Find S ' ( 0 ) and S ' ( 3 ) for the cubic spline { S 1 ( x ) = 3 + b 1 x + x 3 o n [ 0 , 1 ] S 2 ( x ) = 1 + b 2 ( x − 1 ) + 3 ( x − 1 ) 2 − 2 ( x − 1 ) 3 o n [ 1 , 3 ]

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Chapter 3.4, Problem 9E

To determine

Find S'(0) and S'(3) for the cubic spline

{ S 1( x)=3+ b 1x+ x 3 on [ 0,1] S 2( x)=1+ b 2( x−1)+3 ( x−1 ) 2−2 ( x−1 ) 3 on [ 1,3]

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In a small office, there are m = 5 typists who need to use a single typewriter to complete their reports. Assume the time each typist takes to prepare a report follows an exponential distribution with an average of 20 minutes per preparation (A = 3 reports/hour), and the service time for the typewriter to type out a report also follows an exponential distribution, averaging 30 minutes to complete a report (μ 2 reports/hour). Given that the number of typists is finite and all typists = share one typewriter, they will form a waiting queue. (1). Describe this queuing system and explain how it fits the characteristics of the M/M/1/∞0/m model. (2). Calculate the probability that any typist is using the typewriter at steady-state. (3). Calculate the average number of typists waiting in the queue at steady-state. (4). Considering the need to reduce waiting time, if an additional typewriter is introduced (turning into a two-server system, or M/M/2/∞0/m model), analyze the expected impact,…

Answer 2

Question

Chapter 3.4, Problem 9E

To determine

Find S'(0) and S'(3) for the cubic spline

{ S 1( x)=3+ b 1x+ x 3 on [ 0,1] S 2( x)=1+ b 2( x−1)+3 ( x−1 ) 2−2 ( x−1 ) 3 on [ 1,3]

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Answer 3

Question

Chapter 3.4, Problem 9E

To determine

Find S'(0) and S'(3) for the cubic spline

{ S 1( x)=3+ b 1x+ x 3 on [ 0,1] S 2( x)=1+ b 2( x−1)+3 ( x−1 ) 2−2 ( x−1 ) 3 on [ 1,3]

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Answer 4

Question

Chapter 3.4, Problem 9E

To determine

Find S'(0) and S'(3) for the cubic spline

{ S 1( x)=3+ b 1x+ x 3 on [ 0,1] S 2( x)=1+ b 2( x−1)+3 ( x−1 ) 2−2 ( x−1 ) 3 on [ 1,3]

Expert Solution & Answer

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Answer 5

Chapter 3.4, Problem 9E

To determine

Find S'(0) and S'(3) for the cubic spline

{ S 1( x)=3+ b 1x+ x 3 on [ 0,1] S 2( x)=1+ b 2( x−1)+3 ( x−1 ) 2−2 ( x−1 ) 3 on [ 1,3]

Answer 6

Chapter 3.4, Problem 9E

To determine

Find S'(0) and S'(3) for the cubic spline

{ S 1( x)=3+ b 1x+ x 3 on [ 0,1] S 2( x)=1+ b 2( x−1)+3 ( x−1 ) 2−2 ( x−1 ) 3 on [ 1,3]

Answer 7

Chapter 3.4, Problem 9E

To determine

Find S'(0) and S'(3) for the cubic spline

{ S 1( x)=3+ b 1x+ x 3 on [ 0,1] S 2( x)=1+ b 2( x−1)+3 ( x−1 ) 2−2 ( x−1 ) 3 on [ 1,3]

Answer 8

Expert Solution & Answer

Answer 9

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Answer 10

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Answer 11

Ch. 3.1 - Use Lagrange interpolation to find a polynomial...Ch. 3.1 - Use Newtons divided differences to find the...Ch. 3.1 - How many degree d polynomials pass through the...Ch. 3.1 - (a) Find a polynomial P(x) of degree 3 or less...Ch. 3.1 - (a) Find a polynomial P(x) of degree 3 or less...Ch. 3.1 - Write down a polynomial of degree exactly 5 that...Ch. 3.1 - Find P(0), where P(x) is the degree 10 polynomial...Ch. 3.1 - Let P(x) be the degree 9 polynomial that takes the...Ch. 3.1 - Give an example of the following, or explain why...Ch. 3.1 - Let P(x) be the degree 5 polynomial that takes the...

Find S ' ( 0 ) and S ' ( 3 ) for the cubic spline { S 1 ( x ) = 3 + b 1 x + x 3 o n [ 0 , 1 ] S 2 ( x ) = 1 + b 2 ( x − 1 ) + 3 ( x − 1 ) 2 − 2 ( x − 1 ) 3 o n [ 1 , 3 ]

Solution Summary: The author calculates that a cubic spline passes through n data points and satisfies the following properties.

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Find S'(0) and S'(3) for the cubic spline

{ S 1( x)=3+ b 1x+ x 3 on [ 0,1] S 2( x)=1+ b 2( x−1)+3 ( x−1 ) 2−2 ( x−1 ) 3 on [ 1,3]

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Chapter 3 Solutions

Find S ' ( 0 ) and S ' ( 3 ) for the cubic spline { S 1 ( x ) = 3 + b 1 x + x 3 o n [ 0 , 1 ] S 2 ( x ) = 1 + b 2 ( x − 1 ) + 3 ( x − 1 ) 2 − 2 ( x − 1 ) 3 o n [ 1 , 3 ]

Solution Summary: The author calculates that a cubic spline passes through n data points and satisfies the following properties.

Videos

Find S'(0) and S'(3) for the cubic spline { S 1( x)=3+ b 1x+ x 3 on [ 0,1] S 2( x)=1+ b 2( x−1)+3 ( x−1 ) 2−2 ( x−1 ) 3 on [ 1,3]

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Chapter 3 Solutions

Find S'(0) and S'(3) for the cubic spline

{ S 1( x)=3+ b 1x+ x 3 on [ 0,1] S 2( x)=1+ b 2( x−1)+3 ( x−1 ) 2−2 ( x−1 ) 3 on [ 1,3]