Calculate the volume of the section of the ellipsoid x^2 ?+ y^2/9 + z^2/4 =? 1 corresponding to −1 ≤ and ≤ 1.
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Calculate the volume of the section of the ellipsoid x^2 ?+ y^2/9 + z^2/4 =? 1...
2 x-I 3. Find the volume of solids enclosed by a paraboloid z x2+ y2 and an x2y2+z2 =6 ellipsoid 4 Sud, a. 2 x-I 3. Find the volume of solids enclosed by a paraboloid z x2+ y2 and an x2y2+z2 =6 ellipsoid 4 Sud, a.
please answer question 3. 1. Find the integral of the function f(x, y, z)xy+2 z over the region enclosed by the planex +y+z 2 2. Find the volume and center of gravity for the solid in the first octant (x 20, y 20, z20) bounded by 3. Find the center of mass for the solid hemisphere centered at the origin with radius a if the density and the coordinate planes z0,y 0, and x0 the parabolic ellipsoid Z-4-r-y. function is...
4 + x2 + (y-2)2 and the planes z = 1, x =-2, x Find the volume of the solid enclosed by the paraboloid z 2, y 0, and y 4. 4 + x2 + (y-2)2 and the planes z = 1, x =-2, x Find the volume of the solid enclosed by the paraboloid z 2, y 0, and y 4.
5) Find the equation of the tangent plane to the ellipsoid F(x, y, z) = * ++ z2 – 1 = 0 at (0,4,)
9. The upper half of the ellipsoid tr + ty? + Z2-1 intersects the cylinder x2 + y2-y 0 in a curves C. Calculate tfe circulation of v y'i+y+3i k around C by using Stokes Theorem. x2 + y2 intersec ts the plane z y in a curve C. Calculate the circulation 10. The paraboloid z of v 2zi+ x j + y k around C by using Stokes Theorem. 9. The upper half of the ellipsoid tr + ty?...
For random variables X, Y, and Z, Var(X) = 4, Var(Y) = 9, Var(Z) = 16, E[XY] = 6, E[XZ] = −8, E[Y Z] = 10, E[X] = 1, E[Y ] = 2 and E[Z] = 3. Calculate the followings: (b) Cov(−3Y , −4Z ). (d) Var(Y − 3Z). (e) Var(10X + 5Y − 5Z).
Find the volume of the solid region R bounded superiorly by the paraboloid z=1-(x^2)-(y^2), and inferiorly by the plane z=1-y taking into account that when equaling the values of z we obtain the intersections of the two surfaces produced in the circular cylinder given by 1-y=1-(x^2)-(y^2) => (x^2)=y-(y^2), as the volume of R is the difference between the volume under the paraboloid and the volume under the plane you can obtain the dimensions for the integrals and calculate the volume
1. Find the volume of the solid under the cone z= sqrt (x^2 + y^2) and over the ring 4 |\eq x^2 + y^2 |\eq 25. 2. Find the volume of the solid under the plane 6x + 4y + z= 12 and over the disk with border x^2 + y^2 = y. 3. The area of the smallest region, locked by the spiral r\Theta= 1, the circles r=1 and r=3 and the polar axis.
(1 point) Calculate ſls f(x, y, z)ds For y = 4 – z2, Is $(x, y, z) ds = 0 < x, z <7; f(x, y, z) = z
Find the volume of the solid enclosed by the paraboloid z = 4 + x^2 + (y − 2)^2 and the planes z = 1, x = −3, x = 3, y = 0, and y = 3.