Derive three-dimensional heat equation in cylindrical polar coordinate system.

Q: Convert the point (−2/3,  4/3 , 8) from cylindrical coordinates to rectangular coordinates

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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: Wave mechanics are often employed for

A: Given,              ∂2u∂t2=16∂2u∂t2  for all  0≤x≤10 and t≥0.             ...(1)

Q: Convert point (-8,8,-7) from Cartesian coordinates to cylindrical coordinates. Hint: r² = x² + y²…

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

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Q: Convert the point (x, y, z) = (4, 1, 4) to spherical coordinates. Give answers as positive values,…

A: The spherical coordinates of the point x, y, z is ρ, θ, ϕ where ρ = x2+y2+z2 θ = cos-1zr ϕ = tan-1yx

Q: A point has cylindrical coordinates (r, 0, z) = (2, ,2/3). co .Convert to spherical coordinates.…

A: Given cylindrical coordinate is r,θ,z=2,π6,23 ∴ r=2  θ=π6z=23

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: Show that the cylindrical equationr 2(1 − 2 sin2 θ ) + z 2= 1is a hyperboloid of one sheet.

A: The cylindrical co-ordinates is converted into rectangular co-ordinate as x=rcosθ         ⋯⋯1y=rsinθ…

Q: Sketch the graph of the polar equation labeling "critical points and

A: Concept Used: Using the formula               where a≠0   and n is an integer >1, graph the…

Q: . Two trains A and B moving on a horizontal track with velocities Va = (40 + i30 km/h and V = (25 -…

A: Given, VA=40+30ikm/hVB=25-50ikm/h So, the relative velocity from A to B is,…

Q: 9. Identify the surface whose equation in spherical coordinates is given by

A: We have to solve given to problem:

Q: Determine the parametric equations of the curve of of the ellipsoid 4x² + y2 + 4z2 = 4 and the…

A: Solution: Given equation:ellipsoid: 4x2+y2+4z2=4; and half−cone: y2=x2+2z2 To find: parametric…

Q: Find the equation of the tangent line of the parametric equations x = 2 – 3 cos 0, y = 3+2 sin 6 at…

A: Given that: x=2-3cosθ and y=3+2sinθ

Q: Give a vector parametric equation for the line that passes through the point (3, 5, –5), parallel to…

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Q: . Determine the parametric equations of the curve of intersection of the ellipsoid 4x² + y² + 4z² =…

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Q: Transform (0, 5, 2) from rectangular into spherical form (here z is any negative number).

A: given rectangular coordinates is of the form (x, y, z) are (0,5,z) Now we are going to find…

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

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Q: Determine the parametric equations of the curve of intersection of the ellipsoid 4x² + y² + 4z² = 4…

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Q: Find the solution of polar coordinate f(z) = Z+ sine function by using Cauchy-Riemann method.

A: Cauchy Riemann method in polar form

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: Under suitable assumptions derive one dimensional wave equation.

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Q: Convert the point (x,y,z)=(−3,−3,5) to spherical coordinates. Give answers as positive values,…

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Q: Convert the point (x, y, z) = (4, 5, 1) to spherical coordinates. Give answers as positive values,…

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Q: Write the equation of a sphere of radius 3 in all three coordinates--cartesian, cylindrical, and…

A: It is given that the radius of sphere is 3 .We have to find the equation of sphere in all three…

Q: -axis. 5. Evaluate dV, where E is the solid tetrahedron with vertices at (0,0, 0), (2, 0, 0),…

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Q: 1.Convert (0,√3,−1) from Cartesian coordinates to spherical coordinates.

A: We will find spherical coordinates from cartesian coordinated.

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

A: We have to find the coordinates

Q: What is the equation of family of central conics with common foci and axis. Determine its orthogonal…

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

A: We have to find the transformation

Q: 1) In cartesin coordinate system, differential the Rfferential dxdydz. Infer 8 spherical Volume…

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

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Q: Sketch the graph of the polar equation labeling "critical points" and name the type of curve: 0= 一

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Q: Give deep concept about steam line and path line with their mathematical form and all respects? This…

A: The objective is to define the terms streamlines and path lines along with their mathematical forms.

Q: Consider a partially polarized light whose Stokes vector is given by [5,4,0,0]. Obtain the output…

A: Here a partially polarized light whose Stokes vector is given by [5,4,0,0]. We have to calculate its…

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: Convert the point (x, y, z) = (5, 3, – 1) to spherical coordinates. Give answers as positive values,…

A: we have to convert the rectangular coordinates to the spherical coordinates   The given…

Q: Parametrize the circle of radius 7 centered at (-2, 3) in the clockwise direction starting at…

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

Q: Convert the point (x, y, z) = (- 5, – 2, 4) to spherical coordinates. Give answers as positive…

A: We have to find the spherical coordinate

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

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Q: Convert the point (x, y, z) = (0, – 3, 2) to spherical coordinates. Give answers as positive values,…

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Q: Express answer in: 1.) in Cartesian Coordinate System 2.) in Cylindrical Coordinate System 3.) In…

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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 point (z, Y, z) = (5, – 5, 1) to spherical coordinates. Give answers as positive values,…

A: The given point is                               (x, y, z)=(5, -5, 1). Cartesian to spherical…

Q: parametric equations representing the given curve.  Line passing through (0, 2) and (3, 1)

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Q: Find out the general solution of one-dimensional wave equation in spherical polar coordinates by…

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

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Q: polar Co-ovdina 4x²= y²-44+8

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Q: Show the derivation of formula for the conversion from spherical coordinates to rectangular…

A: Rectangular coordinates can be written in spherical coordinates as follows: x=ρ cos θ sin ϕy= ρ sin…