What are the criteria’s involved in choosing mass balances for components?
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ACCOUNTING AND FINANCIAL ENGINEERING - EXAMPLE 34.33 : An engineering corporation that produces a type of healthy food has A number of shares of $B preferred stock and C number of shares of $H common stock outstanding. In a typical financial year, let the net income obtained = D. The amount retained by the corporation = E. (a) Calculate the amount of money distributed to the shareholders if : (i) D > E; (ii) D = E; (iii) D < E. (b) Let preferred dividend = F, common dividend = G, CH > G. Find the values of F and G, in term of A, B, D and / or E when : (i) (D - E) > AB; (ii) (D - E) < AB; (iii) (D - E) = AB.
QUANTUM CHEMISTRY AND CHEMICAL ENGINEERING - EXAMPLE 31.5 : In a wavefunction, let P(x) = A cos kx + B sin kx. By using the boundary conditions of x = 0 and x = l, where P(0) = P(l) = 0, prove by mathematical calculation that P(x) = B sin (npx / l) where p = 22 / 7 approximately, n is a rounded number. A, B and k are constants.
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ACCOUNTING AND FINANCIAL ENGINEERING - EXAMPLE 34.6 : In a random walk, a stochastic process starts off with a score of A. This is a score for a chemical engineering test. At each discrete event, there is probability p chance you will increase your score by B and a (1 - p) chance you will decrease your score by C. The event happens T times. Let D = expected value of score. (a) Form an equation of D as a function of A, B, C, T and p. (b) Find the value of D if A = 60, B = 1, C = -1, T = 50, p = 0.5.
ACCOUNTING AND FINANCIAL ENGINEERING - EXAMPLE 34.11 : Let an Accounting Equation to be : Assets = Liabilities + Equity of Owner. In a biochemical engineering organization, its account balance sheet contains the following information : Accounts payable $2200; accounts receivable $1500; line of credit $500; cash $100; long term debt $3800; inventory $1300; investments $800; plant equipment $6800. Find the equity of owner by applying Accounting Equation.
CHEMICAL MATERIAL BALANCE - EXAMPLE 2.5 : In a non-dilute absorber, the inlet gas stream consists of 8 mol % carbon dioxide in nitrogen. By contact with room temperature water at atmospheric pressure, 65 % of the carbon dioxide from a gas stream has been removed. (a) Find the mole ratio of carbon dioxide and nitrogen gases at inlet and outlet gas streams. (b) The Henry's Law provides y = 1640 x for carbon dioxide in water. Find the mole ratio when x = 0.0000427. Mole ratio is y / (1 - y) for y.
QUANTUM COMPUTING - EXAMPLE 32.4 : A system of linear congruences consists of 3 equations : X ≡ 1 (mod 2), X ≡ 3 (mod 3), X ≡ 4 (mod 5). X has positive values. (a)(i) List the values of these equations from 1 to approximately 40. (ii) Find the first smallest value and second smallest value of X. (iii) Guess the third smallest value of X. (b) Let X ≡ Aa (mod Ma), X ≡ Ab (mod Mb), X ≡ Ac (mod Mc). According to Chinese remainder theorem, X ≡ (Aa x Ya x Md + Ab x Yb x Me + Ac x Yc x Mf) [ mod (Ma x Mb x Mc) ]. (i) Show that Ma, Mb and Mc have the greatest common divisor of Ma x Mb x Mc. (ii) Find the values of Md, Me and Mf if Md = Mb x Mc, Me = Ma x Mc and Mf = Ma x Mb. (iii) Find the values of Ya, Yb and Yc if Ya = Remainder of (Md / Ma), Yb = Remainder of (Me / Mb) and Yc = Remainder of (Mf / Mc). (iv) Use Chinese remainder theorem to find X.
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