The value of Jacobian in cylindrical coordinate system is given by а. r b. 2 sin e с. d. r sin? 0

Q: Find the Grodient (Cylindrical ) V=(2pz?sin"p)op +(pz-sin24)ap + (2p2 sin? o) az

A: Given: V=2ρz2sinϕaρ+ρz2sin2ϕaϕ+2ρ2zsin2ϕaz To find: Gradient of given function.

Q: Use spherical coordinates. ter? + y + z* dV, where E is the portion of the unit ball x2 + y2 + z2 <…

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Q: on? 26. Use spherical coordinates to evaluate: on height Vx? + y² + z² dz 1+[x² + y² + z²1} Jo psing…

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Q: Find an equation in rectangular coordinates for the surface represented by the cylindrical equation…

A: To convert: The equation into rectangular form. Formula used: Convert rectangular into cylindrical.

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

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Q: Problem. Use the spherical coordinatas, I= psin o cos 0, y= psin osin 0, z= pcos o; p = r +y° +z, dV…

A: Let us first analyse E to get the limit values of integration. We are given that E is the solid…

Q: Find the general (d’Alembert's) solution of the equation of spherical waves 1 d³u 72 p2 dr dr c2 Ət?…

A: the solution of Homogeneous Partial Differential equations with constant coefficients is of the…

Q: VI-y? rz²+y? I = f(x, y, z) dz dx dy.

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Q: Convert the following to rectangular coordinates and spherical coordinates. Do not evaluate the…

A: Given: The Tripple integral is ∫02π∫02∫r4-r2r2θdzdrdθ. To convert: The integral into the rectangle…

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: Use cylindrical coordinates to calculate : + y? dV W : a² + y? < 9, 0<z< 8 SSSW(x² + y³) dV =

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Q: Use spherical coordinates to evaluate -VE 0 Vx? + y? +z? dz dx dy

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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: 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: c) Use spherical coordinate to evaluate UTM TM 1²+y? Væ2 + y? + 22 dz dy dx. UTM &UTM

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Q: When written in cylindrical coordinates, the equation (x + y')2 = 1 is (a) r = 1. (c) r' cos'0 = 1.…

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: Q.1 Use cylindrical coordinates to evaluate (x+y )dzdxdy

A: ∫-11∫01-y2∫0xx2+y2dzdxdy =∫-11∫01-y2∫0xdzx2+y2dxdy=∫-11∫01-y2z0xx2+y2dxdy=∫-11∫01-y2xx2+y2dxdy…

Q: Use cylindrical coordinates to calculate : x? + - y dV W : x + y < 25, 0sz<4 SII»(x² + y² ) dV =

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Q: Show AlL work for ALL parts a) convert: x?+y?+2Z*+2z-5=0 to cylindrical

A: (a) Given,                      x2+y2+2z2+2z-5=0                       (1)

Q: Evaluate y*dV, where E is the solid hemisphere x? + y? + z² 0. E (Hint: spherical coordinates)

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Q: ify Stokes' theor d S is the surface

A: INTRODUCTION: Stoke's Theorem:-…

Q: The value of Jacobian in cylindrical coordinate system is given by a. r b. r? sin e c. p2 d. rsin?e

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

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Q: Find the cylindrical equation for (x-4)² + y² = 4². O a.r = 8 cos (theta) o b.r = 0 c. theta = 6.28…

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Q: If the relation between the spherical coordinates ' and the rectangular Cartesian coordinates x is…

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Q: A cone in cylindrical coordinates has the equation z = Vx2 + y? , so in spherical coordinates its…

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Q: 48. Use spherical coordinates to evaluate y'Vx +y +z dz dx dy

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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: The moment of inertia of a surface about the z axis is given by the formula I Sls x2 + y? dS. Find…

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

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Q: Convert the following point from cylindrical to rectangular coordinates: (* ). 11a 6, (x, Y, z) =…

A: The given point in cylindrical coordinates are   6,11π6,9. We know that if cylindrical coordinates…

Q: Use spherical coordinates. SIL Evaluate xyz dV, where E lies between the spheres p = 2 and p = 6 and…

A: Consider the given statement. Let  x=ρsinϕcosθy=ρsinϕsinθz=ρcosϕ Then dV=ρ2sinϕdρdθdϕ The limits…

Q: (b) To change from spherical coordinates to Cartesian coordinates we use the equations x =r cos 0, y…

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Q: Use cylindrical or spherical coordinates to evaluate the integral. 2 cVA-y? cv8-x?_y² z?dzdxdy. A…

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Q: For the following cylindrical coordinate (r, 0, z) of a point, find its associated spherical…

A: Given the cylindrical co-ordinates (r,θ,z)=(2,−5π4,−2)

Q: 3. Evaluate /// x² + y? dV where E is the part of a2 + y? + 2? = 4 with y 2 0, using spherical E…

A: (3) Given integral is ∭Ex2+y2dV, where E is the part of x2+y2+z2=4 with y≥0, using spherical…

Q: Use cylindrical coordinates to calculate : x? + y? dV W : a² + y? < 49, 0<z< 14 SSIW(æ² + y?) dV =

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Q: 9-y2 18-22-y? Example 3 Convert a2 + y? + z? dz dx dy into spherical 1²+y? coordinates.

A: Given that: ∫03∫09-y2∫x2+y218-x2-y2x2+y2+z2  dz dx dy

Q: Use spherical coordinates. I/| y? dv, where E is the solid hemisphere x2 + y2 + z? s 4, y > 0.…

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Q: Find an equation in rectangular coordinates for the surface represented by the cylindrical equation.…

A: We have to find

Q: Evaluate | xz dz dy dx by changing to spherical coordinates.

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Q: Answer true or false in spherical coordinates X,Y,z J p² sin p

A: Given: Jx,y,zρ,φ,θ=ρ2sinφ As we know that; The cylindrical coordinates; x=ρsinφcosθ,…

Q: 2) | cos(r + y)dA, R is the unit disk (i.e. the region inside the unit circle)

A: This double integral can be easily solved in polar coordinates. A brief introduction to polar…

Q: Use cylindrical coordinates to calculate : x² + y? dV W : 2² + y? < 9, 0<z< 14 SSIW(æ² + y?) dV =

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Q: Evaluate the spherical coordinate integral. 7/2 7/3 8 sec 8 sec o Q sin o cos o do do de 5 sec o

A: We have to find the value of given integral.

Q: Use spherical coordinates. Evaluate /| y² dV, where E is the solid hemisphere x2 + y² + z² s 9, y 2…

A: first convert x,y,z coordinates into hemispherical coordinates than perform integral  detailed…

Q: Use spherical coordinates. Evaluate xex + y2 + 22 dV, where E is the portion of the unit ball x2 +…

A: Consider the given: I=∫∫∫Exex2+y2+z2dVE​ is the portion of unit ball x2+y2+z2 that lies infirst…

Q: Given the cylinder (M): (x + 1)² + (y – 1)² = 2. (M) can be presented in cylindrical coordinates as:…

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Q: Use spherical coordinates. Evaluate y² dV, where E is the solid hemisphere x2 + y² + z² s 9, y 2 0.

A: Given  solid hemi sphere is   ;      x2+y2+z2≥  9   , y ≥0