3. A) Evaluate the triple integral xdV, where E is the solid region bounded by the cylinder 4 = y = 3z, x = 0 in the first octant. x² + y², and the planes z = 0,

Q: Find the volume under the paraboloid z-x+y above the triangle enclosed by the lines y=x, x=0 and…

A: Volume is the amount of space occupied by the closed surface. In this problem, we have to calculate…

Q: The integer n = 12700140x3243243 is missing the digit x. a) If n congruent to  3 (mod 9), then what…

A: According to the given information, Consider the given integer n:

Q: a)Given that the volume of the solid under the paraboloid z = x^2+y^2 and above the disk x^2+y^2 ≤…

A: We will find limits for x .y and z for triple integral to find volume . If needed we can change…

Q: 3.Obtain the centroid of the solid formed of the area bounded in the first quadrant by y = 2x7, the…

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Q: 2. Calculate the centroid of the thin plate R which bounded by a = 1, y = 0 and, x² + y² = 4.

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Q: The solid bounded by the paraboloids 2= - 8+z²+ y² and z -3-32²-3y² has volume:

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Q: under the pi = 1.

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

Q: 2. A solid is in the first octant lies inside the hemisphere z = 4 - x² - y², outside the cone z =…

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Q: 2) The solid S consists of the points above xy-plare, below cone x²+y2=2², enclosed by the surfues…

A: According to question,Given cone,x2 + y2 =z2,Given Surfaces,y = x,x = y2.

Q: Evaluate the triple integral z dV where E is the solid bounded by the cylinder y² +z² = 324 and the…

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Q: Evaluate where G is the solid in the first octant bounded by paraboloid : = + y, the cylinder r+ y 9…

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Q: The volume of the solid bound by the two surfaces is z = 8- 3(x² +y?), z= (x² + y?)² - 2.

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Q: 3) Evaluate the double integral fS, dr dy where D is the region bounded by the hyperbolas ry = 2, ry…

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Q: Find the volume of the solid bounded by the paraboloids z = 6 – x² – y? and z = 2x2 + 2y2.Use polar…

A: Given paraboloids z=6-x2-y2 and z=2x2+2y2 We have to find volume of the solid by the given…

Q: u², y = 56)Use the transformation x= v², z = w² to find the volume of the region bounded nby the…

A: Given: Use the transformation x=u2, y=v2, z=w2. To find: The volume of the region bounded by the…

Q: Calculate the line integral fe F. dr, where F = (ry, r? + y? + 22, yz), and C is the boundary of the…

A: Step:-1 Given that a parallelogram with vertices 0, 0, 1, 0, 1, 0, 2, 0, -1, 2, 1, -2 and F→=xy,…

Q: 5. Evaluate Sl. x2 dV where is the solid that lies within the cylinder x² + y² = 4 above the plane z…

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Q: Find a particular solution of the equation y4 -y3 - y" - y' - 2y = 8x^5:

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