Identify the quadratic surface, explain the shape and describe the traces. 1. a) x^2 + y^2 + 1/2 z^2 = 2 b) 1/2 x^2 - y^2 - z^2 = 1 c) z^2 = x^2 + y^2

Q: Explain why the curve of intersection of the surfaces x2 + 3y2 − 2z2 + 2y = 4 and 2x2 + 6y2 − 4z2 −…

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Q: Describe and sketch the surface x + 2y + 3z = 6

A: Given

Q: Sketch the surface..........CYLINDERS.............x2 + 4z2 = 16

A: Here we have to draw the surface of cylinder having equation  x2+4z2=16

Q: Sketch the surface.......... ASSORTED ............... x2 + z2 = 1

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Q: 7. Sketch the surface 15zs9-x' - y² and x'+y' <1

A: To find:

Q: Describe and sketch the surface 4x2 + y2 = 4

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Q: Reduce the equation to one of the standard forms, classify the surface, and sketch it. Label at…

A: y2=16+x2+z2

Q: Sketch the portion of the surface that lies in the first octant: x = y. 12 1.5 1 0.5 0.15 . 0. . 2.

A: The given plane is in first octant and the plane is given by:  x = y

Q: What is the total length of the curve of intersection of the surfaces x2 + y2 + z2 = 4 and y2 + 2z2…

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Q: Sketch the surface with equation x^2 + y^2 + 2z^2 − 1 = 0.

A: The given equation is x2+y2+2z2-1=0

Q: Find the equation of the surface of revolution that is generated by rotating the straight line y = x…

A: The surface of revolution that is generated by rotating x=f(y) around the y-axis is x2+z2=f(y)2 so…

Q: What is a trace of a surface?

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Q: Sketch the curve of intersection of the surfaces. The ellipsoid 2x + 2y + = 3 and the paraboloidz =…

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Q: Explain what it means for a surface to be orientable.

A: They are the surfaces for which we can define clockwise consistently. e.g. Cylinder and spheres are…

Q: Sketch the surfaces 1. x2 + y2 = 4  2. x2 + 4z2 = 16

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

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: 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: Use traces to sketch and identify the surface -x2+ 4y2-z2=4

A: To identify the surface, set each variable to some constant and find what type of surface produces…

Q: the solid cut from the first octant by the surface z = 81-x2-y

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Q: Sketch the surfaces ASSORTED 16x2 + 4y2 = 1

A: we have to sketch the the surface 16x2+4y2=1

Q: Discribe the topology through diagrams of surface and curves

A: Describe topology through diagrams of surface and curves.

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

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Q: Identify the surface whose equation isľ = 3 sec (0). O Circle O Hyperbolic Paraboloid O Cone Sphere…

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Q: Sketch the surface x = 2y2 +3z2

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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 2D curve 4x2 - y2 = 3, generates a surface in 3D by rotationing it out of the xy-plane and…

A: The 2D curve 4x2 - y2 = 3, generates a surface in 3D by rotating it out of the xy-plane and around…

Q: 12. 4x² + 9y² + 9z² = 36

A: Given: 4x2+9y2+9z2=36

Q: classify the quadric surface given by equation and determine its standard form.−8x 2 − 8y2 + 10z2 +…

A: We have the quadratic surface : -8x2-8y2+10z2+32xy-4xz-4yz-24=0…

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: In Exercises 25–26, find the areas of the surfaces generated by revolv-ing the curves about the…

A: Given:

Q: What is the minimum amount of unique shapes that could tessellate a plane?

A: Only three unique shape form tessalate

Q: find the surface of both of the trainagles, all the sides *show all the work*

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

Q: Plot the surface of 6a2- 2x4- y?z2 = 0, for -10 <x, y, z < 10

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

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

Q: Classify the quadric surface ² - y² - x² + 4x = 5. 2 य

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Q: Describe the usual orientation of a closed surface such as a sphere.

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Q: Sketch the surface = 2y + 32².

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Q: Sketch the section of the surface at y = 0. 4 2 -2 -6 -4 -6 -4 4 6. -61

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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: Reduce the equation to one of the standard forms, classify the surface, and sketch on paper.…

A: Express the equation 4y2+z2-x-16y-4z+20=0 in terms of the complete squares of y and z, and then…

Q: Classify the quadric surface. 9x2 + 3y2 − 6z2 = 54

A:

Q: Sketch the surfaces ASSORTED 16y2 + 9z2 = 4x2

A: Solution:- We have to  Sketch the surfaces ASSORTED 16y2 + 9z2 = 4x2

Q: Identify and sketch the section of the surface at x = 0. 4 Type of the surface: 6. 6- 2 -8 -6 -4 4 6…

A: Given the surface

Q: 5. y-z =16

A: Since you have asked multiple questions in a single request so we will be answering only first…

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: Sketch the graph of -x + 9y² – 4z² = 36 and identify the surface. %3D

A: Given a function in terms of x, y and z. Here x and y are independent variables and z is a dependent…

Q: What is a flat surface that extends infinitely in all directions?

A: Plane.

Q: What is the surface generated by a straight line which moves along a fixed curve, and which remains…

A: To determine the name of the surface generated by a straight line which moves along a fixed curve,…

Q: Describe and sketch the surface y = z2

A: Solution: Consider the given surface y = z2 On the y z-plane, it represents a parabola that opens in…

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