please please please anwer super super fast its really important and urgent also please try to write clear and neatthis is not a graded question [20] (2)GIVEN: a>0, The surface, Q2: x+y+z = a, x ≥ 0, y ≥ 0, z ≥ 0.Consider the 3D field: F= (x, 2x, 3x)Orient the surface so that its normal vector has a positive z- component.FIND: The flux of F through 2 with the given orientation.Parameterization of D:D = PROJ, &:D Qxy= {(²₂₂) |0 ≤ y ≤a-x}$(x,y)=(x, y, a-x-y)⇒= (1,0,-1) canonical*y = (0,1,-1)⇒ x = (1,1,1)=parameterizationAaJA = (a,0,0)B = (0, a, 0)C = (0,0,a)F = (x, 2x, 3x)D=ABy=a-xaFLUX = √ F•áŠ = √ (2,22,32)-(1,1,1) dedy= √₂ 6x dx dy = 65 ª 1 * x² dydбуaa6 ["²x (2-x) b = 6 √ ² x ² + ax de6 [ - ‡ a³ + + a²³²]3Y [10] (5): x + y + z = a, x ≥ 0, y ≥ 0, z ≥ 0.(x + y, z, y - x)Orient the surface so that its normal vector to it has a positive z - component.GIVEN: a>0, The surface,Consider the 3D field: FHere is the canonical parameterization of Q:Þ:D →→ Ω, Φ(x, y)(x, y, a- x - y)where D = x, y==0 ≤ x ≤ a0 ≤ y ≤a-FIND: The flux of F throughwith the given orientation.AXΩAdd extrapages, asneeded.A = (a,0,0)B = (0,a,0)C = (0,0, a)BF = (x+y, z, y - x)Y

Answered: Image /qna-images/answer/bbede9e8-266f-4bdb-af23-08a2381127b8.jpg

GIVEN: a>0, The surface, 2: x+y+z = a, x ≥ 0, y ≥ 0, z ≥ 0. Consider the 3D field: F (x+y, z, y - x) Orient the surface so that its normal vector to it has a positive z- component. Here is the canonical parameterization of 22: D:D, P(x, y) = (x, y, a- x - y) where D = {(x, y) = 0 ≤ x ≤ a 0 ≤ y ≤ a- FIND: The flux of F through 2 with the given orientation. A X Ω F = Add extra pages, as needed. A = (a,0,0) B=(0, a,0) C = (0,0,a) B (x + y, z, y - x) Y

GIVEN: a>0, The surface, 2: x+y+z = a, x ≥ 0, y ≥ 0, z ≥ 0. Consider the 3D field: F (x+y, z, y - x) Orient the surface so that its normal vector to it has a positive z- component. Here is the canonical parameterization of 22: D:D, P(x, y) = (x, y, a- x - y) where D = {(x, y) = 0 ≤ x ≤ a 0 ≤ y ≤ a- FIND: The flux of F through 2 with the given orientation. A X Ω F = Add extra pages, as needed. A = (a,0,0) B=(0, a,0) C = (0,0,a) B (x + y, z, y - x) Y

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section: Chapter Questions

Problem 18T

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