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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.
Five years ago a business borrowed $100,000 agreeing to repay the principal and all accumulated interest at 8% pa compounded quarterly, 8 years from the loan date. Two years after
4+8/56.75
Define A*B where: A = | 3 -3 6 | B = | 6 1 | | 0 4 2 | | 0 -5 |
273.98 convert it into BCD code?
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writ the equation that describes the motion of a point on the wheel that has a center of 4m off the ground, has radius of 15 cm, makes a full rotation every 10 seconds and starts a
how to find the minimum distance between any two particles which are in relative motion?
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How do I create an input-output table with the rule -12
Arc length Formula L = ∫ ds Where ds √ (1+ (dy/dx) 2 ) dx if y = f(x), a x b ds √ (1+ (dx/dy) 2 ) dy
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