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iris [78.8K]
3 years ago
12

Suppose there are n chairs in a row. We want to compute the number of ways to put 2 students into seats so that they are not nex

t to each other. Assume that students are interchangeable: e.g., if n = 3, the solution should be 1, because the only way to accomplish this is to use the first and last chairs. For both parts to this problem, you must explain why your answer is correct: it is not sufficient to compute a few values directly and look for a pattern.
a. Write a recurrence relation describing the number of ways to put the 2 students into seats so that they are not next to each other.
b. Repeat part a, but now suppose the chairs are in a circle (hint: it might help if you label the chairs 1, ... n, even though they are in a circle without a 'start' or 'end').

Engineering
1 answer:
icang [17]3 years ago
8 0

Complete Question

The complete question is shown on the first uploaded image

Answer:

a) f_{(n)} = f_{(n-1)} + n-2

b) g_{(n)} = g_(n+1) + (n-2)

Explanation:

The explanation is shown on the second and third uploaded image

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A thin-walled tube with a diameter of 6 mm and length of 20 m is used to carry exhaust gas from a smoke stack to the laboratory
Molodets [167]

Answer:

Explanation:

Mean temperature is given by

T_mean = \frac{T_i + T_ \infinity}{2}\\\\T_mean = \frac{200 + 15}{2}

Tmean = (Ti + T∞)/2

T_mean = 107.5^{0}

Tmean = 107.5⁰C

Tmean = 107.5 + 273 = 380.5K

Properties of air at mean temperature

v = 24.2689 × 10⁻⁶m²/s

α = 35.024 × 10⁻⁶m²/s

\mu = 221.6 × 10⁻⁷N.s/m²

\kappa = 0.0323 W/m.K

Cp = 1012 J/kg.K

Pr = v/α  = 24.2689 × 10⁻⁶/35.024 × 10⁻⁶

              = 0.693

Reynold's number, Re

Pv = 4m/πD²

where Re = (Pv * D)/\mu

Substituting for Pv

Re = 4m/(πD\mu)

     = (4 x 0.003)/( π × 6 ×10⁻³ × 221.6 × 10⁻⁷)

     = 28728.3

Since Re > 2000, the flow is turbulent

For turbulent flows, Use

Dittus - Doeltr correlation with n = 0.03

Nu = 0.023Re⁰⁸Pr⁰³ = (h₁D)/k

(h₁ × 0.006)/0.0323 = 0.023(28728.3)⁰⁸(0.693)⁰³

(h₁ × 0.006)/0.0323 = 75.962

h₁ = (75.962 × 0.0323)/0.006

h₁ = 408.93 W/m².K

4 0
3 years ago
State the mathematical expression to define the availability of equipment over a specified time and operational availability?
Gelneren [198K]

Answer:

Availability=\dfrac{Up\ time}{Down\ time+Up\ time}

Explanation:

Availability:

  It define as the probability of system which perform desired task before showing any failure .

The availability can be define as follows

 Availability=\dfrac{Up\ time}{Down\ time+Up\ time}

Or we can say that

Availability=\dfrac{Up\ time}{total\ time}

Availability can also be express as

 Availability=\dfrac{MTBF}{MTBF+MTTR}

Where MTBF is the mean time between two failure.

MTTR is the mean time to repair.

7 0
3 years ago
An ideal gas undergoes two processes: one frictionless and the other not. In both the cases, the gas is initially at 200 ℉ and 1
Zarrin [17]

Answer:

The process which has friction

Explanation:

The entropy is simply the change in the state of the things or the molecules in the system. It is simply the change in the energy of the system with a focus on the atoms in the system. This is also known as the internal energy of the system and is given the symbol, G. The friction contributes to the change in the energy of the system. This is because friction generates another form of energy - that is heat energy. This energy causes the internal temperature id the system to increase. Hence the greater change in the temperature.

