Find the area of the surface. The part of the surface  2y + 4z − x2 = 5  that lies above the triangle with vertices (0, 0),  (2, 0),  and  (2, 4)

Q: Find the area of the surface. The part of the paraboloid x = y^2 + z^2 that lies inside the cylinder…

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Q: Identify and sketch the surfaces x2 + y2 - z2 = 4

A: Given, The surface is x2 + y2 - z2 = 4

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A: Rearrange the given equation to find y in terms of x and thus f(x). Plot the curve and find the…

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

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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: Describe and sketch the surface (x2/16) + (y2/9) + z2 = 1

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Q: Find the points on the surface x² −yz = 5 that are closest to the origin.

A: Let the point P be (x,y,z). The distance between the point P and origin is given by the formula…

Q: 5. Plot the surface of 6x2 – 2.r – y?z2 = 0, for -10 <r, y, z < 10 %3D | |

A: To plot the given surface.

Q: Classify and sketch the surface 4x2 − 3y2 + 12z2 + 12 = 0.

A: Solution:Given surface4x2 - 3y2 + 12z2 + 12 = 0    — 1divide equation 1 with -12,⇒ x2-3 + y2u - z2 -…

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: Sketch and identify the surface given by x2 + 4y + 4z2 = 0.

A: Equation of the surface is given by:x2+4y+4z2=0 we need to identity the surface and hence sketch the…

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 surface cut from the paraboloid x2 + y + z2 = 2 by the plane y = 0.

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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 area of the surface x^2-2y-2z =0 that lies above the triangle bounded by the lines x=2,y=0…

A: From the given equation. 2z=x2-2yz=x2-2y2z=x22-ydzdx=x, dzdy=-1 From the limits x limits from 0 to 2…

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: Determine the area of the surface. The part of the surface z=1+3x+2y^2 lying on the triangle with…

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Q: Find the center and radius of the sphere. * + + 5z +x+y+z= 4 5x +

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Q: Find the area of the surface. The part of the sphere x2 + y2 + z2 = 16 that lies above the plane z =…

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Q: Find the exact area of the surface z = 1 + 2x + 3y + 4y2, 1 ≤ x ≤ 11, 0 ≤ y

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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. The portion of the sphere  x2 + y2 + z2 = 100  inside the cylinder…

A: To find the area of surface

Q: Find the area of the surface. The part of the sphere x2 + y2 + z² = 81 that lies above the plane z =…

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Q: Find the area of the surface. The surface in the first octant cut from the cylinder y = (2/3)z^(3/2)…

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Q: Describe and sketch the surface x2 + z2 = 4

A: Given- x2+z2=4 To sketch- The graph of the above function and explain it.. Concept Used- The…

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 figure shows the surface created when the cylinder y2 + z2 =1 intersects the cylinder x2 + z2 =…

A: It is given that, the cylinder y2 + z2 =1............... (1) intersects the cylinder x2 + z2 = 1…

Q: The figure shows the surface created when the cylinder y2+z2 = I intersectsthe cylinder x2+z2=1 Find…

A: Given : surface S (say) is created when the cylinder y2+z2=1 intersects the cylinder x2+z2=1 To find…

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: 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: Describe and sketch the surface 16x2 + 16y2 − 9z2 = 0

A: Given surface 16x2+16y2-9z2=0

Q: Describe and sketch the surface y2 + z2 = 9

A: the given equation represents the cylinder where it forms the circle as the base on yz plane and is…

Q: Describe and sketch the surface y2 + z = 6

A: Graph: Given surface y2+z=6 Since one co-ordinate has power 2 and other co-ordinate has power 1. So…

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

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Q: Find the area of the surface. The part of the plane 3x + 2y + z = 6 that lies inside the cylinder…

A: Find the area of the surface. The part of the plane 3x + 2y + z = 6 that lies inside the cylinder…

Q: Find the area of the surface. The portion of the paraboloid z = 16 - x - y in the first octant

A: The given surface is the portion of the paraboloid z=16-x2-y2 in the first octant. The surface area…

Q: Find the area of the finite part of the paraboloid  y = x2 + z2 cut off by the plane y = 4.

A: To find the area of the finite paraboloid y=x2+z2 cutt off by the plane

Q: 6. The part of the surface z = 1 + 3x + 2y² that lies above the triangle with vertices (0, 0), (0,…

A: Given: A surface z=1+3x+2y2 and vertices of triangle (0, 0), (0, 1) and (2, 1). To find: Area of…

Q: Classify and Sketch the surface X2+ Zy² + Z? -4x+4y-2z+3:0

A: The given equation of the surface is x2 + 2y2 + z2 - 4x + 4y - 2z + 3 = 0.The general equation,…

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 surface. The part of the plane z = 7+ 2x + 3y that lies above the rectangle [0,…

A: We have to find the area of the surface of the given problem.

Q: Sketch the surfaces 1. z = y2 - 1 2. 4x2 + y2 = 36

A: Using graphing calculator to sketch themz=y^2-1

Q: Find the area of the part of the sphere x2 + y2 + z2 = a2 that lies inside the cylinder x2 + y2 =…

A: answer is A = a2(π -2) detailed solution with explanation is given below

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

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

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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