Question 63 – Autocad computer program is used to draw a pipe that is used to transport natural gases for processing. Actual length of the pipe is 10 metres. The pipe has cross sectional area of circle in shape with measured circumference of s = 3 metres. (a) If 10 units are used to represent the actual length of the pipe in computerised engineering drawing, find the diameter of the pipe, d that will be shown in the engineering drawing. (b) If one unit in the program equals to 1 centimetre, find the scale used in the computer program.
Answer / kang chuen tat (malaysia - pen
Answer 63 – (a) s = 3.142 d, then d = s / 3.142 = 3 / 3.142 = 0.9548 metres. Since 10 units : 10 metres, then d = 0.9548 units. (b) 1 unit : 1 metre or 1 centimetre : 1 metre for engineering drawing : actual object, then 0.01 m : 1 m or 1 : 100 is the scale used. 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 34.18 : An investor is planning to purchase a small office for biochemical engineering consultancy on loan. In the calculation of the discount of payment in arrears, the following formula is used : y = 1 / (1 + r) ^ 1 + 1 / (1 + r) ^ 2 + 1 / (1 + r) ^ 3 + ... + 1 / (1 + r) ^ n where y = present value, r = interest rate of discount, n = number of payment, ^ = power used in certain computer languages for mathematics. (a) What is the meaning of : arrears? (b) Find a mathematical equation of y (1 + r). (c) Calculate, in less than 3 terms, y as a function of r and n.
ACCOUNTING AND FINANCIAL ENGINEERING - EXAMPLE 34.25 : (a) If an engineering company has a policy to maintain A % debt ratio, it will limit its total debt B, to A % of all company assets with total assets C. Find the value of A as a function of B and C. (b) An engineering consultancy that designs biochemical processing plants has a beginning balance in a bank of value D. The interest paid by the bank to the consultancy for the saving is E. The consultancy withdraws F amount of money from the bank to cover the project cost. (i) Calculate the end balance in a bank of the consultancy by using the symbols of D, E and F etc. (ii) Find the value of the principal due to E and F.
Question 101 - (a) Let | A > = (Aa Ab Ac), | B > = (Ba Bb Bc), | C > = (Ca Cb Cc). Find | A > + | C > - | B > in term of Aa, Ab, Ac, Ba, Bb, Bc, Ca, Cb and Cc. (b) Let d | E > = d (Ea Eb Ec) = (d Ea d Eb d Ec). If | E > = (6 7 8), find the value of 10 | E >.
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