6 0
3 years ago
Read 2 more answers
Write a program that prompts for a line of text and then transforms the text based on chosen actions. Actions include reversing
nlexa [21]

Answer:

public class TextConverterDemo

{

//Method definition of action1337

public static String action1337(String current)

{

//Replace each L or l with a 1 (numeral one)

 current = current.replace('L', '1');

 current = current.replace('l', '1');

 

 //Replace each E or e with a 3 (numeral three)

 current = current.replace('E', '3');

 current = current.replace('e', '3');

 //Replace each T or t with a 7 (numeral seven)

 current = current.replace('T', '7');

 current = current.replace('t', '7');

 //Replace each O or o with a 0 (numeral zero)

 current = current.replace('O', '0');

 current = current.replace('o', '0');

 

//Replace each S or s with a $ (dollar sign)

 current = current.replace('S', '$');

 current = current.replace('s', '$');

 return current;

}

//Method definition of actionReverse

//This method is used to reverses the order of

//characters in the current string

public static String actionReverse(String current)

{

 //Create a StringBuilder's object

 StringBuilder originalStr = new StringBuilder();

 //Append the original string to the StribgBuilder's object

 originalStr.append(current);

 //Use reverse method to reverse the original string

 originalStr = originalStr.reverse();

 

 //return the string in reversed order

 return originalStr.toString();

}

//Method definition of main

public static void main(String[] args)

{

    //Declare variables

 String input, action;

 

 //Prompt the input message

 System.out.println("Welcome to the Text Converter.");

 System.out.println("Available Actions:");

 System.out.println("\t1337) convert to 1337-speak");

 System.out.println("\trev) reverse the string");

 System.out.print("Please enter a string: ");

   

 //Create a Scanner class's object

 Scanner scn = new Scanner(System.in);

 

 //Read input from the user

 input = scn.nextLine();

 do

 {

  /*Based on the action the user chooses, call the appropriate

   * action method. If an unrecognized action is entered then

   * the message "Unrecognized action." should be shown on a

   * line by itself and then the user is prompted again just

   * as they were when an action was performed.

   * */

  System.out.print("Action (1337, rev, quit): ");

  action = scn.nextLine();

  if (action.equals("1337"))

  {

   input = action1337(input);

   System.out.println(input);

  } else if (action.equals("rev"))

  {

   input = actionReverse(input);

   System.out.println(input);

  } else if (!action.equals("quit"))

  {

   System.out.println("Unrecognized action.");

  }

 } while (!action.equals("quit"));

 System.out.println("See you next time!");

 scn.close();

}

}

7 0
3 years ago
A solid circular rod that is 600 mm long and 20 mm in diameter is subjected to an axial force of P = 50 kN The elongation of the
Kay [80]

Answer:

a) V = 0.354

b)  G = 25.34 GPA

Explanation:

Solution:

We first determine Modulus of Elasticity and Modulus of rigidity

Elongation of rod ΔL = 1.4 mm

Normal stress, δ = P/A

Where P = Force acting on the cross-section

A = Area of the cross-section

Using Area, A = π/4 · d²

= π/4 · (0.0020)²  = 3.14 × 10⁻⁴m²

δ = 50/3.14 × 10⁻⁴    = 159.155 MPA

E(long) = Δl/l  = 1.4/600 = 2.33 × 10⁻³mm/mm

Modulus of Elasticity Е = δ/ε

= 159.155 × 10⁶/2.33 × 10⁻³    = 68.306 GPA

Also final diameter d(f) = 19.9837 mm

Initial diameter d(i) = 20 mm

Poisson said that V = Е(elasticity)/Е(long)

= -  <u>( 19.9837 - 20 /20)</u>

        2.33 × 10⁻³                  

= 0.354,

∴ v = 0.354

Also G = Е/2. (1+V)

=  68.306 × 10⁹/ 2.(1+ 0.354)

= 25.34 GPA

⇒ G = 25.34 GPA

5 0
4 years ago
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