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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."
out of 500 randomly chosen grocery shoppers, 320 like cheerios and 380 like total. 275 of the grocery shoppers liked both cheerios and total.
Barney was charged $123.00 for 3 days and 300 miles, while Mary was charged $216.00 for 5 days and 600 miles. What does Best Rental charge per day, for mileage?
A spherical balloon is inflated with a gas at the rate of 500 cm3/min. How fast is the radius of the balloon increasing at the instant the radius is 30 cm?
George and Harry Haygood are building contractors
an open-top box is to be made by cutting small congruent squares from corners of a 30 x 30 sheet and bending it up to the sides. how large should the squares cut from the corners to make the box hold as much as possible?
Find an example online of a graph used in real life. Please provide the link to the web page by using the link button in the editor.
in analyzing hits by v-1 buzz bombs in world war ii south london was subdivided into regions each with an area of
a triangular pyramid begins with these coordinatesp-1 2 0y2 3 0r-3 4 0a-2 1 5the pyramid is then reflected over the
In what direction should the plane head to end up going due east? What is the airplane's speed relative to the ground?
a woman owns a small cash-only business in a state that requires her to charge 7 sales tax on each item she sells. at
describe how quadratic equations are important to a basketball player or a sniper. And give a real world example.
The componets of v=180i+450j represent the respective number of one-day and three day videos rented from a video store. the componets of w=3i+2j represent the prices to rent the one day and three day videos,respectively
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