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find the mass of the lamina that is the portion of the surface y = 4-z...
Find the mass of the lamina that is the portion of the circular cylinder x? +3+ = 4 that lies directly above the rectangle R= {(x, y): 0 < x < 1,0 <y s4} in the xy-plane. Assume the lamina has a constant density of do. Enter the exact answer in terms of do. M= ? Edit
please answer 5-7 in detail
5. Find the center of mass of the rectangular lamina with vertices (0.0), (21.0). (0.12), and (21. 12) for the density p = kxy. Ans: 6. Find the mass of the triangular lamina with vertices (0, 0), (12, 24), and (24,0) for the density p = kxy. Ans: 7. Find the area of the portion of the of the surface z = 4x + 8y that lies above the region R = {(x, y): x...
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...
8) [10 points] Use a surface integral to find the mass of the surface lamina Зл r(u, v)=sin v cosui+sin vsin uj+cos vk where Osus 05 vsa and density is given by 2 P(x,y,z)= x² + y2 +2?. Ba
Could you do number 4 please. Thanks
1-8 Evaluate the surface integral s. f(x, y, z) ds Vx2ty2 -vr+) 1. f(x, y, z) Z2; ơ is the portion of the cone z between the planes z 1 and z 2 1 2. f(x, y, z) xy; ơ is the portion of the plane x + y + z lying in the first octant. 3. f(x, y, z) x2y; a is the portion of the cylinder x2z2 1 between the planes...
Find the mass of the lamina that is the portion of the paraboloid 2z = x² + y2 inside the cylinder x² + y2 = 24 with constant density 80. Mass = Edit
6. Find the center of mass of the rectangular lamina with vertices (0,0), (6,0), (0, 24) and (6, 24) for the density p = kxy. 7. Find the area of the surface given by z =f(x,y) over the region R. f(x,y) = 3 – 2x + 5y R: square with vertices (0,0), (4,0),(4,4),(0,4)
Find the center mass of the solid bounded by planes x+y+z=1, x = 0, y = 0, and z = 0, assuming a mass density of p(x, y, z) = 15/2. (CCM, YCM, 2CM) =
a. Find the center of mass for lamina defined by the interior of
the polar curve r=sin(3) with a density
that varies according to p(r,theta)=1/r
b. Find the volume of the cylinder inside the sphere
For part a I got a mass of 2 but not sure about the x bar and y
bar calculations.
For part b Im stuck on the z bounds for the integral when doing
the problem with the cylindrical coordinate method.
We were unable to...
Evaluate the surface integral of the function G over the surface S. 15) G(x, y, z)-x z: S Is the surface of the wedge formed from the coordinate planes and the planes 15) X +z 4 and y 4 A) 128+ 64 320 320
Evaluate the surface integral of the function G over the surface S. 15) G(x, y, z)-x z: S Is the surface of the wedge formed from the coordinate planes and the planes 15) X +z 4...