A: The region enclosed by the curves y = x 2 + 2 y = 10 − x 2

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Answer 1

Question

Chapter 6.3, Problem 15E

To determine

A:

The region enclosed by the curves $y = x^{2} + 2$ $y = 10 - x^{2}$

To determine

B:

The cross-section perpendicular to x axis at x.

To determine

C:

The volume of the solid obtained by rotating the region about x axis.

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Compute the volume of the solid formed by rotating the region bounded by y = 1 - x2 and y = 0 about the x-axis. (It may help to sketch the region and the solid.)

A solid is generated by revolving the region bounded by y = √ 9 - x2) and y = 0 about the y-axis. A hole, centered along the axis of revolution, is drilled through this solid so that one-third of the volume is removed. Find the diameter of the hole?

In Exercises 47–50, find the volume of the solid generated by revolv-ing each region about the y-axis. 47. The region enclosed by the triangle with vertices (1, 0), (2, 1), and (1, 1) 48. The region enclosed by the triangle with vertices (0, 1), (1, 0), and (1, 1) 49. The region in the first quadrant bounded above by the parabola y = x2, below by the x-axis, and on the right by the line x = 2 50. The region in the first quadrant bounded on the left by the circle x2 + y2 = 3, on the right by the line x = sqrt(3), and above by the line y = sqrt(3).

Answer 2

Question

Chapter 6.3, Problem 15E

To determine

A:

The region enclosed by the curves $y = x^{2} + 2$ $y = 10 - x^{2}$

To determine

B:

The cross-section perpendicular to x axis at x.

To determine

C:

The volume of the solid obtained by rotating the region about x axis.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 6.3, Problem 15E

To determine

A:

The region enclosed by the curves $y = x^{2} + 2$ $y = 10 - x^{2}$

To determine

B:

The cross-section perpendicular to x axis at x.

To determine

C:

The volume of the solid obtained by rotating the region about x axis.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 6.3, Problem 15E

To determine

A:

The region enclosed by the curves $y = x^{2} + 2$ $y = 10 - x^{2}$

To determine

B:

The cross-section perpendicular to x axis at x.

To determine

C:

The volume of the solid obtained by rotating the region about x axis.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 5

Chapter 6.3, Problem 15E

To determine

A:

The region enclosed by the curves $y = x^{2} + 2$ $y = 10 - x^{2}$

To determine

B:

The cross-section perpendicular to x axis at x.

To determine

C:

The volume of the solid obtained by rotating the region about x axis.

Answer 6

Chapter 6.3, Problem 15E

To determine

A:

The region enclosed by the curves $y = x^{2} + 2$ $y = 10 - x^{2}$

Answer 7

Chapter 6.3, Problem 15E

To determine

A:

The region enclosed by the curves $y = x^{2} + 2$ $y = 10 - x^{2}$

Answer 8

To determine

B:

The cross-section perpendicular to x axis at x.

Answer 9

To determine

B:

The cross-section perpendicular to x axis at x.

Answer 10

To determine

C:

The volume of the solid obtained by rotating the region about x axis.

Answer 11

To determine

C:

The volume of the solid obtained by rotating the region about x axis.

Answer 12

Expert Solution & Answer

Answer 13

Expert Solution & Answer

Answer 14

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Answer 15

Ch. 6.1 - Prob. 1PQ Ch. 6.1 - Prob. 2PQ Ch. 6.1 - Prob. 3PQ Ch. 6.1 - Prob. 4PQ Ch. 6.1 - Prob. 5PQ Ch. 6.1 - Prob. 6PQ Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E

A: The region enclosed by the curves y = x 2 + 2 y = 10 − x 2

Solution Summary: The author explains how the two equations intersect at x =2,-2 and the region enclosed by the curves is marked grey.

Concept explainers

Videos

A:

The region enclosed by the curves $y = x^{2} + 2$ $y = 10 - x^{2}$

B:

The cross-section perpendicular to x axis at x.

C:

The volume of the solid obtained by rotating the region about x axis.

Want to see the full answer?

Chapter 6 Solutions

A: The region enclosed by the curves y = x 2 + 2 y = 10 − x 2

Solution Summary: The author explains how the two equations intersect at x =2,-2 and the region enclosed by the curves is marked grey.

Concept explainers

Videos

A: The region enclosed by the curves y=x2+2 y=10−x2

B: The cross-section perpendicular to x axis at x.

C: The volume of the solid obtained by rotating the region about x axis.

Want to see the full answer?

Chapter 6 Solutions

A:

The region enclosed by the curves $y = x^{2} + 2$ $y = 10 - x^{2}$

B:

The cross-section perpendicular to x axis at x.

C:

The volume of the solid obtained by rotating the region about x axis.