Compute the surface area of the ellipse that lies on the plane z=11-3x+2y and inside the cylinder x^2+y^2=9

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

A: Given: y=2x2-4x and y=2x-x2 Graph:

Q: Obtain all the umbilical point of the Hyperboloid of two sheets {x^2+y^2-z^2=1}.

A: consider the equation {x2+y2-z2=1}

Q: Find the centroid of the “triangular” region bounded by the lines x = 2, y = 2 and the hyperbola xy…

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Q: Compute the area of surface generated by revolving the four-cusped of hypocycloid x⅔+ y⅔ =a⅔ about…

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Q: Determine the surface area of the solid obtained by rotating y=v9-x from -2sxs2 about the x -axis.

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Q: Determine the solid bounded by the surfaces 9x2+4y2=30 and the plane 9x+4y−6z=0 in the first octant.

A: Given surface is 9x2+4y2=30 and plane is  9x+4y-6z=0 Bounded region in first octane ⇒x≥0, y≥0, z≥0…

Q: Find the surface area of the part of the spherex +y² +z = 16 that lies above the plane z = 2.

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Q: Determine the centroid bounded by the parabolas x=y^2 and x^2=-8y

A: Consider the given curves. x2=-8yx=y2

Q: parabola

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Q: Find the surface area cut from the cone 2x2 + 2y2 = 5z2, z > 0, by the cylinder x2 + y2 = 2y

A: To find the surface area cut from the cone 2x2 + 2y2 = 5z2, z > 0, by the cylinder x2 + y2 = 2y

Q: Find the dimensions of the rectangular box of maximum volume with faces parallel to the coordinate…

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Q: Find the area of the surface obtained by rotating the curve y = 4x + 4, 0 < x< 8, about %3D the…

A: To find- Find the area of the surface obtained by rotating the curve y2 = 4x + 4, 0 ≤ x ≤ 8, about…

Q: find the centroid of the solid formed by revolving about the x-axis the solid formed by the curve…

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Q: Explain why the explicit description for a cylinder x2 + y2 = a2 cannot be used for a surface…

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Q: Calculate the point on the surface z =1 - x2 - y2 that has a maximum value for the sum of its…

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Q: Find an equation of the surface of revolution obtained by revolving the plane curve 4x² – y² = 4…

A: The given equation of plane curve is 4x2-y2=4. Since the plane curve is rotated about x-axis,…

Q: Find a parametrization of the hyper-boloid of two sheets (z2/c2)-(x2/a2)-(y2/b2)=1

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Q: Sketch the curve of intersection of the surfaces. The ellipsoid 2x + 2y² + z² 24 and the paraboloid…

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Q: Find the centroid of the region between the semicircle y = v1 – x2 and the top half of the ellipse y…

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Q: Find the area of the part of the surface z = x² + 2y that lies above the triangle with vertices…

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Q: Find the area of the surface obtained by rotating the parabola 1 y = 0 <x < 2, about the y-axis.

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Q: Find the centroid of the triangular region cut from the first quadrant by the line x + y = 3.

A: We will find the x and y-intercept of the triangle.  To find x-intercept we plug y=0 and find x…

Q: Find the centroid of the portion of the sphere x2 + y2 + z2 = a2 that lies in the first octant.

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Q: Find the area of the portion of the plane in the first octant passing through the points (0,0,6),…

A: This question can be solved using the area of triangle in three dimensional geometry.

Q: Identify the surface defined by x - y – 4x + z² +6= 0 O hyperboloid of two sheets O elliptic cone O…

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Q: Find the centroid of a thin, flat plate covering the region enclosed by the parabolas y = 2x2 and y…

A: Given,

Q: Find the area of the surface generated by revolving the curve y = √(x2 + 2), 0 ≤x ≤ √2, about the…

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Q: 9. Determine the position of the centroid of a sheet of metal formed by the curve y = 4x - x² which…

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Q: Find the centroid of the region in the first quadrant that is bounded above by the lines y = 2x and…

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Q: Find the centroid of a thin, flat plate covering the region enclosed by the parabolas y = 2x2 and y…

A:

Q: Find the surface area of the portion of the half ball with radius a which cuts off by the cylinder…

A: The equation of a ball with radius a is x2+y2+z2=a2. The surface area of the function z=fx,y over…

Q: classify the quadric surface given by equation and determine its standard form.x 2 + y2 − z2 − 2x −…

A: The given quadric surface is  x2+y2-z2-2x-4y-4z+1=0 To reduce to its standard form,…

Q: termine the solid bounded by the surfaces 9x2+4y2=30 and the plane 9x+4y−6z=0 in the first octan

A: The given solid is bounded by the surface 9x2+4y2=30 and the plane 9x+4y−6z=0 in the first octant.

Q: Classify the quadric surface given by equation  and  determine its standard  form. x2 + y2 + 2z2 −…

A: The quadric surface given to us is: x2+y2+2z2-2xy+4xz+4yz=16 This is compared to the general form of…

Q: Find the area of the surface. The part of the surface z = 1 + 2x + 2y2 that lies above the triangle…

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Q: What is the surface area of the portion of the surface z=x2+y that lays over the triangle on xy-…

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

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Q: Classify the quadric surface given by equation  and  determine its standard  form. x2 + y2 − z2 − 2x…

A: x2 + y2 − z2 − 2x − 4y − 4z + 1 = 0

Q: Identify a generating curve on the rz-plane for the surface of revolution with equation 1² + y² + zª…

A: The equation of the surface of revolution given is as follows:…

Q: The curve y = (64x – 4x³ )m bounds the shaded section on top and the x-axis on the bottom. Determine…

A: Given curve, y=64x-4x3 The shaded region is shown as: Formula for the centroid x, y in a region is…

Q: Find the centroid of the lamina cut by the parabolas y2=x and y=x2.

A: For the clear understanding of curve we have the following graph which is shown below as:

Q: Determine the area of the surface of revolution of x=sqrt{y} from (1,1) to (2,4), rotated about the…

A: The equation is x=y.   Determine the derivative dxdy=12y   The formula for the area of surface…

Q: Find the centroid of the region bounded by the parabola y=x2 and the line y=4.

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Q: area of the surface obtained by rotating the curve y=x^3, x ∈ [0

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Q: Find the centroid of a thin, flat plate covering the region enclosed by the x-axis, the lines x = 2…

A: Given information:

Q: Find the centroid of a thin flat plate covering the region enclosed by the parabolas y = 2x and y =…

A: Solution of question is written in step2 and step3.

Q: Find the centroid of the region bounded by these curves. y=2x+4, y=2x2

A: Consider the provided curves, y=2x+4 and y=2x2. Find the Centroid of the region. Now, the graph of…

Q: Find the surface area obtained by rotating y = V9 – x2 ,-2sxs-1 9– x² -2sxs-1

A: Given,             y=9-x2 , -2≤x≤-1

Q: Find the centroid when revolved in y-axis: y³ = x² ; y = 4.

A: As per the question we are given a solid of revolution obtained by rotating the area between y3 = x2…

Q: Identify the surface defined by x- y - 4x + z2 = 4 O hyperboloid of two sheets O elliptic cone O…

A: Thanks for the question :)And your upvote will be really appreciable ;) option A ) Hyperboloid of…