1-For spherical polar coordinate system Zr Zr (2² exp(- 2a 1 Z. -) sin OCosø 42 `a а Jy„V„dV = 8_ =? %3D px px

Q: Find the spherical equation of the Cartesian equation x2 + y2 +(z - 81)2 = 812. o a. rho = 81 cos…

A:

Q: 7. (a) Find a spherical coordinate equations; for the sphere x²+y²+(z-1)²=1 and the surface…

A: To convert a point from Cartesian coordinates to spherical coordinates, use equations…

Q: 43/2-x f(x,y,z) dzdydx is rewritten in spherical coordinates as g(p.p,0) dpdwde, then…

A: By integral, x2+y2⩽z⩽43-x2-y2----1 0⩽y⩽43/2-x2------2 0⩽x⩽43/2----------3

Q: Convert to spherical coordinates. √9-x2 3 St. Sort So √x² + y² [x² + y² (1) Z aretan, dzdy dx

A:

Q: 24. A particle moves round the polar curve r = a(1+ cos e) with constant angular velocíty w. The…

A: We have constant angular velocity = w  r = a(1+ cosθ)

Q: When 9-x-y (x²+ y² +z²)% dzdydx the t 2n n 3 to spherical coordinates becomes the form !! p…

A: Solve the triple integral.

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: What is the rectangular equivalence to the parametric equations? x (0) = 3 cos 0 + 2, y (0) = 2 sin…

A: .

Q: V18-x2-y Convert (x² + y + z?)dzdxdy into spherical coordinates. 2n/3 3V2 4 p* cos pdpdpdO /2 -n/2

A:

Q: 1) Use spherical coordinates to evaluate 4-x² -y² 4-x2-y2 4-y² LaSNa- y²/x² + y² + z² dzdxdy

A: The given problem is to evaluate the given triple integral using spherical coordinates, We have to…

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: Evaluate spherical 4 √16-4² √16-x² - y² sőösi O -√16-x²-y² cylindrical coordinates. or (x² + y² + z…

A:

Q: In spherical coordinates, if u is a spherical wave, i.e. u=u(r,t), then the wave equation becomes du…

A: Given equation: 1r2∂∂rr2∂u∂r=1c2∂2u∂t2 ....i First Let V=ru ⇒u=Vr substitute this value of u in…

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

A: For the parametric curve x=x(θ), y=y(θ)Curvature K=|x'y''-y'x''|[(x')2+(y')2]32Radius of…

Q: 5. Use spherical coordinates to evaluate /16--2² Not √16¬x² / √x² +yª √x² + y² + z² dz dy dr.

A: The given problem is to evaluate the given triple integral by converting the Cartesian coordinates…

Q: 25) Evaluating in polar coordinates: 6*L*(x² + y²)dydx

A:

Q: Find the spherical equation of the Cartesian equation x2 + y2 +(z - 37)2 = 37². a. rho = 37 cos…

A:

Q: 2. By changing to cylindrical coordinates, evaluate 2 2π Stt. [²* * cos p² sin³ o dp do dô 0

A: To Evaluate: The integral ∫02π∫0π/4∫02/cosϕρ4sin3ϕ dρdϕdθ by converting it to cylindrical…

Q: For spherical polar coordinate system (3² exp(x)sin Cosø 4/2 `a 1 -Zr,„Zr. 2a a |W„Y„dV = 8¸ = ? px…

A:

Q: 5. Given the parameter 7, constants a and c, show that the parametric equations: X(+) = (cosh () –…

A:

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: (b) Graph the curve in R² whose polar equation is r= cos 20. (c) Graph the surface in R whose…

A: Since you have posted multiple subparts. I am answering the first 3 subparts. Please post again for…

Q: 9.) Use spherical coordinates to evaluate 3/2 (x² + y² +2²) ³¹² dydzdx. 9-1² √√9-1²-₂² √√√9-x²-2²

A: To find the given integral using spherical co-ordinate system :-

Q: r cos 0 = -3 2n 5Tt 2 3 Check for symmetry line 0 = = pole polar axis

A: rcosθ=-3 Now when θ=0, rcos0=-3⇒r1=-3⇒r=-3 When θ=π6, rcosπ6=-3⇒r32=-3⇒r=-23 When θ=π3,…

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: For spherical polar coordinate system 1 Z -Zr Zr 3/2 4/2 a exp(-()sin OCoso 2a px a V WmdV = 8 = ?…

A:

Q: 1. Consider a point in Cartesian coordinates given by (-2, 2\3, 4). (a) Find the corresponding…

A:

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: 5 25- y² 50-g² –y² Convert (x² + y² + z²)dzdædy into spherical coordinates. ²+y² 5/2 pª cos ødpdød0…

A: Answer:We have to convert∫50∫25-y20∫50-x2-y2x2+y2x2+y2+z2 dzdxdy into sphercal coordinates∵0≤y≤5…

Q: 4-72-2 2. z dz dy dx 3r2+3y2 from Cartesian coordinates to spherical coordinates.

A: Given Integral is converted from Cartesian to Spherical Coordinates

Q: 1. Describe the graphs of the equation (a) r = cos 20 in cylindrical coordinates. (b) p= sec otan 0…

A: First change cylindrical and spherical coordinates system to Cartesian coordinates system

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

A: Solve the following

Q: 4-22-y2 Compute y? Vx2 +y? + z² dz dx dy by converting to spherical 4-x2- coordinates.

A:

Q: 1. Convert the point (-1,1, v2) from Cartesian to spherical coordinates. (a) (VZ. VZ) (b) (1., vZ)…

A: To convert the point (-1,1,√2) from cartesian coordinates to spherical coordinates.

Q: x2-y는 군.Give the spherical coordingtes.

A:

Q: 1) Converting Cartesian to spherical x +y + (z - 1)? = 1

A: The relationship between cartesian and spherical coordinates are :

Q: iyı , Z2 = x2 +iy2 than Z,Z, in polar forr + 62) – i sin(0, + 02) Z,Z2 = ir2(cos(0, – 02) + i sin O…

A:

Q: Transform C = cos p a, - sin p a, + cos p sin p az into spherical coordinates and then at P (2, T/4,…

A:

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

A:

Q: 2. Find the coordinates of the centre, vertices and foci of the curve with parametric equations: x =…

A:

Q: If Z, = (-V3 + 3i), Z2 = (2+ 2i ) than 4 in polar form is : %3D Z2 Z1 5n 5n (cos +i sin 12 5n (cos…

A: z1=-3+3i,z2=2+2i,z1z2=-3+3i2+2iApply complex arithmetic rule:  a+bic+di = c-dia+bic-dic+di =…

Q: please don't skip any steps

A: Given, ∫03∫09-x2∫09-x2-y2x2+y2+z2dzdydx

Q: 4-x²-y² ) Use spherical coordinates to evaluate ,L /x² + y² + z²dzdydx.

A:

Q: Therefore, the system in polar coordinates is given by i = r(1 – r2 – r² sin? 20) Ô = 1+ 4r2 cos 0…

A: Polar Coordinates:   In terms of Cartesian coordinates, the polar coordinates r (radial coordinate)…

Q: Which of the following expressions are false? I. Spherical coordinates of z2 – y? – z² = 1 is…

A: