Explanation Given : W is the region above the sphere x 2 + y 2 + z 2 = 6 and below the paraboloid z = 4 − x 2 − y 2 Proof : The equation z = 4 − x 2 − y 2 implies x 2 + y 2 = 4 − z . Substituting in x 2 + y 2 + z 2 = 6 and solving for z gives 4 − z + z 2 = 6 ⇒ z 2 − z − 2 = ( z − 2 ... To determine (b) To calculate: The volume of W using polar coordinates.

4th Edition

ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 16.4, Problem 22E

To determine

(a) To prove: The projection of W on the xy plane is the disk $x^{2} + y^{2} \leq 2$ where W is the region above the sphere $x^{2} + y^{2} + z^{2} = 6$ and below the paraboloid $z = 4 - x^{2} - y^{2}$

To determine

(b) To calculate: The volume of W using polar coordinates.

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Chapter 16.4, Problem 21E

Chapter 16.4, Problem 23E

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Chapter 16 Solutions

CALCULUS W/SAPLING ACCESS >IC<

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(a) To prove : The projection of W on the xy plane is the disk x 2 + y 2 ≤ 2 where W is the region above the sphere x 2 + y 2 + z 2 = 6 and below the paraboloid z = 4 − x 2 − y 2

Solution Summary: The author explains that the projection of W on the xy-plane is the disk, where W is above and below the paraboloid.

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(a) To prove: The projection of W on the xy plane is the disk $x^{2} + y^{2} \leq 2$ where W is the region above the sphere $x^{2} + y^{2} + z^{2} = 6$ and below the paraboloid $z = 4 - x^{2} - y^{2}$

(b) To calculate: The volume of W using polar coordinates.

Want to see the full answer?

Chapter 16 Solutions

(a) To prove : The projection of W on the xy plane is the disk x 2 + y 2 ≤ 2 where W is the region above the sphere x 2 + y 2 + z 2 = 6 and below the paraboloid z = 4 − x 2 − y 2

Solution Summary: The author explains that the projection of W on the xy-plane is the disk, where W is above and below the paraboloid.

Videos

(a) To prove: The projection of W on the xy plane is the disk x2+y2≤2 where W is the region above the sphere x2+y2+z2=6 and below the paraboloid z=4−x2−y2

(b) To calculate: The volume of W using polar coordinates.

Want to see the full answer?

Chapter 16 Solutions

(a) To prove: The projection of W on the xy plane is the disk $x^{2} + y^{2} \leq 2$ where W is the region above the sphere $x^{2} + y^{2} + z^{2} = 6$ and below the paraboloid $z = 4 - x^{2} - y^{2}$