The equation of a sphere of radius 5 , centered at the origin in spherical coordinates is: O r2 + z? = 25 O p? = 25 %3D O x² + y² = 25 O r² + z? = 5 O p = 5

Q: (c) dz dy dx

A: Let's find.

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: A hole is drilled through the center of a sphere x²+y² +z? = R,², leaving a ring-shape solid. If the…

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Q: The surface 10x – 9y = z2 can be described in spherical coordinates in the form p = f(0, 4) help…

A: Given 10x-9y=z2

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

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

A: To convert: The equation into rectangular form. Formula used: Convert rectangular into cylindrical.

Q: Question 7 Evaluate the triple by using cylindrical coordinates. ++y)dzdydx

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Q: Use the parametric equations of an ellipse, x = 3 cos (0), y = 4 sin(0), 0≤ 0 ≤ 2T, to find the area…

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

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Q: 4-x² –y² b.) z dz dy dx -VI¬x² J /3x²+3y? from Cartesian coordinates to spherical coordinates.

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Q: 6. By converting to spherical coordinates, evaluate 22 dz dx dy. 0.

A: triple integral

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

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Q: In three dimensions, the cylinder x? + z2 – 10x – 6z – 2 = 0 has radius k i +tj+ and the axis line…

A: Radius =6  r(t)= (5+6cos(thetha))i+tj+(3+6sin(thetha)k

Q: Use spherical coordinates. (x2 + y? + z?)2 dv, where Bis the ball with center the origin and radius…

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Q: A beam whose centre of gravity divides it into two portions, a and b, is placed insıde a smooth…

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

A: Given:y2=10-z2r2=x2+y2x=r cosθy=r sinθz=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: 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: 9. Show that for a ± 0, the equation p = 2a sino cos 0 in spherical coordinates describes a sphere…

A: Given :  The equation ρ = 2 a sin ϕ  cosθ  .   To determine: The equation ρ = 2 a sin ϕ  cosθ  in…

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: 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: In spherical coordinates equation for the paraboloid z = 2- x - y is p(cos o- psin? $) = 2 Select…

A: We have to find out  spherical coordinate

Q: Let N be the lower hemisphere of the sphere of radius 5 and let H • Construct dS for 2. Try using…

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Q: Identify the surface whose equation in spherical coordinates is given by p= 8 cos o

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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…

Q: Use cylindrical coordinates to show that the volume of a sphere of radius a from which a central…

A: If a cylinder of radius b is cut from a sphere of radius a, then the volume of sphere depends on the…

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: Sketch a Saccheri quadrilateral in the spherical model of double elliptic geometry with the…

A: To sketch: A Saccheri quadrilateral in the spherical model of double elliptic geometry with the…

Q: The planet is spherical with a radius of 1 unit in length. Suppose that in a coordinate system whose…

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Q: (d) r2 + x? = 9 in cylindrical coordinates (e) pcos(o) = 1 in spherical coordinates %3D

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Q: Problem 2. Use spherical coordinates to find the volume of the solid within the sphere r2+y? + z2 =…

A: z=ρcos(ϕ)x=ρsin(ϕ)cosθy=ρsin(ϕ)sinθz=x2+y2ρcos(ϕ)=ρsin(ϕ)cosθ2+ρsin(ϕ)sinθ2…

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

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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: 3. Use spherical coordinates to valuate ff, y? dV where E is enclosed by the hemisphere x? + y? + z?…

A: Given that  ∫∫∫Ey2dV and  enclosed by the hemisphere, x2+y2+z2≤9,y≥0 Here to evaluate the integral,…

Q: Question 7 Evaluate the triple by using cylindrical coordinates. LL x²+y)dzdydx

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Q: 1. The parts of spherical triangle are B=120°, C=150°, a=135°. What is the spherical excess? Compute…

A: We know: cos(A) = cos(a) sin(B) sin(C) − cos(B) cos(C)             =cos(135°) sin(120°) sin(150°) −…

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 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: Given that, 11-2-y 12x dzdyda = MT With the help of cylindrical coordinates find the value of m

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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 the area of the surface generated by revolving about the x-axis the portion of the astroid x2/3…

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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: A hole is drilled through the center of a sphere x² + y² + z? = R,², leaving a ring-shape solid. If…

A: given sphere x2+y2+z2=R2s and a drill of cylinderical shape x2+y2=R2d use polar coordinate to…