Find the area of the surface of the part of the cylinder ? + 2² = 4 that lies above the square in the æy-plane with vertices (0,0), (1,0), (0, 1), and (1, 1).

Q: Find the area of the surface 2x^(3/2) + 2y^(3/2) - 3z = 0 above the square R: 0<= x<= 1,…

A: find z.

Q: Find the area of the surface. The portion of the paraboloid  z = 49 − x2 − y2 in the first octant

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Q: Q5/ Find the volume of the Tetrahedron that is determined by three edge vectors â = [1, 0.-3), 5=…

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Q: Find the area of the surface. The part of the sphere x2 + y2 + z² = 4z that lies inside the…

A: Given sphere is x2+y2+z2=4z that lies inside the paraboloid  z=x2+y2. We have to find the area f the…

Q: Find the area of the surface. The part of the surface z = 9 + 5x + 2y2 that lies above the triangle…

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

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Q: C is the hexagon in the xy-plane with vertices (5, −5), (5, 5), (0, 10), (−5, 5), (−5, −5), and (0,…

A: Given : Vertices : (5,-5) , (5,5), (0,10), (-5,5), (-5,-5) and (0,-10) Integral given :…

Q: Fin He ara at tHe surface af the portion oF Hae Plane 2= 5-2X -9y

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Q: Find the area of the portion of the plane 2x + 3y + 4z = 28 lyingabove the rectangle 1 ≤ x ≤ 3, 2 ≤…

A: GIVEN  2x + 3y + 4z = 28  We need to find the area of the plane  lyingabove the rectangle 1 ≤ x ≤ 3,…

Q: Find the point on the plane x-y+z=7 that is closest to the point (2,4,6).

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Q: Find the area of the part of the sphere x2 + y2 + z2 = 4z that lies inside the paraboloid z = x2 +…

A: Given, x2+y2+z2=4z  and  z=x2+y2 Equation of the sphere and paraboloid in cylindrical coordinates is…

Q: Find the dimensions of the largest rectangular box in the first octant (x, y, z > 0) with one corner…

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Q: Find the distance (d) from the point (- 4, 8, 4) to the plane 2x + 5y + 4z = - 50. d =

A: image is attached

Q: Find the area of the surface. The part of the hyperbolic paraboloid  z = y2 − x2  that lies between…

A: In the question we have to find the value of area enclosed by the function of given figures.

Q: Find the area of the surface.The part of the surface 2y + 4z − x2 = 5 that lies above the triangle…

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Q: Find the area of the surface. The surface cut from the bottom of the paraboloid z = x2 + y2 by the…

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Q: 5. Find the surface area of the portion of the surface z = 2x + y? that is above the triangular…

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Q: 3. Find the area of the part of the surface x 2z + y° - 3, that lies above the triangle in the…

A: Given, x=2z+y2-3, i.e. z=12x-y2+3. As it is known that the surface area is given as,…

Q: Find the area of the portion of the surface z = 8x+4y that lies above the triangular region with…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Find the maximum volume of a box that is resting on the xy-plane with one vertex at the origin and…

A: Given the plane is 3x+4y+2z=12

Q: 1. Find the area of the part of the surface z = a? + 2y that lies above the triangle with vertices…

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Q: Find the area of the surface. The portion of the plane z = 6 - 3x – 2y in the first octant

A: We need to find the area of the portion of the plane z=6-3x-2y in the first octant. Let f(x, y) =…

Q: Find the area of the part of the sphere x2 + y2 + z2 = 100z that lies inside the paraboloid z = x2 +…

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Q: Find the maximum volume of a box that is resting on the xy-plane with one vertex at the origin and…

A: Given, equation of the plane is  7x + 6y + 2z = 18 => 2z = 18 - 6y - 7x Therefore, z = ( 1/2)(18…

Q: Find the area of the surface. The part of the cylinder y2 + z2 = 9that lies above the rectangle…

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Q: Find the area of the surface. The part of the surface 2y + 4z - x2 = 5 that lies above the triangle…

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Q: Find the area of the surface of the part of the plane 3x + 2u + z = 6 that lies in the first octant.

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Q: Find the area of the cap cut from the top of the sphere x2 + y2 + z2 = 1 by the plane z = sqrt(2)/2.

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Q: Find the area of the surface. The part of the paraboloid z = x² + y2 that lies inside the cylinder…

A: Area of the surface f(x ,y) above a region R of the xy-plane is given by…

Q: The upper half of the unit sphere x2+y2+z2=1 is z=Square root of 1-x2-y2. Find its centroid

A: Solution Given The intersection gives z2=1-x2+y2we need to find the centroid

Q: Find the area of the surface. The part of the surface  2y + 4z − x2 = 5  that lies above the…

A: According to the given information, it is required to find the area of the surface.

Q: Compute the surface area of the ellipse that lies on the plane z = 11 – 3x + 2y and inside the…

A: The surface area of the surface given by z=f(x,y) where (x,y) is a point from the region D in the…

Q: Find the area of the surface. The surface cut from the “nose” of the paraboloid x = 1 - y2 - z2 by…

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Q: Find the area of the cap cut from the paraboloid y2 + z2 = 3x by the plane x = 1.

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Q: Find the point on the sphere x2 + y2 + z2 = 4 farthest from the point (1, -1, 1).

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Q: Find the area of the surface. The part of the plane z = 7 + 5x + 2y that lies above the rectangle…

A: The given equation is, z=7+5x+2y The partial derivatives are, fx=5fy=2

Q: Find the surface area of the ellipse that lies on the plane z=11-3x+2y and inside the cylinder…

A: The plane z=11-3x+2y and cylinder is x2+y2=9. Obtain the partial derivatives of z=11-3x+2y:…

Q: he cylinder x² + y² = 2y and the plane

A: Shift cylinder at origine as centre

Q: Find the area of the cap cut from the top of the sphere x2 + y2 + z2 = 1 by the plane z = √2/2.

A: Given equation of sphere is    x2+y2+z2=1     And the equation of plane is  z=22=12 But we know that…

Q: 2 Find the area of the ellipse cut from the plane z = 3x by the cylinder x² + y² = 16. Surface area…

A: Given plane z=3x and the cylinder x2+y2=16. The objective is to find the area of the ellipse cut…

Q: Find the area of the surface. The part of the plane z = 4 + 3x + 2y that lies above the rectangle…

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Q: Find the point on the sphere  x2+y2+z2=7056 that is farthest from the point (5,−15,−2)

A: The given question has been solved in detail

Q: Find the area of the surface. 12. The part of the sphere x2 + y2 + z2 = 4z that lies inside the…

A: Solution:GivenSphere:   x2+y2+z2=4zParaboloid: z=x2+y2To find the area of the…

Q: Find the area of the surfaces The surface cut from the “nose” of the paraboloid x = 1 - y2 - z2 by…

A: The surface cut from the '' nose '' of the paraboloid x=1-y2-z2 by the yz plane .…

Q: Find the area of the surface. The part of the plane z = 8 + 5x + 2y that lies above the rectangle…

A: Area of the surface z=f(x,y) A(s)=∬1+fx2+fy2f(x,y)=8+5x+2yfx=5fy=2

Q: The part of the surface z-1+ 3x + 2y that lies above the triangle with vertices (0, 0), (0, 1). and…

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Q: Find the area of the surface. The part of the surface  2y + 4z − x2 = 5  that lies above the…

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Q: Find the point lying on the intersection of the plane x + + z = 0 and the sphere x2 + y2 + z2 = 25…

A: According to the given information, it is required to find a point lying on the intersection of the…

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

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