Which figure represents a three-dimensional solid with only one face?

Q: The solid whose base is the triangle with vertices (0, 0), (2, 0), and (0, 2), and whose cross…

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Q: Find an equation of the sphere that passes through the origin and whose center is (3, 1, 4).

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Q: Find the standard equation of the sphere with the given characteristics. Center: (-1, -9, 7) Radius:…

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Q: Find the standard equation of the sphere with the given characteristics. Center: (-1, -2, 9) Radius:…

A: Given:Center : (-1,-2,9)Radius: 7We will find the equation of the sphere

Q: Describe a method for determining whether four points P, Q , R , and S lie in the same plane?

A: We will show a method for determining whether four points P,Q,R and S lie in the same plane.

Q: Find the equation of the hyperboloid of one sheet passing through the points (±2,0,0), (0, ±7,0) and…

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Q: Find the area of the hyperbolic (geodesic) triangle with vertices (3,0), (4,0) and (5,0).

A: Let P(3,0), Q(4,0) and R(5,0) be three vertices.  It is known that the equation of hyperbolic line…

Q: Draw the front and right views of the solid below. Front Right

A: To draw front view and right view from given figure.

Q: Find the standard equation of the sphere with the given characteristics. Center: (-1, -5, 3) Radius:…

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Q: Describe the intersection of the prism and the plane.

A: Given figure of the rectangular prism is,

Q: The front view of a three-dimensional figure using identical cubes is shown. Front Identify two…

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Q: What is Bimodal?

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Q: Find the coordinates of the centroid of the triangles whose vertices are: a. (5.7), (1, -3), (-5.1);…

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Q: Find the standard equation of the sphere with the given characteristics. Center: (-1, -4, 5) Radius:…

A: topic - standard equation of sphere

Q: Choose two figures which are topologically equivalent to each other 25

A: Solution :-

Q: Find the standard equation of the sphere with the given characteristics. Center: (-1, -3, 5) Radius:…

A: We are given: Centre: (-1, -3, 5)Radius: 7 We need to find the standard equation for the sphere with…

Q: Find the standard equation of the sphere with the given characteristics. Center: (-1, -4, 4) Radius:…

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Q: The area of parallelogram whose adjacent sides are i^-2j^+3k^ and 2i^+j^-4k^ is

A: Given sides arei^-2j^+3k^  &  2i^+j^-4k^

Q: Find the equation of the hyperboloid of one sheet passing through the points (±8,0,0), (0, ±3,0) and…

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Q: the physical dimensions of an object?

A: To define: Physical dimensions of an object.

Q: Find an equation of the sphere that passes through the origin and whose center is (1, 2, 3).

A: I have appended the formula used in the solution part.

Q: In Cartesian space, the point (0,6,0) lies 6 units above the origin. Select one: True False

A: We have to find the point location

Q: Find an equation of the sphere with center (1, –11, 8) and radius 10.

A: Center of sphere=1,-11,8radius of sphere , r=10Sphere has 3-dimensions ,hence equation of sphere…

Q: What are the coordinate planes in three-dimensional space? How are they drawn?

A: The Cartesian coordinate system is used to describe three-dimensional space which consists of an…

Q: Choose two figures which are topologically equivalent to each other

A: Two figures are said to be tropologically equivalent if they can be tranformed into each other…

Q: Which quadric surfaces have both hyperbolas and parabolas as traces?

A: Consider the given: The intersection of a three-dimensional surface and a plane is called a trace.…

Q: Find the standard equation of the sphere with the given characteristics. Center: (-1, -6, 9) Radius:…

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Q: Find the standard equation of the sphere with the given characteristics. Center: (-1, -3, 8) Radius:…

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Q: Find the surface of the regular pyramid.

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Q: Give two examples of a real-world object that is in the shape of a prism.

A: In this question we have to give two examples of a real world object that is in the shape of the…

Q: If (-2, 3), (4, -3) and (4, 5) are the mid-points of the sides of a triangle, find the coordinates…

A: On solving this we will get:-

Q: Find the equation of the hyperboloid of one sheet passing through the points (+2, 0,0), (0, ±6, 0)…

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Q: What is different about the shape in part c?

A: Part (c) is a rectangular shape .

Q: Find the equation of the sphere which passes through (2, 1, 3), (3, 2, 1), (1, –2, –3), (–1,1, 2).

A: Given that the sphere passes through the points (2,1,3), (3,2,1), (1,-2,-3), (-1,1,2).

Q: Find the standard equation of the sphere with the given characteristics. Center: (-1, =7,2) Radius:…

A: Explanation of the answer is as follows

Q: Find the standard equation of the sphere with the given characteristics. Center: (-1, -2, 9) Radius:…

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Q: Find an equation of the sphere that passes through the point (8, 1, -5) and has center (5, 6, 3).

A: The objective of the question is determine the question of sphere .

Q: What is the length of the transverse axis of the hyperbola whose foci are (0, -5) and (0,5), and…

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Q: Front Top Right Side Which could be this three-dimensional figure?

A: In the second option, all three views ( Top view, Front view, and right side view) are satisfying…

Q: Find the standard equation of the sphere with the given characteristics. Center: (-1, -6, 3) Radius:…

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Q: Find the standard equation of the sphere with the given characteristics. Center: (-1, -5, 2) Radius:…

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Q: Find an eguation of the sphere that passes through the point (5,-2,-1) whose whose Center is the…

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Q: Find the equation of the hyperboloid of one sheet passing through the points (+8, 0, 0), (0, +6, 0)…

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Q: The equation of the sphere with center (7,-10, 1) that touches that y-axis is

A: To find the equation of the sphere we need center of the sphere  radius of the sphere.  Here given…

Q: Find equations for the sphere whose center and radius is given in center(0,-7,0) radius 7

A: General equation of sphere is given by:

Q: find the standard equation of the sphere with center (4,3,3) and radius 7

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Q: What is the length of the transverse axis of the hyperbola whose foci are (0, -5) and (0,5) , and…

A: The foci of Hyperbola are:   (0, -5)  and  (0, 5). Length of transverse axis of Hyperbola is:  2a…

Q: How are three-dimensional figures and polygons related?

A: As every figure with faces or edges can be a polygon.

Q: Find the standard equation of the sphere with the given characteristics. Center: (-1, -7, 9) Radius.…

A: We are given center of sphere as (-1, -7, 9) and radius be 6. We have to find standard equation of…

Q: Which figure is being constructed?

A: Given:GH is a line