Let E be the region in the plane between the two ellipses 4x² +9y? = 1 and 4x2 + 9y2 = 4. Evaluate ff, x²y dA. %3D

Q: Consider AABC with its centroid at point G and median at BH. What is the length of GH if BG = 3x + 4…

A: Given Data: The length of BG is: BG=3x+4 The length of GH is: GH=x+10 The ∆ABC with its centroid at…

Q: Evaluate ://| y} dV, where E is the solid tetrahedron with vertices at (0,0, 0), (2,0, 0), (0, 2,0),…

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Q: Find a parametrization of the hyperboloid of two sheets (z2/c2) - (x2/a2) - (y2/b2) = 1.

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Q: Find c > 0 such that the area of the region enclosed by the parabolas y = x² – c and y = c² – a² is…

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Q: (b) Find the surface area of the portion of the paraboloid given by the equation z = 1- x? – y? that…

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Q: Evaluate (x + 2y) dA, where R is the region bounded by the parabolas y = 2x² and y = 1 + r?.

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Q: B- Find the area of the ellipse resulting from the intersection of the plane x+y+z=6 with the…

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Q: Find the area of the ellipse cut from the plane z = cx (c a constant) by the cylinder x2 + y2 = 1.

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Q: Show that the area of that portion of the surface of the paraboloid x² + y² = 4z included between…

A: Here we need to find area between given plane and x*x + y*y = 4z

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: Find the area of the portion of the paraboloid z=x^2+y^2 that lies inside the cylinder x^2+y^2=4.

A: Given that ,  paraboloid   z=x2+y2 cylinder        x2+y2=4

Q: Use the given transformation to evaluate the integral. 7x2 dA, where R is the region bounded by the…

A: Given : R is the region bounded by the ellipse 9x2+25y2=225 given transformation x=5u,y=3v We want…

Q: Evaluate ||(x+2y)dA ,where D is the region bounded by the parabolas y = 2x² D and y=1+x².

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Q: Consider the region R bounded by the parabolas y = and y = r - 3.r, as depicted in the graph below.

A: Since you have posted multiple questions but according to guidelines, we will solve the first…

Q: ind the volume of the solid that lies under the hyperbolic paraboloid z = 3y2 - x2 + 4 and above the…

A: Using the double integral formula.

Q: Find the centroid of the boomerang-shaped region between the parabolas y2 = -4(x - 1) and y2 = -2(x…

A: Parabolas are

Q: Find the points on the surface z2 = xy + 4 closest to the origin.

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Q: Use the given transformation to evaluate the integral. | 5x2 dA, where R is the region bounded by…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the centroid of the portion of the sphere x2 + y2 + z2 = a2 that lies in the first octant.

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Q: || 9x2 dA, where R is the region bounded by the ellipse 9x2 + 25y2 = 225; x = 5u, y = 3v

A: Here we use transformation to solve this problem.

Q: Which of the following equals to the area of the plane region bounded by the ellipse 4x²+y² = 4.…

A: Option 1 is true.

Q: Explain why C lies on the surface of the cylinder x² + y² = 1.

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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: Consider D to be the region below the paraboloid z = 3+x² + y² , inside the cylinder x + y² =1 and…

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Q: The portion of the surface z = 2x + y2 that is above the triangular region with vertices (0, 0), (0,…

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Q: Let E be the solid ellipsoid bounded by the surface y? = 1, a2 62 c2

A: Given that, the solid ellipsoid bounded by the surface x2a2+y2b2+z2c2=1 The volume of the unit…

Q: Integrate g(x, y, z) = x + y + z over the portion of the plan 2x + 2y + z = 2 that lies in the first…

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Q: 5/10 Determine the coordinates of the centroid of the shaded area. y * = ky? a b.

A: Given:

Q: Find the average height of the paraboloid z = x2 + y2 over the square 0<= x <= 2, 0…

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Q: Find the region in the xy-plane in which the following equation is hyperbolic: ((x- y)? - 1]u + 2u,…

A: Given partial differential equation x−y2−1uxx+2uxy+x−y2−1uyy=0 We have to find the region in the…

Q: Evaluate [xydxdy where D is the region D in the first quadrant of the ellipse 9x +4y = 36 in the…

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Q: Q4(a) Find the surface area of the part of the paraboloid z=10-x -y' that lies above the plane :=1.

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Q: Find the area of the ellipse cut from the plane z= 3x by the cylinder x + +y? =4

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Q: Consider the figure below, point D is the centroid of △ABC with DF = 4x − 1 and BD = 6x + 4. Use the…

A: Figure of triangle is given, where point D is centroid with DF=4x-1 and BD=6x+4.

Q: Which of the following equals to the area of the plane region bounded by the ellipse 4x²+y² = 4.…

A: Here we find area for given ellipse.

Q: Let R be the region enclosed by the loop of the t², y = t³ – 3t. parametric curve x =

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Q: XydA, D is the triangular region with Vertices (0,0), Cu,0], and Cor) SketchD onthe XY planel

A: 8/3

Q: =valuate the double integral [2aydA, 2xy dA, where D is the triangular region with vertices (0,0),…

A: Given that a double integration and given  D is  triangular region with vertices (0,0) (1,2) and…

Q: Find the volume of the solid that lies under the hyperbolic paraboloid z = 3y2 – x2 + 2 and above…

A: To find the volume of the solid that lies under the hyperbolic paraboloid  z=3y2-x2+2 and above the…

Q: Find the centroid of the lamina cut by the parabolas y2=x and y=x2.

A: For the clear understanding of curve we have the following graph which is shown below as:

Q: Use the given transformation to evaluate the integral. 8x2 dA, where R is the region bounded by the…

A: According to the given information, It is required to calculate the given integral using the given…

Q: Find the centroid of the parabolic spandrel shown in the figure.

A: We have given a diagram of parabolic spandrel;

Q: Evalute ff Rx²dA, where R is the region in the first quadrant bounded by the hyperbola xy = 16 and…

A: The given integral: ∫∫Rx2dAWhere R is the region in the first quadrant bounded by the hyperbola…

Q: y. y:3x- 31 to

A: Consider the figure, which is given below

Q: Find the area of the part of the paraboloid x = y2 + z2 that lies inside the cylinder y2 + z2 = 1

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Q: calculate ∫ ∫ ∫Ty dv, being the T region inside the paraboloid z= 1/(x2+y2)the sphere x2+y2+z2=5

A: We need to calculate the triple integral ∫ ∫ ∫Ty dv, where T being the region inside the paraboloid…

Q: Find the area of the surface generated by removing about the x-axis the upper half of the ellipse…

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Q: Graph the surface 1 = y2 + z2 –- by first sketching at least three cross sections in each of the xy…

A: We have to sketch the graph of the following surface in the 3D space: . First we have to sketch the…