dA, where K is the disk r + (y 2 +?

Q: - || e dA, where D is the open disk D = {(x, y) : x² + y² < 4}.

A:

Q: In AABC, X is the centroid. If CW = 15 , find XW. %3D

A: Given,           In △ABC, X is the centroid and CW¯=15

Q: Find the moving tri hedral of f R CE) = t, 2E> at %3D

A: This is a problem of differential Geometry.

Q: A) || Jx2 + y2 dA , R is the disk x2 + y? < 9

A: We have to use polar coordinates here.

Q: Evaluate x² zdS, where S is the part of the plane z = 3 + 4x + y above the rectangle [0, 4] × [0,…

A:

Q: x² y? + z = 1 4 9.

A: Given equation  x^2/9 - y^2/4 +z = 1 this is equation of hyperbolic Paraboloid.  Quadratic Surface…

Q: Find the points on the cone z = x+y' that are closest to the point (-2,3,0) 22

A:

Q: Fin He ara at tHe surface af the portion oF Hae Plane 2= 5-2X -9y

A:

Q: Please solve this problem

A: Given integral is,

Q: Determine the image of the upper half plane {z € C : Im(z) > 0 }

A: In this question, we use the transformation under g(z) we find the image set.

Q: Let D be the half-disc in the xy-plane given by x +y <9. Calculate e-(x2+v)dA

A:

Q: Determine whether the statement is true or false. If D is the disk given by x2 + y2 s 49, then 49 x2…

A:

Q: A surface in R³ is defined by the equation 4z = x² + 4y“.

A:

Q: Find the point on the sphere x +y +z = 4 that is close O A. V11 V11 9. V11 (유 O B. 11 V11 V11

A: Solution of the problem as follows

Q: a) Evaluate ff, (2x – z) dS, where S is part of the plane 3x + 2y +z = 1 that lies above the…

A:

Q: 2. Find the area of the part of the sphere x² + y² + z² = 4z that lies inside the paraboloid z = x²…

A:

Q: WY bisects ZXWZ and ZXYZ. Complete the proof that AWXY E AWZY. Y. W

A: Given that WY bisects ∠XWZ and ∠XYZ. We know that when a line bisects an angle, it means it divide…

Q: Use the Disk Method Y= x^(3/2) , Y = (3/2)x , revolved around X = 5

A: First we have to design the integral using the given conditions,  and for that obtain functions of…

Q: Enclosed by the paraboloid z = x² + 3y? and the planes x = 0, y = 1, y = x, z = 0

A: We know that, volume under surface z=fx,y and above the region D in xy-plane is given as…

Q: Evaluate // x² zdS, where S is the part of the S 1 + 4x + 3y above the rectangle plane z = [о, 2] x…

A:

Q: Evaluate (image) over the sphere D = { (x,y,z) | x2 + y2+z2 ≤ R2 }

A: Given integral is ∭x2+y2+z2xyzdxdydz over the sphere D = { (x,y,z) | x2 + y2+z2 ≤ R2 } Change…

Q: Find the barycentric coordinates of p with respect to the affinely independent set of points that…

A: Given 11, 35, 06, p=23 let a=11, b=35, c=06, p=23 Now we write the points in augmented matrix form…

Q: What are the perpendicular generators on (D) 좋 =3 %3D2 (P) 16 2. of the surface

A:

Q: Use the flux form of Green's Theorem to evaluate |(6xy + 8y°) dA, where R is the triangle with…

A: Greens' Theorem : Let D be the region bounded by the curve C. Let F(x,y)=P,Q be the vector field…

Q: Find the area of the part of the paraboloid z=x² + y² that lies under the plane z=9.

A:

Q: Sketch the surface r = 2y? + 32².

A:

Q: dx dy, where D is the disk x2 + y² < 9. (x² + y?)3/2 Evaluate

A: The given integral is,

Q: Explain why C lies on the surface of the cylinder x² + y² = 1.

A:

Q: Evaluate f 3z2dz over C, where C is the upper half circle |z – connects points O and 1+i. -글히 %3D플…

A:

Q: SSx x dA; R is the portion of the disk x +y s 16 in the second quadrart

A: According to the given information, it is required to find the value of the given integral.

Q: Find the area of the surface. The part of the paraboloid z = 1 – x2 - y? that lies above the plane z…

A:

Q: Evaluate x2 zdS, where S is the part of the S plane z = 1+ 2x + 3y above the rectangle [0, 2] × [0,…

A: We have to evaluate ∬Sx2zdS, where S is the part of the plane z=1+2x+3y above the rectangle 0,2×0,3.…

Q: JJs where S is the sphere x² + y2 + z2 = 1.

A: Given S is the sphere                         x2+y2+z2=1 To evaluate:             ∫∫S3x+3y+z2dS…

Q: Find the area of the cap cut from the paraboloid y2 + z2 = 3x by the plane x = 1.

A:

Q: Find the area of the part of the plane 4x + 3y + z = 12 that lies in the first octant.

A: to find:- surface area, A.

Q: Let R be the triangle in the xy-plane with vertices (0,0),(0, 1),(1,0). Find C[n(2 – x – y) dA.

A: Given vertices of triangle now we have to find the area as shown below

Q: Evaluate I ( V9 - x2 - y2 dA, where D is the disk x? + y < 9, by interpreting it as a known volume.…

A:

Q: Find the point on the surface r – 2xy + 2y² – x+ y = 0 closest to the point (1, 2, –3).

A: Consider the provided question, We have to find the point on the given surface closest to the point…

Q: Evaluate ([(3xi +2yi)-d$ -d$ where S is a sphere x +y +z? =9.

A: To evaluate the below integral. ∫∫S3xi+2yj⋅ds Here S is a sphere x2+y2+z2=9

Q: a) Evaluate ff, (2x – z) dS, where S is part of the plane 3x + 2y + z = 1 that lies above the…

A: Surface integral

Q: ce cut from the first octant by the cylinder z = 12 – 3y, and the plane x + y = 2

A:

Q: Find the point on the surface r² – 2ry + 2y² – x +y = 0 closest to the point (1, 2, –3).

A:

Q: Determine whether the statement is true or false. If D is the disk given by x2 + y2 < 4, then I V4-…

A: Given the given relation is

Q: ZI and Q[r, y) are not Euclidean domains

A: Prove that ℤx and ℚx, y are not Euclidean domain. Every Euclidean domain is a Principle Ideal…

Q: 3. Show that every sphere through the circle x2 +y-2ax+r²=0, z=0 cuts orthogonally every sphere…

A: This is a co-ordinate geometry problem

Q: SSx x dA; R is the portion of the disk x + ys 16 in the second quadrart

A: I use polar conversion method

Q: What are the perpendicular generators on (D) 등 =D3 %3D (P) -= of the surface

A: Given equations are  x216-y24=z ......(1)x3=y2=z-4  ......(2) Equation of generators of the…

Q: se the disk method or the shel y = x2 y = 0 x = 3 (a) the x-axis 243

A:

Q: Evaluate JJ (² where o is the first-octant portion of the plane 2x + y + 2z = 6 (x² + 2yz)dS

A:

Q: Given F(x.y.z) (x+y+Zi +(x-yj+(xz-2)k what is CurlF at the point (1,-1,3)? You should write your…

A: