The part of the surface z =1  + 3x+ 2y 2 that lies above the triangle with vertices (0, 0), (0, 1) and (2, 1)

Q: Find the area of the surface. The portion of the plane z = 24 - 3x - 2y in the first octant

A: ⇒Given:-  Equation of plane                      z=24-3x-2y  in 1stoctant In intercept form,…

Q: Find the surface area for the portion of the surface f(x,y)=1-x² + y that lies above the triangular…

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Q: Consider the surface z = (x+ 1)² + (y – 2)² – 1 Does the point (1, 3, 1) belong to this surface?

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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: Classify the quadric surface. x2 - y2 + z = 0 O hyperboloid of one sheet O hyperboloid of two sheets…

A: Classify the quadratic surface.

Q: Find the center C and the radius a for the sphere 1. 3x2 + 3y2 + 3z2 + 2y - 2z = 9 2. x2 + y2 + z2 -…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: A 2-D surface was found in one research group of scientists and a surface equation has been derived…

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Q: Sketch the curve of intersection of the surfaces. The paraboloids z = x² + y² and z = 16 – x – y.…

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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: Integrate G(x, y, z) = xyz over the triangular surface with vertices (1,0, 0), (0, 2, 0), and (0, 1,…

A: To Determine: integrate Gx,y,z=xyz over the triangular surface with vertices (1,0,0),(0,2,0) and…

Q: the normal line of the surface [z = (4x^2 + y^2] at the point (1,1,5) O 8x-2y+z=5 O 8x+2y+z=5…

A: We have to find the normal line of the surface.

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 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 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: 9. Write the equation of the quadric surface in standard form then identify the quadric surface…

A: The standard form of quadric surface : Ax2+By2+Cz2+Dxy+Exz+Fyz+Gx+Hy+Iz+J=0…

Q: The quadric surface 2z-x²-4y² = 0 is O Hyperboloid of two sheets. O Elliptic paraboloid. O…

A: We have to solve given problem:

Q: Sketch the quadric surface: r +4y2 +4z2 16. Note: The x, y, & z axes are depicted in red, green, &…

A: The given function is: x2+4y2+4z2=16

Q: Sketch the curve of intersection of the surfaces. The paraboloids z = x² + y² and z = 25 – x – y².…

A: Given that: z=x2+y2      ......(1)z=25-x2-y2      ......(2)

Q: Find parametrizations The portion of the paraboloid z =-(x2 + y2)/2 above the plane z =-2

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Q: 4 and the plane Find the point on the curve of intersection of the paraboloid x- + y- x - y + 2z = 0…

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Q: sketch the given surface. x2 + y2 − z 2= 1

A: Given: x2 + y2 − z 2= 1

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: The portion of the surface z = 2x + y2 that is above the triangular region with vertices (0, 0), (0,…

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Q: Verify Stoke's theorem for A=(2x-y)i-yz²j-y*zk where S is the upper half 5A. surface of the sphere *…

A: Consider the given vector and sphere equation. A→=2x−yi−yz2j−y2zk and x2+y2+z2=1 Since S is the…

Q: Find the center and radius of the sphere. x2 + y2 + z2 - 18y + 12z + 36 = 0 (x, y, z) = ( 0,9, – 6…

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Q: Find an equation of the surface consisting of all points P(x, y, z) that are twice as far from the…

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Q: Evaluate the surface z =1,0<x,y <1.

A: To solve this we will use divergence theorem.

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: Sketch the surfaces 1. . z = x2 + 4y2  2. x = 4 - 4y2 - z2 3. x2 + y2 = z2

A: The given surfaces are sketched using online 3D calculator.

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: 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 equation of the xy-trace of the sphere. (x + 2)2 + (y + 1)2 + (z − 3)2 = 25

A: The equation of the sphere: - The general equation of a sphere is (x – a)2+(y-b)2+(z-c)2=r2 if (a,…

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: (b) Integrate (x, y,z)=(y+z)+1 the paraboloid 4x - y-z -0 by the plane x 1. over the surface cut…

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Q: Classify the quadric surface. −49x2 + y2 + z2 = 49

A: Given query is to find the shape of the surface.

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

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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: The part of the sphere x^2+y^2+z^2=4z that lies inside the paraboloid z=x^2+y^2

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Q: Find parametrizations The portion of the paraboloid y = 2(x2 + z2 ), y&lt;=2, that lies above the…

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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: Identify the surface y-3=x²+z² paraboloid cylinder cone hyperboloid

A: y-3=x²+z²

Q: Describe and sketch the surface y2 + z2 = 16

A: Given equation is y2+z2=16

Q: Sketch the surfaces 1.z = 1 + y2 - x2  2. z =-(x2 + y2 ) 3. 4y2 + z2 - 4x2 = 4

A: Used graphing calculator to graph:z = 1 + y^2 - x^2 from two viewing angles

Q: 7. Sketch the surface 1≤z≤2-x² - y²

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