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

Q: Write the ellipsoid 4.x2 + 16x + 3y? – 12y + 22 – 2z + 28 = 0 using spherical coordinates. Find the…

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Q: Find an equation of the form p = f(0, $) in spherical coordinates for the surface z3 = 4(x2 + y2)…

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Q: 1. Convert the equation of the sphere : x + y +6y+z? = 0 Into. a) Cylindrical coordinates (An…

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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: Q4. (a) Express the given equation into cylindrical and spherical coordinates: (x + y)2 – z2 + 4 = 0…

A: Sperical co ordinate

Q: Match the surface to its corresponding equation in spherical coordinates. 37 4 -3 -2 -1 0 1 2 3 3…

A: To solve this we have to find the relation of equation

Q: (a) Find a spherical coordinate equations; for the sphere X²+y²+(z-1)²=1 and the surface…

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

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Q: Find a spherical coordinate equation for the sphere x². + y? + (z – 1)2 = 1 Select one: а. p = cos Ø…

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Q: Use the parametric equations of an ellipse, x = a cos 0, y = b sin 0, 0 < 0 < 2m, to find the area…

A: Given Parametric Equation of ellipse  x=acosθ and y=bsinθ ,0≤θ≤2π To find the area of the Ellipse

Q: Determine the number of cusps for the hypocycloid described by the parametric equations x(t) =…

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Q: find an equation of the form ρ = f (θ , φ) in spherical coordinates for the following surfaces  z 2…

A: Coordinate systems are used to define the position of a point on an n-dimensional system. Some of…

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: 8. The position of a particle moving in the xy-plane is given by the parametric equations x =…

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Q: Find an equation of the form p = ƒ (0, 4) in spherical coordinates for the surface z = 16 (Use…

A: The equation in spherical coordinates for the surface is determined as shown below

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 of the form r = f (θ , z) in cylindrical coordinates for the following surfaces.…

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Q: Find a spherical coordinate equation for the cone Z =Vx² + y2? Select one: а. 4 b. TT 4 С. 4 d. Non…

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Q: Find an equation of the form p = f (0, $) in spherical coordinates for the surfac z = 8

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Q: (c) Evaluate zdz dy dr using spherical coordinates.

A: Triple integral is used to integrate the function of three variable over the three-dimensional…

Q: In three space, find the parametric equations of the curve C of intersection of the cylinder S: x2 +…

A: Here we have to find the parametric equations of the curve C of intersection of the cylinder S:x2+y2…

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

A: To convert z=x2+y2, in spherical coordinates, substitute z with ρ cosϕ, x with ρ sinφ cosθ and y…

Q: Find the spherical equation for the hyperboloid of two sheets x² – y² – 2² = 1.

A: Given information :  Equation of hyperboloid of two sheets x2-y2-z2 = 1

Q: Let x²+y? -6y = 0 be the equation of a surface S in xyz-rectangular coordinates. Give the equation…

A: We are given Equation of a surface S : x2+y2-6y=0 ---(1) To write this Equation  in the cylindrical…

Q: Use the parametric equations of an ellipse, x = 5 cos(0), y = 4 sin(0), 0 < 0< 2n, to find the area…

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Q: Determine the parametric equations of the curve of intersection of the paraboloid x? – y? + z² = 0…

A: Detailed explanation mentioned below

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

A: Given,  The equation of the surface by cylindrical equation r=3,  To convert a cylindrical equation…

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

A: In this question, the concept of conversion of the coordinate system is applied. Cartesian…

Q: Use the parametric equations of an ellipse, x = a cos(0), y = b sin(0), 0 s 0 s 2T, to find the area…

A: Given: Use the parametric equations of an ellipse, x = a cos θ, y = b sin θ, 0 ≤ θ ≤ 2π,  to find…

Q: Find a spherical coordinate equation for the sphere x² + y? + (z – 1)? =1 Select one: а. p = 3cos Ø…

A: Let us consider rectangular coordinates x,y,z and spherical coordinates ρ,θ,φ. Equations which…

Q: Use spherical coordinates to evaluate V4-x² 4-x²-y² + y² + z² dz dy dx V4-2² Jo Do not forget to…

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

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Q: Use the parametric equations of an ellipse, x = a cos(0), y = b sin(0), o sos 2r, to find the area…

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Q: Find an equation in rectangular coordinates for the cylindrical equation p2 + z? = 16

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Q: YouTrylt 1 Sketch the graphs of the equations given in cylindrical coordinates. (a) r =1 (b) 4 (c) =…

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Q: 9. (a) Find the equation of the cone 3.x2 +3y2 in spherical polar coordinates. (b) Use spherical…

A: Given

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

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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: A cone in cylindrical coordinates has the equation z = Vx2 + y? , so in spherical coordinates its…

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Q: Find the center C and the radius a for the spheres (x - 1)2 + (y - 2)2 + (z + 1)2 = 103 + 2x + 4y -…

A: Standard equation of sphere is given as x-x12+y-y12+z-z12=r2, where x1,y1,z1 is center of sphere and…

Q: Use the parametric equations of an ellipse, x = 2 cos(8), y = 3 sin(8), 0 < 0 < 27, to find the area…

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Q: Find an equation of the form p = f(0, $) in spherical coordinates for the surface. x2 - y2 = 36 p =…

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Q: The equation z = 1+r² in cylindrical coordinates represents Select one: O a paraboloid O a circle O…

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Q: 5. Use spherical coordinates to evaluate [[[ (x² + y² + 2²) ² dv D where D is the solid hemisphere…

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Q: 4. (i) Use the parametric equations of an ellipse, z = a cos (t) , y = bsin (t), 0 < t< 2r, to find…

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Q: Let r²+y?-6y = 0 be the equation of a surface S in ryz-rectangular coordinates. Give the equation of…

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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: Find a spherical coordinate equation for the sphere x² + y² + (z – 1)² = 1 Select one: a. Non of…

A: We have to solve given problem:

Q: What is the Cartesian form of the parametric equations æ(t) = 4cost – 1 and y(t) = 5sint + 2?…

A: Here I am attaching image so that you understand each and every step.