EQUATION The accounting equation can be described as of the basis of accounting. This is because it describes the double entry principle of book-keeping. It is a representation of how funds are raised to finance Assets. The equation is illustrated below: Asset = Capital + Liabilities For example‚ a girl needs to buy a laptop costing £500. She already had £250 in personal savings and then took a loan of £250 from her boyfriend. Here is the equation again: Asset Capital
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timing signals has become more and more difficult. Present-day transistors can process data so quickly that they can accomplish several steps in the time that it takes a wire to carry a signal from one side of the chip to the other. Keeping the rhythm identical in all parts of a large chip requires careful design and a great deal of electrical power. Wouldn ’t it be nice to have an alternative? Clock less approach‚ which uses a technique known as asynchronous logic‚ differs from conventional
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Global Variations in the Potato Crisps and Potato Chips Market It’s fair to assume that consumer snacking habits are likely to differ from country to country‚ particularly across different regions and cultures. A clear example is the consumption of potato crisps / potato chips which can be seen in the bar chart below. 86% of consumers throughout the USA and France consume potato crisps / potato chips closely followed by 84% of GB consumers. On the other end of the scale is the Chinese market
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Introduction Two Popular Microarraying Platforms Spotted microarrays Commercially available microarray www.molgen.mpg.de cDNA: PCR products (500-2‚000bp) synthesized oligos >10‚000 probes www.the-scientist.com Affymetrix “Gene Chip” 500‚000 probes 25 mer
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