QUANTUM COMPUTING - EXAMPLE 32.3 : A system of linear congruences consists of 3 equations : X ≡ 1 (mod 3), X ≡ 3 (mod 5), X ≡ 4 (mod 6). X has positive values. (a) List the values of these equations from 1 to 35. Then find the minimum value of X. (b)(i) Find the least common multiple (LCM) of b = 3, 5 and 6 where X ≡ a (mod b). (ii) If b - a has the same value of all equations above, then X + (b - a) is divisible by LCM. Find the value of minimum value of X via LCM division.
QUANTUM COMPUTING - ANSWER 32.3 : (a) X ≡ 1 (mod 3) = 1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34. X ≡ 3 (mod 5) = 3, 8, 13, 18, 23, 28, 33. X ≡ 4 (mod 6) = 4, 10, 16, 22, 28, 34. All equations have minimum value of X = 28. (b)(i) LCM for b = 3, 5 and 6 = (30 / 10, 30 / 6, 30 / 5) is 30. (ii) Since b - a = 3 - 1 = 5 - 3 = 6 - 4 = 2, then X + (b - a) is divisible by LCM. X + 2 is divisible by 30. X = 30 - 2 = 28. The answer is given by Kang Chuen Tat; PO Box 6263, Dandenong, Victoria VIC 3175, Australia; SMS +61405421706; chuentat@hotmail.com; http://kangchuentat.wordpress.com.
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ACCOUNTING AND FINANCIAL ENGINEERING - EXAMPLE 34.26 : In a construction accounting for a biochemical processing plant, $A has been spent to date, and another $B is expected required to complete the construction project. The biochemical processing plant is expected to generate a total revenue of $C. Calculate the : (a) estimated total costs; (b) percentage completion of project; (c) total estimated profit; (d) profit to date.
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ACCOUNTING AND FINANCIAL ENGINEERING - EXAMPLE 34.35 : A voluntary accountant is performing Du Pont Analysis for a charitable engineering organization. References for 3-step Du Pont formula are : (ROE) = (Net Income $) / (Equity $), where ROE is Return On Equity. (ROS) = (Net Income $) / (Sales $), where ROS is Return On Sales. (Asset Turnover) = (Sales $) / (Assets $). (Leverage) = (Assets $) / (Equity $). From the balance sheet and income statement, the company has Assets of $3753.19 this year and $3216.86 last year. Sales for this year is $2292.34. Let ROE = 0.37 and ROS = 0.21. (a) Calculate the Asset Turnover of the organization. (b) Find the value of the organizational Leverage. (c) Calculate the Net Income $ of the organization.
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