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- Identify the roots of the DE from its auxiliary equation: y"" бу" + 11у' — 6у %3D 0 Select one: O a. Case 1 Real and Distinct Roots O b. Case 3 Complex and Distinct Roots O c. Case 4 Complex and Repeated Roots O d. Case 2 Real and Repeated RootsEvaluate: 1 dx 2(х — 1)2 Оа. 1 + C - 2(х-1) 1 + C Ob. 2x O c. --+C С. 1 d. + C 2(х-1)If z1 = (3,7) and 22 (5,-6), then 2122 is equal to what? A. (57, 17) В. (15, - 42) С. (15, 42) D. (57,-17)
- 12,,28 Simplify: V32r"y²z°.Pf of 2xy(-x² + y) + xe", what is ду If ду? Select one: 4ху — 2х3 + хеУ а. ду? 2x(-x² + 1) + xe" b. dy? = 2x + e ду? d. dy? 2x(-x² + 1) + e 4ху — 2х3 + еу е. = - ду?x+y b). Use the change of the variables u=5 and v= Mathematical verify using mathematica code also. thanks y-x √2 to evaluate 00 -dxdy.. [Verify using 1-xy
- SIMPLIFY THE EXPRESSION AND RATIONALIZE THE DENOMINATOR A) V-64 2V 2 B) V16a®b 2 C) x'y- ,12 V 5x? 125x D) 3x'"y³ 9x? 3 E) 8x3 4x 2x y? F) V5xy V15x³y SrV 31. Simplify: a. (x2y)2 / xy = xy5 b. x2 X y4 X x3 / (2x2)2 c. (3x2y2)2 X x2y2 d. (2x3y)3 / x2yWhich set of coordinates follows these two rules? • X-coordinate: Start with 4 and add 4 to each term. • y-coordinate: Start with 4 and multiply each term by 2. @ (4, 4), (8, 8), (12, 16) ® (4, 4), (8, 8), (16, 16) ©(4, 4), (6, 16), (8, 64) O (4, 4), (8, 6), (12, 8)