Find the outward flux of F= (x')i+(y²)}+(z²)k across the boundary of the region D, where D is the cube cut from the first octant by the planes x =1, y=1, and z=1.

Q: Let S be the closed cylinder bounded by the surface r2 + 2² = 4, and the planes y = 1 and y = 4. Use…

A: Let's find.

Q: find the outward flux of F across the boundary of D. F =-2x i - 3y j + z k D: The upper region cut…

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Q: use the Divergence Theorem to find the outward flux of F across the boundary of the region F = (5x3…

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Q: Let F(x, y) = 3 i + j + 2k, and let S be a square whose side lengths are 3, parallel to the…

A: Flux is F.dA Where F is the Field and A is the area

Q: Compute the flux of F = 3(x + z)i +j+ 3zk through the surface S given by y = x2 + z2, with 0 0, z 2…

A: flux is determined as shown below

Q: Find the flux F(x, y, z) = (xy²,x²y, ln(x + y)) directed outwards through the surface of the solid…

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Q: 17. Use the Divergence Theorem to find the outward flux across the boundary of the region D where F…

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Q: Find the flux of F(x,y,z) = sin(xyz) i+ xy j + ze*/5 k across the part of the cylinder y? + 2 z? = 4…

A: According to question,Fx,y,z= sin xyzi +xy j + z ex5 k,equation of cylinder,y2 + 2z2 =4planes, x = 1…

Q: The region W lies between the spheres x2+y2+z2=1 and x2+y2+z2=9 and within the cone z=x2+y2−−−−−−√…

A: Given: The region W lies between the spheres       x2 + y2 + z2 = 1 and x2 + y2 + z2 =9 with in the…

Q: Find the center of mass and the moment of inertia about the x-axis of a thin rectangular plate…

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Q: Consider a thin plate of length L and width W governed by the heat equation Uf = k(uxx + uyy) for u…

A: Let  U(x,y,t)=X(x) Y(y) T(t)ut=k(uxx+uyy)T'kT=X''X+Y''Y     ......(1) Here T is function of t. and…

Q: Determine the centroid of the lamina bounded by y=sin x, y= cos x and x= 0 in the interval 0,

A: Plot the curve and find the area of the area enclosed by the curves. The shaded region is the area…

Q: Compute the flux of F = 3(x + z)i +j+3zk through the surface S given by y = x2 + z2, with 0 0, z >…

A: From given data we see that the surface is oriented towards xz plane,  Hence,  d→s=dxdzj→

Q: use the Divergence Theorem to find the outward flux of F across the boundary of the region F = x2i -…

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Q: Let v = zk be the velocity field (in meters per second) of a fluid in R3. Calculate the flow rate…

A: Concept: Similar to circle sphere is a two dimensional space where the set of points that are at the…

Q: Find the x coordinate of the centroid of the solid formed in the first octant bounded above by…

A: Given the solid E is bounded by z=1-y2,x=1,x+y=3 in the first octant. Find the x coordinate of the…

Q: Use Divergence Theorem to evaluate SF. Nds and find the outward flux of F(x,y,z) = xi+y²j−zk through…

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Q: Compute the line integral of the scalar function f(x,y,z)=2x2+8zf(x,y,z)=2x^2+8z over the curve…

A: To find the line integral, obtain dS as follows.

Q: Let S be the closed cylinder bounded by the surface x2 + z2 = 4, and the planes y =1 and y = 4. Use…

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Q: Calculate the scalar line Integral where the function is f(x,y)= 1 / x²+y²+1 and the curve is the…

A: We have given function fx,y=1x2+y2+1 and the curve joining the point 0,0 1,0 1,1 0,1. Let A0,0,…

Q: Find the volume of the solid bounded from above by the surface z = (64 − 4x^2 − 9y^2)^(1/3) and from…

A: To find - Find the volume of the solid bounded from above by the surface z = 64 - 4x2 - 9y213 and…

Q: Find the outward flux of F through S. F-Ñ dS where F(z, y, z) = -3zî+y³j+yk, and S is the surface of…

A: The general form of a vector valued function in three dimensions is given by F→=F1i^+F2j^+F3k^,…

Q: Use cylindrical coordinates to evaluate the triple integral ∫∫∫E √(x2+y2)dV, where E is the solid…

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Q: Compute the flux of F = (5(z + 2), 5, 52) through the surface S given by y = ² + 2, with 0 0, z 2 0,…

A: We have to find flux.

