Given the bases B = {u1,u2} and B'= {u'1, u'2} for R, where and The transition mat rix P8-B from B to B'is: 1 OA. O 1 1 1 OB. 0 -1 -1 1 o OC. 2 -1 1 1 OD. 1 -1 -1

Q: In AMNP, T is the centroid. If MR=30 find MT. N R T M S

A: We are given that T is the centroid and MR=30. We know that the centroid divides each median in a…

Q: Given the vector field E = 4zy² cos 2xa, +2zy sin 2xay + y² sin 2xa₂ for the region [x], [y], and…

A: The general form of a vector-valued function in three dimensions is given by F=F1ax+F2ay+F3az, where…

Q: Use the Chain Rule to find Əz/əs and əz/ət. z = x°y', x= s cos(t), y = s sin(t) az as %3D az %3D at

A: Total derivative

Q: (a) Let F = 4x27 + y} - (z – 1)k. Compute I7. dA where S is a square of side 5 units centered at…

A: Given that, the vector is F→=4x2i→+yj→-z-1k→. Determine the value of ∫SF→·dA→.…

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: Use Green's Theorem to evaluate the line integral |v - x)dx + (2x – y)dy for the given path. C: x =…

A: Answer

Q: Find the decomposition of a(t) a = arT + anN into tangential and normal components for r(t) =…

A: Given

Q: Find Laplace ice transforms of the ictions: suonpun f(t) = t – 2e3t

A:

Q: Find the Jacobian for the transformation x = 3u + v and y = u+ 3v. NEXT, use this transformation to…

A:

Q: Find a mat rix P such that p-l 1 0 1 0 %3D 3 2 -1 0 P%3D OA. 3. 13 P = В. 0 1 1 0 P = C. 3 1 1 0 [1…

A: In the question we have to find P matrix.

Q: Evaluate the triple integral. 16.  ∫∫∫T  xz dV , where T is the solid tetrahedron with vertices…

A: The solid tetrahedron T with vertices 0, 0, 0, (1, 0, 1), (0, 1 ,1) and 0,0, 1. The solid region is…

Q: 10. Use Green's Theorem to evaluate the integral fe y dx + 2xy³ dy, where C is the square with…

A: Introduction: By applying Green's theorem, one can determine line integral through surface integral.…

Q: 17. Integrate G(x, y, z) = xyz over the triangular surface with vertices (1, 0, 0), (0, 2, 0), and…

A:

Q: Use the Chain Rule to find ôz/ðs and ôz/ôt. z = tan(u/v), u = 9s + 8t, v = 8s – 9t as az at

A:

Q: 1) Find the outward flux of F across the region D where F= (6x² + 2xy, 2y + x²z, 4x² y³ ) and the…

A: The vector field is,F¯=6x2+2xy, 2y+x2z, 4x2y3The region D is cut from the first octant by the…

Q: Let R be the trapezoid with vertices (1,-1), (3,3), (3,-3) and (9,9). Give a change of variables to…

A: Given that ,  R be the trapezoid with vertices (1,-1) , (3,3) ,(3,-3) and (9,9) . Let , the vertices…

Q: Carry out the affine transformation | u = (x + y)/V2 lv= (y - x)/V2 in the improper double integral…

A:

Q: 5) Find the work done by the force field F(r, y, z) = ri-zj+y k in moving an object along the…

A: Work = Force X Displacement

Q: Find the Jacobian w/ respect to UVW X=U(3-v), Y= uv(3-w), Z=Uw

A: Our aim is to find the jacobian of x=u(3-v), y=uv(3-w) and z=uvw⇒x=3u-uv ,   y=3uv-uvw and…

Q: Evaluate the triple integral ryd xydV where E is the solid tetrahedon with vertices (0,0,0), (10, 0,…

A:

Q: For this problem why did we integrated from -90degre to 90degree, instead of integrating from…

A: To discuss the suggested solution for the length of the given curve

Q: Considering f(, Y, z) = z + x²y and S as part of the cylinder y² + z² = 25 that is between the plans…

A: It is given that surface S is the part of the cylinder y2+z2=25 lies between the planes x = 0 and x…

Q: Calculate the circulation of A = p cos ap + z sin o az around the edge L of the wedge defined by 0 ≤…

A: Yes , we can solve using stokes theorem. Note that all the cases z = 0

Q: Evaluate the triple integral. 6xyz dV, where T is the solid tetrahedron with vertices (0, 0,0), (1,…

A:

Q: Use the Chain Rule to find dz/ðs and əz/ət. z = tan(u/v), u = 5s + 8t, v = 8s – 5t %3D az %3D as az…

A: We have to use chain rule to find the partial derivatives of z.

