Mathematical Library Methods

Chapter 7

Mathematical Library Methods

Class 10 - Logix Kips ICSE Computer Applications with BlueJ

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Assignment Questions and Answers

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Question 1

How do user-defined methods differ from library methods?

Answer

A user-defined method is a method defined by the user whereas library methods or built-in methods are the methods created by the developers of Java which are available in the form of packages.

Question 2

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

Answer

Question 3

What is wrong with the following statements? Explain.

i. result = (5/10) * Math.sqrt( a );

Answer

(5/10) will lead to integer division as both numerator and denominator are integers. So result of (5/10) will be 0 instead of 0.5 and the entire expression will always result in 0.

ii. result = math.sqrt(b * b - 4 * a * c) / ( 2 * a );

Answer

math should be written as Math. As Java is case-sensitive so it treats math and Math differently.

Question 4

Explain the following Math functions in Java:

i. Math.abs()

Answer

Returns the absolute value of its argument. Its return type is same as the type of its arguments. For example, Math.abs(-5) will return 5.

ii. Math.sqrt()

Answer

Returns the square root of its argument as a double value. For example, Math.sqrt(25) will return 5.0.

iii. Math.cbrt()

Answer

Returns the cube root of its argument as a double value. For example, Math.cbrt(27) will return 3.0.

iv. Math.random()

Answer

Returns a positive double value, greater than or equal to 0.0 and less than 1.0.

v. Math.round()

Answer

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.

vi. Math.ceil()

Answer

Returns the smallest double value that is greater than or equal to the argument and is equal to a mathematical integer. For example, Math.ceil(65.5) will return 66.0.

Question 5

Write Java expressions for the following:

i. The square root of a + 5b³

Answer

Math.sqrt(a + 5 * Math.pow(b, 3))

ii. The cube root of x³+ y³+ z³

Answer

Math.cbrt(x*x*x + y*y*y + z*z*z);

iii. The square root of b² + 4ac

Answer

Math.sqrt(b * b + 4 * a * c)

 

Question 6

Write the following as Java expressions:

i.

Answer

Math.cbrt(x * x + 5 * y * y * y)

ii. ∣x + y∣

Answer

Math.abs(x + y)

iii. ∣x³ + y² − 2xy∣

Answer

Math.abs(Math.pow(x, 3) + Math.pow(y, 2) - 2*x*y)

 

iv. ${\displaystyle \frac{\pi }{6}}(z^4-2\pi )$

Answer

Math.PI / 6*(Math.pow(z, 4) - 2*Math.PI)

 

v. $\sqrt[3]{z^2-\pi }$

Answer

Math.cbrt(z*z - Math.PI)

 

vi. $\sqrt[4]{x^3-y^3}$

Answer

Math.pow(x*x*x - y*y*y, 1/4)

 

vii. ${\displaystyle \frac{amount\ast rate}{1-{\displaystyle \frac{1}{(1+rate{)}^n}}}}$

Answer

(amount*rate) / (1 - (1 / Math.pow(1+rate, n)))

 

viii. ${\displaystyle \frac{(-b+\sqrt{b^2-4ac})}{2a}}$

Answer

(-b + Math.sqrt(b*b - 4*a*c)) / (2*a)

 

ix. $\sqrt[4]{{\displaystyle \frac{1}{LC}}-{\displaystyle \frac{R^2}{4C^2}}}$

Answer

Math.pow((1 / L*C) - ((R*R)/(4*C*C)), 1/4)

 

Question 7

Write valid statements for the following in Java:

i. Print the rounded off value of 14.49

Answer

System.out.println(Math.round(14.49));

 

ii. Print the absolute value of -0.09

Answer

System.out.println(Math.abs(-0.09));

 

iii. Print the largest of -67 and -50

Answer

System.out.println(Math.max(-67, -50));

 

iv. Print the smallest of -56 and -57.4

Answer

System.out.println(Math.min(-56, -57.4));

 

v. Print a random integer between 25 and 35

Answer

int range = 35 - 25 + 1;

int num = (int)(range * Math.random() + 25);

System.out.println(num);

 

vi. Print 47.5 raised to the power 6.3

Answer

System.out.println(Math.pow(47.5, 6.3));

 

vii. Print minimum of -4, -7

Answer

System.out.println(Math.min(-4, -7));