Compute the volume of the ellipsoid obtained by rotating the ellipse 16 1 around the x-axis. O 40 O 247 647 3 O 327 32л

Q: Q3: Find the centroid of the next shaded area. 4m

A: Solution :-

Q: An ellipse + 1 is revolved around the y-axis. The volume generated by the solid of revolution if a =…

A: Let us first calculate the y value on the ellipse at x = t.   From the equation of the ellipse, at x…

Q: = Find the volume of the ellipsoid x² + y² + 6z² 64.

A: Given,                x2+y2+6z2=64.

Q: 4.x² + y = 4

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Q: Determine the relative to the or two curves whos

A: Given,          x2+4x2-8x=0                    x2-8y=0

Q: Let a, b > 0. (a) Calculate the area inside the ellipse given by the equation 1. 62 || a²

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Q: A three dimensional solid is created by rotating a circle about one of its diameters. What is the…

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Q: Find the centroid of the area shown in figure 1.

A: The figure is  There are four rectangles 1, 2, 3, 4.

Q: 2. Find the center of a tetrahedron that is cut off the first octant by the plane z+ y + z = 2. Due…

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Q: FIND THE AREA OF THE SURFACE FOR THE PORTION OF THE PARABOLOID Z = 49-x² - y² IN THE FIRST OCTANT

A: Formula: The surface area of the function z=fx, y over the region D is: SA=∫∫D1+zx2+zy2 dA The given…

Q: 1. a. Draw the ellipse x? + y/4 = 1 and label its x and y intecepts. b. View the ellipse as a type I…

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Q: = The region bounded by the parabolas y2 r-axis. The two curves intersect at x = solid is 16 5x and…

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Q: Determine the x- and y-coordinates of the centroid of the shaded area. Assume c = 7, a = 1.35, b =…

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Q: Q2. Fin the mass of an octant of the ellipsoid =1,

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Q: Center of Mass. (a) Prove that each median of a triangle divides the triangle into two subtriangles…

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Q: 2 Find the volume of the ellipsoid 2y 7z 16

A: Volume of the ellipsoid for the equation,

Q: Complete the following problems. a. Express the area A of the cross-section cut from the ellipsoid…

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Q: 6) Find the centroids of the shaded region. Indicate the typical rectangles and derive the values…

A: As you post multiple questions  I only answered first one

Q: 5) Using transformation and integration, find the area of the region that is enclosed by the ellipse…

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Q: A rectangular box is to be inscribed inside the ellipsoid 2x< + y2 + 4z2 = 12 Find the largest…

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Q: Identify the following quadric surface. x²1²²=² + 8 10 14 =1 O ellipsoid O hyperboloid of one sheet…

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Q: Y 60 cm 40 cm 15 cm +45 cm 15 cm Figure(1)

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Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.