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& y varies from 0 to 2 and z varies from 0 to 4.

Q: Evaluate the triple Integral. 3xyz dV, where T

A:

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: Compute the flux ∮∂D F • n ds of F(x, y) = {x3, yx2) across the unit square D using the Flux Form of…

A: Given the equation F(x, y) = (x3, yx2)  The closed surface is the unit square the limits of x and  y…

Q: FD is the region in the first octant between the spheres x2+y2+z²=1 and x2+y2+z²=16, then dV =

A: Converting into spherical coordinates

Q: z dV, where E is the solid tetrahedron with vertices (0,0,0), (2,0,0), E Find (0,6,0), and (0,0,3)

A:

Q: Find the Jacobian d(x,y,z)/ d(u,v,w) of the transformations below. a. x = u cos v, y = 4u sin v, z…

A:

Q: Find the Jacobian a(x, y) / a(u, v) for the indicated ch x = e-u sin v, y = e-U cos v a(x, y). a(u,…

A:

Q: Solve by Laplace transform Utt - 9urz = 0, 0 0 u(0, t) = u(T, t) = 0, %3D u, (x,0) = 0, u(x,0) = 2…

A: Use Laplace.

Q: Let T(r,s,t) = (r cos(s) sin(t), r sin(s) sin(t), r cos(t)) Find the Jacobian of T at (3, π/4, π/3)

A:

Q: Evaluate the double integral I2 = || y'dzdy T where T is a triangle with vertices (-4, 0), (0, 1),…

A:

Q: Choose an appropriate form for a panticular Soln of y"+ qy =f8cos@t) evaluate the constants in the…

A: To find - Choose an appropriate form for a particular solution of y'' + 9y = t2cos(3t) and then…

Q: 13. Point P is the centroid for AMNO. Calculate OQ if ON = 17. Round to the nearest tenth if…

A:

Q: Use the Fourier transform to solve the IBVP U = a² (urz + Uyy), 0 < x < 0, 0 < y < o. u (x, y,0) = f…

A:

Q: Use the Chain Rule to find az/ds and az/ôt. z = tan(u/v), u = 3s + 6t, v = 6s - 3t az as az at II

A:

Q: .The primal form of SVR with soft margin is M 1 min |w+CE(6i + &;) i=1 s.t. y) – w"x1) – b < e+ §i,…

A:

Q: #1. Evaluate (2x – 5y) dA, R where R is the parallelogram with vertices (0,0), (2,3), (–1,4) and…

A: The given region R is a parallelogram with vertices as shown in below graph. We have to use change…

Q: Compute the Jacobian of the mapping at the given point. O(r, 0) = (8r cos(0), 8r sin(0)), (r, 0) =…

A:

Q: Let r(t)=⟨sin(t),cos(t),9sin(t)+3cos(2t)⟩. Find the projection of r(t)r(t) onto the xz-plane for…

A: Set y=0 as the answer is asked for xz plane.

Q: Consider the functions z = - e* In y, x= In (u cos v), and y = u sin v. dz dz (a) Express du and dv…

A:

Q: Let z = f(x, y) and r =r cos 0, y = r sin 0. Use the chain rule to express: af %3D 11. af dy Te and…

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: Use the Chain Rule to find ôz/ds and ôz/ðt. z = tan(u/v), u = 5s + 9t, V = 9s – 5t az as az at

A:

Q: The Jacobian J (r, Ø) for the transformation x =r cos(Ø) + 100000 y = r sin(Ø) + 500000000 at r= 2,…

A:

Q: 1. The accompanying figure shows two polygonal paths in space joining the origin to the point (1, 1,…

A: Given: The function with two polygonal paths in space joining the origin to the point (1, 1, 1).…