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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.
Non Linear Relationships If the correlation coefficient and the scatter diagram do not indicate linear relationship, then the relationship may be nonlinear. Two such relations
If two vertices of an equilateral triangle are (0, 0) and (3, 0), find the third vertex. [Ans: 3/2 , 3/√ 3/2 or 3/2, -3√ 3/2] Ans: OA = OB = AB OA 2 = OB 2 = AB 2
f(x)=sin(x),All x belongs to [p/6, p]
uses of vector in daly life
The Stefan-Boltzmann law can be employed to estimate the rate of radiation of energy H from a surface of copper sphere with radius = 0.15 ±0.01 m, as in H=AesT^4 where H is in watt
There is a number. If the sum of digits is 14, and if 29 is subtracted from the number, the digits become equal. Find the number.
If sec A = x+i/x, prove that sec A + tan A = 2x or 1/2x
1. Find the slope and the y-intercept of the line whose equation is 5x + 6y = 7. 2. Find the equation of the line that is parallel to 2x + 5y = 7 and passes through the mid poin
who created math?
what is the answer
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