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Suppose that we are given a set of vectors {x(1),...,x(p)}, x(i) n, i = 1,...,p. Find the vector x n such that the average squared distance (norm) between and x(1),..., x(p), is minimized. Use the SOSC to prove that the vector found above is a strict local minimizer. How is related to the centroid (or center of gravity) of the given set of points {x(1),...,x(p)}?" "Prove the following generalization of the second-order sufficient condition: Theorem: Let Ω be a convex subset of n, f 2 a real-valued function on Ω, and x* a point in Ω. Suppose that there exists c , c > 0, such that for all feasible directions d at x* (d ≠ 0), the following hold: 1. d∇f(x*) ≥ 0. 2. dF(x*)d ≥ c||d||2. Then, x* is a strict local minimizer of f."
Find the height of the flag pole from the word problem and determine the total number of student-tickets sold from given word problem
a moving truck rental company has a total of 24 trucks in its lot. The trucks are either 4-wheelers or 18-wheelers. How many of each kind of truck does the company have if the total number of wheels is 138?
budget rental cars charges 35 a day plus 0.40 per mile. enterprise charges 20 a day plus 0.55 per mile. wirte and solve
90% confidence interval for the difference in average absorption time for the two drugs. Does it appear that one drug is absorbed faster than the other (at the 90% level)? Explain
Find all values of: tan^(-1) * (1 + i). The format for the final answer should be similar to this one:
Use the Newton-Raphson method of finding roots of equations to find the minimum number of computers that need to be sold to make a profit. Conduct three iterations to estimate the root of the above equations.
find the three qualitatively different regimes of growth from the given data.human populations are sometimes modeled by
If the fund earns interest at the rate of 10% year compounded quarterly, determine the size of each (equal) quarterly installment that should be deposited in the fund.
Using one of the tests for convergence (comparison, limit, integral, nth term, etc.), show whether the following series converges or diverges:
Deon races his bicycle for . A wheel of his bicycle turns times as the bicycle travels this distance. What is the diameter of the wheel?
Evaluate the Equation of the line which passes through the two given points and Write down the equations of the line described in the following questions
A car traveling at 40 ft/sec decelerates at a constant 8 feet per second squared. How many feet does the car travel before coming to a complete stop? I end up getting 200 but it comes up as incorrect.
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