use Green's Thearum. to fina the counterclockwise Circulation. and outward Flux for the flela F and curve C ° i 3. + 2xt yex *..... F=3X y (0,0) .......... **. ...
Q: Let F = Use Stokes' Theorem to evaluate · dī, where C is the curve of intersection of the parabolic…
A: To find the curl , ∇×F=i^j^k^∂∂x∂∂y∂∂zxy5z7y=i^7-5-j^0-0+k^0-x=2i^-xk^ To find the normal vector,…
Q: If KN=2x+1 and NJ=3x+5, what value of x makes point N the centroid? K, J M
A: (1). If in the given triangle N is the centroid then the point N divides the line HL, JK and LM in…
Q: Let C be the curve that consists of 4 straight intervals, beginning at (0, 0, 0) , going to (5, 2,…
A: Consider the given: F=8x+6y+3z+yz ,8x+16y+3z+xz,2x+3y+6z+xy and the points:(0,0,0),(5,2,2),(8,5,6)…
Q: Given the space curve r(t) = (t, 2e", e²²), find the tangential and normal components of…
A: The tangential component of acceleration can be found by using the formula r'(t).r''(t)r'(t) The…
Q: Let F = %3| Use Stokes' Theorem to evaluate curlF · dS , where S is the hemisphere x? + y? + z² =…
A:
Q: Suppose F(x, y) = (4x – 3y)i + 4xj and C is the counter-clockwise oriented sector of a circle…
A:
Q: For which regions of flow is the Laplace equation ∇-›2? = 0 applicable? (a) Irrotational (b)…
A:
Q: Let S be the cylinder x +y a, 0szsh, together with its top, x +y sa, z=h. Let F= -7yi + 7xj + 7x k.…
A: Given data: S is the cylinder, with its top x2+y2≤a and height0≤z≤h. Also Given a vector F→ Such…
Q: Let F = < rY, 3z, 4y Use Stokes' Theorem to evaluate | F . dī, where C is the curve of intersection…
A: Here we have, F→=xy, 3z, 4y Using the stoke theorem, we have to evaluate the ∫CF→·dr→=? Where C is…
Q: Use the divergence theorem to find the outward flux of F across the boundary of the region D. F=x'i-…
A:
Q: Use Stokes' theorem to evaluate Ĝ - dĩ, vhere Ĝ(1, Y, 2) = (2r, y,0) and D is any closed curve.
A:
Q: use the Laplace frans forme to solve U - U = 100 u (Xi0) = ut (Xio) =uCoit) %3D %3D limu( X; t ) =0,…
A: The partial differential equation given to us is as follows: utt-uxx=100, x>0, t>0 With the…
Q: Calculate the arc length of the following vector function. E(1) = 4 In i+j+ 4t k; 1sts2.
