Find D at P(0,0,8) due to a disk of surface charge 15nC/m2, p< 5 m lies on the z=0 plane

Q: Evaluate the surface integral F. dS where F = (4x, -5z, 5y) and S is the part of the sphere x² + y +…

A: The solution is given below:

Q: Find the centroid of the solid hemisphere of radius a that is enclosed between the ry-plane and z =…

A: Given solid hemisphere of radius a enclosed by xy-plane and z=a2-x2-y2 The centroid is given by the…

Q: Find the mass and center of mass of the S solid bounded by the paraboloid z = 8x? + 8y2 and the…

A: We have to find mass and enter of mass of the S solid.

Q: A hole is drilled through the center of a sphere x² + y² + z² = R,², leaving a ring-shape solid. If…

A: A per your request , (b) The equation of sphere is given as , x2+y2+z2=Rs2 and Radius of drill=Rd…

Q: Evaluate the surface integral. x dS, S is the part of the plane 16x + 8y + z = 16 that lies in the…

A:

Q: Evaluate the surface integral. xz ds, S is the part of the plane 2x + 2y + z = 4 that lies in the…

A:

Q: Find the area of the portion of the cylindrical surface Y = 4 – x² in the first octant that is…

A:

Q: The area of the plane z = 2x + 1 above the disk of radius 1 centered at the origin is (а) 4л. (b)…

A: As we know, z=fx,y defines a surface in xyz-space.  Formula for the surface area of the surface…

Q: Find the flux ofF across the oriented surface S' by evaluating the surface integral F.î dS. F = zî +…

A:

Q: Use cylindrical coordinates to evaluate the integral 2²dV where E is the solid that lies within the…

A:

Q: Evaluate the surface integral. + y2 + z2) ds S is the part of the cylinder x² + y2 = 16 that lies…

A: We will solve this problem in some steps

Q: (c) Evaluate dx dy 1– x² – y² where R is the right half-disk of radius % and centered at (0, % ).

A: R: (x-0)2+(y-1/2)2=1/4, x≥0 x2+(y-1/2)2=1/4

Q: Find the area of the plane xtay-zt 10=0 that lies above the disk xy-plare

A: Given that, Area of plane is x+2y-z+10=0 It lies above the disk {(x,y)/x2+y2≤4} in x,y plane. The…

Q: Find the parametrization r(t) = [x(t), y(t), z(t)] of the curve obtained by intersecting the…

A:

Q: Evaluate the surface integral  ffR(x+y)dS where σ is the portion of the plane z = 6 − 2x − 3y in the…

A:

Q: Find by using polar coordinates in R^2 the volume of the region bounded by the parabolic z=…

A:

Q: |Use cylindrical coordinates to evaluate the triple integral |/L Vz? + y² dV, E is the solid bounded…

A:

Q: Find the surface area of that part of the plane 9x + 6y + z = 4 that lies inside the elliptic…

A:

Q: Let S be the portion of the paraboloid z = r² + y? below z = 4 together with the disk a2 + y² < 4 in…

A:

Q: Evaluate the surface integral. /| xz ds, S is the part of the plane 2x + 2y + z= 4 that lies in the…

A: We need to find surface integral.

Q: Compute the surface area of the cone with parametrization p(r, 0) = (r cos 0, r sin 0 , r) where 0 <…

A: Differentiate the function φr,θ=rcosθ,rsinθ,r partially with respect to r and θ, to compute φr×φθ.…

Q: Find the surface integral ls yz dS, where S is the plane surface z = x + 3y lying above the…

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: At which of the points below is the tangent plane to the surface z - 2y + z?+ yz = 2 vertical?…

A:

Q: Evaluate the surface integral: x dS,  S is the part of the plane  12x + 6y + z = 12  that lies in…

A: From the given statement, the plane is 12x + 6y + z = 12 and it is lies in the first octant.

Q: Find the volume of a right circular cylinder of radius a = 4.00 with a paraboloid of revolution…

A:

Q: Consider the parametrization y: [0,47] → R, (t) = (t cos t, t sin t), of a counter-clockwise spiral…

A:

Q: Find the area of the surface of the part of the plane 3x + 2y + z = 6 that lies in the first octant.

A:

Q: Find the centroid of the region cut from the solid ball r2 + z2&lt;= 1 by the half-planes u =…

A:

Q: Suppose that C is the curve of interesection between the plane z = x and the cylinder x² + y? be the…

A: Consider the given function. z=x and x2+y2=1 As, the function S be the interior of this ellipse…

Q: Calculate the flux integral (9i+95+9k)· dà where S is a disk of radius 8 in the plane x +y + z = 1,…

A:

Q: Find the average of the function f(r,0)=r sin(0/2) over a disk of radius R centered at the origin.

A: Given function: f(r,θ)=r2*sinθ2Disk description: radius=R0 and center at the origin To find: Average…

Q: Calculate the flux integral f(2i + 2j + 2k) · dA where S is a disk of radius 5 in the plane æ + y +…

A: Given F=2i+2j+2k,radius=5 and x+y+z=1 plane

Q: Evaluate the integral //, (x² + y²) dA where R is the quarter disk of radius 3 centered at the…

A:

Q: Calculate the positive value of m so that the x+y+2z=m plane is tangent to the spherical surface…

A:

Q: Evaluate the integral // Fn ds where F = (2r+32)i-(rz+y)3+(y² +2)& and S is the surface of the…

A:

Q: Find the circulation of F= (xy)i+(yz')j-(2xyz)k around the curve C in the counterclockwise direction…

A:

Q: Use spherical coordinates to evaluate the triple integral ∫∫∫ √(x^2 + y^2 + z^2) dv where G is the…

A:

Q: Find the surface area of the plane 3x + 2 y + z = 6 that lies in the first octant.

A: The surface area of the plane z=f(x,y) is given by the formula                          S=∬D…

Q: Compute the scalar line integral xy ds where C is the part of the circle of radius 3, centered at…

A:

Q: Assume that S is the disk 2 + y² <4 in the plane z 0 oriented upwards with positively oriented…

A:

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

A:

Q: If F=xi+yj, prove that JF.ñds equals [V.FdA, where R is the disk of radius C R "a" and centre at the…

A: Given Data: F =xi  +yjTo Prove:∫C F . n ds =∫R∇·F dA where R is the disk of radius ''a'' and centre…

Q: The spherical surface S is tangent to the z=0 and x+y+3z−2=0 planes, with (−1,2,0) being one of the…

A: Explained below

Q: use a parametrization to find the flux ∬S F . n dδacross the surface in the specified direction. F =…

A: Given surface, F=2xyi+2yzj2xzk           ...(1) Given plane, x+y+z=2a                ...(2) Where…

Q: Find the average height of the (single) 34. Average height of a cone cone z = Vx² + y² above the…

A:

Q: Find f[fp Vx2 + y2 + z² dV, where D is the sphere of radius a centered at the origin.

A: We need to find the integral:∫∫∫Dx2+y2+z2dVwhere D is the sphere of radius a centered at the…

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: (a) Find the surface area of the plane 3x +2y + z = 6 that lies in the first octant.

A: If z=fx, y then surface area is, AS=∫∫D1+zx2+zy2dA