ENGINEERING NUMERICAL METHODS - EXAMPLE 19.1 : Solve the simultaneous equation using simple Excel program : r + s - t = 7, 2r - s = 0, 3r + 2t = 15. Explain the use of functions of MINVERSE and MMULT together with the keyboard C (Ctrl) + S (Shift) + E (Enter).
ENGINEERING NUMERICAL METHODS - ANSWER 19.1 : By using Microsoft Excel, r = 3.22, s = 6.44, t = 2.67. MINVERSE, or =minverse is used to inverse the 3 x 3 matrix with constants of r, s, t. MMULT, or =mmult can be used to obtain the answers by functions (inversed matrix of 3 x 3, constants of 7 and 0 and 15). CSE is an Excel function to perform quick calculations for the cells. 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.
sir, kindly explain to me that how to calculate volume of torrispherical vessel which is used in pharma company ss reactor bottom dish volume. thank u.
For a heat exchanger, will the overall heat transfer coefficient increase along with an increase in lmtd (log mean temperature difference) around the unit?
QUANTUM BIOLOGY - EXAMPLE 33.8 : (a) Let ^ be the symbol of power where 1 ^ 2 = 1 x 1 = 1, 2 ^ 2 = 2 x 2 = 4. Let the number of electrons in a human body to be 10 ^ 28 = A, the number of all of the grains of sand on Earth planet to be 7 x (10 ^ 20) = B, the number of all the stars in the visible sky to be 8 x (10 ^ 3) = C. By assuming that every star in the visible sky has the same number of grains of sand as on Earth planet, prove by mathematical calculations that there are more electrons in one human body compared to the number of all of the grains of sand on the stars in the visible sky. (b) The incoming solar radiation to the Earth's surface is mainly from sun. Around 51 % of the radiation is absorbed by Earth's surface. Around 19 % is absorbed by atmosphere and clouds. In term of reflection, 4 % of the radiation is from surface of Earth, 6 % is reflected by atmosphere and the rest is reflected by clouds. Find the percentage of radiation absorbed by and reflected by biological beings on Earth, with reason for your response.
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Question 57 – There are 2 simultaneous equations : (A1) x + (B1) y = D1 and (A2) x + (B2) y = D2. (a) By using Excel program, find the values of x and y when A1 = 80, A2 = 150, B1 = 52, B2 = 100, D1 = 3.5 and D2 = 2.3. (b) Write the expression of Excel in the form of =MMULT(MINVERSE(W:X),Y:Z) in order to get the values of x and y. W, X, Y and Z may be A1, A2, B1, B2, D1 and D2.
COMPUTER PROGRAMMING FOR ENGINEERS - EXAMPLE 17.1 : 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.
How 'saltation velocity' is used in designing pneumatic conveying systems?
ENGINEERING DRAWING - EXAMPLE 18.1 : For a Vernier scale of representative fraction (RF) = 1 / 25, calculate the length of the scale for the reading up to 4 metres.
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