Let E be the solid region in the first octant that lies inside the sphere x^2+y^2 + (z − 1)^2 = 1. The density at (x, y, z) is given by function f(x, y, z) = (x^2 + y^2 +z ^2)3⁄2. Do the following. (a). Use cylindrical coordinates and the set-builder notation to describe E, and set up, but DO NOT evaluate, the integral(s) that represent the mass of E. (b). Repeat (a) using the Spherical Coordinates.

Q: 3. Find the area of the part of the surface x 2z + y° - 3, that lies above the triangle in the…

A: Given, x=2z+y2-3, i.e. z=12x-y2+3. As it is known that the surface area is given as,…

Q: Find a parametrization of the surface x³ + 15xy + z² : = 10 where x > 0 and use it to find the…

A:

Q: Where does the plane tangent to z = At z = 5exy at (7, 7, 5) meet the z-axis?

A: We find equation of tangent plane to z=5e^(x-y) at (7,7,5)

Q: Find the centroid of the region W lying above the sphere x² + y² + z² = 30 and below the paraboloid…

A: Given the sphere x2+y2+z2=30 and below the paraboloid z=18-x2-y2. And the density of δx, y, z=1.

Q: termine the solid bounded by the surfaces 9x2+4y2=30 and the plane 9x+4y−6z=0 in the first octan

A: The given solid is bounded by the surface 9x2+4y2=30 and the plane 9x+4y−6z=0 in the first octant.

Q: 3. Consider the parametric vector equation of a cone r(u, v) = u cos vi + u sin vj + uk with 1<u < 2…

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

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Q: Calculate F - dS where F = (e" sin y, e" cos y, yz²) S is the surface of the box bounded by the…

A: Given F¯={exsiny,excosy,yz2)

Q: Surface S is the portion of the cylinder x^2 + y^2 = 9 lying above the plane z = 1 and below the…

A: