Write the equation for the sphere of radius 1 centered at the prigin in the each of the following coordinate systems. (a) Cartesian (b) Spherical (c) Cylindrical

Q: Show that the equation represents a sphere, and find its center and radius: 2x2+2y2+2z2=8x-24z+1

A: To show that the equation represents a sphere, and find its center and radius: 2x2+2y2+2z2=8x-24z+1

Q: Write the equation of Spheres with radius R.

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Q: Find the equation in rectangular coordinates of the quadric surfaceconsisting of the two cones φ =…

A: The relation between spherical and rectangular coordinates in polar form is given by the following…

Q: A sealed-beam headlight is in the shape of a paraboloid of revolution (parabolic shaped). The bulb,…

A:

Q: Suppose that a cylindrical container of radius r and height L is filled with a liquid with volume V…

A: Consider the given:  Express volume in terms of “h”, “r” and “w”.…

Q: Find the standard equation of the sphere with the given characteristics. endpoints of a diameter:…

A: Equation of the sphere

Q: Find the standard equation of the sphere with the given characteristics.

A:

Q: Find the standard equation of the sphere with the given characteristics. Endpoints of a diameter:…

A: Given endpoints of diameter ::

Q: A bridge is to be built in the shape of a semielliptical arch and is to have a span of 100 feet.The…

A: Given: A bridge is to be built in the shape of a semielliptical arch and is to have a span of 100…

Q: 5. Find the equation for the sphere whose center is at (-1, 1/12-13) and radius is

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

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Q: A cooling tower, such as the one shown in the figure, is a hyperbolic structure. Suppose its base…

A: Let the tower be a hyperbola centered at the origin as shown in the figure. Since the lowest…

Q: Find the standard equation of the sphere with the given characteristics. Endpoints of a diameter:…

A: Solution: The objective is to find the standard equation of the sphere

Q: state whether the given equation defines an elliptic paraboloid, a hyperbolic paraboloid, or an…

A: Rearrange the equation, 3x2-7y2=z by dividing both sides by 21 and obtain x27-y23=z21. The general…

Q: Show that the parabolas $r=c /(1+\cos \theta)$ and $r=d /(1-\cos \theta)$ intersect at right angles.

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Q: A] Find the length of the arc of the semi-cubical parabola y² = x3 (1,1) and (5,5V5). between the…

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Q: 1.) A gateway is a parabolic shape whose vertex is 20 ft. From the ground, (0,20), and the width of…

A: Given, a gateway  is a parabolic shape whose vertex  is 20 ft. From the ground, (0, 20), and the…

Q: 1-sketch the following hyperboloid z² – x² – y² = 1 %3D

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Q: The Cassegrain telescope design (dating back to 1672) makes use of the reflective properties of both…

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Q: Find the standard equation of the sphere with the given characteristics. endpoints of a diameter:…

A: Use standard equation of sphere

Q: a) [. Show that the equation 6x + 6y6z + 3x² + 3y² + 3z² = 18 represents a sphere, and find its…

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: i) Find the solution of Vu O in spherical co-ordinates.

A: The given Laplace's equation is,∇2u=0Now this equation can  be written as in the spherical…

Q: Find the standard equation of the sphere with the given characteristics. endpoints of a diameter:…

A: To find the standard equation of sphere.

Q: The Hubble Space Telescope was launched into space in 1990 and now orbits the Earth at 5 mi/sec at a…

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Q: satellite dish shaped like a paraboloid, has a diameter 2.4ft and depth 0.9ft. If the receiver is…

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Q: Find the length of the arc of the semicubical parabola x  sq = ycu . betweenthe points (2,2 )  ; (4,…

A:

Q: State whether the given equation defines an elliptic paraboloid, a hyperbolic paraboloid, or an…

A: 3x2-7y2=z On simplification, we get ⇒z=x213-y217⇒z=x2132-y2172⇒z=x132-y172

Q: parabolic antenna follows the equation y^2 + 4x 0. Which of the following is the coordinates of its…

A: Topic = Parabola

Q: Write the equations in cylindrical coordinates. (a) 7x2 - 8x + 7y2 + z2 = 7 (b) z = 2x2 – 2y²

A: We have to find cylindrical form of the given equation.

Q: The parabola y = x² is shifted up by 4 unit %3D What is the equation of the new parabola?

A: Parabola:y=x2  shifted up by 4 units

Q: Find the standard equation of the sphere with the given characteristics - Center: (3, −2, 6);…

A: We have to find the standard equation of the sphere where, center is given as 3, -2, 6 and radius is…

Q: A searchlight is shaped like a paraboloid of revolution. If the light source is located 4 feet from…

A: Given: A search light is shaped like a paraboloid of revolution. If the light source is located 4…

Q: Find equations for the sphere whose centers and radii are given in center(1,2,3) radius sqrt(14)

A: To determine the equation of a sphere.

Q: The center of a clock is 60cm above the ground. The minute hand on the clock is 23cm long and starts…

A: topic- trigonometric equations

Q: Find the standard equation of the sphere with the given characteristics. Endpoints of a diameter:…

A: Given endpoints of a diameter of sphere is 2,1,3 and 1,3,-1. The standard equation of sphere is…

Q: Find the standard form of the equation of the sphere with the given characteristics. Endpoints of a…

A: The standard form of the equation of sphere is given by Where ( x0, y0, z0) is the center and r is…

Q: Find the parametric equations of the li segment that passes through the point

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Q: In a right spherical triangle ABC, B=90°. Using Napier’s first rule, what is the simplified form of…

A: There are two Napier's rules that are used to solve the right spherical triangles.

Q: Find the equation of the sphere in standard form that satisfies the given conditions. diameter PQ,…

A:

Q: 1 in (r', y')-coordinates, if (iii) Find the equation for the hyperbola ry 0 = 1-

A: Find the equation of hyperbola in x'y' system

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

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Q: Match the following equations with appropriate ones. 물 %3 11 Ses- Seç. Seç. Seç. Seç. Hyperbolic…

A: Solutions We have to match each equation as in options

Q: The surface of equation + 1 is: 16 A circular cylinder An ellipsoid

A: An ellipsoid is a surface that may be obtained from a sphere by deforming it by means of directional…

Q: A satellite dish is shaped like a paraboloid, with the receiver placed at the focus. It is to have a…

A: The base of the dish is the vertex of the parabola. The parabola is upward oriented. Let the vertex…

Q: Eliminate the parameter 0 and obtain the standard form of the rectangular equation. hyperbola: x = h…

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Q: Which is the corresponding equation of the hyperbola with foci located at (−8, 0) and (8, 0) and a…

A: Given data is : Foci are -8,0 and 8,0 The transverse axis is 14 unit

Q: what is the equation of the geodesic in the hyperbdic upper half-plane that joins -1+i with Iti

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Q: Find the standard equation of the sphere with the given characteristics Endpoints of a diameter: (0,…

A: Given: Endpoints of a diameter of sphere: a1, b1, c1 ≡(0, 0, 4) and a2, b2, c2 ≡(4, 6, 0)

Q: Find the equation of the sphere in standard form that satisfies the given conditions. diameter PQ,…

A: Distance between two points A(x1, y1, z1) and B(x2, y2, z2) is AB = x2-x12 + y2-y12 + z2-z12   The…