9) Find the center of mass (also known as the centroid) of the triangular region with vertices (0,0), (2,0), (2,6) Note that this is a continuous region not three individual point masses. You may assume that the region has a uniform density.

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A: To find the centroid x, y ,z of the region bounded by the xy-plane, the cylinder x2+y2=1369 and the…

Q: A solid in the first octant is bounded by the two spheres x^2 + y^2 + z^2 = 1 and x^2 + y^2 + z^2 =…

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Q: Consider the two-dimensional surface (“lamina”) bounded by y = e^x , y = 0, and x = 1 and whose…

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Q: Using Pappus' theorem, find the centroid of the upper region bounded by the graph of X² + Y² = R²…

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Q: 2. bounded by the axis of the region Volume of the body of rotation created by rotating it Oround ?

A: Given that  y = 1 -x2, x =0 , y = 0   x2 = 1- y The limits of y :-  from y = 0 to y = 1

Q: Find the centroid of the region bounded by y=x^2 and y=2.

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Q: Determine the volume of the solid formed when a circle that passes through the points (l , 3), (3 ,…

A: As per the question we are given a circle passing through the three points : (1, 3) ; (3, 1) ; (1,…

Q: 38. f(x) = x² at x = -1 %3D

A: Solution Question 38 Given, The curve  fx=x2 We have to find the equation of the tangent at point x…

Q: Find the mass of the lamina in the shape of the portion of the plane with equation 4x + 8y + z = 8…

A: Surface integral

Q: A solid is formed by revolving about the y-axis, the area bounded by the curve x^3=y, the y-axis,…

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Q: Calculate the volume of the solid above the xy plane delimited by = 9-x² - y²

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Q: Let S be the passage of R ^ 2 defined by the parabola with equation y = 18-x ^ 2 and by the line…

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Q: y-coordinate of the centroid of the plane region bounded by 17 What is the the x-axis and the…

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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 center of mas of the region bounled bry y - 28 - x, x = 0, y - 0 with mass density &x, y) -…

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Q: Find the centroid of the triangle bounded by the x-axis, the y-axis, and the line 2x + y = 5. The…

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Q: Calculate the volume of the sphere x^2 + y^2 + z^2 = a^2, using both spherical and cylindrical…

A: Given the equation of the sphere is       x2+y2+z2 = a2 ,where a is the radius of the sphere.

Q: Use Polar coordinate to evalute ff gdA, 8 where R is the region Bounded by the life line yet, the…

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Q: Find the centroid of the quarter circle x² + y² ≤7, y> [x] assuming the density 6(x, y) = 1. (Use…

A: Given that x2+y2≤7, y=x In polar coordinate we can write x=r cos θ, y=r sin θ and the point of…

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: What is the center of gravity of the region bounded by the graphs of equations y = x2 -2x+1, y =…

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Q: In Exercises 19 - 26, find the center of mass of the lamina de- scribed by the region R in the plane…

A: To find the center of mass of the lamina described by region R and density function δx,y. The region…

Q: A semi-circular lamina of redius R is bounded by the curve x2+2=4 and the x- axis. Find (a) the…

A: Given A semi-circular lamina of radius R is bounded by the curve x2+2=4 and the x-axis.

Q: A thin plate with uniform density is placed in the region bounded by the circle ² + y² = 25 in the…

A: Given that a thin plate with uniform density is placed in the region bounded by the circle x2+y2=25…