A fluid has density 1200 kg/m3 and flows with velocity ī measured in meters, and the components of ū are = xi + yj + zk, where x, y, and z are measured in meters per second. Find the rate of flow outward through the part of the paraboloid z = 49 – x² – y? that lies above the xy plane. -

Q: Evaluate (3x + 2y)dV, where S is the solid bounded above by the plane z=4, below by plane z=0 and…

A: Evaluation of the triple integrals

Q: A fluid has density 1200 kg/m and flows with velocity = i + yj + zk, where x, y, and z are measured…

A:

Q: A fluid has density 1200 kg/m³ and flows with velocity ū = xi + yj + zk, where x, y, and z are…

A: Use the integral formula of flow rate given by stoke's theorem to calculate its value. Determine the…

Q: y dV, where B is the portion of the unit ball B = {(x, y, z) : x² +y² + z² < 1} which lies below the…

A:

Q: Suppose that a curved lamina o with constant density 8(x, y, z) = 8o is the portion of the…

A: mass=∫∫∫δx,y,z dv

Q: Find the flux of F(x,y,z) = sin(xyz) i+ xy j + ze*/5 k across the part of the cylinder y? + 2 z? = 4…

A: According to question,Fx,y,z= sin xyzi +xy j + z ex5 k,equation of cylinder,y2 + 2z2 =4planes, x = 1…

Q: A fluid has density 1000 kg/m³ and flows with velocity = ci +yj + zk, where x, y, and z are measured…

A: We have to find the rate flow outward through the part of paraboloid . We can to use the methods of…

Q: (a) Integrate g(x,y,z) = Inx+y over the surface of the region cut from the plane 4x+3y+2z=1 by the…

A:

Q: Find the center of mass and the moment of inertia about the x-axis of a thin rectangular plate…

A:

Q: The solid in the first octant bounded by the coordinate planes and the plane z = 8 – x – y dz dy dx

A:

Q: A fluid has density 1000 kg/m3 and flows with velocity ū = xi + yj + zk, where x, y, and z are…

A: A fluid density 1000 kg/m3 andflows with velocity v→=xi→+yj→+zk→where x,y and z are measured…

Q: Find the vo lume oF the solid OF revolution when the regiON bounded by y = x +1, the solid X-axis,…

A: Given problem:- Find the volume of the solid of revolution when the region bounded by y = x + 1 the…

Q: Find the polar moment of inertia about the origin of a thin triangular plate of constant density d =…

A:

Q: a) A laminar with density &(x, y) = lies in the first quadrant is bounded y3 by two circles a2 + y²…

A: Given that, the density function is: δ(x,y)=xy3 Now, Ix=∫∫x δ(x,y) dy dx   =∫∫xxy3dy dx   =∫∫x2y3dy…

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

A:

Q: Find the mass, in kilograms, of the portion of the cone x² + y² = z² 1 and z = 3 if the area density…

A: Given the portion of the cone x2+y2=z2 between the planes z=1 and z=3. and density δx,y,z=y2z2

Q: Use the Divergence Theorem to find the rate at which a fluid with flux F = through the cube formed…

A: We are asked to find the rate at which a fluid with flux F→=x2+exy, y2+exz, z2+exy through the cube…

Q: What is the center of gravity of the solid formed when the plane region bounded by y^2 = 4x in the…

A:

Q: A fluid has density 800 kg/m³ and flows with velocity i = ri + yj+ zk, where x, y, and z are…

A:

Q: Find the moment of inertia about the z-axis of the surface of the cube cut from the first octant by…

A:

Q: Use cylindrical coordinates to evaluate the triple integral ∫∫∫E x^2 dV, where E is the solid that…

A: Given, E is the solid that lies within cylinder, above plane, and below the cone is

Q: Find Iz and the center of mass of a thin shell of density d(x, y, z) = z cut from the upper portion…

A:

Q: Express |[[y d V in cylindrical coordinates, where Q is the solid that lies between cylinders x+y =…

A: Consider the given information.

