16-y Convert (z² + y² + z²)dzdrdy into spherical coordinates.

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: Convert the point from rectangular coordinates to spherical coordinates. 13. (4,0,0) 14. (J3.1.2/3)

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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: y³ /r² + y² + z²dzdrdy

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Q: Convert from spherical to rectangular coordinates. (3, 0, π/2)

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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: V4-y? '8-x²-y² By converting to spherical coordinates, evaluate 2? dz dx dy.

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Q: Convert to polar coordinates in the xz-plane, similar to Example 3 in the book. r2 63 – 2x? – 2z? –…

A: The limits lead to interpretation that,   From (2), Comparing the above result with  r=3

Q: Find the parametric equation of x, y, z where : . z2 = x2 + y2 p. 9 = x2 + y² Nhat is the name of…

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Q: Convert from cylindrical to rectangular coordinates ( a) ( 4, π/6, 3 (b) (8, Зт/4, -2) (c) (5, 0, 4)…

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Q: Given a point in spherical coordinate (5, ) find its equivalence in cylindrical coordinate. Draw the…

A: Introduction: Apart from the rectangular coordinate systems, there are two other coordinate systems…

Q: Jo Jo Jo 5. Use spherical Coordinates to evaluate Av16 -r² 00O00

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Q: Determine the angle of rotation necessary to transform the equation in x and y into an equation in X…

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Q: Convert from rectangular to cylindrical coordinates. (1, √3, 7)

A: Given: 1,3,7 To convert rectangular form to cylindrical co-ordinate.

Q: . Convert the Cartesian coordinates (2, 2, 2) to Cylindrical and Spherical Coordinates

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Q: Convert to spherical coordinates and evaluate: 4-x2-y2 4-x2 -4²+x²+z?)² dzdy dx

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

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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: Convert the rectangular equation r +2y? + 2? = 42 + 6x to an 4) equation in cylindrical coordinates.…

A: Consider the rectangular equation: x2+2y2+z2=4z+6x. To convert rectangular equation into equation in…

Q: 5. Evaluate /9 z² y² yVx² + y? + z² dzdrdy by converting to spherical coordinates.

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Q: Evaluate by changing to spherical coordinates: /2–x²-y² xydzdydx x²+y2

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Q: Transform to spherical coordinates: F 102-8ỹ+6ż at point P (10, 8, 6)

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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: Use polar coordinates to evaluate 2/2 dydx. 3 1 0, (x²+y?)? O 5 Оз 6 O 2 O 1 O 4

A: To determine: The value of the integral  using polar coordinates, ∫12∫0x22x2+y232dydx.

Q: 1) Use spherical coordinates to evaluate 4-y² c4-x²-y² 4-x2-y2 Li L y²/x² + y² + z² dzdxdy

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Q: H. Evaluate coordinates. 4-y² 4-x²-y² 1 x²+y²+z² So dzdxdy by using spherical or cylindrical

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

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Q: Calculate the imaginary part of  ∮C(Re(z)+3.78)(2z^2+ 5z+ 13 / z)dz  where C:|z|=1  Use FOUR…

A: We have to find the imaginary part of the integral ∮ fzdz, where fz=Rez+3.782z2+5z+13z over the…

Q: Write the equations in spherical coordinates 3x+4y+7z=1

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Q: Rewrite the equation in (a) cylindrical and (b) spherical coordinates. 4x? + 4y? + 9z² = 36.

A: In the  Cylindrical co-ordinate system  a point in space is represented by the ordered triple…

Q: Write the equation in spherical coordinates. 9. (a) x2 + y2 +z2 = 9   (b )x2 - y2 - z2 = 1

A: Here we have to write the equation in spherical coordinates. 9. (a) x2 + y2 +z2 = 9   (b )x2 - y2 -…

Q: II. Determine the number of solutions of the right Spherical triangle 1. b= 42°18' B = 42°18'

A: Given: b=42°18' B=42°18'   To determine: The number of solutions of the given right spherical…

Q: Convert the point from rectangular coordinates to cylindrical coordinates. (6V2, -6V2,9) (r, 0, z) =…

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Q: Determine the angle of rotation necessary to transform the equation in x and y into an equation in X…

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Q: Find an equation in spherical coordinates whose graph is the parapoloid Z=(X^2)+(Y^2)

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Q: 77 Convert 1. T from 4 spherical to cylindrical coordinates

A: We have to 1st convert to rectangular coordinates then to cylinderal coordinates.

Q: Convert the rectangular equation x2 + y2 + z2 = 27 to an equation in (a) cylindrical coordinates and…

A: Given: Rectangular equation x2 + y2 + z2 = 27

Q: Find an equation equivalent to x²+ y² + 2z²+ 2z - 5 =0 in spherical coordinates.

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

A: To convert the given point into spherical coordinates (x,y,z)=(0,-3,-2)

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

A: Given equation is x2+y2=z2  ....1

Q: c) Use spherical coordinate to evaluate x dz dy dr 4-x²-y²

A: Sketch the region and find range of variable

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

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Q: Convert the rectangular equation x2 + y2 = 4y to an equation in (a) cylindrical coordinates and (b)…

A: Given- x2+y2=4y To find- An equation in (a) cylindrical coordinates and (b) spherical coordinates.…

Q: Determine the rectangular form of z (1 + i)!-i

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Q: c) Use spherical coordinate to evaluate V1-x2 1 Vx2 + y? + 22 dz dy dr.

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

Q: Convert the rectangular equation x2 + y2 + z2 − 2z = 0 to an equation in (a) cylindrical coordinates…

A: (a) Convert to  cylindrical coordinates as follows: Substitute x=rcosθ,y=rsinθ,z=z.…

Q: Convert the following point from spherical to rectangular coordinates: (17) - 4 4 (x, y, z) =

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