Chapter 4, Problem 8RE

a.

Program Plan Intro

Program:

//Import necessary packages

import java.io.*;

import java.math.*;

//Define the class "Sample"

public class Sample

{

    //Define the main method

    public static void main(String[] args)

    {

         /*Declare required variables and

         assign the values to it*/

         double x = 2.5;

          double y = -1.5;

          int m = 18;

          int n = 4;

          //Print the statement

        System.out.println(x + n * y - (x + n) * y);

        System.out.println(m / n + m % n);

        System.out.println(5 * x - n / 5);

System.out.println(1 - (1 - (1 - (1 - (1 - n)))));

        System.out.println(Math.sqrt(Math.sqrt(n)));

    }

}

Output:

6.25

6

12.5

-3

1.4142135623730951

b.

Explanation of Solution

 Value of the second expression:

• In the above given program, four variables such as “x”, “y”, “m” and “n” are declared and are assigned with values “2.5”, “-1.5”, “18”, and “4” respectively.
• The given expression is evaluated by considering the BODMAS (Bracket, Of, Division, Multiplication, Addition, and Subtraction) rule.
  • The BODMAS rule describes the order of operations to solve an expression.
  • If an expression consists of brackets, then first solve the braces or simplify the braces followed by of (powers, roots, and so on), division, multiplication, addition and subtraction from left to right.
• The modulo operation is used to find the remainder after division of one number by another...

c.

Explanation of Solution

 Value of the third expression:

• In the above given program, four variables such as “x”, “y”, “m” and “n” are declared and are assigned with values “2.5”, “-1.5”, “18”, and “4” respectively.
• The given expression is evaluated by considering the BODMAS (Bracket, Of, Division, Multiplication, Addition, and Subtraction) rule.
  • The BODMAS rule describes the order of operations to solve an expression.
  • If an expression consists of brackets, then first solve the braces or simplify the braces followed by of (powers, roots, and so on), division, multiplication, addition and subtraction from left to right...

d.

Explanation of Solution

 Value of the fourth expression:

• In the above given program, four variables such as “x”, “y”, “m” and “n” are declared and are assigned with values “2.5”, “-1.5”, “18”, and “4” respectively.
• The given expression is evaluated by considering the BODMAS (Bracket, Of, Division, Multiplication, Addition, and Subtraction) rule.
  • The BODMAS rule describes the order of operations to solve an expression.
  • If an expression consists of brackets, then first solve the braces or simplify the braces followed by of (powers, roots, and so on), division, multiplication, addition and subtraction from left to right.
• Thus, the given expression “$1-(1-(1-(1-(1-n))))$” is evaluated as follows:

      $\begin{array}{l}1-(1-(1-(1-(1-n))))\\ 1-(1-(1-\end{array}$

e.

Explanation of Solution

 Value of the fifth expression:

• In the above given program, four variables such as “x”, “y”, “m” and “n” are declared and are assigned with values “2.5”, “-1.5”, “18”, and “4” respectively.
• The given expression is evaluated by considering the BODMAS (Bracket, Of, Division, Multiplication, Addition, and Subtraction) rule.
  • The BODMAS rule describes the order of operations to solve an expression.
  • If an expression consists of brackets, then first solve the braces or simplify the braces followed by of (powers, roots, and so on), division, multiplication, addition and subtraction from left to right.
• In Java programming, the “Math.sqrt” function is used to find the square root of the number that is passed as the parameter to the function.
• Thus, the given expression “$Math.sqrt(Math.sqrt(n))$” is evaluated as follows:

      $\begin{array}{l}Math.sqrt(Math\end{array}$