7) Find the mass and the center of mass of the lamina with density 8(x, y) = grams/cm² and occupies x² + the rectangular region 1sx5√√3 and 1sys4.

Q: Consider the disk x² + y² ≤ 4 in the second quarter. Find its center of mass if the density at any…

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Q: 10. The part of the paraboloid x = y² + z² that lies inside the cylinder y² + z² = 9

A:

Q: Calculate the volume of the solid that is limited superiorly by the sphere x2+y2+z2=9 and inferiorly…

A: To Calculate: Volume of the solid bounded superiorly by x2+y2+z2=9 and inferiorly by x2+y2=z2.

Q: Find  the Volumeof the largest rectangular box lying above the xy-plane, with y less that or equal…

A: considerlength of rectangular box =x width of rectangular box  =yheight of rectangular box =z

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Q: Suppose that a pencil holder is in the shape of a right circular cylinder, which is open at one of…

A: Data from the question÷

Q: Find the surface area of the part of the sphere x² + y² + z² = 16 that lies above the cone z = √√x²…

A:

Q: Sketch the cylinder given by x = 4- Z*2（z square）in three-dimensional space.

A: Given: The equation is x=4-z2. To sketch: The given equation in three-dimensional space.

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Q: Find the surface area of that part of the plane 8x + 6y + z = 5 that lies inside the elliptic…

A: Given that the equation of a plane                                         8x+6y+z=5. To find the…

Q: Calculate the surface area of the z=x²+y surface on the triangular region with vertices (0,0), (1,0)…

A: Let z=fx,y. Differentiate the function fx,y with respect to x and y, to obtain fxx,y and fyx,y.…

Q: Verify the Divergonce Theorem for F=(2x-x)+x*y} -aż? taken over the bounded by x -o, X=1, y=0,…

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Q: Q5) Find volume of body bounded by z² + y² + x² = 9.

A: Explanation of the answer is as follows

Q: 6) Find the area of the part of the sphere X² + y² + Z² = 4 that lies within the cylinder X² + y² =…

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Q: 1,2 40 40 cm 40 cm 40 xp, 40 Saỹ dA y SadA 0, 40 1 x'dx Jo 40 What is written instead of '?'

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Q: U %3D {x\x € R лх> 14} А 3D [-2,25), В %3 [15,30]. Find: a) AUB =? b) Ā =? c) AnB =?

A:

Q: Give an example of a plate such that its center of mass does not occur at any point on the plate.

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Q: Q6/ Find the volume of the parallclogram-sided determined by: u- -3i +7j +5k, v -3i + 7j-3k, and w-…

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Q: Find the volume of the solid bound by the surface z=(2x-y)^2+(x-y-1)^2 and the plane z=4. Question:…

A: Given that a solid is bounded by the surface and plane.

Q: Compute the volume of the column with a square base R= {(x,y): |x|< 3, |y| <3} cut by the plane z =…

A: We have to find volume whose base is square-

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Q: Which is the equation of a sphere with a center at (1,0,-2) with a volume of 36(pi)(u^3)? a.…

A: We first defined the equation of sphere and centre,volume . Using this formula we have equation (a)…

Q: iv) The region bounded by the semi-circle x = centroid (x,y). a) Explain why y = 0. b) Find the…

A: The objective of this question is to find the centroid of the region bounded by the semi-circle x =…

Q: Find the surface area of the portion of the cone x² + y² = z² above the region inside the…

A: