Question 27 – By using Excel or other easiest programming package, explain how I, the integral of sin x dx from 0 to 3.142 could be approximated using random number. Find the exact value of I.
Answer / kang chuen tat (malaysia - pen
Answer 27 : When Excel is used, let column A=RAND() and column B=ASIN(A1). Stretch the columns A and B vertically. The data is transferred to Word, then reinserted into column C and D in order to prevent changes in column A. By using the sort function from the lowest to highest, arrange the data in column C and D, followed by trapezoidal rule performance in column E=0.5*(C1+C2)*(D2-D1). The 2 times summation of values in column E will approximate I≈2 gradually as the random numbers used increase. Exact value of I = -2(-1) = 2 units. 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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ENGINEERING NUMERICAL METHODS - EXAMPLE 19.2 : For a mixture of benzene (B), toluene (T) and xylene (X), the equation applies where x for B, T and X will sum up to 1. The equation of x for each component is x = (L / V + 1) (F) / (L / V + K). The data of F for each component are : 0.5 for B, 0.35 for T, 0.15 for X. The data of K for each component are : 1.98 for B, 0.76 for T, 0.24 for X. When x for B + x for T + x for X = 1, find the values of (a) L / V; (b) x for each component of B, T, X respectively. You may use Excel program - Data : What-If-Analysis for Goal Seek to perform the iterative calculations.
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In a triple effect evaporator, the heat transfer for an evaporator is calculated as q = UA (TI – TF) where TI is the initial temperature, TF is the final temperature; U and A are constants. Given that heat transfer for the first evaporator : q(1) = UA (TI – TB); second evaporator : q(2) = UA (TB – TC); third evaporator : q(3) = UA (TC – TF) where q(x) is the heat transfer function, TB is the temperature of second inlet and TC is the temperature of third inlet, prove that the overall heat transfer Q = q(1) q(2) q(3) = UA (TI – TF).
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ACCOUNTING AND FINANCIAL ENGINEERING - EXAMPLE 34.29 : An engineering company that produces small biochemical tools applies Installment Sales Method in its accounting. Let A = Installment Sales, B = Cost of Installment Sales, C = Gross Profit, D = Gross Profit Ratio. In year 20X8, let A = $400, B = $250, C = $150. In year 20X9, let A = $450, B = $315, C = $135. If the value of D = 37.5 % in year 20X8 : (a) find the value of D for year 20X9; (b) calculate the realized gross profit = ED / 100, for year 20X8 when the cash collected from sales is E = $100.
types and working of compressor
ACCOUNTING AND FINANCIAL ENGINEERING - EXAMPLE 34.12 : You, as an engineer, buy a piece of biochemical instrument to start a servicing business. The instrument has a useful life of 3 years, that costs $60k. The instrumental business generates $100k per year. The labor costs $50k per year. The $60k new instrument depreciates in its value evenly up to 3 years, thereafter the old instrument needs to be replaced by another piece of new instrument. (i) In the first year of this engineering business : (a) what is its starting cash? (b) calculate the depreciation value of the instrument. (c) find the operating profit generated. (d) what is the capital expense of the business? (e) calculate the cash from operation. (f) calculate the ending cash. (ii) Based on the income statement of the business in the second year : (a) find the capital expense of the business. (b) what is its starting cash? (c) calculate the depreciation value of the instrument. (d) find the operating profit generated. (e) calculate the cash from operation. (f) calculate the ending cash.
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