Formulas (to differential equations) Math. A3‚ Midterm Test I. sin2 x + cos2 x = 1 sin(x ± y) = sin x cos y ± cos x sin y tan(x ± y) = tan x±tan y 1∓tan x·tan y differentiation rules: (cu) = cu ′ ′ ′ ′ ′ (c is constant) cos(x ± y) = cos x cos y ∓ sin x sin y (u + v) = u + v (uv)′ = u′ v + uv ′ ′ ′ u ′ = u v−uv v v2 df dg d dx f (g(x)) = dg dx sin 2x = 2 sin x cos x tan 2x = sin x = 2 cos 2x = cos2 x − sin2 x 2 tan x 1−tan2 x 1−cos 2x ‚ 2 integration rules: cos x = 2
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DERIVATION OF FORMULAS constant acceleration In order to be accurate‚ the title of this section should be "One Dimensional Equations of Motion for Constant Acceleration". Given that such a title would be a stylistic nightmare‚ let me begin this section with the following qualification. The equations of motion are valid only when acceleration is constant and motion is constrained to a straight line. Given that we live in a three dimensional universe in which the only constant is change‚ you may
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Ingredients for Success of Five Guys Burgers and Fries By Edna Odish Contemporary Business Dr. Ronna Campbell Oct.23th‚ 20012 Determine how Five Guys’ philosophy sets it apart from other fast-food chains. In my opinion what makes Five Guys’ Burgers and Fries different from other fast food chains are the following characteristics: a) Quality: Ingredients such as meat which cannot be frozen‚ bread which has to be made at least the night before and potatoes produced in locations that
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a way that conforms to the rules of the language and culture in the TL community. In general‚ this procedure is used as an effective way to deal with culturally-bound words/expressions‚ metaphors and images in translation. That is‚ the translator resorts to rewriting the SLT according to the characteristics of the TLT. Monia Bayar (2007)[16] argues that adaptation is based on three main procedures: cultural substitution‚ paraphrase and omission. Cultural substitution refers to the case where the
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ONE-SCHOOL.NET Physics Equation List :Form 4 Introduction to Physics Relative Deviation Relative Deviation = Mean Deviation ×100% Mean Value Prefixes Prefixes Tera Giga Mega Kilo deci centi milli micro nano pico Units for Area and Volume 1 m = 102 cm 1 m = 10 cm 2 4 2 Value 1 000 000 000 000 1 000 000 000 1 000 000 1 000 0.1 0.01 0.001 0.000 001 0.000 000 001 0.000 000 000 001 Standard form 1012 109 106 103 10-1 10-2 10-3 10-6 10-9 10-12 Symbol T G M k d c m μ n p (100 cm) (10
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• Profitability Procter & Gamble’s Gross Profit Margin (GPM) increased in 2010 by 2.41%‚ however it decreased in 2011 by 1.34%‚ while Net Sales continued to increase from 2009 to 2011. This trend was due to a price fluctuation in Cost of Goods Sold. The GPM directly affected the Operating Profit Margin (OPM)‚ which also increased in 2010 by 0.25% and decreased in 2011 by 1.14%. The Operating expenses were somewhat stable‚ which resulted in the OPM ratios following a similar trend as the GPM
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TWO (2) examples of each of Substantive Analytical Procedures in Payroll & Personnel Audit Cycle when auditing the accounts below: i- Payroll Expense Accounts ii- Payroll-Related Accrual Accounts 3. Describe the duties that are performed within the personnel‚ timekeeping‚ and payroll processing functions. 4.a. Describe what are the key authorisation points in a payroll system. b.Explain the importance of establishing control procedures over the classification of payroll transactions.
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MECHANICAL PROPERTIES Table I lists minimum yield strength‚ minimum ultimate tensile strength‚ and minimum elongation values. Yield strength‚ ultimate tensile strength‚ and elongation property values are determined with standard test method ASTM B557. This table also includes hardness screening criteria values‚ indicated in parentheses. As applicable‚ minimum electrical conductivity values are also specified. TABLE I Minimum Ultimate Tensile Strength3 (ksi) 38.0 38.0 35.0 26.0 38.0 38.0 38.0 25
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HULL 1. Stem 2. Forefoot 3. Keel 4. Rudder post 5. Rudder 6. Propeller 7. Propeller boss 8. Stem 9. Anchor 10. Draught marks 11. Load line markings 12. Deck line HULL INTERIOR 13. Hawse pipe 14. Deck stores 15. Windglass machinery room 16. Spurling pipe 17. Chain locker 18. Fore peak tank 19. No.1 Upper tween deck 20. No.1 Lower tween deck 21. No.1 Lower hold 22. No.1 Double bottom tank 23. No.2 Upper tween
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Homework 2 Solution Key Problem 1. Suppose that you sell short 500 shares of Intel‚ currently selling for $40 per share‚ and you give your broker $15‚000 to establish your margin account. Assume Intel pays no dividends. a) If you earn no interest on the funds in your margin account‚ what will be your rate of return after one year if Intel stock is selling at (i) $44; (ii) $40; (iii) $36? The gain or loss on the short position is 500 P . Invested funds are $15‚000. Therefore‚ your rate
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