6a 7 - 8a3 (a >0) I cacose ava2-r2 Jo Jo z"dzdrd0 =

Q: What is the surface area of the three dimensional solid formed by rotating the following parametric…

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Q: 2 ² J z=0x= -√4-2² 4-x²-2 y=0 N dydxdz

A: The given integral is: ∫z=02∫x=-4-z24-z2∫y=04-x2-z2 z dy dx dz Convert the given integral into…

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 the ratio as a ratio of whole numbers using fractional notation 12 to 1

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Q: et H be a solid hemisphere of radius 5 whose density at any point is proportional to its distance…

A: Let H be a solid hemisphere of radius 5 whose density at any point is proportional to its distance…

Q: Use cylindrical coordinates. Evaluate III Vx2 + v² dV, where E is the region that lies inside the…

A: We have to evaluate ∭Ex2+y2dV, where E is the region that lies inside the cylinder x2+y2=9 and…

Q: Please review the screenshot attached to this request and solve the problem :)

A: Let's break down the steps involved in converting the original integral from Cartesian to…

Q: sketch the solid whose spherical coordi- nates (p, 4, 0) satisfy the given inequalities. 0<p<2/cos…

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Q: 6. Show that (an)neN C R is bounded if and only if lim supn→∞ an < +∞o.

A: To Prove:  ann is bounded sequence if and only if limsupan&lt;+∞.

Q: 2. Change Vx? + y? dz dy dx into cylindricalcoordinates, then evaluate. J-1 Jo

A: Given I=∫01∫-1-x21-x2∫x2+y22-x2-y2x2+y2 dz dy dx

Q: #5. Find the rectangular coordinates of the point (3,57/4, 7/6) given in spherical coordi- nates.

A: We have given a spherical coordinates:…

Q: cimals to at least one decimal place,

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Q: Use cylindrical coordinates to show that the volume of a sphere of radius a from which a central…

A: If a cylinder of radius b is cut from a sphere of radius a, then the volume of sphere depends on the…

Q: Given o V4-r2 4-r2-y2 -2-V4-12 x dzdydx 0. Choose the correct triple integrals in cylindrical…

A: Given

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: 14. ƒƒƒÂ(x² + y² + z²) dV, where D is the solid region inside the sphere p = 2 cos & and outside the…

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Q: Convert the point (x, y, z) = (2, 1, — 4) to cylindrical coordinates. Give answers either as…

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Q: Use cylindrical coordinates to evaluate SG √x²++y² dV, where G is the solid above z = 9 - x² - y²…

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Q: Evaluate II| 6x(x2 + y2) dv, where E is the solid in the first octant that lies beneath the…

A: Since the integral lies in first octant so 0≤θ≤π/2 and z≥0.  Converting into cylindrical coordinates…

Q: Use cylindrical coordinates. JIJ x² dv, where E is the solid that lies within the cylinder x2 + y2 =…

A: x=rcosθy=rsinθx2+y2=r2dV=rdzdrdθx2+y2=4⇒r2=4⇒r=2 z2=49(x2+y2) ⇒z2=49r2 ⇒z=7rI=∭x2dV

Q: The equation p = 2 cos 0 sin o in spherical coordinate defines a sphere of center P and radius R,…

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Q: The Cartesian equation associated with a sphere of radius 2 centred at (0, 0, 2) is x² + y² + 22 –…

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Q: る The quadric surfaces 3x y and 5z: = x² – y intersect in a curve. %3D %3D Parametrize this curve.…

A: To find the parametrized curve of the intersection curve we first find the intersection curve…