The region above the xy-plane that is inside both the sphere 2? + y2 + x2...
Find the mass of the region above the cone z = (x2 + y2 and inside the sphere x2 + y2 + 22 = 2 which has density 8(x, y, z) = 2
plane, and outside the cone z-5V x2 (1 point Find the volume of the solid that lies within the sphere x2 ,2 + z2-25, above the x (1 point) Find the mass of the triangular region with vertices (0,0), (1, 0), and (0, 5), with density function ρ (x,y) = x2 +y.
plane, and outside the cone z-5V x2 (1 point Find the volume of the solid that lies within the sphere x2 ,2 + z2-25, above the x
(1...
(1 point) Find the volume of the solid that lies within the sphere x2 +y2 .2 16, above the xy plane, and outside the cone 2
(1 point) Find the volume of the solid that lies within the sphere x2 +y2 .2 16, above the xy plane, and outside the cone 2
(1 point Find the volume of the solid that lies within the sphere x2 + 2 + z-64 above the xy plane, and outside the cone z 8V x2 y2
(1 point Find the volume of the solid that lies within the sphere x2 + 2 + z-64 above the xy plane, and outside the cone z 8V x2 y2
Q3(a) Let W be the region above the sphere x2 + y2 + z2 = 6 and below the paraboloid z = 4 - x2 - y2 as shown in Figure Q5(a) below: Z=4-x-y? x2 + y + z = 6 Figure Q3(a) (i) Find the equation of the projection of Won the xy-plane. (ii) Compute the volume of W using polar coordinates. [16 marks] (b) Using double integral in polar coordinates, compute the following: $$*** (2x+3y) dedy [7 marks]...
Evaluate the triple integrals JR V and JSSR zdv, where R is the region bounded above by the sphere x2 +y2+22 : 4, below by the cone 3za_ x2 + y2, and such that y 2 0
Evaluate the triple integrals JR V and JSSR zdv, where R is the region bounded above by the sphere x2 +y2+22 : 4, below by the cone 3za_ x2 + y2, and such that y 2 0
Calculate the volume of the region inside the cylinder x +y = 4, above the XY-planea below the paraboloid z = x2 + y2. 3) Calculate the volume of the region enclosed by the R2 - R functions f and g given by f(x, y) = 8 - x2 - y2 and g(x, y) = x2 + y2.
Please show all steps. Thank you, need to verify what I'm doing
wrong.
1. (20 points) Suppose B is the solid region inside the sphere 2+ y2 +2 4, above the plane = 1, and in the first octant (z, y, z 0)、z, y and z are measured in meters and the density over B is given by the function p(z, y, z)-(12 + y2 + ?)-1 kg/m3 (a) Set up and write the triple integral that gives the mass...
All of 10 questions, please.
1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...
Let E be the solid that lies inside the cylinder x^2 + y^2 = 1,
above the xy-plane, and below the plane z = 1 + x. Let S be the
surface that encloses E. Note that S consists of three sides: S1 is
given by the cylinder x^2 + y^2 = 1, the bottom S2 is the disk x^2
+ y^2 ≤ 1 in the plane z = 0, and the top S3 is part of the plane z...