Let D be the unit disk: x² + y² ≤ 1. Evaluate √√ 4exp(x² + y²) dx dy by making a change of variables to polar coordinates. 4ñ( e − 1)

Q: Q17:- In polar coordinates prove that** 第。

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Q: Evaluate √√x² + y² dA, where D is the domain in the figure and a = 10. -X (Give your answer in exact…

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Q: Evaluate in polar coordinate 5. So 0 √1-x² (x² + y²)dydx

A: The given integral is ∫01∫01-x2x2+y2dydx. The objective is to calculate the value of the given…

Q: Find the parametrization for the line segment beginning at P1 and ending at P2. P1(-3,0,-5)…

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Q: (08.01 MC) Given point M (6.-6√3), which is located on the rectangular coordinate plane, what are…

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Q: Find the polar coordinate for (-1, √3) where r>0 and 0≤Ø<2π

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Q: 5. Find u-dr for a unit square in the first quadrant with vertex at the origin by Stokes's C theorem…

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Q: Determine the angle of rotation necessary to transform the equation in x and y into an equation in X…

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Q: 2. Use polar coordinates to evaluate √9-1² 2 L √4+x² + y² dy dx.

A: This is a problem related to integral of polar curves. Based on the substitution in cartesian…

Q: 7. Evaluate JJ S² S² √x² + y²dydx + by converting to polar coordinates. 2√2 1/2v² √²² √2³² + 1²³dyde

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Q: 3. Find the polar form of the Cartesian equation: x² + y² = (3 + 2x)² %3D

A: Solution-

Q: in C6. Evoluate the Rxpiession, write your ans wer polar and rectangulor form

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Q: Find the cosine of the angle between the following two planes. -1x -4x cos 0 = [3]/[2(sqrt(15))] +2y…

A: -x+2y+5x=-1-4x+3y-5x=1

Q: How do you solve this using polar coordinates?

A: We will find out the required result.

Q: 3. The point D is the centroid of AABC. Find the value of the distance DC if : GD = 2x – 8 and GC =…

A: It is known that the centroid of a triangle is the point at which the 3 medians of the triangle…

Q: Consider the following. x2 + 2 sqaureroot of 3  xy − y2 + 8 = 0 (b) Use a rotation of axes to…

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Q: 3. Find the dot product of à = and B =. 4. Find the scalar product of P = 10î – 4f + 7k and Q = -2î…

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Q: Find the area of the triangle with vertices O (0,0), P (6√3, π / 6), P (12, π / 3) on a plane formed…

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Q: The center of Dis R. Rare}

A: As the centre of group D4 is {R0,R180}•

Q: Evaluate ([cos (x – y)sin(x+ y)dA, where R is the triangle with vertices (0,0), R (-1,7), and (7,7)…

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Q: Convert to Polar coordinates. (r 20 & 0 < 0 < 2n) (x, y) = ( -1, v3 )

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Q: 3. Evaluate LLA" (4- y2) dydx by using polar coordinates.

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Q: 1. Convert to polar form (a) −3+4j (b) –10j

A: a) -3+4jb) -10j

Q: R] [CLO 8] Give an example of a point in Quadrant III of the rtesian plane.

A: we will find the required.

Q: 2(V3 – i) (1 + 1)?

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