Use the transformation u = y – 3x, v = y + 6x to evaluate // (2y + 12x) dA on the parallelogram R with sides R y = 3x + 3, y = 3x + 12, y = –6x – 24, and y = -6x – 18.

Q: Find the Jacobian of the transformation x = 5u + 6v, y = u² + 7v

A: Let us consider the function x=x(u,v) , y=y(u,v) The Jacobian of the function is obtained as…

Q: Find the Jacobian of the transformation. x= 3u/v, y 8v/w, z= 7w/u a(x, y, z). - a(u, v, w)

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Q: Given ABCD and its image EFGH in the plane, which type of transformation has taken place?

A: There are many different rules that are used to transform a figure into another figure. We an…

Q: Use the rule (x, y) → (3x, 2y) to find the image for the preimage defined by thepoints. Determine…

A: Steps to solve this problem1st find the image of the preimage of the points by the given…

Q: Use the transformation x = 2u + v and y=u+2v to evaluate where R is the triangular region with…

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Q: Use the given transformation to evaluate the integral. | &x +y) d4, where R is the square with R…

A: To find- Use the given transformation to evaluate the integral. ∬Rx + y dA, where R is the square…

Q: Use the given transformation to evaluate the integral. (8x + 8y) da, where R is the parallelogram…

A: Given that vertices of parallelogram is −3,9,3,−9,4,−8  and −2,10 And transformation is x=14u+v  and…

Q: Use the given transformation to evaluate the integral.   (15x + 15y) dA   R,  where R is the…

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Q: Find // (4x + 3y)dA where R is the parallelogram with vertices (0,0), (-3,1), (-4,-5), and (-7,-4).…

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Q: Use the transformation u = x – 2y, v = 2x + y to find x – 2y R 2x + y Where R is the rectangular…

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Q: Use the given transformation to evaluate the integral. (12x + 12y) dA, where R is the parallelogram…

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Q: Use the given transformation to evaluate the integral.   (9x + 12y) dA   R,  where R is the…

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Q: Find (4x +5y)dA where R is the parallelogram with vertices (0,0), (-3,-5), (-1,-4), and (-4,-9). Use…

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Q: 2. Use the transformation u = x – 2y, v = 2x + y to find x – 2y 2.x + y Where R is the rectangular…

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Q: Find /| (4x + 5y)dA where Ris the parallelogram with vertices (0,0), (5,-4), (1,-2), and (6,-6). Use…

A: Given integral, ∫∫R4x+5ydA Here R is the parallelogram with vertices 0,0, 5,-4, 1,-2 and 6,-6. To…

Q: For the transformation below, find д(х, у) d(u, v) и%3D 3х — 5у, v = 2x + y -

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Q: Evaluate (6x-3y)dA where Ris the parallelogram with vertices (2,0), (5,3), (6,7) and (3,4)using the…

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Q: et D be a parallelogram with vertices (0,0), (= nd a linear transformation x-x(u,v), y-y(u,v)a (x…

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Q: Q4 Evaluate S SR (x + 2y) dA where R is the triangle with the vertices (0, 3).(4, 1) and (2,6) using…

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Q: Q1//A:- +ydA where Ris the trapezoidal region with vertices given by Evaluate 5 5 2 2 2u + 3v and…

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Q: Use the transformation u = x2 –- y²,v = x² + y² to find ff, xydA where R is the region in the first…

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Q: Find (2x + 3y)dA where Ris the parallelogram with vertices (0,0), (-5,-1), (1,-2), and (-4,-3). Use…

A: Here, we need to find ∬R2x+3y dA where R is the parallelogram with vertices (0, 0), (-5, -1), (1,…

Q: b) Use the transformation u = 2x – y, v = x + 3y to find p (2x-y)3 dA, x+3y where R is the…

A: .

Q: For the solution of the PDE x*uz + y?u, + x² + 4x + 6y = 0 Which transformation can be used?

A: use special form of charpit auxiliary equation

Q: Find the Jacobian of the transformation. x = 6e5 +t, y = 2es - t a(x, y) = a(s, t)

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Q: Find the Jacobian of the transformation. x = 7es +t, y = 3e5 - t a(x, y) = a(s, t)

A: We have to solve

Q: Find the Jacobian of the transformation. V y 2и + 7v y 3= 4и - бу

A: To find the jacobian of the given transformation.

Q: Find // (3x + 5y)dA where R is the parallelogram with vertices (0,0), (4,2), (-1,5), and (3,7). Use…

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Q: Calculate 121x dxdy where R is the parallelogram with vertices (0,0), (6,2), (7,6) R 1 -(v — Зи), у…

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Q: under the linear transformation T: R² → R² consisting of a reflection in the y-axis followed by a…

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Q: Use the given transformation to evaluate the integral. + v), y = v - 3u) (16x + 16y) dA, where R is…

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Q: Find the Jacobian of the transformation. x = 8v + 8w², y= 5w + 5u2, z = 3u + 3v2 дх, у, z) a(u, v,…

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Q: Find the Jacobian of the transformation. x = 4v + 4w?, y = 9w + 9u?, z = 5u + 5v2 Ә(х, у, 2) d(u, v,…

A: Given transformation: x=4v+4w2y=9w+9u2z=5u+5v2 We have to find the jacobian  ∂(x, y, z)∂(u, v, w).

Q: Find the Jacobian of the transformation x 2u, y = 2uv and sketch the reg

A: (a) Given,             x=2u, y=2uv

Q: Q3//B:- Evaluate | 2? – zy + y² dA where Ris the ellipse given by R 2? – ay + y? < 2 and using the…

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Q: Use the given transformation to evaluate the integral. u + v), y = v (16x + 16y) dA, where R is the…

A: Given  ∬R16x+16ydAWhereR is the parallelogram with vertices -3,9, 3,-9, 4,-8, -2,10and x=14u+v ,…

Q: For which transformation would triangle RST have image R'S'T'?

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Q: Find the area.

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Q: 2) Use the change of variables formula and an appropriate transformation to evaluate ff, xy dA where…

A: Jacobian is for n functions in n variables, the Jacobian is the determinant of the Jacobian matrix.…

Q: Find the Jacobian of the transformation x = 5u – 2v, y = u + 2v

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Q: Use the transformation u = r- 2y, v = 2r +y to find a - 2y dA 2.r + y Where R is the rectangular…

A: To evaluate: ∫∫Rx-2y2x+ydA where R is the rectangle region enclosed by the lines…

Q: Use the given transformation to evaluate the integral.   (12x + 12y) dA   R,  where R is the…

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Q: Find /| (5x + 3y)dA where R is the parallelogram with vertices (0,0), (4,1), (5,3), and (9,4). Use…

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Q: Find the Jacobian of the transformation T : (u, v) → (x, y) when x = y = 4и — v 5u + 4v -

A: Jacobian of the Transformation.

Q: 15 Find / (4x + 3y)dA where Ris the parallelogram with vertices (0,0), (-3,-4), (5,-1), and (2,-5).…

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Q: Find the Jacobian ∂(x,y) ∂(u,v) for the transformations x=4ucos(6v)​, y=4usin(6v) and x=4usin(6v)​,…

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Q: Find the Jacobian of the transformation. x = 7es +t, y = 3e5 - t a(x, y) - a(s, t) -42e25

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

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Q: Use the given transformation to evaluate the integral. (9x + 9y) dA, where R is the parallelogram…

A: This question is based on the concept of change of variables in double integral whose formula is…

Q: Find the Jacobian of the transformation z = 4u – 6v, y = u² − 2v

A: The objective of the question is determine the jacobian transformation.

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.