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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.
a) Using Karnaugh map, show X': A'BC'D'+ ABC'D'+ A'BCD'+ ABCD' (b) If R is an equival
Mimi is filling a tennis ball can along with water. She wants to know the volume of the cylinder shaped can. Which formula will she use? The volume of a cylinder is π times the
find the value of 0 that makes cos 21 degrees = sin 0 statement true.
what is the tenths place
Take the carburizing of a steel bar to make a hard surface. To obtain the desired hardness, we require to control the diffusion of carbon into the surface and the phases obtained d
Example of Graphing Equations: Example: By using the above figure, find out the distance traveled if the average speed is 20 mph and the time traveled is 40 minutes. T
Example of line - Common Polar Coordinate Graphs Example: Graph θ = 3Π, r cos θ = 4 and r sin θ = -3 on similar axis system. Solution There actually isn't too much to
A number x is selected from the numbers 1,2,3 and then a second number y is randomly selected from the numbers 1,4,9. What is the probability that the product xy of the two
int*sin^-1 x dx=?
a sail has a spread of canvas as measured 12'',12'', 15'' and 9'' and it has 90 degrees. Find the area of one side of the sail
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