The equation of a surface in spherical coordinates is ϕ = π/4. Find the equation of the surface in cylindrical coordinates and in rectangular coordinates.

Q: Describe how the surface with spherical equation p²(1 + A cos² ¢) = 1 depends on the constant A.

A: Given : ρ2(1+Acos2ϕ)=1To describe: How the surface with spherical equation  ρ2(1+Acos2ϕ)=1depends on…

Q: (a) Sketch the surface whose equation is given by = 5π/6 (b) Convert the equation = 5π/6 to…

A: We have to use relation between cartesian and spherical system  x=ρ sinφ cosθ , y= ρ sinφ sinθ , z=…

Q: Find an equation in spherical coordinates for the surface represented by the rectangular equation x2…

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Q: An equation of the sphere (x-1)² + y² + (z-2)² = 5 in spherical coordinates 18:

A: A coordinate system is a convention that is used to represent a point uniquely using a set of…

Q: Find an equation in rectangular coordinates for the surface represented by the spherical equation,…

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Q: The equation of a surface in spherical coordinates is given by p= 6. Rewrite this equation in…

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Q: Convert the given equation, -z2- y2 +=1, z20 to an equation in cylindrical coordinates.

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Q: 4. For each equation of a surface given in spherical coordinates, sketch the surface and describe it…

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Q: Find an equation in spherical coordinates for the surface represented by the rectangular equation x2…

A: Given rectangular equation can be written as x2-y2-2z2=0. The co-ordinates in terms of spherical…

Q: Convert the following quadric surface into spherical coordinates.

A: Convert the quadric surface into spherical coordinates.

Q: Identify the surface whose equation in spherical coordinates is given by p= 2 cos o

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Q: The equation of a surface in spherical coordinates is ϕ = π/4. Find the equation of the surface in…

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Q: Find an equation in cylindrical coordinates for the surface represented by the rectangular equation.…

A: We have z=x2+y2-4we need to convert (x,y,z) ≡(ρ,θ,z)where ρ =x2+y2θ =tan-1yxz=z

Q: Find an equation in rectangular coordinates for the surface represented by the cylindrical equation…

A: Cylindrical co-ordinates of the point P are (r,θ,z) rectangular co-ordinates of the point P are…

Q: For each equation of a surface given in cylindrical coordinates, sketch the surface and describe it…

A: Given: a) r = 7 b) θ =π2 c) z = 2

Q: find an equation of the form ρ = f (θ , φ) in spherical coordinates for the following surfaces  x2…

A: Solution:- x2-y2=4 x=ρ sinφ cosθ y=ρ sinφ sinθ   ρ sinφ cosθ2-ρ sinφ sinθ2=4 ρ2 sin2φ cos2θ-ρ2 sin2φ…

Q: Eliminate the parameter in the parametric equations x(t) = e³t and y(t) = 3e' to a Cartesian form of…

A: Givenx(t)=e3t    ....(1)y(t)=3et     ....(2)

Q: Find an equation in rectangular coordinates for the surface represented by the spherical equation. p…

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Q: Find an equation in rectangular coordinates for the surface represented by the cylindrical equation…

A: To find an equation in rectangular coordinates for the surface represented by the cylindrical…

Q: d) Find the parametric equations for the line of intersection of the two planes.

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Q: Express the equation z = rroot2 cos2tita, which is given in cylindrical coordinates, in…

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Q: find an equation in rectangular coordinates for the equation given in cylindrical coordinates r= 2z

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Q: Find an equation in spherical coordinates for the surface represented by the rectangular equation.…

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Q: Find an equation in spherical coordinates for the surface represented by the rectangular equation y…

A: given that the rectangular equation y=2

Q: find an equation in cylindrical coordinates for the equation given in rectangular coordinates z=…

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Q: Try to sketch by hand the curve of intersection of the circu- lar cylinder x + y² = 4 and the…

A: Given, Circular cylinder, x2+y2=4 Parabolic cylinder, z=x2

Q: (a) Plot the point with cylindrical coordinates (2, 27/3, 1) and find its rectangular coordinates.

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Q: Identify the surface whose equation in spherical coordinates is given by p = 2 cos o %D

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Q: Find an equation for the paraboloid z = x2 + y² in spherical coordinates. (Enter rho, phi and theta…

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Q: Suppose you have the parametric equations x = 4cos(6) y= 6sin( 6 ) %3D Eliminate the parameter and…

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Q: Find an equation in rectangular coordinates for the surface represented by the spherical equation. 프…

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Q: Find the rectangular coordinates of the point, whose cylindrical coordinates are given. (a) (4, T/4,…

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Q: Part a) Convert the spherical equation p = to cylindrical coordinates. sin(4) Part b) Give a plain…

A: Let's find.

Q: Find an equation in spherical coordinates whose graph is the parapoloid Z=(X^2)+(Y^2)

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Q: Find a spherical coordinate equation for the sphere x² + y? + (z – 1)² = 1

A: All real numbers can be represented on a line called the number line. The number zero corresponds to…

Q: b) Find the area of the triangle with vertices P, Q, R. c)Write down parametric equations for the…

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Q: Plot the point with spherical coordinates (2, -5pi/6, pi/6) and describe its location in both…

A: We have to use relation between rectangular and spherical co ordinates and then between rectangular…

Q: Find an equation in spherical coordinates for the surface represented by the rectangular equation.…

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Q: Sketch, or describe in words, the following surfaces whose equations are given in cylindrical…

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Q: 18. x = et, y = e2t - 1

A: Solution

Q: Match the equation (written in terms of cylindrical or spherical coordinates)  = 5, with its graph.

A: Solution: Consider the general equation of the sphere is x-a2+y-b2+z-c2=r2 we have a relationship…

Q: Find the Cartesian form of the equation in spherical coordinates given by p = 2 cos p.

A: We have to solve above question and find cartesian form

Q: For the surface x? + y? = 2z? a) Find an equation in cylindrical coordinates b) Find an equation in…

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Q: Find an equation in rectangular coordinates for the surface represented by the cylindrical equation.…

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Q: 11.) Find a rectangular equation for the Surface whose Spherical equation is a sin ($) Sin (e)

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Q: Find an equation for the paraboloid z = x2 + y? in spherical coordinates. (Enter rho, phi and theta…

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Q: The equation r = 2 sin(0) in cylindrical coordinates describes a surface. Convert this equation to…

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

Q: Change the spherical equation below into cylindrical coordinates! tan2(Φ) = 1

A: Any point in the cylindrical coordinate system is represented as r,θ,z . Any point in the spherical…