R) show that the pints ACI,l,4), B(2,2,2), c (o,1,5) and D(1,0,5) are coplanear (in the Same plane).

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: 4. Find the centroid of each of the given plane region bounded by the following curves: у? %3 2х, у…

A: Based on the integration concept we will answer the question.

Q: (15) Let D be the half-disk x² + y? 0. Compute / | (a + y) dA D

A:

Q: Let T be the tetrahedron with vertices (2, 0, 0), (0, 3, 0), (0, 0, 5) and the origin. Write (a, y,…

A:

Q: D

A:

Q: 7. In AVYX, the centroid is Z. Use the diagram to solve the problems. If VP = 51, find VZ and ZP.

A: We use the property ,the centroid divides each medians in the ratio 2:1.

Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (5,0,0), (0,2,0), and (0,0,4)

A: # Given integral is      ∫∫E∫ zdv

Q: ind the valume of the portion of the Solid. Sphere x+y2,+2-10 that les between the Surfaces

A: We need to find the volume of the portion of the solid sphere x2+y2+z2 = 10 that lies between the…

Q: The value of the triple integral 6zdV where E is the upper half E of the sphere of x² + y? + z? = 1…

A:

Q: (b) Let the distance between two adjacent planes parallel to the plane (hkf) in the direct lattice…

A:

Q: Compute the distance d from y to the plane in R' spanned by u1 and uz.

A: We have to find the distance d from y to the plane in R^3.

Q: Use Green's Theorem to evaluate pxcosydx – ysinxdy, where the curve C is the square with 0), (TT,…

A:

Q: Find the volume of the parallelepiped having adjacent edges u, v, and w; for u = (1,-1,0), v =…

A: Given u=1,-1,0, v=0,2,2 and w=1,3,1

Q: If point N is the centroid of AHIJ, IM = 18, KN = 4, and HL = 15, find JN. %3D %3D %3D K /N/

A:

Q: The volume of the pyramid formed in the first octant by the plane 6x + 10y + 5z-30 = 0 is: О 45 О зо…

A: We can solve as follows

Q: 4. Show that the set of points (z, w) e C with w2 = sin z is naturally a Riemann surface. %3D

A: Let, S=z,w∈ℂ2|w2=sinz be the set in equation. The multivalued analytic function fz=sinz can be…

Q: Let T be the tetrahedron with vertices (3, 0, 0), (0, 5, 0), (0, 0, 4) and the origin. Write /| f(x,…

A:

Q: Q) show that the pánts ACI,1,4), B(2,2,2), C (o,1,5) and D(1,0,5) ave coplanear (in the Same plane).

A: The given points are: A=1,1,4B=2,2,2C=0,1,5D=1,0,5 To prove: A, B, C and D are coplanar (they lie in…

Q: (6) I. adv, where E is bounded by the planes z=0, y = 0, =0, y+= =1 and +=1, as shown in the figure…

A: Given that,

Q: Show that, in the triangular region with vertices (0,0), (1,0) and (1,1) the following double…

A: Double integral

Q: In AQUW, point T is the centroid, and VT = 5 . Find QT and VQ. W V QT= VQ =

A: We know centroid divide each median in 2:1 ratio.

Q: WX || ZY and Zs Z and Y are supplementary WXYZ is a parallelogram Given: Prove: W Y

A: It is given that,  WX ¯|| ZY¯  and ∠Z and ∠Y are supplementary To prove :- WXYZ is a parallelogram

Q: In ANPQ, U is the centroid. If NS=15 find US. R S U

A:

Q: 7. Which surface is parameterized by ř(u, v) = (u, uv, v) for –1 < u <1 and –1< v< 1?

A: r→(u, v) = u, uv, v for -1≤u≤1 and -1≤v≤1The parametric curve is  Option C is correct.

Q: I, Use Stoke's theorem to evalueate S.Fidr, where F Cau2)= - it +x3 + 2î aind C is the Ceurve of…

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: Let C be the positively oriented square with vertices (0, 0), (3, 0), (3, 3), (0, 3). Use Green's…

A:

Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (1,0,0), (0,2,0), and (0,0,4)

A: x varies from 0 to 1&amp; y varies from 0 to 2 and z varies from 0 to 4.

Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (1,0,0), (0,3,0), and (0,0,5)

A:

Q: 4. A 5m x 5cm is cut from a corner of 20cm x 30cm. cardboard, find the centroid from the longest…

A:

Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (4,0,0), (0,3,0), and (0,0,2)

A: we have to find triple integral

Q: 4 Calculate the directed curvilinear integral I where L is the perimeter of triangle ABC with…

A:

Q: 4 6 Let y = 7 2 40 Compute the distance d from y to the plane in IR spanned by ui and uz d =

A:

Q: Let C be the positively oriented square with vertices (0,0), (3,0), (3,3), (0,3). Use Green's…

A:

Q: Calculate ff A.n ds If A = yi + 2xj – zk and S is a 2x + y = 6 plane surface in the first octane cut…

A:

Q: Locate the centroid of the plane area shown. 20 in. Ans: 9.00 20 in- Fig. P5.12

A:

Q: 12- Evaluate JJI (x2 + y? + z?)dvwhere B is a ball with center the origin and radius 5. B

A: Given problem is :

Q: Evaluate J CurIF. [cariF- nas F(x,v,z) = - yi + xj + zk, and S is part of the sphere z =9-x2 - y?…

A:

Q: Find the volume of the parallelepiped shown having    u = 3i − 5j + k ,            v = 2j − 2k and w…

A: Givenu=3i−5j+kv=2j−2kw=3i+j+k

Q: Let T be the tetrahedron with vertices (4, 0, 0), (0, 3, 0), (0, 0, 5) and the ori I f(x, y, z) dV…

A:

Q: 8. Evaluate the double integral // ydrdy where T is the triangle with vertices (0,-1), (0,5), (4,…

A:

Q: O 9/ Compute I - [.lryz) , uhere s is the part g the plane y +x that lies inside the half-cylinder…

A: We know that, dS=1+∂z∂x2+∂z∂y2dydx where S is the part of plane z=y+x. ∂z∂x=1∂z∂y=1 dS=1+(1)2+(1)2…

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: 8. Use Green's Theorem to evaluate px*dx+xydy where C is the triangle with vertices (0,0), (1,0),…

A: As we know from the Green's theorem: ∫CMdx+Ndy=∫∫R∂N∂x-∂M∂ydA And The expression for the equation of…

Q: Compute 5xy ds, where S is the surface of the tetrahedron with sides z = 0, y = 0, x + z = 1, and x…

A:

Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (5,0,0), (0,6,0), and (0,0,3)

A: This question is related to triple integral, We will solve it using given information.

Q: Find ¹JJ²₁ z dV, where E is the solid tetrahedron with vertices (0,0,0), (3,0,0), (0,2,0), and…

A: The solid E is the tetrahedron with vertices 0, 0, 0, 3, 0,0, 0, 2,0 and 0, 0, 1. Draw the solid E:…

Q: he region bounded by the cylinder x2 + y2 = 9 and the planes z=0 and x +z =9 O 243 O 81T 27TT 729TT

A: Follow next step

Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (2,0,0), (0,4,0), and (0,0,1)

A: We have to find the volume integral of the given function.