2) The double integnal | 3x ekdy, whetzeT is the tniang le of VErtices 6,0),c2,0) ond (eti-2), equals. 8. B) 24 ) 21 D 12

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: What is an equation for the largest ball centred at (0,0, 1) that can fit in the paraboloid z = 3 -…

A: To find the equation for the largest ball centered at (0, 0, 1) that can fit in the below equation…

Q: 6. For any closed surface S, prove that || CurlF.N dS=0.

A:

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

A: Sketch the tetrahedron T with vertices (2,0,0), (0,3,0), (0,0,5) and the origin.

Q: Consider a radix 3 (possibly non-linear) code C of length n = 5 and minimum distance d(C) = 5. What…

A: In sphere packing bound, the code length is is 1 greater than the value of C.  i.e. Covering radius…

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

A:

Q: 13-Evaluate JSS zdV E where E lies between the spheres x2 + y? + z² = 1and %3D x? + y? + z? = 4 in…

A:

Q: Label the following statement as either true or false. The regular hexagon possesses both rotational…

A: To find: The regular hexagon possesses both rotational and reflective symmetry…

Q: Suppose P,Q,R,S are four collinear points such that: a. Q is between P and R. b. Ris between Q and…

A:

Q: C is the hexagon in the xy-plane with vertices (5, −5), (5, 5), (0, 10), (−5, 5), (−5, −5), and (0,…

A: Given : Vertices : (5,-5) , (5,5), (0,10), (-5,5), (-5,-5) and (0,-10) Integral given :…

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

A:

Q: In the figure, ABCD is a cyclic quadrilateral. AB // DC in circle with centre O. BC and AD produced…

A:

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: 10. Find all the planar and hyperbolic points on the surface o(u, v) = u-3uv².

A: A point on a surface is said to be a hyperbolic point if the Gaussian curvature at p,i.e., κp<0.…

Q: Use Green's Theorem to evaluate (V1+r) dr+2ry dy, where C is the triangle with vertices (0, 0),…

A:

Q: 3 Show thot tfe fundion fae Ax +26T* +C with A = AT E IR E IR", CE IR is strongly Convex if and only…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: a) Evaluate (-ri-yj+2z k) n dS, where a is the portion of the paraboloid : 3x +3y between the planes…

A: We have to Evaluate the Integral using polar coordinate

Q: 2. Given: WX = YZ; ZWXZ = ZYZX Prove: WXYZ is a parallelogram

A: Parallelogram

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: 6. Use Stoke's Theorem to evaluate fF dr, where F =, and C is the part of the paraboloid z = 4 - x2-…

A:

Q: 1. If C₁ is the segment from (x₁, y₁) to (x2, y2), find Ja x dy - y dx in terms of the four…

A: Using Green 's theorem line integral to double integral

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: What is the projection of r(t) = ti + t4j + etk onto the xz-plane?

A: Given: r(t)= ti+t4j+etk

Q: Let E be the solid parallekepiped with vertices Co,0,o).(LLO).co,l,3),(1,0,). C1,2,3),Cし,4).(2,1,1)…

A: Here, vertices are given in 3D. So, for taking limits of X and Y, we'll look for the projection of…

Q: Suppose ABCD and AB'C'D' are two squares in the plane that a) have rertex A in common, b) have the…

A: Let we have small letter corresponding to each vertex denotes the corresponding complex number.…

Q: 3. If point P is the centroid of AMNO, which statements can be deduced? Select all that apply. M R S…

A:

Q: The sphere x² + y² +z² = 100 has the center (0,0,0) and a radius of length 50. Select one: True…

A:

Q: or tho gonal Use the least, me thad to find the squones projetiom of bz Ġ 2 -a anto the salwmin of…

A: Consider the given:         A=011211and  b=12-2T=12-2

Q: 10 11 3 vertices at a parallelograni AaCD are shown in the appiet What are the coordinates of point…

A:

Q: Use the Green's theorem to calulate So (3x²y – xy? – 3.x²y²) dx + (x³ – 2.x³y+ x²y) dy, where C is…

A:

Q: 1. MATH is an isosceles trapezoid 1. 2. MH AT 2. 3. MA = MA 4. AH MT 5. ΔΗΜΑ ΔΤΑΜ 5. 6. ZMHA = ZATM…

A: Given query is to give the reason for the statement.

Q: obtain the value of b. regaring e conomethies and the forme 4= bo t bi Xi Y=bot bixitei

A: For the given linear regression line and its estimate: Y = b0 + b1Xi + ei y^ = b0 + b1 Xi We need to…

Q: Find the orthogonal traiectories ofthe one-narameter fomilyy2 - v2

A:

Q: Verify Green's theorem Where C is the boundary of the triangle formed by x=3 , y=0 , x2= 3y

A: Verify Green's theorem Where C is the boundary of the triangle formed by x=3 , y=0 , x2= 3y

Q: The middle points of the three diagonals of a complete quadrilateral are collinear. Let ABCD be the…

A:

Q: XydA, D is the triangular region with Vertices (0,0), Cu,0], and Cor) SketchD onthe XY planel

A: 8/3

Q: Show that the auto- Carre la Eton tunctan of X(+) = at e ult) for ayo does not exist. %3D 3 Find the…

A: Autocorrelation is simply the cross correlation  of a function with itself, For the first function…

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: 1) Prove that T = { diag ( eia eip, eilxip)) | a,B E [0,27()} ís maximal torus in sul 3).

A:

Q: 13-Evaluate JSS zdV E where E lies between the spheres x2 + y? + z² = 1and x2 + y? + z? = 4 in the…

A: To find- Evaluate ∭Ez dV where E lies between the spheres x2 + y2 + z2 = 1 and x2 + y2 + z2 = 4 in…

Q: Given that o is the part of the surface z = 4 – x in

A: Given, the surface z = 4 - x in the first octant from y = 0  to  y = 2. If ψx, y, z=xyz, F(x, y, z)…

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

A: Given T is a tetrahedron with vertices (5,0,0) , (0,2,0), (0,0,5) and  (0,0,0)…

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: 6. If UV bisects XY at point W, which statements must be true? Select all the true statements. (A UW…

A:

Q: Show that the points E(2, 2, 2), F(2, 0, 1), G(4, 1, -1) and H(4, 3, 0) are coplanar and that they…

A:

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: 7. What additional piece is needed to prove JMLK is a rhombus ?

A:

Q: Evaluate the double integral / ydrdy where T is the triangle with vertices (0,-1), (0, 5), (4, 3).

A: First, draw the region of integration. Then, use the region to setup the double integral.

Q: Show that a indeed perojective plane of gives 0rder BİBD (n+n+,n+),!

A: We need to prove that a projective plane of order n indeed gives a BIBD (n2+n+1, n+1, 1)