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Consider two regions separated by the plane defined by f(r,y, )-2r 3y -4z1 as described in...
a) A concentration of a carbon monoxide in a tank is described by f(X,y,z) X2 + y2 + Z2. Based on Fick's Law, the d...
a) A concentration of a carbon monoxide in a tank is described by f(X,y,z) X2 + y2 + Z2. Based on Fick's Law, the diffusion happens in the direction of maximum decrease of concentration Point P is at (1, -2, 3) in the respective tank. Find a vector field to describe diffusion field that happens in the tank. 1. Determine a unit vector in the direction of diffusion at P. ii. Determine unit vector(s) in the direction of zero change...
Consider the vector field F(x, y, z) -(z,2x, 3y) and the surface z- /9 - x2 -y2 (an upper hemisph...
Consider the vector field F(x, y, z) -(z,2x, 3y) and the surface z- /9 - x2 -y2 (an upper hemisphere of radius 3). (a) Compute the flux of the curl of F across the surface (with upward pointing unit normal vector N). That is, compute actually do the surface integral here. V x F dS. Note: I want you to b) Use Stokes' theorem to compute the integral from part (a) as a circulation integral (c) Use Green's theorem (ie...
Consider the vector field F(x, y, z) = 8x^2 + 3y, −5x^2y − 4y^2, 6x^2 + 7y − 8 which is defined on all of double-struck R3, and let F be the rectangular solid region F = {(x, y, z) | 0 ≤ x ≤ a, 0 ≤ y...
Consider the vector field F(x, y, z) = 8x^2 + 3y, −5x^2y − 4y^2, 6x^2 + 7y − 8 which is defined on all of double-struck R3, and let F be the rectangular solid region F = {(x, y, z) | 0 ≤ x ≤ a, 0 ≤ y ≤ b, −1 ≤ z ≤ 1} where a > 0 and b > 0 are constants. Determine the values of a and b that will make the flux of F...
Vector field F = î 3y + ŷ (5 – 2x) + î (22 – 2)...
Vector field F = î 3y + ŷ (5 – 2x) + î (22 – 2) is given. Find: (e) The surface integral of the normal component of the curl of F over the open hemisphere x + y2 + z = 4 above the x-y plane.
rty. I 5. [16 pointsj Consider the function f(x, y,z) Let S denote the level surface consisting of all points in space such that f(,y,z)-4, and let P- (2,-2,1), which is on S. a) Calculate Vf. b) Det...
rty. I 5. [16 pointsj Consider the function f(x, y,z) Let S denote the level surface consisting of all points in space such that f(,y,z)-4, and let P- (2,-2,1), which is on S. a) Calculate Vf. b) Determine the maximum value of Daf(P), where u is any unit vector at P c) Find the angle between Vfp and PO, where O denotes the origin. d) Find an equation for the tangent plane to S at P
rty. I 5. [16...
(1 point) Let F(2, y, z) be a vector field, and let S be a closed...
(1 point) Let F(2, y, z) be a vector field, and let S be a closed surface. Also, let D be the region inside S. Which of the following describe the Divergence Theorem in words? Select all that apply. L A. The outward flux of F(x, y, z) across S equals the triple integral of the divergence of F(2, y, z) on D. IB. The outward flux of F(x, y, z) across S equals the surface integral of the divergence...
Could you please 1.question ЕЕ211 Electromagnetic Field Theory 1 Homework 2 Due by 12th of Nov,...
Could you please 1.question
ЕЕ211 Electromagnetic Field Theory 1 Homework 2 Due by 12th of Nov, 2018 at 5 PM ANTALYA BILIM UNIVERSITY Homework 2 Q1. Given three vectors A, B, and C A-a +2a, -3a, Find (a) unit vector along A. (b) IA -BI (c) A.B (d) the angle between vectors A and B (e) The vector component of A in the direction of C. (f) AxC (g) A. (x C) and (A x B).C (h) (A x B)...
Problem 1: Let F(, y,) be a function given by F(, y, z) (r2+y)e. Let S be the surface in R given ...
Problem 1: Let F(, y,) be a function given by F(, y, z) (r2+y)e. Let S be the surface in R given by the equation Fr, y, 2) 2. (a) Find an equation of the tangent plane to the surface S at the point p(-1,1,0) (b)Find the directional derivative -1,1,0) of F(,y,2) in the direction of the unit vector u = (ui, t», t's) at the point p(-1,1,0) - In what direction is this derivative maximal? In what direction is...
