9-22 c9-a2-y2 In cylindrical coordinates, S x² + y² dz dy dx = Select one: c9-r2 S S L* ,² dz dr de O b. None of these O c. S So S-r* r dz dr d0

Q: 2. Use cylindrical coordinates to evaluate √√9-x² 9-x²-y² [dz x² dz dy dx. √9-x2 0

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Q: Write a second order liner D.E. for which y=e°' sin(7 t) is a solution. y" - 12 y' +85 у%3D0 None У'…

A: Write a second order linear D.E for which y = e6tsin7t is a solution

Q: y² + 1 dy (y – 1)²(y + 1) 1.

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Q: Use spherical coordinates to evaluate f (ử+y° +z°)* dydzdx. 3/2

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Q: 9. Use spherical coordinates to evaluate ¹-² 1-x²-y² (x² + y² + z²)² dz dy dx

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

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Q: Given x = 2 cost + 38 and y = 5 sin2t %3D

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Q: d² y dx² Linear Equatoin/ variatoin parametee + y = tan x

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Q: Eliminate the parameter on t to write the parametric function as a Cartesian equation in y = form.…

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Q: Calculate Li eax 1 + ex -dx for 0 < a < 1 using the rectangular contour -R → R → R+ 2πi → -R+ 2πi…

A: If f(z) is regular, except at a finite number of poles within a closed contour C and continuous on…

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: 5. (x, y) (x - 6, y – 1) B A 1 2 3 4 5 Image Coordinates A'(__) B'( _) C'( -) n す 21

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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: dy for the following parametric equation: dx Calculate

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Q: Please solve asap: 9. Give a parametric description of the form r(u,v) for the equation 6x - 3y +…

A: To obtain a parametric description of the equation 6x−3y+2z=18, write it in terms of two variables,…

Q: Change from rectangular to cylindrical coordinates. (Let r 2 0 and 0 s 0 s 27.) (a) (-3, 3, 3) (b)…

A: Cylindrical coordinates are (r, θ, z)

Q: /16–y² /32–2²-y² n[L 2² + y* + z®)dzdzdy in nvert 1²+y² •1/2 4/2 -/2 Jo п/2 " T p* sin ódpdődý •4/2…

A: from the integral limits are as  follows 0 ≤ x ≤ 16-y2 0 ≤ y ≤ 4  x2+y2 ≤ z ≤ 32-x2-y2

Q: Vi-x² 2-x²-y² Change Vr +y² dz dy dx into cylindrical coordinates, then evaluate.

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Q: Use polar coordinate to find S² So 1-(x-1)2 x+y x² + y² dydx

A: A double integral ∫02∫01-x-12x+yx2+y2dydx To Find: Use polar to find the above integral. "As per the…

Q: 2. Solve the DE: (2x + dx + 2y ) dy = 0 1+ x?y? 1+ x?y?

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Q: 2 Evaluate the feltowing cartesian integrats by changing them inte equivalent Pelarintegrals: ff dy…

A: As per our guidelines we can solve first question for you .You can ask the remaining questions…

Q: (-3x) dxtxdy C is part of the ellipse 5x2+6y=30 fromC0,-V5) to cra,O). X,

A: Line integral Given ellipse is  From .

Q: Coute : 2y da + 3x dy, where D is described by 0 < a < 1, 0 < y < 1.

A: We have to find the given integral. For this we can use Green's theorem

Q: 3. Use cylindrical coordinates to evaluate 3 √9-x² [² [³²*² [√²²+³ (2² + y²) ³¹ dzdydz 0 Jo

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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: - z²) – 2x + 30y = 0 da? What is the larger root from the indicial equation

A: Given differential equation, 1-x2d2ydx2-2xdydx+30y=0 Find the largest root from the indicial…

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.