A wire with density ρ(x, y, z) = 4x^2 + 4y^2 + 4z, occupies the intersection of the quadric surfaces x^2 + y^2 + z^2 = 5 and x^2 + y^2 + (z + 4)^2 = 25 in the first octant. Find the mass of the wi

Q: Find the centroid of the region bounded by the xy-plane, the cylinder x² + y² = 1369, and the +3=1.…

A: To find the centroid x, y ,z of the region bounded by the xy-plane, the cylinder x2+y2=1369 and the…

Q: Verify Stokes theorem ㅋ F² = (2x²-y)=² - y²²} - y²zk, where -y s is of and the the с upper sphere.…

A: Given: F=2x-yi-yz2j-y2zk where S is the upper half surface of sphere x2+y2+z2=1 and C is its…

Q: At what point on the ellipsoid x² + y² + 9z² = 1 is the tangent plane parallel to the plane x + 2y +…

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Q: The circular cross-section of the cylinder, y + z? = 4, can be obtained by cutting it along any…

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Q: Point masses of equal size are placed at the vertices of the triangle with coordinates (a, 0), (b,…

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Q: Q) S = the part of the paraboloid z = 10-x^2-y^2 above z = 1 F = [x^3, xy, z] Find the flux of F…

A: Step:-1 Given that S is part of paraboloid z=10-x2-y2 above z=1 Since, given that z=10-x2-y2 and…

Q: A solid in the first octant is bounded by the two spheres x^2 + y^2 + z^2 = 1 and x^2 + y^2 + z^2 =…

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Q: what is the formula to find centroid of triangular prism

A: Centroid of triangular prism is determined as shown below.

Q: Given F(x,y,z) = (xz-y, yz+x, z^2) (F: R^3->R^3) How do I find the flux of F through the sphere x^2…

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Q: 1) Consider the closed surface: z = h – x^2 – y^2, h>0, and z=0. Let F=(x^2,y^2,z^2). Find the flux…

A: Consider the given information: The given surface is  z=h-x2-y2,     h>0z=0 Also F→=x2, y2, z2 To…

Q: Consider the two-dimensional surface (“lamina”) bounded by y = e^x , y = 0, and x = 1 and whose…

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Q: Let T be the tetrahedron with vertices at the origin and (4,0,0), (0,5,0) and (0,0,2). A fluid flows…

A: Given, Vertices of the Tetrahedron are, , , and Velocity of fluid:

Q: usuƏp seu pin 100 kg/m and flowS With Ve Zk, whei y, and z are measurec in meters, and the…

A: Density of fluid=1100kg/m3 Flow with velocity v=xi^+yj^+kz^ To find the rate of flow outward through…

Q: Use the triple scalar product to find the volume of the parallelepiped having adjacent edges: u = i…

A: We have to find the volume of parallelepiped used the scalar triple product.…

Q: Find the mass of the solid bounded below by the circular paraboloid z=x^2+y^2 and above by the…

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Q: use triple scalar product to find the volume of the parallelpiped u= v= w=

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Q: Volume of the slice, then the Mass of the slice, the Force needed to lift it, and the Work needed to…

A: Volume: Volume of this slice = πr2dhMass:Mass of this slice = Volume of slice Density of waterForce…

Q: Find the most suitable system of coordinates to describe cylindrical shell of height 10 determined…

A: Given: 1) Determine the best coordinate system to describe a cylindrical shell with a height of 10,…

Q: The roof of the Monterrey Campus gymnasium has the shape of the hyperbolic paraboloid given by the…

A: Here we have to use directional derivative  Directional derivative of a function f(x,y,z) in the…

Q: 5. a) Find the volume of the solid bounded by the paraboloid z= 2(x? + y²) +3 and the cylinder x? +…

A: (a)  Find the volume of the solid bounded by the paraboloid z=2x2+y2+3 and the cylinder x2+y2=1 and…

Q: Calculate the volume of the sphere x^2 + y^2 + z^2 = a^2, using both spherical and cylindrical…

A: Given the equation of the sphere is       x2+y2+z2 = a2 ,where a is the radius of the sphere.

Q: 4- A thin plate with uniform density is placed in the region bounded by the circle 16 in the first…

A: given circle x2+y2=16 here r=4 area =14πr2                                            in first…

Q: - Cone o Find the volume of the solid region above the cone (zv3)" (z 2 0) and below the sphere x² +…

A: Using spherical coordinates,

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Q: Determine if F(n.y,z) =x+y+Z have a maximum/minimum value when m,9, z) lies on unit sphere:x'+yiZ=1•…

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Q: Find the mass of a wire segment if the density of the density of the wire is delta(x,y) = (x^2) +…

A: Let density of a wire segment is r(x,y) and its endpoints are (a.b) and (c,d). Then mass of this…

Q: A thin hubcap is modeled by the part S of the sphere x² + y² + z² = 4 that lies above the plane z =…

A: From the given information: