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Example1 : Solve the subsequent system of equations. -2x 1 + x 2 - x 3 = 4 x 1 + 2x 2 + 3x 3 = 13 3x 1 + x 3 = -1 Solution The initial step is to write d
Parametric objective-function problems
what is the difference between North America''s part of the total population and Africa''s part
how do you divide fractions?
Bikes are on sale for 30% off the original price. What percent of the original price will the customer pay if he gets the bike at the sale price? The original price of the bike
Example of subtraction: Example: Subtract 78 from 136. Solution: 2 136 -78 ------ 58 While subtracting the units column, 6 - 8, a 10 that is b
advanteges of duality
Method to determine solution is absolute minimum/maximum value Let's spend a little time discussing some methods for determining if our solution is in fact the absolute minimum
f(x)+f(x+1/2) =1 f(x)=1-f(x+1/2) 0∫2f(x)dx=0∫21-f(x+1/2)dx 0∫2f(x)dx=2-0∫2f(x+1/2)dx take (x+1/2)=v dx=dv 0∫2f(v)dv=2-0∫2f(v)dv 2(0∫2f(v)dv)=2 0∫2f(v)dv=1 0∫2f(x)dx=1
Q. Describe the Laws of Sines? Ans. Up to now we have dealt exclusively with right triangles. The Law of Sines and the Law of Cosines are used to solve oblique triangles
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