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Consider the solution of following linear systemx1 - 2x2 + 3x3 = 2, 3x1 - 2x2 + x3 = 7, x1 + x2 - x3 = 1by an unconstrained optimisation method. Design a mathematical model for solving this problem and use any gradient method to ?nd an approximation to the solution of the system (either perform 3 iterations manually or use a Matlab/Mathematica program). Hint: minimise the distance between the right- and left-hand sides.
Description of Probability : Random Selection, Suppose there are two vendors and each provides 50% of the items. The lifetime (in days) of an item from the first vendor is Exp
find the intervals on which f(x) is increasing and decreasing and find the x- and y- coordinates of all the local extrema
boolean algebric mulitiple choice question
Prove that there cannot be a nilpotent group N generated by two elements with the property that every nilpotent group generated by two elements is a homomorphic image of N
Air is pumped into a spherical balloon, so the balloon expands. The volume of a sphere of radius R is . If the radius of the sphere after t seconds is 2t centimeters, at what rate is air being pumped in when t=5?
Minimizing the cost
A manufacturer produces cardboard boxes that are open at the top and sealed at the base. The base is rectangular and its length is double its width.
Find the two mean proportionals between two cubes guaranteed by Proposition VIII-12.
Let R(t) be the field of rational functions. Answer the following (with proofs): If we identify the rational numbers with a subset of R(t), what function corresponds to a given rational number r?
Write an equation that illustrates this situation. Use the same variables you used in Part a. c. Use elimination to determine how many houses are available in each floor plan. Explain how you arrived at your answer.
Find new estimates using ten rectangles in each case.
If a blueprint 1/4 inch equals 12 inches, what is the actual length in feet of a steel bar represented on the blue print by a line 3 3/8 inches long?
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