6. Find the mass of the upper half of the sphere r²+y² +z² < 4, z > 0, if the density at any point in the solid is given by the function p(x, y, z) = /x2 + y² + z². %3D

Q: (b) A cubc has sidcs length of a cm and it is made of a matcrial of variable density. If one corner…

A: Given: Cube of side length a cm, and density function of cube  is δx,y,z=b+xyz gm/cm3 where one…

Q: he x-axis and the curve y = moint (x,y) is 8(x) = 2x². 20 x²¹ 5≤x≤7, if the plate's density at a

A: The solution of step 1 is

Q: (10) Sketch the solid in the first octant bounded by x + z = 1 and y+ 2z = 2. If 8(x, y, z) = x…

A: The given region lies in the first octant, so x≥0, y≥0 and z≥0. To get the points on the planes,…

Q: 6. Determine the volume of the solid (shown below) E between the sphere 1? + y? + 22 = 4, the…

A: Solve by triple integration

Q: If u = and , then what is the magnitude of 2 + . Round to the nearest hundredth. Answer:

A:

Q: a) Compute the area of the surface z=4−(x^2)−(y^2) in upper half space {z≥0}. b) If F = (x)i +…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Find the area of the part of the hyperbolic araboloid z = y² – x² nat lies between the cylinders x²…

A:

Q: Find the centroid of the quarter circle x + y Ix| assuming the density ő(x, y) = 1. (Use symbolic…

A:

Q: Find the center of mass of a thin plate covering the region between 20 the x-axis and the curve y=-…

A:

Q: A lamina occupies the part of the disk x² + y² ≤ 16 in the first quadrant. Find its center of mass…

A:

Q: 3 27 Find the center of mass of a thin plate of constant density & covering the region bounded by…

A: Center of mass of a body is a point at which it can be considered that entire mass of body is…

Q: A planar region is given by D = {(x, y) : x² + y² 0, y 2 0} . The density of this region is given…

A: We have to find the mass of the given region.

Q: = Find the mass of the solid bounded by the the graphs of y 8x², y = 5, z = 0, and z = 2, in the…

A:

Q: Use V=SSSDdV and the substitutions u = x/a, v = y/b, w = z/c to show that the volume of the…

A:

Q: The boundary of a lamina consists of the semicircles y=√16-x² and y= √36-x2 together with the…

A: Here we have to find the centre of the mass of the lamina.

Q: Find the centroid of the quarter circle x² + y² ≤7, y> [x] assuming the density 6(x, y) = 1. (Use…

A: Given that x2+y2≤7, y=x In polar coordinate we can write x=r cos θ, y=r sin θ and the point of…

Q: Calculate the volumes of the solids of revolution obtained by rotating the curve y = x², 0 < x < 2…

A: Given: The curve is given by:                  y=x2,             0≤x≤2 To find: We have to determine…