Write the equations in cylindrical coordinates. (a) 5x2 – 2x + 5y² + z² = 3 (b) z = 3x2 – 3y2

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

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Q: From Example 1, recall that x2 +y2 = 1 is the equation of the cylinder with radius 1, whose axis of…

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Q: write the equation in spherical coordinates a) 3x2 − 4x + 3y2 + 3z2 = 0

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Q: Write the equations in cylindrical coordinate (a) 8z = 5x2 + 5y2 (b) 3x2 + 3y2 = 2y

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

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Q: Write the equation in spherical coordinates. (a) 7z2 = 5x2 + 5y2 (b) x2 + 2z2 = 7

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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.

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A: topic:- coordinate system

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

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

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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: 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

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Q: 7) Find a rectangular equation equivalent to the given pair of parametric equations. x=2t-1 „y=t^2;…

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Q: Write the equations in cylindrical coordinates. (a) 8x2 - 6x + 8y2 + z? = 9 (b) z = 8x2 – 8y2

A: We have to find

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: Q2:- Find the parametric equations for the following Cartesian equations. 1) x=(/y² + 4 + 2) 2) 4x2…

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

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Q: 3 3 Let P be a point in R³ with rectangular coordinates (,,-13). v3). 2 (a) Give the cylindrical…

A: For cylindrical coordinates (r,theeta,z) r^2 = x^2+y^2 tan (theeta) = y/x  z=z

Q: Write the equations in cylindrical coordinates. (a) 3x² – 6x + 3y2 + z² = 5 z = 7x2 – 7y2

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

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

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Q: 5. Find the parametric equations of a line through (1, 0, -1) and parallel to the line -(x-4) 1 y =…

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Q: Write the equations in cylindrical coordinates. (a) 7x2 - 8x + 7y2 + z2 = 7 (b) z = 2x2 - 2y²

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

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Q: (a) Write the equation 3x2 + 3y? +3z2 - 15 = 0 in spherical coordinates (b) What does this equation…

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

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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: Write the equations in cylindrical coordinates. (a) 4x² + 4y² - z² = 9 (b) 7x - y + z = 3

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Q: Solve the following system of equations. (Enter your answers as a comma-separated list. If there are…

A: Given2x - 16y - 6z= 33……………..……….(i)-4x + 32y +12z = -44…………………(ii)

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

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Q: Write the equation in spherical coordinates. (a) 5z2 3x2 + 3у2

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

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Q: x2+y2+z2=2x write the spherical and cylindrical equations

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Q: Write the equation  x2 + z2 -(y-1)2  = 0 in cylindrical system . Which surface does it represent?…

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Q: Write the equations in cylindrical coordinates. (a) 6x2 - 8x + 6y² + z? = 9 (b) z = 7x2 - 7y2

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

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Q: . Find the cylindrical equation for the ellipsoid 4r² + 4y² + z² = 1.

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Q: Q7. Convert the rectangular coordinates to both Spherical and cylindrical coordinates; A (-1, 1,…

A: x,y,z=-1,1,-2 r=x2+y2+z2 r=-12+12+-22 r=1+1+2 r=4 r=2 . θ=tan-1yx θ=tan-11-1 θ=135  degree θ=3π4…