Interpret the results of the optimization problem.

Substitute (y−2)2−4 ( y - 2 ) 2 - 4 for y2−4y y 2 - 4 y in the equation x2+y2−2x−4y=4 x 2 + y 2 - 2 x - 4 y = 4 . ) Volume = √ √ S (3-3x-241) dy dx. Y=2-2x. = S (3Y-3xY~ ~²) | x - - xxx. O. =S (3x²-6x+3) dx. (x³-3x²+3x) 16 = 1 dx. X. 2. 07. Y=x3 z = 1/2 (6-6x-3×). S = 3-3x- ... May 31, 2021 ... ∇f(x, y) = 2x + 4y − 2, 4x + 6y2 + 12y − 20. We obtain now the Hessian matrix. H f(x, y) = 2. 4. 4 12y + 12. We have D1 = 2 > 0, D2 =8+24y. So ... Feb 20, 2014 ... 2x + 2y = 7, x^2 - 4y^2 = 8 solve by simultaneous equation. 2 Answers By Expert Tutors By: Best Newest Oldest 1 Answer. Alan P. Dec 5, 2015. (x−1)2+(y−(−2))2=(√6) ... (xA+yB)·C = (x+5y, x+2y,−x−4y)·(2,2,3) = 2x+ 10y +2x+4y −3x−12y = x+2y. Therefore (xA + yB) · C = 0 if and only if x = −2y. This means that the vectors xA + ... Jan 14, 2024 ... Solution For Find the separate equations of the lines represented by the equation x^2 - 4y^2 - 2x + 4y + 0.Ans: x -2y -2 = 0, x -2y = 0. ... (x, y) = x2 + y2 − 2x − 4y is ~i +j. Solution: The direction of fastest change is in the direction of ∇f =< 2x−2, 2y−4 > . Therefore we want ∇f =< 2x−2, 2y −4 > ... ... x - y = -9 → y = x + 9. 5y + 4(7y - 31) ... x - 2(2) - z = -4 x + z = 0 x - z = 0. 2x = 0 x = 0. 0 + 2 + z = 2 z = 0. REF: 062311aii. 8 ANS: 2. 2x + 4y - 2z = 2. - ... ... y = tan(π/4 − ln x). (c) If sin xe−3x + 3y + dy dx. = 0, y(0) = 2, then y = e−3x cos x + e−3x. (Answer 15) y = p(x − 5)2 − 16. The solution is valid for all x < ...