Q7. Convert the rectangular coordinates to both Spherical and cylindrical coordinates; A (-1, 1, –V2)

Q: Find the rectangular coordinates of the point whose cylindrical coordinates are given. a) (3, pi,…

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Q: Convert from rectangular to cylindrical coordinates. (6.2V3, 3) (Use symbolic notation and fractions…

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Q: The cylindrical coordinates of the point with rectangular coordinates (-V2, -v2, v2) are (v2, , V2).…

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Q: Consider a point in Cartesian coordinates given by (-2, 2v3, 4). (a) Find the corresponding…

A: Given,

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

A: Cylindrical (ρ,θ,z) to cartesian (x,y,z) conversion formula is -: x = ρ × cosθ  y = ρ × sinθ  z = z…

Q: Convert the given equation, -z2- y2 +=1, z20 to an equation in cylindrical coordinates.

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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: "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: 4-x²-y² 1 Evaluate ²4-y² So coordinates. x²+y²+z² dzdxdy by using spherical or cylindrical

A: Here we can use spherical coordinates to find the value of the integral. In spherical coordinates…

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: If a point A has the rectangular coordinate (v2, v2, V3), so its cylindrical coordinates are (2, 5,…

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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: Write the equation in spherical coordinates. (a) 2x2 – 3x + 2y2 + 2z2 = 0 (b) 5x + 4y + 7z = 1

A: To write the given equations in spherical coordinates a 2x2-3x+2y2+2z2=0(b) 5x+4y+7z=1

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: Find an equation in spherical coordinates for the equation given in rectangular coordinates. x² +y²…

A: Explanation of the answer is as follows

Q: Express the following points in cylindrical and spherical coordinates: (а) Р(1, — 4, — 3) | (b) Q(3,…

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

A: Given the equation:

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

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Q: Find an equation in spherical coordinates for the equation given in rectangular coordinates. x2. +…

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Q: 5. Use spherical coordinates to evaluate r2+ y2 +22 dz dy dr. 16-

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Q: Find the rectangular coordinates of the point, whose cylindrical coordinates are given. (a)    (8,…

A: ρ, θ, z=8, π4, 3⇒ρ=8, θ=π4, z=3  Now rectangular coordinates are, x=ρcosθ, y=ρsinθ, z=z⇒x=8cosπ4,…

Q: find an equation in rectangular coordinates for the equation given in cylindrical coordinates r= 2z

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Q: find an equation in cylindrical coordinates for the equation given in rectangular coordinates z=…

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Q: Find an equation in rectangular coordinates for the equation given in cylindrical coordinates. p2 +…

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Q: Find an equation in rectangular coordinates for the cylindrical equation p2 + z? = 16

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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: Evaluate: , S 9-2²-y? x² dz dy da, using cylindrical coordinates. 3 245 243 245 243

A: As we know that the cylindrical coordinates: x=rcosθ;y=rsinθz=z x2+y2=r2 dydx=rdrdθ Given:…

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

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

A: y=4 a). rsinθ=4   ∵x=rcosθ,  y=rsinθ,  z=z⇒r=4sinθ⇒r=4cscθ

Q: Find a spherical coordinate equation for the sphere x² + y? + (z – 1)² = 1

A: All real numbers can be represented on a line called the number line. The number zero corresponds to…

Q: YouTrylt 3 Find the rectangular and cylindrical coordinates of the point with spherical ( 2, 7 /…

A: To convert the spherical to rectangular and cylindrical 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: 1. Consider a point in Cartesian coordinates given by (-2, 2v3, 4). (a) Find a corresponding…

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

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Q: Convert from rectangular to cylindrical and spherical coordinates. z2 = x? + y?

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

A: Sketch the region and find range of variable

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

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

A: Cylindrical to rectangular transformation is made by following rule,

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

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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: 5. Use spherical coordinates to evaluate LIVE √√= ²+ y² + 2² dz dy dr.

A: Given ∫-44∫-16-x216-x2∫x2+y24x2+y2+z2 dzdydx

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.