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Let A⊆ ℜn be a convex set. LetMbe an n×n matrix and define,B:={Mx:x∈A}i.e.B is the set of all points in ℜn that can be obtained by selecting a point x∈Aand applying the transformationx→Mx.(a) Show that B is convex.(b) Suppose thatMis invertible and considerz∈A, hence Mz∈B.Show thatzis an extreme point ofAif and only if Mz is an extreme point of B
Find the dimensions of the enclosure that is most economical to construct.
We are learning Rolle, Lagrange, Fermat, Taylor Theorems in our Real Analysis class. We just finished continuity and are now studying differentiation.
A circle is the set of points that lie at a constant distance from one point, the center of the circle. This solution explains the equation of a circle with a center point that can exist anywhere on the coordinate plane.
A solution was prepared by mixing 4.00 ml 0.20 M NH3, 1.00 ml of 0.20 M HCl, and 5.00 ml of water. Calculate the concentration of NH3 and NH4+ in the final diluted solution.
snell's law total internal reflection between two materials is seen to occur if a critical angle of 60° is exceeded. if the index of refraction of the material that the light is entering is 1.98, find the index of refraction of the material in whi..
Pulsar also manufactures a series of 19-in color television sets. The quantity x of these sets demanded each week is related to the wholesale unit price p by the following function.
A formula is derived for the n-th derivative of a function that is a product of two other functions, f(x)=u(x).v(x). This formula is used to write down the n-th derivative of f(x) = e^x/(1 − x).
A reconnaissance airplane leaves its airport on the east coast of the United States and flies in a direction 85 degree. Because of bad weather, it returns to another airport 230 km due north of its home base.
Write a differential equation for A, the amount of caffeine in the body t hours after 7am and give the particular solution to this differential equation. How much caffeine is in the person's body at 5pm?
s to have an area of 230 in2 with 1 inch margins at the bottom and sides and a 3 inch margin at the top. What dimensions will give the largest printed area? (Give your answers correct to one decimal place.)
Use Taylor's expansion to arrange the function in ascending order - explain briefly how the Taylor expansions tell you what order the functions
For a given event, if the payoffs for alternatives 1, 2, and 3 (the only alternatives) are 50, 125, and -50 respectively, what is the regret associated with alternative 1?
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