A:
Q: Let F: = . Use Stokes' Theorem to evaluate curlF · dS, where S consists of the top and the four…
A:
Q: Show that ¥(x,t)= Asin(wt+kx) describes a wave motion
A: Given: ψx,t=Asinwt+kx
Q: Suppose F(r, y) = (2x – 2y)i + 3xj and C is the counter-clockwise oriented sector of a circle…
A:
Q: Find the center of mass, the moment of inertia about the coordinate axes, and the polar moment of…
A:
Q: Let F = 0, oriented upwards
A: Stokes theorem
Q: Let F = . Use Stokes' Theorem to evaluate curlF · dS , where S is the hemisphere x? + y? + z2 = 9,…
A: Given that, F=x2eyz,xexz,z2exy Given hemisphere that S:x2+y2+z2=4,z≥0 From stoke's theorem, ∬Scurl…
Q: Use Stokes' Theorem to evaluate curl F· dS. F(x, y, z) = zeYi + x cos(y)j + xz sin(y)k, S is the…
A:
Q: Let F(z, y, 2) = 12?ri + (ty + tan(z))j + (1z?z+ 4y?)k. Use the Divergence Theorem to evaluate f, F…
A: We must apply the Divergence theorem on a closed solid, but the surface S is not closed (it is just…
Q: Let F = . Use Stokes' Theorem to evaluate / curlF · d5, where S is the hemisphere x² + y² + z² =…
A:
Q: Compute the flux of F= xi+yj+ z*k across the cone z =Vx2 + y? , 0szs1, in the downward direction.…
A: We have to find the flux in the downward direction. Let us assume that x=rcosθ, y=rsinθ, z=r Then…
Q: Given the force field F, find the work required to move an object on the given oriented curve r(t).…
A:
Q: Let F = Use Stokes' Theorem to evaluate / F. dī, where Cis the curve of intersection of the…
A:
Q: A. From the Laplace table, determine F(s). 4. f(t) = e-3t(t – 2)20 %3D
A:
Q: Find the outward flux across the domain D xi + yj + zk x2 +y? + z? F(x,v,z) = across the sphere x2…
A:
Q: S,F•dr, and C is the triangle, with Use Stokes Theorem to evaluate where F(x,y; =) = (x+ y² )i+ (vy+…
A: Given: Fx,y,z=(x+y2)i+y+z2j+z+x2k and C is the triangle with vertices 1,0,0 ,0,1,0 and 0,0,1 We know…
Q: Suppose F(2, y) = (2x – 4y)i + 5æj and C is the counter-clockwise oriented sector of a circle…
A: The circulation of a vector field F→ around the curve C is evaluated by finding the value of the…
Q: Let F = %3D So Use Stokes' Theorem to evaluate F · dī, where C is the curve of intersection of the…
A: Here, the given function is F=xy,5z,4y To use Stroke's theorem: ∫CF·dr=∫∫S∇×F·N^ dA And,…
Q: :) Use Stokes' theorem to evaluate RF dr where C F = z?i + yj + xk and C is the triangle with…
A:
Q: Use the Divergence Theorem to calculate the outward flux of F = (r3 + y, y + z3, z3 + 23) across S:…
A:
Q: Use the divergence theorem to find the outward flux of F across the boundary of the region D. F=x*i-…
A:
Q: 2) Given vector Á = r?cos²Øâ, + zsinøâg, and function f = r?cosØ + z, find the followings: a) Div.…
A:
Q: Let F < ryz, ry, r'yz Use Stokes' Theorem to evaluate curlF dS, where S consists of the top and the…
A: The given surface is a cube, where the bottom face is not considered. The surface in question has 4…
Q: The work done by the force F = in the displacement along the path C: r(t)=from the point (1,0,0) to…
A: To find the work done by a force
Q: Let F . F. dr, where Use Stokes' Theorem to evaluate C is the curve of intersection of the…
A: The given vector function: F→=<xy,2z,3y> To find ∫CF→.dr by using Stokes theorem. The Formula…
Q: Let F = . curlF dS, where Use Stokes' Theorem to evaluate S S is the hemisphere a + y? + z² = 16, z…
A: Given that F=x2eyz,xexz,z2exy Then S is the hemisphere x2+y2+z2=16 The objective is to find the…
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: Use Stokes' Theorem to find m # 0 satisfying F · dr = -5, whereF(r,y, z) = (3yx² + z³, y², 4yx²) e C…
A: Given:
Q: Suppose F(x, y) = (3x – 4y)i + 2xj and C is the counter-clockwise oriented sector of a circle…
A: Suppose F(x,y) = (3x-4y)i + 2xj and C is the counter-clockwise oriented sector of a circle centered…
