Let T be the tetrahedron with vertices (2, 0, 0), (0, 2, 0), (0, 0, 3) and the origin. Write I.f(r, y, 2) dV in the form: 3 u(z) cu(y,z) f(x, y, z) dx dy dz u(2) = ข(บ, 2) =

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: 7) z dV, E is the solid enclosed by the cylinder r2 +y = 1, and the E planes z = 0 and z 3.

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Q: Compute the triple integral and please show work

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Q: Evaluate O xy?dx + a°dy, where C is the rectangle with vertices (0,0), (6,0), (6,3), and (0,3)

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Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (1,0,0), E (0,4,0), and (0,0,2)

A: The vertices of the tetrahedron are (0,0,0),(1,0,0),(0,4,0),(0,0,2).  x varies from x:0→1y varies…

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: 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: Integrate H(x, y, z) = x2sqrt(5 - 4z), over the parabolic dome z = 1 - x2 - y2, z>=0.

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

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Q: Evaluate the triple integral |// xy dV where E is the solid tetrahedon with vertices (0,0,0), (7, 0,…

A: Consider the following: Equation of plane passing through 7,0,0,0,5,0,0,0,10x7+y5+z10=1x ​ranges…

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: Let S be the solid tetrahedron bounded by the four planes a = 0, y = , z = 30, and z = 4x + y. !!…

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Q: 2x2 dv, where T is the solid tetrahedron with verticies (0, 0, 0), (1, 0, 0), (0, 1, 0), and (0, 0,…

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Q: If E is the solid shape bounded by x 2 0,y 20 ,z 2 0 and the plane 2x + 3y +z = 6 evaluate (x + y)…

A: The given question is solved below

Q: Sſcos( dxdy y-x y+x D

A: Given and u=y-x,  v=y+x where D is the trapezoid with vertices (1, 0), (2, 0), (0, 2) and (0, 1).

Q: I need help finding the absolute maximum and minimum values of f on the set D.

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Q: 6. Evaluate (a + y) da dy dz, where D is the tetrahedron with vertices (0,0,0), (1,0, 0), (0, 1, 0)…

A: Introduction: The triple integral is applicable to find the volume of a solid enclosed by given…

Q: Let G be the solid enclosed by the plane z= y, the xy-plane, and the parabolic cylinder y = 1-x². If…

A: Consider the given information,

Q: Z is the centroid of AUVW. What is UY if UZ = 8? O A. 4 о с. 6

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Q: Evaluate the triple integral∭E xy dV where E is the solid tetrahedon with vertices…

A: Given Data : Triple Integral ∬∫ExydV and E is the solid tetrahedron with vertices 0,0,0,…

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: Let T be the tetrahedron with vertices (3, 0, 0), (0, 5, 0), (0, 0, 4) and the origin. Write /| f(x,…

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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: Considering f(x, y, z) = z + x²y and S as part of the cylinder y? + z² = 25 that is between the…

A: Given that, fx,y,z=z+x2y and S is the part of the cylinder y2+z2=25 that is between the planes x=0…

Q: If S is the solid bounded by the paraboloid z = 3x2 + 3y and the plane z = 4 (with constant…

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Q: Evaluate // e² dV where E is enclosed by the paraboloid z = 2 + x² + y², the cylinder E x² + y? = 3,…

A: Since we are given with the multiple number of questions and answered according to the guideline.

Q: Evaluate the triple integral xy dV where E is the solid tetrahedon with vertices (0, 0,0), (6, 0,…

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Q: Let C be the positively oriented square with vertices (0, 0), (2,0), (2, 2), (0, 2). Use Green's…

A: Let the given square be OABC which is positively oriented.

Q: Let B be the ball with center at the origin and radius 1 SS S2(z² + y² + z²)dV = %3D 8M 16x 5. 24x

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

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Q: 5. Evaluate y* dV, where E is the solid tetrahedron with vertices at (0,0,0), (2,0,0), (0, 2,0), and…

A: we can evaluate the given integral. ∫∫∫R f(x,y,z) dV =∫∫∫R f(x,y,z) dzdydx

Q: 2. Set up the triple integral f[Sp I+y+zdV, where D is the tetrahedron with vertices at (0,0,0),…

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Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (4,0,0), (0,3,0), and (0,0,2)

A: we have to find triple integral

Q: The simple solid Q, drawn in the first octant and generated by the surfaces y – 1 = (x – 2)² 3x + 2z…

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Q: Consider the solid Q that is generated in the first octant by the surfaces S, : 2x + 3y + 3z = 6 S,:…

A: The region S2 is clearly a parabola y2 = 2-x and it is symmetrical in the x-axis.

Q: Let T be the tetrahedron with vertices (4, 0, 0), (0, 5, 0), (0, 0, 5) and the origin. Write f(x, y,…

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Q: Consider the solid lih S,: X=4-y² そ=2

A: Surface: Surface, A two-dimensional collection of points (flat surface), a three-dimensional…

Q: Evaluate the triple integral II. x* dV, where T' is the solid tetrahedron h vertices (0, 0, 0),…

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Q: Evaluate the triple integral.  (x2 + y2) dx dy dz; W is the pyramid with top vertex at (0, 0, 2)…

A: The given triple integral is,

Q: Let B be the ball with center at the origin and radius 1 SS f6(n² + y² + z² )dV

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Q: Let T be the tetrahedron with vertices (4, 0, 0), (0, 3, 0), (0, 0, 5) and the ori I f(x, y, z) dV…

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Q: where F(x, y, z) = (ry, x²y, y) Use Gauss's theorem to calculate where is the paraboloid z = 4 – x²…

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Q: A solid G is bounded by the paraboloid z = 4 – r - y², the cylinder 2+ y = 4 and the plane z = 5.…

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Q: Let V be a solid enclosed by x2 + y? + z² = 4 and z = 0, which can be illustrated by (0,0,4) (0,4,0)…

A: The given curve is: x2+y2+z2=4          and         z=0

Q: Consider the solid bounded by surfaces S1, S2, S3, S4, S5, and S6 with vertices A, B, C, D, E and O,…

A: In this question, we use the given sketch of the surface and find the parametrization for each…

Q: 3.use Greens theorem s (1+x5 dx + 2xy dy ,where C is triangle With vertices (0,0),(1,0),(1,3)…

A: Apply greens theorem

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: Let T be the tetrahedron with vertices (3, 0, 0), (0, 4, 0), (0, 0, 5) and the origin. Write f(x, y,…

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Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (2,0,0), (0,4,0), and (0,0,1)

A: We have to find the volume integral of the given function.