Q: Integrate R(x,y,z)=x (xy2 +z) over the surface of the cylinder x2 + y2 = 9 that lies between the…

A:

Q: Use cylindrical coordinates to evaluate the triple integral |||| Væ² +y² dV, where E is the solid…

A: Mentioned below is the answer

Q: Consider the solid that lies above the square (in the xy-plane) R = [0, 2] x [0, 2], and below the…

A: (a) For the lower left corner we have: (0,0)-(0,1)-(1,0)-(1,1) and evaluate the function at these…

Q: A fluid motion is given by V=(y+z)i+(z+x)j+(x+y)k. Is this motion irrotational? If the velocity…

A:

Q: A fluid with density 1,330 flows with velocity v = yi +j+ zk. Find the rate of flow upward through…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: If E is the solid shape bounded by x 20,y 20,z 20 and the plane 6x + 4y + 3z = 12 evaluate %3D (y +…

A:

Q: Compute the flux of F = (r, y, z*) across the cone z = x2 + y?, %3D 0<<1, in the downward direction.

A:

Q: Find the flux of F= through of the total surface of the closed cone y=(x2+z2)0.5 with 0 < y < 2…

A:

Q: „ Compute the flux of F = xi + yj + zk through the curved surface of the cylinder x? + y² = 1…

A: Consider the vector field:

Q: Find the volume of the solid that lies under the plane 4x + 10y – 2z + 19 = 0 and above the…

A:

Q: Express [[[vdV in cylindrical coordinates, where 2 is the solid that lies between cylinders x+y = 1…

A: Region is between the cylinders  x2+y2=1x2+y2=4  Thus,  1≤x≤2  1≤x≤2    Thus, changing to…

Q: Let D = 4xyäx + 4yzäy + 2(x² + y²)āz C/m². Find the total charge enclosed in the rectangular…

A: Given, D=4xyax+4yzay+2x2+y2az  C/m2 0&lt;x&lt;2,   0&lt;y&lt;5,   0&lt;z&lt;3

Q: * Q. (41), p.305 : Find the volume of the solid generated of revolving V3 1 y V1 + x2 SxS V3 3 < x s…

A: The volume of a solid obtained by revolving the curve   about the x-axis from to is given by the…

Q: O Find the mass of the solid defined by Jx²+yz <Z s Janx?yz Knowing that the denoity in each point…

A: A cartesian coordinate system contains three mutually perpendicular number lines named x-axis,…

Q: A: Determine the mass and center of mass of the solid that bounded by the paraboloid z = 9y? + 9x?…

A:

Q: Find the moment of mass from the x-axis for y = x In(x) – 3x and y density is equal to 0.37…

A:

Q: 2. Calculate the volume of the solid that is bounded by the surface x²+y²-4y%3D0, inferiorly by the…

A:

Q: Find the valume of the Solid bounded by the para boloid そ- 28-x2 152the cylinder x2+y?= 24 and xy-…

A:

Q: Find the flux of F across S, where F(x, y, z) = xyi + y²j + zk and S is the part of the paraboloid z…

A: According to question given that F(x,yz,)=xyi^ + y2 j ^+z k^S is the part of the paraboloid z=x2+y2,…

Q: (7) Determine the upward flux of V x F through the part of the elliptical cone C = {(x, y, z)2 =…

A:

Q: A fluid has density 600 kg/m3 and flows with velocity ū = ri + y. measured in meters, and the…

A: Here we have, Velocity v→=xi^+yj^+zk^ where x,y, and z are measured in meters.  the equation of…

Q: Find the flux of F = 5zi+ 3y²j+ 2xk through of the total surface of the closed cone y = Vx² + z²,…

A: Flux of vector F through a surface S  can be given by  flux= ∫∫SF.ds We will use Divergence theorem…

Q: A fluid has density 1200 kg/m³ and flows with velocity v = xi + yj + zk, where x, y, and z are…

A:

Q: ~F = z(x2+ y2) ~k through the disk of radius 4 in the plane z = 2, centered on the z-axis, oriented…

A:

Q: Express the volume of the solid that lies between two cylinders a² + y2 = 1 and ² + y² = 4 and…

A: Consider the given equation of the cylinders, x2+y2=1x2+y2=4 and the paraboloid, z=9-x2-y2. In the…

Q: Use cylindrical coordinates to evaluate the triple integral x² + y dV, where E is the solid bounded…

A: