(a) To prove: The horizontal cut at height y has length 4 − 2 3 y . Also find M x ( with ρ = 1 ) .

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Answer 1

Question

Chapter 9.3, Problem 9E

To determine

(a)

To prove:

The horizontal cut at height y has length 4−23y.

Also find Mx(with ρ=1).

To determine

(b)

To prove:

My=0 using symmetry Principle and alsofind the center of mass.

Expert Solution & Answer

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(10 points) Let f(x, y, z) = ze²²+y². Let E = {(x, y, z) | x² + y² ≤ 4,2 ≤ z ≤ 3}. Calculate the integral f(x, y, z) dv. E

(12 points) Let E={(x, y, z)|x²+ y² + z² ≤ 4, x, y, z > 0}. (a) (4 points) Describe the region E using spherical coordinates, that is, find p, 0, and such that (x, y, z) (psin cos 0, psin sin 0, p cos) € E. (b) (8 points) Calculate the integral E xyz dV using spherical coordinates.

(10 points) Let f(x, y, z) = ze²²+y². Let E = {(x, y, z) | x² + y² ≤ 4,2 ≤ z < 3}. Calculate the integral y, f(x, y, z) dV.

Answer 2

Question

Chapter 9.3, Problem 9E

To determine

(a)

To prove:

The horizontal cut at height y has length 4−23y.

Also find Mx(with ρ=1).

To determine

(b)

To prove:

My=0 using symmetry Principle and alsofind the center of mass.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 9.3, Problem 9E

To determine

(a)

To prove:

The horizontal cut at height y has length 4−23y.

Also find Mx(with ρ=1).

To determine

(b)

To prove:

My=0 using symmetry Principle and alsofind the center of mass.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 9.3, Problem 9E

To determine

(a)

To prove:

The horizontal cut at height y has length 4−23y.

Also find Mx(with ρ=1).

To determine

(b)

To prove:

My=0 using symmetry Principle and alsofind the center of mass.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Chapter 9.3, Problem 9E

To determine

(a)

To prove:

The horizontal cut at height y has length 4−23y.

Also find Mx(with ρ=1).

To determine

(b)

To prove:

My=0 using symmetry Principle and alsofind the center of mass.

Answer 6

Chapter 9.3, Problem 9E

To determine

(a)

To prove:

The horizontal cut at height y has length 4−23y.

Also find Mx(with ρ=1).

Answer 7

Chapter 9.3, Problem 9E

To determine

(a)

To prove:

The horizontal cut at height y has length 4−23y.

Also find Mx(with ρ=1).

Answer 8

To determine

(b)

To prove:

My=0 using symmetry Principle and alsofind the center of mass.

Answer 9

To determine

(b)

To prove:

My=0 using symmetry Principle and alsofind the center of mass.

Answer 10

Expert Solution & Answer

Answer 11

Expert Solution & Answer

Answer 12

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Answer 13

Ch. 9.1 - Prob. 1PQ Ch. 9.1 - Prob. 2PQ Ch. 9.1 - Prob. 3PQ Ch. 9.1 - Prob. 4PQ Ch. 9.1 - Prob. 5PQ Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E

(a) To prove: The horizontal cut at height y has length 4 − 2 3 y . Also find M x ( with ρ = 1 ) .

Solution Summary: The author explains that the triangle is symmetric with respect to the y -axis and hence M_y=0.

Videos

(a)

To prove:

The horizontal cut at height y has length 4−23y.

Also find Mx(with ρ=1).

(b)

To prove:

My=0 using symmetry Principle and alsofind the center of mass.

Want to see the full answer?

Chapter 9 Solutions

(a) To prove: The horizontal cut at height y has length 4 − 2 3 y . Also find M x ( with ρ = 1 ) .

Solution Summary: The author explains that the triangle is symmetric with respect to the y -axis and hence M_y=0.

Videos

(a) To prove: The horizontal cut at height y has length 4−23y. Also find Mx(with ρ=1).

(b) To prove: My=0 using symmetry Principle and alsofind the center of mass.

Want to see the full answer?

Chapter 9 Solutions

(a)

To prove:

The horizontal cut at height y has length 4−23y.

Also find Mx(with ρ=1).

(b)

To prove:

My=0 using symmetry Principle and alsofind the center of mass.