H.W: Find the center of mass of a solid of constant density & bounded below by the disk R: x² + y² <4 in the plane z = 0 and above by the paraboloid z=4-x² - y² c.m. 2=4-x²-y² 20 x² + y² = 4

Q: Find the centroid of the solid hemisphere of radius a that is enclosed between the ry-plane and z =…

A: Given solid hemisphere of radius a enclosed by xy-plane and z=a2-x2-y2 The centroid is given by the…

Q: What is an equation for the largest ball centred at (0,0, 1) that can fit in the paraboloid z = 3 -…

A: To find the equation for the largest ball centered at (0, 0, 1) that can fit in the below equation…

Q: If the point density of the solid is determined by the function p(x, y, z) = 3x kg/m³ and if the…

A: To find the mass of the solid that is bounded by the below equations and has a density function of…

Q: Find the flow of F=xzi-yk through the upper part of plane z-1 in the x +y² +z = 4sphere. %3D

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

Q: Calculate F· dS where F = (4x*z, 4y°z, 3:*) S is the surface of the solid bounded by the hemispheres…

A: Given

Q: Ex: Find the center of mass of the solid whose density &z and bounded above by the plane z=y, below…

A: What is Center of Mass: The unique location where the weighted relative position of the distributed…

Q: Consid‎er a la‎mina t‎hat is in the fir‎st quad‎rant, ins‎ide the ci‎rcle whos‎e equ‎ation is x2 +…

A:

Q: b) Given F(r, y, z) = (r³ + cosh z) i+ (2y3 – 3r*y)j – (2² + 4y²z) k. Use Gauss's theorem to…

A:

Q: 2. Calculate the centroid of the thin plate R which bounded by a = 1, y = 0 and, x² + y² = 4.

A:

Q: the z-axis and above the x-y plane. Use Stokes' Theorem to calculate the circulation of F = (x + y?,…

A:

Q: x² + y? that is below the plane Find the surface area of that portion of the paraboloid z = z = 2.

A: Given paraboloid z=x2+y2 Surface area, AS=∫∫R∂z∂x2+∂z∂y2+1dA AS=∫∫R2x2+2y2+1dA…

Q: A solid body with mass density o(x, y, z)=√√x2 + y2 kg/m³ occupies the region in space below the…

A:

Q: A: Determine the mass and center of mass of the solid that bounded by the paraboloid = 9y? + 9x2 and…

A:

Q: Ex: Find the center of mass of the solid whose density &z and bounded above by the plane z=y, below…

A:

Q: Find the center of mass of a solid of constant density bounded below by the paraboloid z = x² + y²…

A: Given information: The solid is bounded below by the paraboloid .The solid is bounded above by the…

Q: et Q be the part of the sphere of radius 3 centered at the origin which lies above z = 1, and let D…

A:

Q: What is the surface area of a hyperbolic paraboloid described by parametric eqn: z = xy, where x,…

A: The surface area of a hyperbolic paraboloid described by the parametric equation z = xy, where x = u…

Q: Find the surface area of the part of the plane z = 2x - y − 3 that lies inside the - cylinder x² +…

A:

Q: Write down a parametrization r(u, v) for the portion of the plane x - y+ z = 3 that lies inside the…

A: r(u, v) = ( u cos v , u sin v,  3 - u cos v + u sin v)  Where u € [0, 1]           v€ [ 0,2π]

Q: 4. A surface consists of parts of the planes z = 0, z = 1, y = 0, y = 2, z = 1, in the first octant.…

A: To verify stokes theorem

Q: Evaluate f. F dS where F(x,y, z) = (4x³z, 4y³z, 3z*) and S is the surface of the solid bounded by…

A:

Q: Use Stokes' theorem to evaluate where = 3x²1+8x³yj + 3x²yk (V x F) - dA and S is the portion of the…

A: Given that S is the portion of the  plane that lies inside the box defined by the .

Q: /|F . d5 where Calculate F = (3zy°, ze", 2ª) Sis the surface of the solid bounded by the cylinder y?…

A: