In changing variables to spherical coordinates, the dV in I f(2, y, z) dV becomes o dp do do. Cos

Q: (c) dz dy dx

A: Let's find.

Q: Question 3 In changing variables to cylindrical coordinates, the dV in JO f(x, y, z) dV becomes p dz…

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

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Q: Problem. Use the spherical coordinatas, I= psin o cos 0, y= psin osin 0, z= pcos o; p = r +y° +z, dV…

A: Let us first analyse E to get the limit values of integration. We are given that E is the solid…

Q: Which of the following correctly changes the integral rdrde from polar coordinates to rectangular…

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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.

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

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: In changing variables to spherical coordinates, the dV in I| f(x, y, z) dV becomes p cos o dp do de.…

A: By using formulaes for change of integral from Cartesian to spherical

Q: the LLE + y² + z*)% dzdydx 2n n 3 to spherical coordinates becomes the form TI sin(4)dpdød® True…

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Q: Which of the following is the cylindrical coordinates of (-1, 3,-2)? Oa (2, 즐,-2) O b. (2, ,-2)…

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Q: Which of the following is the cylindrical coordinates of (-1, -/3,2)? O a. (2, 품, 2) O b.(2, – 5, –…

A: Explanation of the answer is as follows

Q: Converted into polar coordinates, the integral r1/2 1-y L" Pydzdy becomes Select one: r3 cos? 0 sin…

A: We will first identify the region of the integration then we will obtain the limits in polar…

Q: Use spherical coordinates to find [[[, z2 dV.

A: In this question, we find the triple integral by using spherical coordinate with a sketch of solids

Q: Use spherical coordinates. Evaluate (6 – x2 - y?) dv, where H is the solid hemisphere x2 + y² + z² <…

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Q: Find a spherical coordinate equation for the cone Z =Vx² + y2? Select one: а. 4 b. TT 4 С. 4 d. Non…

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

A: Here, we will be transforming C=cos φ aρ-sin φ aφ+cos φ sin φ az into spherical coordinate and then…

Q: describe the given set in spherical coordinates  y2 + z2 ≤ 4, x = 0

A: y2+z2≤4,  x=0. Now consider, y2+z2≤4⇒x2+y2+z2≤4+x2⇒x2+y2+z2≤4             ∵x=0⇒ρ2≤4⇒0≤ρ≤2 Now since…

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: Change each of the following points from rectangular coordinates to spherical coordinates and…

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Q: Evaluate y*dV, where E is the solid hemisphere x? + y? + z² 0. E (Hint: spherical coordinates)

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Q: describe the given set in spherical coordinates x2 + y2+ z 2 ≤ 1

A: Given: x2+y2+z2≤1 Spherical coordinates: x,y,z→ρ,θ,ϕ ρ2=x2+y2+z2

Q: The value of Jacobian in cylindrical coordinate system is given by a. r b. r? sin e c. p2 d. rsin?e

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Q: The spherical coordinate equation of (x – 4)² + y² + z? = 16 is p= 8sinØcose

A: The spherical coordinates are given by  x=ρcosθsinφy=ρsinθsinφz=ρcosφ The given equation is…

Q: Exercise 2 Use spherical coordinates to evaluate f[[(9-x² - y³ ) dV , where E is the solid…

A: Introduction: When we perform a triple integral over a spherical region, it is convenient to follow…

Q: Evaluate the spherical coordinate integ A1 8 sin o | ? sin d dp dɖp de do de 0 0 512 2 O A. -

A: Here we have to calculate I= ∫0π∫0π∫08 sinϕ ρ2 sinϕ dρ dϕ dθ

Q: p = 4 cos 0 sin

A: Given: ρ=4cosθsinϕ To Find: Give the corresponding equation in Cartesian coordiantes considering…

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

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

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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: The equation p = 2 cos 0 sin o in spherical coordinate defines a sphere of center P and radius R,…

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Q: 48. Use spherical coordinates to evaluate y'Vx +y +z dz dx dy

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Q: Which of the following is a correct conversion formula when changing from spherical to cylindrical…

A: We know that the following formula are used to change from spherical to cylindrical coordinates:…

Q: Convert X-6A Into an integral of spherical coordinates 4 5 SE So p?sinodpdøde 6coso psinodpdode…

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Q: By changing to spherical coordinate, evaluate (a) z' Vx² + y² +z² dz dy dx (b) " ST* E x² + y° +z?…

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Q: (b) To change from spherical coordinates to Cartesian coordinates we use the equations x =r cos 0, y…

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Q: Convert the following rectangular equation: x^2 + y^2 = z^2 into spherical coordinates.

A: Given equation is x2+y2=z2  ....1

Q: For the following cylindrical coordinate (r, 0, z) of a point, find its associated spherical…

A: Given the cylindrical co-ordinates (r,θ,z)=(2,−5π4,−2)

Q: 3. Evaluate /// x² + y? dV where E is the part of a2 + y? + 2? = 4 with y 2 0, using spherical E…

A: (3) Given integral is ∭Ex2+y2dV, where E is the part of x2+y2+z2=4 with y≥0, using spherical…

Q: Which of the following is the spherical coordinates of the point (0, V3, 1) which is given by…

A: We will use the conversation formulae from rectangular to spherical coordinates.

Q: 5. Use spherical coordinates to evaluate [[[ (x² + y² + 2²) ² dv D where D is the solid hemisphere…

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Q: (e) Graph the surface in R' whose spherical equation is p = cos 20.

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Q: The value of Jacobian in cylindrical coordinate system is given by а. r b. 2 sin e с. d. r sin? 0

A: For the cylindrical co-ordinate system:                           The value of Jacobian can be…

Q: Show that the acceleration of a point particle in polar coordinates (d²r dr de +2 d0 |Ô0 is…

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Q: Use spherical coordinates. Evaluate TI (x2 + y2 + z²)² dv, where B is the ball with center the…

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Q: Change the spherical equation below into cylindrical coordinates! tan2(Φ) = 1

A: Any point in the cylindrical coordinate system is represented as r,θ,z . Any point in the spherical…

Cylindrical Coordinate System

The distance from a selected reference axis, the direction from the axis relative to a selected reference direction, and also the distance from a selected reference plane perpendicular to the axis area unit, all accustom outline purpose positions in a cylindrical reference frame. Counting that the aspect of the reference plane faces the purpose, the latter distance is expressed as a positive or negative variety.