(a) r = 3 in cylindrical coordinates (b) = T/3 in spherical coordinates (c) 0 = T/4 in cylindrical coordinates (d) r2 + x2 = 9 in cylindrical coordinates (e) pcos() = 1 in spherical coordinates

Q: 9-22 c9-a2-y2 In cylindrical coordinates, S x² + y² dz dy dx = Select one: c9-r2 S S L* ,² dz dr de…

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Q: Find an equation in rectangular coordinates for the cylindrical equation r = 5 cos(0)

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Q: 4. Find the general solution of the Laplace equation in spherical coordinates when the potential has…

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Q: V1-x² c2 Evaluate xyz dz dy dr in cylindrical coordinates.

A: As per the guidelines I can solve only first question. I request you to kindly repost second…

Q: Line integrals: 1) Evaluate the following line integral:S, (x² + y² + z²) ds where Cis parametrized…

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Q: 1.35. Use cylindrical coordinates to find the area of the curved surface of a right circular…

A: (1.36) Given      radius = a      height = h

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

A: We need to find the geometry of the given integral.  Then find the limits in terms of spherical…

Q: se spherical coordinates. valuate ||| (x² + v2) dV. where E lies between the spheres x2 + = 9 and x2…

A: Given query is to find the value of integral using spherical coordinates.

Q: r4–x²-y² x²y dz dx dy /2-y² Jx²+y² x² + y² by converting to cylindrical coordinates.

A: We will evaluate the given integral.

Q: 4) A cylindrical coordinates equation for the cone z² = ²+1/² is: a. z² = 97² b. 9z=r c. 9z² = 7² d.…

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Q: V1-x /25-x-y Use cylindrical coordinates to evaluate , S zdz dy dx.

A: Here we will evaluate the required value.

Q: Transform in cylindrical coordinate at the point specified 6 ax -3 ay-6 az at P ( r=5; p= 120…

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Q: Q11) Converting Cartesian to spherical x + y + (z- 1)2 = 1

A: We have to convert given equation from Cartesian to spherical coordinates.

Q: Write the equations in cylindrical coordinates. (a) 2x2 - 5x + 2y2 + z2 = 7 8,2 +z? – 5r cos(0) =7…

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Q: (a) 0 = /4 in cylindrical coordinates (b) r = 5 in cylindrical coordinates (c) ø = T/3 in spherical…

A: The graph for part (a) is

Q: CHAPTER ONE: 1-1: For a cylindrical coordinate prove that p = Vy? + x2 1-2: Given a part of cylinder…

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Q: 8. Describe the motion of a particle with position (x, y): x = 3sin (t),y 4cos (t)

A: To describe the motion of a particle for below curve. x=3sint, y=4cost

Q: LS -² dz dy dx, using cylindrical coordinates. 9-r r9-z²-y? 3. Evaluate:

A: Given,             ∫-33∫-9-x29-x2∫09-x2-y2x2dzdydx=

Q: 6. A particle at (1,0,0) starts moving in space in such a way that its position vector at any time t…

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Q: (b) SI Evalucite using cylindrical Coordinates. T = T. (c)

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Q: 6. A particle at (1,0,0) starts moving in space in such a way that its position vector at any time…

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Q: 21. Moments of inertia Find the moments of inertia of the rect- angular solid shown here with…

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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: Evaluate - y² No- 9 - x2 – y2 dz dx dy -2 14 - y² 0 by transforming to cylindrical or spherical…

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Q: 64-x² 64-a 64-x² Jo -8 Use cylindrical coordinate to evaluate La L- So 2x²dzdydx.

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Q: Vi-x² 2-x²-y² Change Vr +y² dz dy dx into cylindrical coordinates, then evaluate.

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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: There are two parts of question a and b parts

A: (a)Given Cartesian coordinate in the following,

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

A: The relationship between cartesian and spherical coordinates are :

Q: (a) r2 < z < 8 – r² in cylindrical coordinates (b) p< 1, 0 < $ <T/6, 0 < 0 <T in spherical…

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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: Find the cylindrical equation for (x-4)² + y² = 4². O a.r = 8 cos (theta) o b.r = 0 c. theta = 6.28…

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Q: 18-z-y? Example 3 Convert + y² + z² dz dx dy into spherical coordinates.

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Q: 1.35. Use cylindrical coordinates to find the area of the curved surface of a right circular…

A: Solution for 1.35 Image is attached,

Q: Evalucite using (b) T = cylindrical Coordinates. T VA (c) sin +y

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Q: 1.32. Find the distance between (2, x/6, 0) and (1, A, 2), where the points are given in cylindrical…

A: We will find out the required distance between two given points.

Q: 4) Find the critical points of the parametric equations x = 5 – In t y = t + Int

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Q: (d) p= 3 in spherical coordinates (e) 0 = 4T/3 in spherical coordinates (f) z = 4 – r2 in…

A: Given: ρ =3. In spherical coordinates, ρ denotes the radius of sphere. Therefore, ρ =3 denotes a…

Q: (h) p= sin(0) sin(ø) in spherical coordinates (i) p2 (sin? (ø) sin? (0) + cos² ()) = 9 (j) 0 <0<T/2;…

A: For (h), We are given the equation of the surface as ρ = sin(θ) sin(ϕ) in spherical coordinates.

Q: Q9) A differential volume in spherical coordinates is shown in Figure below For the volume element,…

A: Answer of all lines elements..(a),(b),(c)

Q: 9-y2 18-22-y? Example 3 Convert a2 + y? + z? dz dx dy into spherical 1²+y? coordinates.

A: Given that: ∫03∫09-y2∫x2+y218-x2-y2x2+y2+z2  dz dx dy

Q: 17-20 Use cylindrical or spherical coordinates to evaluate the integral. 17. x² dz dy dx (a > 0)…

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Q: A hiker in the woods travels along the path described by the parametric equations X = 80 − 0.7T Y=…

A: Hiker  X=80-0.7T Y=0.3T   Bear  X=0.2T Y=20+0.7T

Q: Question 1 Find a normal vector and derite a parametric representation of the cylinder of revolution…

A: To find- Find a normal vector and derive a parametric representation of the cylinder of revolution

Q: Q.No 05: Find the expressions for the spherical harmonics Y30 (0, 9) and Y3,+1(0, 9). Y30 (0, 9) =…

A: Given  Y3,0θ,φ=716π5cos3θ-3cosθY3,±1θ,φ=2164πsinθ5cos2θ-1e±iφ

Q: √1-x² 16 By changing to cylindrical coordinate, evaluate So So √x²+y2x² dzdydx

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Q: Q3/|A:- Verify that dV = p² sin o dp do dp when using spherical coordinates. %3D

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Q: Point -masses mi are located on the x-axis as shown. Find the moment M of the system about the…

A: A diagram is given in which at some values of x, the point masses mi are located. The objective is…

Q: V2,V2-x V4-x2-y2 b b2 If the integral f(x,y,z) dzdydx is rewritten in spherical coordinates as…

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