UTT MATH1002 Weeks 3&4 Notes Systems of ODEs First-order linear equations with constant coefficients [pic] [pic] Let [pic] [pic] Taking Laplace transforms of (1) and (2) [pic] [pic] From (3) and (4) [pic] [pic] We solve this system algebraically for [pic]and [pic] and obtain [pic] by taking inverse transforms. Example [pic] [pic] [pic] We have [pic] [pic] [pic] From (5) and (6) [pic] [pic] [pic]
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Synthesis of Salicylic Acid and Potentiometric Determination of its Purity and Dissociation Constant ------------------------------------------------- Abstract The purpose of the study is to synthesize salicylic acid from the ester‚ methyl salicylate‚ and determine the acid’s dissociation constant and purity. The ester was converted to salicylic acid by base hydrolysis. The products were refluxed and recrystallized‚ to ensure maximum purity‚ and filtered‚ dried‚ and weighed. The melting point
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Question E Assume that Bon Temps is a constant growth company whose last dividend (Dₒ‚ which was paid yesterday) was $2.00 and whose dividend is expected to grow indefinitely at a 6% rate. (i) What is the firm’s expected dividend stream over the next 3 years? Temp Force is a constant growth stock. Its dividend is estimated to increase at a constant rate of 6 percent per year. 0 1 2 3
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Guilt is a common feeling that humans feel when they have done something wrong. The poets Gabriel Okara and Dennis brutus both express this feeling of guilt in their personas backgrounds. Therefore‚ okara’s “Once Upon a Time” and brutus’s “It is the Constant Image of Your Face” are poems portrayed with guilt‚ but they show it in different situations. The body of both poems have a specific situation happening. in the poem “Once Upon a Time” the persona wishes to be young again an forget all the lessons
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Distant stars and distant galaxies aren’t completely featureless‚ but actually has specific spectral features. When we look at their spectrum‚ we can see an absorption of spectrum. Redshift and blueshift are two different terms that describe how the light changes as objects moves closer or further away from us. The reason that these two terms can describe whether or not objects moves closer or further away from us‚ is the fact that when a certain object in space is shifted to the red part of the
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Franklin Delano Roosevelt believed in saving the arts by educating the public‚ along with director Hallie Flanagan establishing the Federal Theater Project (FTP). With high expectations for the FTP to help the arts‚ it failed. With there being constant conflict between the commercial theater advocates and independent non-profit theater supports about funding‚ theaters began to slowly rise. “Hard hit by both the Depression and the rise of the cinema‚ the commercial theater had been trying unsuccessfully
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When World War II ends the United States and the Soviet Union became enemies‚ better knows as the Cold War. It consisted on the constant tension between both countries in starting a war. Both sides had power in nuclear weapons which made people be afraid of the start of a nuclear war. Also both countries disagree in many things. The Soviet Union had a Dictator‚ one political party (Communist) and an economic system (socialism) in which the government run all the industries. USA had an elected president
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DETERMINING THE EQUIVALENT MASS AND DISSOCIATION CONSTANT OF AN UNKNOWN WEAK ACID BY TITRIMETRY INTRODUCTION Acids are substances that donate hydrogen ions and bases are substances that accept hydrogen ions. Acids and bases react with each other by transferring hydrogen ions. One way to distinguish an acid is by its equivalent mass‚ which is the number of grams of the acid needed to transfer one mole of hydrogen ion to a base. For a monoprotic acid‚ which only transfers one hydrogen ion‚ its
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Carbon Dioxide in Water under Constant Pressure Beijing World Youth Academy Subject: Chemistry Student name: YeiYoung Choo Candidate number: 000791 011 January 21‚ 2009 Teacher Helen Xu The Effect of Temperature on the Solubility of Carbon Dioxide in Water under Constant Pressure (Evaluated for Design) Research Question What is the effect of temperature on the solubility of carbon dioxide gas in de-ionised water under constant pressure? Introduction
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How successful can the management of fragile environments be‚ given the constant and increasing demand for their exploitation? A fragile environment is an area where the flora and fauna have adapted to a specific climate and evolved to occupy many different niches due to extremely high competition for resources. Furthermore due to the constant abiotic conditions‚ specialisation and symbiotic relationships have occurred to such a degree that even the slightest ecological or environmental disruption
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