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

Q: Draw a two-dimensional figure that could be rotated using a vertical axis of rotation to give the…

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Q: Write the equation of the sphere with centre at ( 0,0,0) and radius = 2

A: The center of the sphere is:(h, k, j)=(0, 0, 0)The radius of the sphere is:r=2

Q: Which three dimensional figures when sliced by a plane cannot have a cross section that is a square?

A: When a rectangular pyramid is sliced by a plane then the obtained section will not be square.

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: 5. Find the standard form equation of a sphere that has a diameter with endpoints (3, -2, 4) and (7,…

A: Given : The end points of a diameter of a sphere are  (3, -2, 4) and (7, 1, 4). To find : We have to…

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: Identify and sketch the surface 9x² + y² − 2z² — 18x - 4y - 12z - 9 = 0. - Explain the position and…

A: The given surface is: 9x2+y2-2z2-18x-4y-12z-9=0. The given equation can be written as:…

Q: Write the equation of a sphere of radius 3 in all three coordinates--cartesian, cylindrical, and…

A: It is given that the radius of sphere is 3 .We have to find the equation of sphere in all three…

Q: Put the quadric surface equation 4X (-8y + 4Z+39 = 0 into one of the standard forms, specify the…

A: The given quadric surface equation is           4x2+y2-z2-24x-8y+4z+39=0 Write the like terms…

Q: 2. Find the center and radius of the sphere *+y ++4x-2y+8-4 0

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Q: Does every second-degree equation in x, y, and z represent a quadric surface? Explain.

A: the equation of a quadric surface in space is a second degree equation in three variables. The…

Q: 2) The diameter of a sphere has endpoints given by points P = equation of the sphere in standard…

A: The diameter of a sphere has endpoints given by points The Equation of sphere whose center and…

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

A: Only three unique shape form tessalate