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

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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: √√(x + y + 2) ds, 0sus 5, 0≤v≤1 S is the parallelogram with parametric equations x = u + v, y = u -…

A: Solution is here

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

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Q: Match the surface to its corresponding equation in spherical coordinates. |p = 4 cos() 1.5 -1 -0.5 0…

A: To match the given surface to their given Equation in spherical coordinates.

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: Find the radius of curvature at 0 = t of the parametric equations x = 3(0 + cos 0), y = 3(1 – cos…

A: To find the radius of curvature, first find out dxdθ and d2xdθ2. x=3θ+cos θdxdθ=31-sin θd2xdθ2=-3cos…

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

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Q: VI-y? rz²+y? I = f(x, y, z) dz dx dy.

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Q: 17. Find the cartesian equation of the parametric curvex =1+e²*, y= e'. (a) z² = y? – 1 (b) 7 = 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 x2…

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

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

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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: 3. Express the equation y = mx + b, where m and b are constants, in plane polar coordinate.

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

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

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Q: Find an equation of the tangent plane to the following parametric surface, r(u, v) = (u2 + 6) i+ (v³…

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Q: Determine the total distance covered from t = 1 to t = 3 from the given parametric equations: x =…

A: Let's find the total distance covered. = d

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 the equation of the surface in spherical coordinates. x^2+y^2+z^2=2z

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Q: What is the cylindrical equation of the surface whose spherical equation is p = 4? Select one: a. r²…

A: Let us consider spherical coordinates ρ,θ,φ and cylindrical coordinates r,θ,z. Conversion of…

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…

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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: The surface 22 = x² +y? – 4x + 5 remains unchanged when rotated about the line L in R³ Which of the…

A: The given surface is z2=x2+y2-4x+5, which is as shown below: This is a hyperboloid paraboloid.…

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

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Q: 3. Find the exact area of the surface obtained by rotating the curve described by the parametric…

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

A: The equation of the paraboloid z = x2+y2                                       ........(1) To…

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

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Q: The cylindrical equation z = r2 represents which of the following? O a paraboloid O a semisphere O a…

A: The cylindrical equation z=r2

Q: Try to sketch by hand the curve of intersection of the parabolic cylinder y = x² and the top half of…

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Q: The surface z? = x² + y? – 4x + 5 remains unchanged when rotated about the line L in R Which of the…

A: The given surface is z2=x2+y2-4x+5, which is as shown below: This is a hyperboloid paraboloid.…

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

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

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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: 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: Consider the ellipsoid a? + y? + 4z2 = 12. 1. Find the general equation of the tangent plane to the…

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

A: we have to find an equation in cylindrical coordinates for the surface represented by the…

Q: The object shown in the figure is axially symmetric and its curved surface is described in…

A: To calculate the volume of the solid bounded by below surface for 0≤z≤4. r=−z+4

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

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

A: We have to find

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

A: Consider the following equation: x2+y2-2z2=5                                             ...... 1…

Q: Find the point at which the line with parametric equations x = 3 + 4t, y = 5 – 2t, z = 4 + 7t…

A: According to question,Given equation of line in parametric form,x = 3+4t,y = 5-2t,z= 4 +7t,Equation…

Q: Identify the surface whose equation in spherical coordinates is given by p= 6 cos

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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: 1. Describe in words the surface represented by the equation in cylindrical coordinates. (a) 0 = (b)…

A: Consider the provided question, Hello. Since your question has multiple sub-parts, we will solve…

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

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