Operations Research : Applications and Algorithms
4th Edition
ISBN: 9780534380588
Author: Wayne L. Winston
Publisher: Brooks Cole
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Solve the following equations using Gaussian Elimination Method:
2x1 + 10x2 +6x3 = 4
x1 +x2 + 2x3 = -5
x1 + 5x2 +6x3=5
Q. Taylor Series expansion of sine for x is computed as follows:
sin x=x - x^3/3! + x^5/5! - x^7/7!+...
Let the value of x be 30, hence radian value for 30 degree is 0.52359
sin(0.52359) = 0.52359 - 0.52359^3/3! + 0.52359^5/5! - 0.52359^7/7!+ ...
(a)Write a function in c++ that takes value of x in degrees and returns the value of x in radians.
(b)Write a function in c++ that calculates and returns the factorial of a number.e.g. 3!=6
(c)Write a function in c++ that calculates and returns power of a number. e.g. 23=8.
(d)Use the above three functions to find the taylor expansion of sine for in degrees as given above.(Calculate first 3 terms)
Estimate the integral of f(x)=sin(x)/x between 0 and 1 using Simpson's 3/8 rule. Use n=12
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Operations Research : Applications and Algorithms
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- A discharge factor is a ratio which compares the mass flow rate at the end of a channel or nozzle to an ideal channel or nozzle. The discharge factor for flow through an open channel of parabolic cross-section is: K = 1.2 [V16x +1+ In(V16x² +1+4x)]³ 4x where x is the ratio of the maximum water depth to breadth of the channel at the top of the water. Determine the discharge factors for x in the range 0.45 to 0.90 in steps of 0.05. Script e C Reset I MATLAB Docume 1 %Give values for x: 2 3 %Solve for K: 4arrow_forwardQuestion 1 Use K-map to obtain the minimized sum of products form of the function f (x.y,z,w) = SEGMA (0,4,5,7,8,12,13,15) %3D A xy'+yw B x'y'+yw C zw'+yw zw+ywarrow_forwardUse the Gauss-Siedel method to approximate the solution of the following system of linear equations. (Hint: you can stop iteration when you get very close results in three decimal places.) 5x1 - 2x2 + 3x3 = -1 %3D -3x1 + 9x2 + x3 = 2 2x1- X2-7x3 = 3arrow_forward
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