5 -8 points Use spherical coordinates to find the total mass M and the moments of...
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
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
5. Use spherical coordinates to evaluate 1952/x + y? + dv ", over the solid bounded below by the cone z= V8 + y2 and, and above by the sphere z= 11- x2 - y2
Ex: Use Spherical Coordinates to find the mass of the solid bounded -by z /x²y3 and the plane Z=2, where s= R(x² + y² + 2?)
Bonus. (8 pts) Many of the definitions we used for two-dimensional mass and moments can be extended to three dimensions rather easily. For example, mass = ///. P18,9, 2) dv would represent the mass of the solid Q where p(x, y, z) is the density at any point (x, y, z). Find the mass of the solid bounded laterally by the cylinder zº + y2 = 2x and bounded above and below by the cone 2? = 2² + y2....
Bonus. (8 pts) Many of the definitions we used for two-dimensional mass and moments can be extended to three dimensions rather easily. For example, mass = ESSA 1, 2) av would represent the mass of the solid Q where p(x, y, ) is the density at any point (x, y, z). Find the mass of the solid bounded laterally by the cylinder 2? + y2 = 2x and bounded above and below by the cone x2 = x2 + y2....
Use spherical coordinates to find the mass m of a solid Q that lies between the spheres x2 + y2 +z" 1 and x2 + y2 + z2-4 given that the density at each point P(x, y, z) is inversely proportional to the distance from P to the origin and 8(o, 3,02 15 pts] (0, 1,0)-2/m3 from P to the origin and Use spherical coordinates to find the mass m of a solid Q that lies between the spheres x2...
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 spherical coordinates. Find the centroid of the solid E that is bounded by the xz-plane and the hemispheres y = V 1-x2-z2 and y (x, y, z) V4-x2- Use spherical coordinates. Find the centroid of the solid E that is bounded by the xz-plane and the hemispheres y = V 1-x2-z2 and y (x, y, z) V4-x2-
Question 4 (3.6 points) Use spherical coordinates to find the volume of the solid that lies below the cone z = Vx2 + y2 and above the sphere x2 + y2 +22 = 1. Write V= =("sin ødpdøde 1. 0 2. 1 d= > 3. e= > 4. 2 II < 5. < a= 6. Í < C= 7. 2a b= < 8. 9. 34