Consider the velocity field F(x, y, z) = (r + 5/ỹ, y – 10r³, 2). Let S be the portionof 2x – y – 5z = 0 bounded by x = 4 in the first octant.(a) Find the flux of a fluid with velocity F as it flows through S with a positiveorientation.(b) Let C be the boundary of S. Set-up a surface integral equal toF. dR.

given F→x,y,z=x+5y , y-10x3 , z S: 2x-y-5z=0 bounded by x=4 in first octant (a) find the flux of a…

Answered: Consider the velocity field F(x, y, z)…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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F (x,y,z) =(2x+ cos(yz) )i +(xe^-z -y)j+ zk vector field D: x^2 + y^2 =4 , x+z=2 , z=0 Calculate the outward flux of the spatial region over the boundary surface S. (Draw the spatial body D)
Let z = g(x, y) = f(3 cos(xy), y + e") provided that f(3, 4) = 4, f1(3, 4) = 2, f2(3, 4) = 4. %3D i) Find g1 (0, 3). i) Find g2 (0, 3). i) Find the equation of the tangent plane to the surface z = f(3 cos(xy), y + e#') at the point (0, 3). Türkçe: f(3, 4) = 4, f1(3, 4) = 2, f2(3, 4) = 4 olmak üzere z = g(x, y) = f(3 cos(xy), y + e™") olsun. %3D %3D i) 91 (0, 3) değerini bulunuz. ii) 92 (0, 3) değerini bulunuz. iII) z = f(3 cos(ry), y + e#") yüzeyine (0, 3) noktasında teğet düzlemin denklemini bulunuz. O i) 12, ii) 4, iii) 12x + 4y - z = 8 i) 12, ii) 4, ii) 12x - 4y - z = 0 O i) 12, ii) 12, iii) 12x + 12y + z = 32 O i) 36, ii) 4, iii) 36x - 4y - z = -28 O i) -24, ii) 12, iii) -24x + 12y + z = -16 ) 36, i) -8, ii) 3бх -8y - z3D -16 O i) -12, ii) -8, iii) -12x -8y - z = 8 О) -24, i) 16, i) -24x + 16у -z%3D 8
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Consider a surface defined by F(x, Y, z) = 0 whose gradient is (cos(r2), z² e", 2ze"). The equation of the tangent plane to the surface at the point (-2,0, 1) is O x + y+ 2z -1 = 0 x - y – 2z + 4 = 0 x – z + 3 = 0 O x + y + 2z = 0
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Compute the flux of F = xi + yj + zk through just the curved surface of the cylinder ²2 + y² = 16 bounded below by the plane x + y + z = 1, above by the plane x + y + z = 4, and oriented away from the z-axis. flux =
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