Q: Let F = . Use Stokes' Theorem to evaluate / curlF · d§, where S is the hemisphere a? + y? + z? 16,…
A: Given function is F=x2eyzi+xexzj+z2exyk (i) S is the hemisphere x2+y2+z2=16 , z≥0 oriented…
Q: Use the Divergence Theorem to find the flux of F accross S; that is calculate LlF• nds where F(x, y,…
A: Topic : vector calculus
Q: (a) Consider the flow i (Vr, Vy) = (y², x). Determine the circulation T = ū • dl about the square…
A:
Q: Let S be the cylinder x² + y² =a²2, 0≤zsh, together with its top, x² + y² sa², z = h. Let F = -7yi +…
A: Given : Surface S is the cylinder x2+y2=a2, 0≤z≤h, together with its top, x2+y2≤a2, z=h and F→=-7y…
Q: fund the laplace of Cos it CoS Bt dt
A:
Q: Use Stokes' Theorem to evaluate |/. CurlF dS, where F(r, y, 2) = xyzi + xj + e" cos zk and S is the…
A:
Q: 'Use Stokes' Theorem to compute | 1 F. dr where C is the curve where the cylinder a? + y? = 1…
A:
Q: Calculate the circulation of the flow v=-8xy i+4y j around the triangle with vertices (0, 0), (3,…
A: According to our policy, we are supposed to answer the first question (question2). By using the…
Q: Use Stokes' Theorem to evaluate curl F. ds. F(x, y, z) = xyzi + xyj + x²yzk, S consists of the top…
A: The given problem is to evaluate the surface integral using stokes theorem where S is the surface of…
Step by step
Solved in 3 steps with 3 images
- Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?1. (Section 17.7) Use Stokes’ Theorem to calculate the work done by −→F (x, y, z) = ex2ˆı − 2xzˆj + xˆk in moving a particle aroundthe closed path determined by the intersection of positively oriented surface S : x + 4y + 2z = 4 and the coordinate planes.Use Gauss's law to find the charge enclosed by the cube with vertices (±1,±1,±1) if the electric field is E(x,y,z)=5xi+1yj+2zk.
- You are now allowed to assume that the half-planes determined by the line with the equation ax+by +c = 0 correspond to the points (x, y) so that ax + by + c < 0 and ax + by + c > 0, respectively. Usingthis, show that axiom B4(i) holds. (Hint. Suppose (q, r) and (s, t) are on the same side of the given lineand that (s, t) and (u, v) are on the same side of the given line. en construct the parametrized linethrough (q, r) and (u, v). Consider the mappingλ γ7→ a(q − qλ + uλ) + b(r − rλ + vλ) + c and note that it is continuous and either increasing or decreasing. Use this fact to show that, for everyλ, γ(λ) > 0 or γ(λ) < 0, depending on which half-plane the points are on.)A point moves along the curve of intersection of the paraboloid z=x^2+5y^2 and the plane x=3. At what rate is z changing with y when the point is at (3,-1,14)?Consider the spherical surface E with center at C= ( 4, 3, 2 ) and radius 4 . Let π be the tangent plane to E at the pointP=C+ 4u,where u is the reverse of the vector v = ( 4, 3, 4 ).If the general equation of π is given byπ:ax+y+cz=d, so the value of d is:
- Consider the curve C in R3 whose parameterization is given by: eq. in image If is there a point on C P( 3/2, 1/2, √2) A vector tangent to C in P corresponds to options in imageWhich of the following statements is correct?(a) The flux of curl(A) through every oriented surface is zero.(b) The flux of curl(A) through every closed, oriented surface is zero.For which regions of flow is the Laplace equation ∇-›2? = 0 applicable? (a) Irrotational (b) Inviscid (c) Boundary layer (d ) Wake (e) Creeping
- A mass m moves along the x-axis subject to an attractive force given by 19mx/2 and a retarding force given by , where x is its distance from the origin and is a constant. A driving force given by , where A is a constant, is applied to the particle along the x-axis. D)what is the Q value?Given vector valued function Q(t) = <t3+2, -2t3+1, -2t3+3> a. Reparametrize using arc length from point A(2,1,3) to increasing tb. if particle moved 8 units from A, what is the position of the particle