Q: use a parametrization to find the flux ∬S F . n dδacross the surface in the specified direction. F =…

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Q: Use Divergence theorem to find the outward flux of F = 2xz i - 2xy j – z2 k across the boundary of…

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Q: 16. Use the Divergence Theorem to find the outward flux across the boundary of the region D where F…

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Q: Compute the flux of F = 3(x + z)i +j+ 3zk through the surface S given by y = x2 + z2, with 0 <y<9, x…

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Q: Evaluate the surface integral /F- ds for the veetor field F = (y. -r, 2:), where S is the hemisphere…

A: Surface integration

Q: Find the counterclockwise circulation and the outward flux of thefield F = (-sin y)i + (x cos y)j…

A: Use tangential form of Green's Theorem to find the counterclockwise circulation. Counterclockwise…

Q: Among all rectangular regions 0&lt;=x &lt;=a, 0&lt;=y&lt;=b, find the one for which the total…

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Q: Use Green's Theorem to calculate the work done by the force F on a particle that is moving…

A: Given ,                                                                             F(x,y) =…

Q: 7. Find the flux of F(x, y, z) = x î+ y ĵ+ z² k across the sphere of radius 1 centered at the origin…

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Q: 5/ MATH

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Q: 5. Find the flux of F (x,y,z) = y cos(z)i-yx sin(x) j+ xy³k through the outward oriented cube of…

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Q: „ Compute the flux of F = xi + yj + zk through the curved surface of the cylinder x? + y² = 1…

A: Consider the vector field:

Q: Solve the problem. 15) Find the centroid of the solid with constant density a enclosed between the…

A: Given :- The centroid of the solid with constant density α enclosed between the sphere of radius 2…

Q: 17. Use the Divergence Theorem to find the outward flux across the boundary of the region D where F…

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Q: use divergence theorem to find the outward flux of f =2xzi-3xyj-z^2k across the boundary of the…

A: By divergence theorem

Q: Compute the scalar line integral xy ds where C is the part of the circle of radius 3, centered at…

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Q: Find the flux of F=(x, y, z) across the solid that is enclosed by the hemi = 0. Assume an outward or…

A: The Gauss Divergence Theorem states that the volume integral of the divergence of a vector field A…

Q: Find the flux of F(x, y, 2) = (r, y, 2) across the surface o which is the surface of the solid…

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Q: 16. Use the Divergence Theorem to find the outward flux across the boundary of the region D where F…

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Q: Find the flux of F(x,y,z) = (-x,-y, z³) , across S. Where S is the part of the cone z = /x² + y²…

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Q: Find the flux of F across S, where F(x, y, z) = xyi + y²j + zk and S is the part of the paraboloid z…

A: According to question given that F(x,yz,)=xyi^ + y2 j ^+z k^S is the part of the paraboloid z=x2+y2,…

Q: Use Divergence theorem to find the ouward flux of F = 2xz i - 3xy j – z2 k across the boundary of…

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Q: find the outward flux of F across the boundary of D. F = xz i + yz j + k D: The entire surface of…

A: Consider the given vector field. F = xz i + yz j + k

Q: find the outward flux of F across the boundary of D. F = (6x + y)i - (x + z)j + 4yz k D: The region…

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Q: Use Divergence theorem to find the ouward flux of F = 2xz i - 3xy j – z2 k across the boundary of…

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