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Problem 1. Find the maximum and the minimum distance from the origin to the ellipse
x2 + xy + y2 = 3.
Hints: (i) Use x2 + y2 as your objective function; (ii) You can assume that the constraint qualification condition and the second order conditions are satisfied in this problem, as well as in problems 2 and 3.
Problem 2. Maximize f (x, y, z) = yz + xz subject to y2 + z2 = 1 and xz = 3.
Problem 3. (a) Maximize f (x, y) = x2 + y2 subject to 2x + y ≤ 2, x ≥ 0 and y ≥ 0.
(b) Use the Envelope Theorem to estimate the maximal value of the objective function in part
(a) when the first constraint is changed to 2x+ 9/8y ≤ 2, the second constraint is changed to x ≥ 0.1,and the third to y ≥ -0.1.
Prove that a simple graph is connected if and only if it has a spanning tree. Ans: First assume that a simple graph G has a spanning tree T. T consists of every node of G.
(x+3)>3
1+1
Compare and contrast African immigrants with our immigrant groups? How are they different? What are the implications of these differences for their adjustment to the larger society
Homework help???
Consider a database whose universe is a finite set of vertices V and whose unique relation .E is binary and encodes the edges of an undirected (resp., directed) graph G: (V, E). Ea
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
Use green's theorem to computer the integral F . dr where F = ( y^2 + x, y^2 + y) and c is bounded below the curve y= - cos(x),, above by y = sin(x) to the left by x=0 and to the r
#quesSuppose we have a stick of length L. We break it once at some point X ~ Unif(0;L). Then we break it again at some point Y ~ Unif(0;X). Use the law of iterated expectation to c
without using a calculator how would you know is cos theta(20) is greater than cos theta (35)
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