Use cylindrical coordinates to find the mass of the solid Q of density ρ.
Q={(x, y, z): 0 ≤ z ≤ 9-x-2 y, x²+y² ≤ 25}
ρ(x, y, z)=k \sqrt{x²+y²}
Use cylindrical coordinates to find the indicated characteristic of the cone shown in the figure.
Assume that the density of the cone is ρ(x, y, z)=k \sqrt{x²+y²} and find the moment of inertia about the z-axis.
Use cylindrical coordinates to find the mass of the solid Q of density ρ.
Use cylindrical coordinates to find the mass of the solid Q of density p. Q = {(x, y, z): 0 sz s 9 - x - 2y, x2 + y2 s 49} P(x, y, z) = k/x² + y²
Find the volume of the solid Use spherical coordinates to find the mass of the solid bounded below by the cone z=« .) and above by the sphere x+y+ =9if its density is given by 8(x,y,2) = x+ y+Z. JC Use spherical coordinates to find the mass of the solid bounded below by the cone z=« .) and above by the sphere x+y+ =9if its density is given by 8(x,y,2) = x+ y+Z. JC
3. 3D stuff. cylindrical coordinates. A cone of uniform mass density Po has its tip at the origin and its axis of symmetry is aligned with the z axis. The base of the cone is at H and has radius R. Draw a big picture! Compute the following things a. the total mass of the cone. b. the center of mass of the cone. c. its moment of inertia I2z around the z axis
3x23y2 and the plane z = 9 if the mass density of the solid is Use spherical coordinates to find the total mass M and the moments of inertia I, I,, and I, of the solid bounded by the cone z = o(x, y, z) z kg/m3. 21877T М 3 kg 4 432879 kg-m2 X = 8 kg-m2 kg-m2 = II
5 -8 points Use spherical coordinates to find the total mass M and the moments of inertia x y» and z of the solid bounded by the cone z - y2 and the plane z-5 if the mass density of the solid is 0(x, y, z) = z kg/m kg kg-m kg-m2 kg-m2 Submit Answer
If R is a solid in space with density ρ(x, y, z), it's centre of mass is the point with coordinates i, y, 2, given by za(x, y, z) dV, where z, y, z) dV is the mass of the object. Find the centre of mass of each solid R below (a) Rls the cube with 0 < x < b, 0· у<b, 0-2-band ρ(x, y, z) = x2 + y2 + 22; (b) R is the tetrahedron bounded by...
Use polar coordinates to find the centroid of the following constant-density plane region The region bounded by the cardioid r4+4cos0. Set up the double integral that gives the mass of the region using polar coordinates. Use increasing limits of integration. Assume a density of 1 dr d0 (Type exact answers.) Set up the double integral that gives My the plate's first moment about the y-axis using polar coordinates. Use increasing limits of integration. Assume a density of M,-J J O...
밈 Gheth. solid bounded above by the ghre ρ-aand bek_ by them csoep a) H spherical coordiastes (6)(3pts) Fud the mass and the cester ol grwvity of the lamins with dessity OO o 5)Opla) Let G be the solid bounded above by the sphere p- a and below by the cone ф- /3. Find v, by using a) cylindrical coordinates: b) spherical coordinates. (6)(3pts) Find the mass and the center of gravity of the lamina with density 82, v) =...
Hi, I need help solving number 13. Please show all the steps, thank you. :) Consider the solid Q bounded by z-2-y2;z-tx at each point Р (x, y, z) is given by mass of Q [15 pts] 9. x-4. The density Z/m 3 . Find the center of (x, y, z) [15 pts] 10. Evaluate the following integral: ee' dy dzdx [15 pts] 11. Use spherical coordinates to find the mass m of a solid Q that lies between the...
1. Using polar coordinates in the x-y plane, find the volume of the solid above the cone z r and below the hemisphere z= v8-r2. As a check the answer is approximately 13.88 but of course you have to calculate the exact answer 2. At the right is the graph of the 8-leafed rose r 1+2cos(40) Calculate the area of the small leaf. As a check the answer is 0.136 to 3 places of decimal (But of course you have...