Vector a lies in the yz plane 49.0° from the positive direction of the y axis,...
Vector a lies in the yz plane 49.0° from the positive direction of the y axis, has a positive component, and has magnitude 5.60 m. Vector lies in the xz plane 47.0° from the (d) the positive direction of the x axis, has a positive 2 component, and has magnitude 1.60 m. Find (a) 8-5.(b) the x-component of a x. (e) they component of axb.co z-component of a xő, and (c) the angle between a 6 and (a) Number Units...
The axis of a smooth fixed ciular cylinder of radius R is horizontal. A particle of mass m is att...
The axis of a smooth fixed ciular cylinder of radius R is horizontal. A particle of mass m is attached to a model string and is initially at rest level with the cre of the cylinder with the string draped over the top, whee t slids without frictian as if on a model pulley, s shown in the diagram below. A constant force P of magnitude P pulls the model string downwards. Let 0 denote the angle subtended at the...
a) A concentration of a carbon monoxide in a tank is described by f(X,y,z) X2 + y2 + Z2. Based on Fick's Law, the diffusion happens in the direction of maximum decrease of concentration Point P is at (1, -2, 3) in the respective tank. Find a vector field to describe diffusion field that happens in the tank. 1. Determine a unit vector in the direction of diffusion at P. ii. Determine unit vector(s) in the direction of zero change...
Consider the vector field F(x, y, z) -(z,2x, 3y) and the surface z- /9 - x2 -y2 (an upper hemisphere of radius 3). (a) Compute the flux of the curl of F across the surface (with upward pointing unit normal vector N). That is, compute actually do the surface integral here. V x F dS. Note: I want you to b) Use Stokes' theorem to compute the integral from part (a) as a circulation integral (c) Use Green's theorem (ie...
Vector field F = î 3y + ŷ (5 – 2x) + î (22 – 2) is given. Find: (e) The surface integral of the normal component of the curl of F over the open hemisphere x + y2 + z = 4 above the x-y plane.
rty. I 5. [16 pointsj Consider the function f(x, y,z) Let S denote the level surface consisting of all points in space such that f(,y,z)-4, and let P- (2,-2,1), which is on S. a) Calculate Vf. b) Determine the maximum value of Daf(P), where u is any unit vector at P c) Find the angle between Vfp and PO, where O denotes the origin. d) Find an equation for the tangent plane to S at P
rty. I 5. [16...
(1 point) Let F(2, y, z) be a vector field, and let S be a closed surface. Also, let D be the region inside S. Which of the following describe the Divergence Theorem in words? Select all that apply. L A. The outward flux of F(x, y, z) across S equals the triple integral of the divergence of F(2, y, z) on D. IB. The outward flux of F(x, y, z) across S equals the surface integral of the divergence...
Could you please 1.question
ЕЕ211 Electromagnetic Field Theory 1 Homework 2 Due by 12th of Nov, 2018 at 5 PM ANTALYA BILIM UNIVERSITY Homework 2 Q1. Given three vectors A, B, and C A-a +2a, -3a, Find (a) unit vector along A. (b) IA -BI (c) A.B (d) the angle between vectors A and B (e) The vector component of A in the direction of C. (f) AxC (g) A. (x C) and (A x B).C (h) (A x B)...
Problem 1: Let F(, y,) be a function given by F(, y, z) (r2+y)e. Let S be the surface in R given by the equation Fr, y, 2) 2. (a) Find an equation of the tangent plane to the surface S at the point p(-1,1,0) (b)Find the directional derivative -1,1,0) of F(,y,2) in the direction of the unit vector u = (ui, t», t's) at the point p(-1,1,0) - In what direction is this derivative maximal? In what direction is...
Vector a lies in the yz plane 49.0° from the positive direction of the y axis, has a positive component, and has magnitude 5.60 m. Vector lies in the xz plane 47.0° from the (d) the positive direction of the x axis, has a positive 2 component, and has magnitude 1.60 m. Find (a) 8-5.(b) the x-component of a x. (e) they component of axb.co z-component of a xő, and (c) the angle between a 6 and (a) Number Units...
The axis of a smooth fixed ciular cylinder of radius R is horizontal. A particle of mass m is attached to a model string and is initially at rest level with the cre of the cylinder with the string draped over the top, whee t slids without frictian as if on a model pulley, s shown in the diagram below. A constant force P of magnitude P pulls the model string downwards. Let 0 denote the angle subtended at the...
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