A solid is bounded below by the cone z = /x< +y and above by the plane z= 1. Find the center of mass and the moment of inertia about the z-axis if the density is 8(r,0,z) = 3z. The center of mass is (x.y,z) = (O). (Type integers or simplified fractions.)

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: Find the surface area of the surface parametrized by φ(u, v) = (u2 + v, u, v) with 0 ≤ v ≤ 4 and…

A: The given surface is:ϕ(u, v)=u2+v, u, v

Q: "ind the centroid of the quarter circle x + y <7, y 2 |x| assuming the density ő(x, y) = 1. Use…

A: We need to find mass(M) and moment of inertia about x and y axis of the lamina  Mass of lamina…

Q: Let T be a triangle with the vertices (0,0), (1,0) and (1,2). Also, let V be the volume of the solid…

A:

Q: Find div(curl F) = V. (V x F). F(x, y, z)= xyzi + yj + zk

A: If vector field then from the question

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

A:

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

A:

Q: A solid is bounded from below by the cone z = √x² + y² and from above by the plane z = 1. The…

A:

Q: A fluid has density 900 kg/m³ and flows with velocity v = zi+yj + zk, where x, y, and z are measured…

A: Given: Density ρx,y,z=900 kg/m3  , v→=xi^+yj^+zk^. To find: The rate of flow outward through the…

Q: Find the centroid of the lamina with uniform density 8(r, y) = 1 bounded by the parabola y = 2 – 3r²…

A:

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: A fluid has density 600 kg/m³ and flows with velocity xi+yj + zk, where x, y, and z are measured in…

A: From the given information we get:

Q: Suppose the temperature at a point (x, y, z) of a solid D bounded by the coordinates planes and…

A: Let's find average temperature over the solid.

Q: 1 Find moment inertia of the halfdisk with mass density 8(x, y) = a. About the x axis b. About the…

A: We will find out the required value.

Q: F(1, y.:)= (x², 2x²y*, 5yz*) Given: Find (a) div F (b) curl F

A:

Q: The solid region bounded below by the xy plane is above by the function z= y/(x2+y2) and on the…

A: The sketch of the solid region bounded is given below.

Q: Evaluate z* + x dS where S is the cylinder x2 + y? = 36 between the planes z = -3 and z = 1,…

A:

Q: The triangular plate shown in Figure has a constant density ofd = 3 g/cm2.(a) Find the plate’s…

A: These questions are example of applications of integrals where an infinitesimal element can be…

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

A: Given,The curve .Aim: To find the center of the mass of a thin plate of constant density  covering…