Question 1

Question 1Distinguish between Math.ceil() and Math.floor() methods.

Accepted Answer

Math.ceil( )Math.floor( )Returns the smallest double value that is greater than or equal to the argument and is equal to a mathematical integerReturns the largest double value that is less than or equal to the argument and is equal to a mathematical integer.double a = Math.ceil(65.5);In this example, a will be assigned the value of 66.0 as it is the smallest integer greater than 65.5.double b = Math.floor(65.5);In this example, b will be assigned the value of 65.0 as it is the largest integer smaller than 65.5.

Question 2

Question 2Explain the following Math functions in Java:i. Math.sqrt()

Accepted Answer

Returns the square root of its argument as a double value. For example, Math.sqrt(25) will return 5.0.ii. Math.cbrt()Returns the cube root of its argument as a double value. For example, Math.cbrt(27) will return 3.0.iii. Math.random()Returns a positive double value, greater than or equal to 0.0 and less than 1.0.iv. Math.round()Rounds off its argument to the nearest mathematical integer and returns its value as an int or long type. If argument is float, return type is int, if argument is double, return type is long. At mid-point, it returns the higher integer. For example, Math.round(2.5) will return 3.

Question 3

Question 3Write the following as Java expressions:i. ∣x3−y2−2xy∣\lvert x^3 - y^2 -2xy\rvert∣x3−y2−2xy∣

Accepted Answer

Math.abs(Math.pow(x, 3) - Math.pow(y, 2) - 2*x*y)ii. π6(z4−2π)\dfrac{\pi}{6}(z^4 - 2\pi)6π​(z4−2π)Math.PI / 6*(Math.pow(z, 4) - 2*Math.PI)iii. z2−π3\sqrt[3]{z^2 - \pi}3z2−π​Math.cbrt(z*z - Math.PI)iv. x3−y34\sqrt[4]{x^3 - y^3}4x3−y3​Math.pow(x*x*x - y*y*y, 1/4)v. amount∗rate1−1(1+rate)n\cfrac{amount*rate}{1 - \cfrac{1}{(1 + rate)^n}}1−(1+rate)n1​amount∗rate​(amount*rate) / (1 - (1 / Math.pow(1+rate, n)))

Question 4

Question 4Write valid statements for the following in Java:i. Print the rounded off value of 234.49

Accepted Answer

System.out.println(Math.round(234.49));ii. Print the absolute value of -9.99System.out.println(Math.abs(-9.99));iii. Print the largest of -45 and -50System.out.println(Math.max(-45, -50));iv. Print the smallest of -56 and -57.4System.out.println(Math.min(-56, -57.4));v. Print a random integer between 50 and 70int range = 70 - 50 + 1;
int num = (int)(range * Math.random() + 50);
System.out.println(num);vi. Print 10.5 raised to the power 3.8System.out.println(Math.pow(10.5, 3.8));

Question 5

Question 5Write a program in Java to find the minimum of three numbers using Math.min() method.

Accepted Answer

import java.util.Scanner;

public class KboatSmallestNumber
{
    public static void main(String args[]) {
        
        Scanner in = new Scanner(System.in);
        
        System.out.print("Enter First Number: ");
        int a = in.nextInt();
        System.out.print("Enter Second Number: ");
        int b = in.nextInt();
        System.out.print("Enter Third Number: ");
        int c = in.nextInt();
        
        int s = Math.min(a, b);
        s = Math.min(s, c);
        
        System.out.println("Smallest Number = " + s);
    }
}Output

Question 6

Question 6Write a program to print:i. p to the power qii. the square root of pThe values of p and q are 64 and 2 respectively.

Accepted Answer

public class KboatNumber
{
    public static void main(String args[]) {
        int p = 64;
        int q = 2;
        
        double r1 = Math.pow(p, q);
        System.out.println("p to the power of q = " + r1);
        
        double r2 = Math.sqrt(p);
        System.out.println("Square root of p = " + r2);
    }
}Output

Question 7

Question 7Write a program to generate random integers in the range 10 to 20.

Accepted Answer

public class KboatRandom
{
    public static void main(String args[]) {
        int min = 10, max = 20;
        int range = max - min + 1;
        int num = (int)(range * Math.random() + min);
        System.out.println("Random number in the range 10 to 20: " + num);
    }
}Output

Question 8

Question 8Write the equivalent Java statements for the following, only using the mathematical functions:i. Print the positive value of -101.

Accepted Answer

System.out.println(Math.abs(-101));ii. Store the value -125 in a variable and print its cube root.int a = -125;
System.out.println(Math.cbrt(a));iii. Store the value 89.99 in a variable and convert it into its closest integer that is greater than or equal to 89.99.double a = 89.99;
System.out.println(Math.round(a));

Mathematical Library Methods