B-Find the center of mass of the region bounded above by the half circle y = √a²-x² and below by the lines y-0 and y=-x.

Q: F(x, y) = (2x + y3, 3y - x4} across the unit circle

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Q: Find the maximum value of ƒ(x, y) = x²y6 for x, y ≥ 0 on the unit circle. fmax =

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Q: Find the center of mass of a thin plate of constant density & covering the region bounded by the…

A: For center of mass of a region R with constant density k mass  of the region M=∫∫RkdA Moment about x…

Q: 6. Find the area of the surface generated when y = v4x + 6 is revolved about the x- axis on the…

A: 80π

Q: Use Green's Theorem to find the work done by F(x,y)=x(3x+y)i+xy^2j in moving a particle from the…

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Q: Find the area of ​​the rotating surface that occurs by turning circle x2+y2=4 around line x=2 .

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Q: Find the area of the vertical wall whose base is the semicircle {(x, y) | x² + y² = 1 and y>0} and…

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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: Find the centroid of the thin plate bounded by the graphs of g(x)=x² and f(x) = -x + 56. Use the…

A: The region is bounded by the graphs fx=x2 and gx=-x+56. We have to find the centroid of the region.

Q: Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y = x and y =…

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Q: Suppose F(x,y)=. Use Green's Theorem to calculate the circulation of F around the perimeter of the…

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Q: Find extrema of f (x, y) = 2x² + 4y² on the unit-circle x + y² = 1.

A: To find the extrema of the function ƒ(x, y) = 2x² + 4y² on the unit-circle x² + y² = 1, we need to…

Q: Show that the maximum value of f (x, y) = x 2 y3 on the unit circle is

A: We should maximize f(x,y)=x2y3 under the constraint gx,y=x2+y2 where x2+y2=1. Now, ∇f=2xy3,…

Q: enclosed betw parabola y = x2

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Q: Find the center of mass of a thin plate of constant density 8 covering the given region. The region…

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Q: Find the centroid of the thin plate bounded by the graphs of g(x)=x² and f(x) = x + 6. Use the…

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Q: Pu subject to the initial conditions u(1,0) = f(x), and du (z, 0) = g(x). a. Using the…

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Q: Plot the function f(x, y) = x² – y² over the square region bounded by the lines y =x - 2, y =x+ 2, y…

A: Given the function fx,y=x2-y2

Q: Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y = x and y =…

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