To deriving the square root scaling law for the time spent passing through a bottleneck, show that T b o t t l e n e c k = c r b and determine b and c. Concept Introduction: By deriving the square root scaling law for the time spent passing through a bottleneck, we can find T. For finding T, use residue integral theorem as ∫ − ∞ ∞ f ( x ) d x = 2 π i ∑ R

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Answer 1

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Chapter 4.3, Problem 10E

Interpretation Introduction

Interpretation:

To deriving the square root scaling law for the time spent passing through a bottleneck, show that Tbottleneck=crb and determine b and c.

Concept Introduction:

By deriving the square root scaling law for the time spent passing through a bottleneck, we can find T.

For finding T, use residue integral theorem as ∫−∞∞f(x)dx=2πi∑R

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Answer 2

Question

Chapter 4.3, Problem 10E

Interpretation Introduction

Interpretation:

To deriving the square root scaling law for the time spent passing through a bottleneck, show that Tbottleneck=crb and determine b and c.

Concept Introduction:

By deriving the square root scaling law for the time spent passing through a bottleneck, we can find T.

For finding T, use residue integral theorem as ∫−∞∞f(x)dx=2πi∑R

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Answer 3

Question

Chapter 4.3, Problem 10E

Interpretation Introduction

Interpretation:

To deriving the square root scaling law for the time spent passing through a bottleneck, show that Tbottleneck=crb and determine b and c.

Concept Introduction:

By deriving the square root scaling law for the time spent passing through a bottleneck, we can find T.

For finding T, use residue integral theorem as ∫−∞∞f(x)dx=2πi∑R

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Answer 4

Question

Chapter 4.3, Problem 10E

Interpretation Introduction

Interpretation:

To deriving the square root scaling law for the time spent passing through a bottleneck, show that Tbottleneck=crb and determine b and c.

Concept Introduction:

By deriving the square root scaling law for the time spent passing through a bottleneck, we can find T.

For finding T, use residue integral theorem as ∫−∞∞f(x)dx=2πi∑R

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Answer 5

Chapter 4.3, Problem 10E

Interpretation Introduction

Interpretation:

To deriving the square root scaling law for the time spent passing through a bottleneck, show that Tbottleneck=crb and determine b and c.

Concept Introduction:

By deriving the square root scaling law for the time spent passing through a bottleneck, we can find T.

For finding T, use residue integral theorem as ∫−∞∞f(x)dx=2πi∑R

Answer 6

Chapter 4.3, Problem 10E

Interpretation Introduction

Interpretation:

To deriving the square root scaling law for the time spent passing through a bottleneck, show that Tbottleneck=crb and determine b and c.

Concept Introduction:

By deriving the square root scaling law for the time spent passing through a bottleneck, we can find T.

For finding T, use residue integral theorem as ∫−∞∞f(x)dx=2πi∑R

Answer 7

Chapter 4.3, Problem 10E

Interpretation Introduction

Interpretation:

To deriving the square root scaling law for the time spent passing through a bottleneck, show that Tbottleneck=crb and determine b and c.

Concept Introduction:

By deriving the square root scaling law for the time spent passing through a bottleneck, we can find T.

For finding T, use residue integral theorem as ∫−∞∞f(x)dx=2πi∑R

Answer 8

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Answer 9

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Answer 10

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Answer 11

Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E Ch. 4.1 - Prob. 7E Ch. 4.1 - Prob. 8E Ch. 4.1 - Prob. 9E Ch. 4.2 - Prob. 1E

Solution Summary: The author explains the square root scaling law for the time spent passing through a bottleneck using the complex variable and residue theorem.

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