Convert the rectangular equation x2 + y2 + z2 = 27 to an equation in (a) cylindrical coordinates and (b) spherical coordinates.

Q: Find the spherical equation of the Cartesian equation x2 + y2 +(z - 81)2 = 812. o a. rho = 81 cos…

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Q: Find the rectangular coordinates of the point whose cylindrical coordinates are given. a) (3, pi,…

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Q: Convert from spherical to cylindrical coordinates (2, π/3, π/6)

A: Spherical to cylindrical (r,θ,ϕ)->(ρ,θ,Ζ)ρ=r sinϕθ=θz=r cosϕ

Q: Write the equations in cylindrical coordinates. (a) 5x2 – 2x + 5y² + z² = 3 (b) z = 3x2 – 3y2

A: The solution of above question is written below.

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

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Q: 8-a2-y By converting to spherical coordinates, evaluate 2² dz dx dy

A: Let us consider the rectangular coordinates (x,y,z) then the relation between spherical coordinate…

Q: Consider the spherical coordinate point (3,1,) Convert to cylindrical coordinates.

A: we have the spherical coordinate point and convert into cylindrical coordinates

Q: 1. Convert the point (-1,1, v2) from Cartesian to spherical coordinates.

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Q: Write the equation in spherical coordinates. (a) 7z2 = 5x2 + 5y2 (b) x2 + 2z2 = 7

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Q: Convert the rectangular equation to an equation in cylindrical coordinates and to an equation in…

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Q: find an equation in spherical coordinates for the equation given in rectangular coordinates x^2 +…

A: We have to find spherical coordinates form

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

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

A: Solution is given below:

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

A: We have to convert the given equation x2+y2=16 into spherical coordinates

Q: . Convert the Cartesian coordinates (2, 2, 2) to Cylindrical and Spherical Coordinates

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Q: 1. Convert | 1,-/3, 3 from rectangular coordinates to cylindrical coordinates

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

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Q: Write the equation in spherical coordinates. (a) 2x2 – 3x + 2y2 + 2z2 = 0 (b) 5x + 4y + 7z = 1

A: To write the given equations in spherical coordinates a 2x2-3x+2y2+2z2=0(b) 5x+4y+7z=1

Q: Write the equation 5x2+10y-z=5 in cylindrical coordinates.

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Q: Convert from rectangular to cylindrical coordinates (a) (4 /3 ,4, -4)

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Q: Convert the point from cylindrical coordinates to spherical coordinates. 4 (ρ, θ, φ)

A: Explained below

Q: Show that the cylindrical equation ,2(1 – 2 sin² 0) + z² = 1 is a hyperboloid of one sheet.

A: Given a cylindrical equation r21-2sin2θ+z2=1 To show that this equation is a hyperboloid of one…

Q: Find an equation in spherical coordinates for the equation given in rectangular coordinates. x² +y²…

A: Explanation of the answer is as follows

Q: Write the equations in cylindrical coordinates. (a) 3x² – 6x + 3y2 + z² = 5 z = 7x2 – 7y2

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Q: Find an equation in spherical coordinates for the equation given in rectangular coordinates. x2. +…

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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: Convert the point from rectangular coordinates to cylindrical coordinates and spherical coordinates.…

A: Given the rectangular coordinates as -3,3,-4 To find the cylindrical coordinates and spherical…

Q: Find an equation for the plane y=3 in cylindrical coordinates

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Q: . Find the rectangular coordinates of the point (T,5, –2) which is in cylindrical coordinates.

A: To find: The rectangular coordinates of the given point. Given information: The cylindrical…

Q: Convert the point from rectangular coordinates to cylindrical coordinates. 11. (0,5,1) 12.…

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

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

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Q: Find an equation in spherical coordinates for the equation given in rectangular coordinates. x2 + y2…

A: The equation in rectangular coordinate is given by x2+y2+z2-3z = 0…

Q: Convert the rectangular equation y = 4 to an equation in (a) cylindrical coordinates and (b)…

A: y=4 a). rsinθ=4   ∵x=rcosθ,  y=rsinθ,  z=z⇒r=4sinθ⇒r=4cscθ

Q: 1. Consider a point in Cartesian coordinates given by (-2, 2v3, 4). (a) Find a corresponding…

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Q: Find an equation equivalent to x²+ y² + 2z²+ 2z - 5 =0 in spherical coordinates.

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Q: Convert the Cartesian equation Z z = 6-√√36-x² - y² into spherical coordinates.

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Q: 11. Convert the cylindrical coordinates (4,,-2) to rectangular coordinates

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Q: 4-x²-y² ) Use spherical coordinates to evaluate ,L /x² + y² + z²dzdydx.

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Q: Convert the rectangular equation x2 + y2 = 4y to an equation in (a) cylindrical coordinates and (b)…

A: Given- x2+y2=4y To find- An equation in (a) cylindrical coordinates and (b) spherical coordinates.…

Q: Give an equation of a sphere of radius 5, centered at the origin, in: 1. rectangular coordinates 2.…

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Q: Convert the rectangular coordinates to both Spherical and cylindrical coordinates; A (-1, 1, −√2)

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Q: Convert the rectangular equation x2 + y2 + z2 − 2z = 0 to an equation in (a) cylindrical coordinates…

A: (a) Convert to  cylindrical coordinates as follows: Substitute x=rcosθ,y=rsinθ,z=z.…

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…

Q: Q7. Convert the rectangular coordinates to both Spherical and cylindrical coordinates; A (-1, 1,…

A: x,y,z=-1,1,-2 r=x2+y2+z2 r=-12+12+-22 r=1+1+2 r=4 r=2 . θ=tan-1yx θ=tan-11-1 θ=135  degree θ=3π4…

Cylindrical Coordinate System

The distance from a selected reference axis, the direction from the axis relative to a selected reference direction, and also the distance from a selected reference plane perpendicular to the axis area unit, all accustom outline purpose positions in a cylindrical reference frame. Counting that the aspect of the reference plane faces the purpose, the latter distance is expressed as a positive or negative variety.