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

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

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

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Q: b.) √4-1²-² √3x²+3y² TEN nates. z dz dy dx from Cartesian coordinates to spherical coordi-

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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: 2² dz dx dy By converting to spherical coordinates, evaluate

A: Given:  ∫02∫04-y2∫x2+y28-x2-y2z2dzdxdy we need to find following integeral by using spherical…

Q: 3. Given the function, W=x²+y²-z?, using spherical coordinates equations, find the aw aw dw and дө

A: It is given that, w=x2+y2-z2 It is known, that cartesian coordinates can be written in spherical…

Q: Q3// B Verify that dv3p'sin Ddpd@d owhen using spherical coordinate

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

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Q: Q3//A:- Verify that dV = p² sin p dp d0 do when using spherical coordinates.

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

Q: "s): The cylindrical coordinates of the point that has spherical coordinates (5, п /4,2п/3)is

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Q: T 27 Convert ( 5, from 3 spherical to cylindrical coordinates -5V3 ㅠ 5 5V3 5/3 7 5 4 2 (등급) 5V3 T 2…

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Q: Express the following points in cylindrical and spherical coordinates: (i) P(l, -4, -3); and

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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: 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: Write the equations in cylindrical coordinates. (a) 7x + 5y +z 2 z-2-(5 sin(0) +7 cos(8)) (b) -3x-3y…

A: To convert the given equation to cylindrical coordinates we have to put the value., x = rcosθ y =…

Q: 6. By converting to spherical coordinates, evaluate 22 dz dx dy. 0.

A: triple integral

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

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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: (a) Express the following points in cylindrical and spherical coordinates: (i) P(1, -4, -3); and…

A: We need to find cylindrical and spherical coordinates.

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…

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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: Find an equation of the form p = f (0, $) in spherical coordinates for the surfac z = 8

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Q: (c) Evaluate zdz dy dr using spherical coordinates.

A: Triple integral is used to integrate the function of three variable over the three-dimensional…

Q: In changing variables to spherical coordinates, the dV in J f(x, y, z) dV becomes p² cos o dp do do.

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

A: We have to represent a differential element.

Q: find an equation of the form ρ = f (θ , φ) in spherical coordinates for the following surfaces  z =…

A: To convert z=x2+y2, in spherical coordinates, substitute z with ρ cosϕ, x with ρ sinφ cosθ and y…

Q: find an equation of the form ρ = f (θ , φ) in spherical coordinates for the following surfaces  x2…

A: Solution:- x2-y2=4 x=ρ sinφ cosθ y=ρ sinφ sinθ   ρ sinφ cosθ2-ρ sinφ sinθ2=4 ρ2 sin2φ cos2θ-ρ2 sin2φ…

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. 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: (a) Express the following points in cylindrical and spherical coordinates: (i) P(l, -4, -3); and…

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Q: Which of the following is the rectangular coordinates of the point which is given by cylindrical…

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Q: Convert the point (x, y, z) = ( – 5, 1, – 1) to 6. spherical coordinates. Give answers as positive…

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

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Q: Find an equation of the form p = f(0, $) in spherical coordinates for the surface. x2 - y2 = 36 p =…

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Q: Convert the Cartesian equation Z z = 6-√√36-x² - y² into spherical coordinates.

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Q: 5. Convert the integral 9-x2 9-x²-y² Vx? + y? + z² dzdydx to spherical coordinates then evaluate.

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

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

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Q: (b) Use spherical coordinates to evaluate l y²dV_where E is the solid hemisphere a? +y² + z² 0. E

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Q: Given that, 11-2-y 12x dzdyda = MT With the help of cylindrical coordinates find the value of m

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

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Q: Solve the BVP in spherical coordinates v²u = 0, 1< p< 2, 0< ¢ < ñ. u (1, ø) = 3P2 (cos o), u (2, 0)…

A: Given that ∇2u=0, 1&lt;ρ&lt;2, 0&lt;ϕ&lt;πu1,ϕ=3P2cosϕ, u2,ϕ=P3cosϕ

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.