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

Q: Find an equation for the paraboloid z = 3 – (x² + y) in cylindrical coordinates. (Type theta for 0…

A: The given equation of the paraboloid is: z=3-x2+y2 To find the equation of the paraboloid in…

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: Convert from the Spherical Coordinate to the Cylindrical Coordinate AO 3 3 37 2 2'2 BO 3' 2 Co 3 3 3…

A: Conversion of spherical coordinates to cylindrical coordinates

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

A:

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

A: Given,

Q: Convert the point (x, y, z) = (2, 4, – 4) to cylindrical coordinates. Give answers either as…

A: Given point x,y,z=2,4,-4. The cylindrical coordinates can be given by, x=rcosθ    ...1 y=rsinθ…

Q: Find and equatin for the parabolid z = x^2+y^2 in spherical coordinates

A: Given query is to find equation of paraboloid in spheo coordinates.

Q: Transform (4, 7/3, ) from spherical into cylindrical form (here o is any angle).

A:

Q: Which of the following is the cylindrical coordinates of (-1,-V3,2)? Oa (4, 품, 2) O b. (2, 5,2) O…

A:

Q: and an equation in cylindrical coordinates for the equatic = 25x²+25y²-2

A: topic:- coordinate system

Q: 15. Find the radius of curvature at 0 = ÷n of the parametric equations x = 3(0 + cos 0), y = 3(1 —…

A: Given two parametric equations, x=3(θ+cosθ),y=3(1-cosθ) To find the radius of curvature at θ=π3

Q: Sketch the solid that has the given description in spherical coordinates           0 ≤   ≤ 2 , /4 ≤…

A: Concept: Calculus helps in understanding the changes between values that are related by a function.…

Q: Express x2y2+ z2 = 2z in cylindrical and spherical coordinates.

A: Given,

Q: Consider a point in Cartesian coordinates given by (3√√/3, −3, −8). (a) Find a corresponding…

A: The given Cartesian coordinates are: (x,y,z)=(33,-3,-8) Now, the Cylindrical coordinates is given…

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

A:

Q: Evaluate ∫W z dV, where W is the first-octant portion of the solid sphere of radius 2 centered at…

A:

Q: If point P has cylindrical coordinates 6, 8 then its rectangular coordinates are 3 (x, Y, 2) =

A: Finding the rectangular (or) Cartesian coordinates

Q: Find the position of a point given as (5, 2π/3, 2) in cylindrical coordinates, in cartesian and…

A:

Q: Use cylindrical coordinates to evaluate Vio-ri-p2xy dzdydx

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

Q: i) Find the solution of Vu O in spherical co-ordinates.

A: The given Laplace's equation is,∇2u=0Now this equation can  be written as in the spherical…

Q: Verify that dV = p sin o dp de dy when using spherical coordinates. %3D

A: We have to represent a differential element.

Q: 2. Convert the point (V6, , V2 ) from cylindrical to spherical coordinates. (a) (V2,플, ) (b) (vz. )…

A: Option C is correct answer.

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: Express the following points in cylindrical and spherical coordinates: (а) Р(1, — 4, — 3) | (b) Q(3,…

A:

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: 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 B = xa,. Express B in %3D (a) cylindrical coordinates, (b) spherical coordinates.

A:

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

A:

Q: 8. Find a Cartesian equation for the surface whose spherical equation is p= 2 sin() sin(0).

A: Solve the following

Q: are the rectangular coordinates of the point whose cylindrical coordinates are (r = 6, 0 = 2, z = 6)…

A: To convert cylindrical coordinates to rectangular coordinates.

Q: 1. Given a point (r, 0, z) = (2, 1/4, 1 /3) in cylindrical coordinates, what is its %3D rectangular…

A: We have to find the rectangular coordinates of given point in cylindrical coordinates.   According…

Q: 2. Convert the cylindrical coordinates [2, 1/6, –2] to Cartesian coordinates and to spherical…

A: We have to find the coordinates

Q: Translate the spherical equation below into a cylindrical equation! tan2(Φ) = 1

A: We have to find the transformation

Q: Express the point (x, y, z) = (-2, 2, 2/2) in spherical coordinates.

A:

Q: Transform the vector C = cospâ – sinpô + cospsinp2 into spherical coordinates and then evaluate it…

A: Given cylindrical co-ordinates system as                                               we know that…

Q: Convert the point (x, y, z) = ( – 5, 1, – 1) to | - spherical coordinates. Give answers as positive…

A: To convert the given cartesian coordinates (x,y,z)=(-5,1,-1) into spherical coordinates (rho, theta,…

Q: Find the Cartesian coordinates of the point (6, 4. VIT) given in cylindrical coordinates

A: First we have to determine (r,∅,z) then calculate respective Cartesian co-ordinates

Q: The equation of a sphere of radius 3. centered at the origin in cylindrical coordinates is + = 9.…

A:

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

A:

Q: Convert the point (1, , V3) from cylindrical to spherical coordinates. A. (2. 5. 5) 4' 6 В. 2,

A: To convert cylindrical coordinates (r, θ, z) to spherical coordinates ( ρ, θ, φ) we use following…

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

A:

Q: Find the point on the y-axis which is equidistant from (2,5,-3) and (-3,6,1). After getting the…

A: Since the point lies on the y-axis therefore the x and z coordinate will be zero. So, let the point…

Q: The surface 9z = 7x + 3y can be described in cylindrical coordinates in the form = f(0, z) = help…

A: Given surface 9z=7x+3y We know to convert from cartesian coordinate to cylindrical coordinate, we…

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

A:

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

A: r2cos2θ+z2+1=0

Q: 5. Use spherical coordinates to evaluate LIVE √√= ²+ y² + 2² dz dy dr.

A: Given ∫-44∫-16-x216-x2∫x2+y24x2+y2+z2 dzdydx

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…

Q: Convert the point from cylindrical coordinates to spherical co (3,2,0) (p, 0, 4) = || X

A: