Further Pure 1 Revision Notes • Proof by induction To prove by induction that a statement (C) involving an integer n is true for all [pic]‚ prove that‚ i) (C) is true for [pic]; ii) if (C) is true for [pic]then (C) is true for [pic]. And then bring these parts together to complete the proof. • Summing series using formulae To sum series‚ use a combination of the following formulae. Second two are given in formula book. [pic] [pic] [pic] e.g. Q:
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between the intensity of electromagnetic radiation and distance from a source is an example of the inverse square law: I d12 Electromagnetic radiation attenuates over distance‚ i.e. the further you are away from an electromagnetic source the less the intensity will be. This can be applied to light‚ as if you move away from a light it will be less bright. The Intensity is proportional to the inverse of the distance square‚ or I d12 5. outline how the modulation of amplitude or frequency of visible
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and use them to derive the corresponding division facts add‚ subtract‚ multiply and divide using commutative‚ associative and distributive laws understand and use inverse operations use brackets and the hierarchy of operations solve problems set in words; for example‚ formulae given in words understand reciprocal as multiplicative inverse understand that any non-zero number multiplied by its reciprocal is 1 know that zero has no reciprocal because division by zero is undefined perform money calculations
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DETERMINATION OF THE HEAT OF SOLUTION BY THE VANT HOFF ISOCHORE METHOD Jan Vincent Arafiles‚ Merry Joy Arzaga‚ Anne Louise Ayson‚ Lovely Jenny Buenaflor Group 2 3A-Biochemistry chem401 laboratory ABSTRACT Thermodynamic values can be determined using the Vant Hoff isochore method. This method entails the use of equilibrium systems to determine the change in enthalpy of the solution‚ which can b related to the change in internal energy of the solution. The van ’t Hoff isochore relates
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However the data points had a low correlation to the line of best fit with an R2 of 0.6762 and resembled an inverse curve. The most directly proportional relationship between the ionic strength and percent ionization was determined to be an inverse of the square root of ionic strength: α∝1/√I‚ where α is percent ionization and I is ionic strength (M). The graph between percent ionization and the inverse square root of ionic strength has a nearly perfect R2 value of 0.989‚ suggesting that this relationship
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MGT 547 Fixed Income Security Analysis Professor Hongjun Yan YALE SCHOOL OF MANAGEMENT Solutions to Problem Set 7: Caps‚ Floors‚ Collars 1) Use the interest rate tree below. The first number at each node is the 0.5-year rate at that node. The next number is the price of $1 par of a 0.5-year zero at that node. The next number‚ at the time 0 node‚ is the price of $1 par of a 1-year zero. Time 0 Interest Rate Model Time 0.5 5.526% 0.973113 4.9% 0.976086 0.952587 4.345% 0.978737
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order to produce a specific given number. Logarithmic and exponential functions are often used together because they are inverse functions‚ and therefore “undo” one another. The natural exponential function and the natural logarithm are frequent examples. These functions have a base of the constant e‚ or Euler’s number. The natural exponential function is written as f(x)=ex. Its inverse‚ the natural logarithmic function‚ is written as f(x)=ln(x). The decay of radioactive substances can be represented
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Working Capital Management Submitted to: Submitted by: Mr. Mukesh Hans Swati Chaudhry MBA-IIsem Working Capital Management The working capital management is a delicate area in the field of financial management. Every business needs investment to procure fixed assets‚ which remain in use for a longer period. Money invested in these assets is called ‘Long term Funds’ or ‘Fixed Capital’. Business also needs funds for short-term purposes to finance current operations. Investment
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RESULTS AND DISCUSSION Now that we have applied all the tools necessary for hypothesis testing‚ the final results can be discussed in detail. All variables with respect to their relation to the capital structure will be discussed separately. Not only the figures have been interpreted as per the mathematical rules‚ but they have also been analyzed according to the prevalent conditions in the cement industry during the period of analysis. Therefore‚ it is necessary to give the industry scenario
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form the basis of much of modern day eigenvalue computation. In this paper‚ we outline five such iterative methods‚ and summarize their derivations‚ procedures‚ and advantages. The methods to be examined are the power iteration method‚ the shifted inverse iteration method‚ the Rayleigh quotient method‚ the simultaneous iteration method‚ and the QR method. This paper is meant to be a survey of existing algorithms for the eigenvalue computation problem. Section 2 of this paper provides a brief review
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