Use Spherical coordinates to evaluate Cx*+ ya+22)² dV where Bis the B. ball with anter at the ongin and. radius 5.

Q: Use spherical coordinates to evaluate /R Vx2 + y² + z² dV , where B is the ball x² + y? + z? < 10 В

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Q: Use Cartesian coordinates to evaluate JIJ y² dv 2 D where D is the tetrahedron in the first octant…

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Q: Use spherical coordinates to evaluate // | eva*+*** dV, where E is enclosed for E by the sphere x² +…

A: Please see the below picture for detailed solution.

Q: 2. Convert the point (V6, , v2 ) from cylindrical to spherical coordinates. (12등, ) (b) (vZ;. )…

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Q: Q3// B Verify that dv3p'sin Ddpd@d owhen using spherical coordinate

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Q: Use spherical coordinates. Evaluate ∭z dV, where E is between the spheres x ^ 2 + y ^ 2 + z ^ 2 = 16…

A: Triple integral is used to integrate function of three variable in three dimensional region.

Q: 9. Use spherical coordinates to find the volume of the part of the ballps 4 that lies between the…

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Q: Find parametrizations The portion of the hemisphere x2 + y2 + z2 = 10, y&gt;= 0, in the first octant

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

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Q: 5. Use spherical coordinates to evaluate /16--2² Not √16¬x² / √x² +yª √x² + y² + z² dz dy dr.

A: The given problem is to evaluate the given triple integral by converting the Cartesian coordinates…

Q: 6. By converting to spherical coordinates, evaluate 22 dz dx dy. 0.

A: triple integral

Q: In which part of the (x, y) plane the following equation is elliptic? Uzr + 4ury + (x² + 4y*) uyy =…

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Q: Let B be the ball with center at the origin and radius 1 SS [3(x² + y² + z²)dV =

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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: Convert the following point from cylindrical to rectangular coordinates: 10, (x, y, z) = Usage: To…

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Q: 23. Evaluate II (x² + y? + z²)² dV, where B is the ball with center the origin and radius 5.

A: Given, ∫∫∫Bx2+y2+z22 We know that ρ is 0 to 5 because in spherical coordinates, ρ is the radius.…

Q: Use spherical coordinates. Evaluate (x2 + y2) dv, where E lies between the spheres x² + y2 + z² = 9…

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Q: | a2 dA, where D is the part of the unit disk where r+y 2 0.

A: To find :         ∬Dx2 dA where D is the part of the unit disk where x+y≥0

Q: Convert the following point from rectangular to cylindrical coordinates: (4, –4v3, 10). (r, 0, z) =

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Q: Exercise 2 Use spherical coordinates to evaluate [[[(9-x - y³) dV , where E is the solid hemisphere…

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Q: In spherical coordinates equation for the paraboloid z = 2- x - y is p(cos o- psin? $) = 2 Select…

A: We have to find out  spherical coordinate

Q: Let N be the lower hemisphere of the sphere of radius 5 and let H • Construct dS for 2. Try using…

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Q: Use spherical coordinate to evaluate Vr2 + y? + 22 dz dy dr. 0.

A: We have to use spherical coordinate to evaluate the triple integral…

Q: Let B = xa,. Express B in %3D (a) cylindrical coordinates, (b) spherical coordinates.

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Q: describe the given set in spherical coordinates x2 + y2+ z 2 ≤ 1

A: Given: x2+y2+z2≤1 Spherical coordinates: x,y,z→ρ,θ,ϕ ρ2=x2+y2+z2

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

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Q: 8. Evaluate ze+y´+z² dV, where E is the portion of the ball centered at E the origin of radius 5, x?…

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Q: Use spherical coordinates. SI. Evaluate Vx2 + y2 + z2 dV, where E lies above the cone z = Vx2 + y2…

A: The spherical coordinate system is a polar coordinate system used to translate cartesian plane to…

Q: Use spherical coordinates. Evaluate z dv, where E lies between the spheres x2 + y2 + z² = 1 and x2 +…

A: Using spherical  coordinate we can solve it very easily.

Q: Exercise 2 Use spherical coordinates to evaluate f[[(9-x² - y³ ) dV , where E is the solid…

A: Introduction: When we perform a triple integral over a spherical region, it is convenient to follow…

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

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Q: 1- Find Aue Volume the Paralle RPed by usi+j-21k and V= -i_-k ,W = 2i44j-2K %3D

A: As we know that the volume of the parallelepiped is: V=u→·v→×w→ Given:…

Q: Use spherical coordinates. Evaluate y²z² dV, where E lies above the cone o = 1/3 and below the…

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Q: Use spherical coordinates. I/ y2z2 dv, where E lies above the cone o = n/3 and below the sphere p =…

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Q: O Convert this Entegral From rectangular Coordinate to Spherical Coordina tes (Donot eval vate the…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Use spherical coordinates. Evaluate ||| (x² + y²) dv, where E lies between the spheres x2 + y? + z²…

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

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Q: Use spherical coordinates. Evaluate z dv, where E lies between the spheres x2 + y2 + z2 = 9 and x2 +…

A: Given equations of spheres: x2+y2+z2=9 x2+y2+z2=36 For spherical coordinates: x=ρ cosθ sinϕy=p sinθ…

Q: Use spherical coordinates to evaluate the triple integral [[[ 2² + 3² + 2²dV, where E is the ball:…

A: We will first change it into spherical coordinate and then solve it.

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

A: Sketch the region and find range of variable

Q: The r in cylindrical coordinates must be positive or zero. O True O False

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Q: Use spherical coordinates. Evaluate //| y²z2 dv, where E lies above the cone o = 1/3 and below the…

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Q: 5. Convert the integral 9-x2 9-x²-y² Vx? + y? + z² dzdydx to spherical coordinates then evaluate.

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Q: Let B be the ball with center at the origin and radius 1 SSS 4(2² + y² + z?)dV = O 24 5. 127 16

A: We will evaluate the given integral.

Q: (b) Use spherical coordinates to evaluate l y²dV_where E is the solid hemisphere a? +y² + z² 0. E

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Q: Use spherical coordinates. // xex2 + y2 + z? dv, where E is the portion of the unit ball x2 + y2 +…

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Q: Use spherical coordinates. y2 + z2 where E is enclosed by the sphere x2 + y? + z = 49 in the first…

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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: Use spherical coordinates. Evaluate TI (x2 + y2 + z²)² dv, where B is the ball with center the…

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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.