OFind the V of He solid obtacred by rolating the ) Tle egun Under y x+2 [o,a] region aloout the y-afis. b) The under y = x²+ 2 rotated neguon about X=3,

Q: 3. The centroid (#, 9) of an area D can be calculated by To dA To dA (a) Use Green's Theorem to show…

A:

Q: Does the sphere x + y + ? = 25 have symmetry with %3D respect to a) the xy-plane? b) the line e: (x,…

A: we have the sphere x2+y2+z2=25  here the radius is 5

Q: Sdve the folosing Dfferenthal equations by using the method of Laplace Transforms: caly'+4y =4x…

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Q: Integrate h(x, y) = yi-xj over the triangle with vertices (-2, 0), (1, 0), and (0, 1) traversed…

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Q: 2) Evaluate the vategral if cis any Seetion al Smooth Curve from 10,0,0) to (lilil). .(-3p²+2y-Z) da…

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Q: A.W:-Evalwte the intagral Ic2 - i) dz where c is; line OThe straight 9= 2x jeining Aceso) to BC1,) A…

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Q: 5Let MH)=Hit2costj + (2shnt-3k a) Find unit tingent vector TH) of rtH)

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Q: 5) Using the de finition of the contour integral compuute the integral of f 12)= 1+i-2ž from Zo =0…

A: Contour integral

Q: Let S be the torus parametrized by G(e,p) ((a bcos(p)) cos(0), (a +bcos(p)) sin(0), bsin(p)) for θ,…

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Q: Consider the solid mmited by the following surfaces: S,: x=4-7 SziytZ=Z S3: 2xty+ z= 2 C) 2=2- 2z…

A: Here we find the projection of the solid on the xz-plane.

Q: E) If F(x, y, z) = 3x²i + 3zj-3xk

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Q: dx, y) Find the Jacobian du, v) x=9u cos 6v, y=9u sin 6v, z = 3w 1458v 972v 972u 1458u or dx, y, z)…

A: Given x = 9u cos 6v,   y = 9u sin 6v,   z = 3w

Q: a) Find the points at which the twisted cubic F(t) = ti + t} +tk intersects the plane 4.x +2y+z = 24…

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Q: 2 22 2.2 り= ptasp;t P3 %3D 2

A: As per guidelines, we will solve only first question. Let us consider the vector space V3ℝ and…

Q: Find the area of the region between the curve 1 6t = - e and the x-axis from t = 0 to 7 A) 7 x = et…

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Q: Consider the 2nd order equation 2²y+ Sin dy y² +y = Choose the ight assertion A) the linearized…

A: consider the 2nd order equation d2ydx2+sindydt+y2+y=0 this is a non linear homogenous differential…

Q: . Evaluate || (2- 1) do, where S is the part of the cone z = Vr + y² which lies under the plane z =…

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Q: 14 Find the surfuce area the part of the parabolic cy linder 2=y? that the triangle with vertices…

A: According to the given information, it is required to find the surface area of the part of the…

Q: Evaluate: ∬▒ 〖4X d A〗 over the region R bounded by the parabola Y = X ^ 2 and the line X = Y-2. A)9…

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Q: oo Use Hhe Quotient Rule to differentionle the funchion 0. secca) ) Simplify the expression it…

A: Differentiation

Q: Prove that dr-V3Ta? where こis the intersection of the plates: x²+ and and F=ly,Z,x)

A:

Q: 4ay ana y" 4ax is to be revolved aro or the: ) Plane Area ) First Moment with respect to x - axis…

A: Note- “Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: Consider the curve C which is the intersection of the surfaces shown in the attached figure.

A: To evaluate the below integral. ∫Cx−y−2zds