Let v(x, y, z) = (9x² + 5y²z)i + (2xz + 6y)j + (10x³y +62) k be the velocity field of a fluid, and let S be the outward- J oriented surface of the solid E = {(x, y, z) |0 ≤ x ≤ 4,0 ≤ y ≤ 5, 0≤ z ≤9}. Find the flux S across S. Enter an exact answer. Provide your answer below: Fluid flux = vds of the fluid

Q: Compute the flux of F = xi+yj+zk through the curved surface of the cylinder x² + y² = 1 bounded…

A: The given vector field is F→=xi+yj+zk. The goal is to evaluate the flux or surface integral of the…

Q: Find the flux of the vector field F(x, y, z) = [xy, yz, zx] through the cylinder x2+y2 <= 1, 0 <= z…

A: The given problem is to find the flux of the vector field through the given surface of the cylinder…

Q: Find the flux of the vector fleldF = (x – y*)i+ 4yj + x'k out of the rectangular solid [0, 1] x [1,…

A:

Q: II. Let S be the portion of the cylinder x² - 6x + z = 4, oriented by upward-slanting normal…

A:

Q: II. Let S be the portion of the cylinder x² - 6x + z = 4, oriented by upward-slanting normal…

A:

Q: Suppose the vector field v(x, y, z) = (4xy2, -4xz², 5x) represents the velocity field of a fluid.…

A:

Q: Find the flux through through the boundary of the rectangle 0 < x < 6,0 < y < 5 for fluid flowing…

A:

Q: Compute the upward flux of F across the surface defined by R(u,v) = where 0 ≤ u ≤ 2 and 0 ≤ v ≤ 1.

A: The given surface is Ru, v=&lt;2u, 3v, u2-v2&gt;.......(i), where 0≤u≤2 and 0≤v≤1 and F→x, y,…

Q: Find the flux of the vector field V(x, y, z) = 2xy²i+ 5x²yj + 3z³k out of the unit sphere. Flux =

A: Denote the unit sphere by S If the sphere is closed,  then the flux of v(x, y, z) out of S is given…

Q: Find the flux of F = 3zi + 5y? i+ 3x k out of the closed cone y = Væ2 + z2, with 0 < y < 1. flux =

A:

Q: Find the flux of G(x, y, z) = (xz)i+ (yz)j+(z²)k outward across the part of the sphere x² + y² +z² =…

A: Here, surface, S={(x,y,z): x2+y2+z2=9, and 1≤z≤2}. For z=1, we get x2+y2=8 and for z=2, we get…

Q: Find the flux of the vector field F(x, y, z) =(x)i+(y)j+(z)k through the surface S of the…

A:

Q: Find the outward flux of F = (4x +25y*,0,) 10z through the surface 25 4 9

A: Solution:-

Q: Find the work done when a particle moves in the force field 3x² i + (2xz-y)j + zk a) The straight…

A:

Q: Let S be the portion of the cylinder x² - 6x + z = 4, oriented by upward-slanting normal vectors,…

A: The given vector field is F = xy, 3xz2, yz. Our aim is to find the flux or surface integral of the…

Q: Let F = –9zi+ (xe"² – 2xe³) }+ 12 . Find ſg F ·dÃ, and let S be the portion of the plane 2x + 3z = 6…

A: The vector field is F→=-9zi→+xexz-2xex2j→+12k→ The equation of the plane is 2x+3z=6⇒ gx, y=6-2x3.…

Q: Suppose the vector field v(x, y, z) = (2z − 1) i + (−2y − 3) j+ (3z − 2) k represents the velocity…

A: The given problem is to find the circulation of the given vector field over the path C of triangle…

Q: b) F(x,y) represents a velocity field of a fluid over a surface S defined by z= 6-3x-2y. If the…

A: The flux over the surface S in the first octant is given by the following integral: Flux=∫SF⋅ndS…

Q: The velocity field for a flow is given by V = ut + vj + wk where u = 3x, y = -2y and w = 2z. Find…

A:

Q: Calculate the flux of the vector field F(x, y, z) = (5x + 9)ỉ through a disk of radius 3 centered at…

A:

Q: (x*z, 3 – 4xyz, xz") be the velocity field of a fluid. Compute the flux of v across the surface 16x?…

A: Use the Divergence Theorem to calculate the flux. Partial differentiate the flux and substitute the…