Q1. Arrange the rational numbers -3/5, 7/10, and -5/6 in
descending order.
Q2.
Write three rational numbers between 2 and 1/3.
Q3.
Write three rational numbers between -4/5 and -2/3.
Q4. Draw the number line and represent the following
rational numbers on it.
b. -6/7
Q5. Write two rational numbers equivalent to 2/3.
a. 34
Q6. Write true/false:-
a)
Sum of two rational numbers is always a rational number.
b)
All decimal numbers are also rational numbers. ,
c)
Every fraction is a rational number.
d)
1 is a positive rational number.
e)
Zero is a rational number.
Answers
Answer:
In geometry, the parallel postulate, also called Euclid's fifth postulate because it is the fifth postulate in Euclid's Elements, is a distinctive axiom in Euclidean geometry. It states that, in two-dimensional geometry:
If the sum of the interior angles α and β is less than 180°, the two straight lines, produced indefinitely, meet on that side.
If a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles.
This postulate does not specifically talk about parallel lines;[1] it is only a postulate related to parallelism. Euclid gave the definition of parallel lines in Book I, Definition 23[2] just before the five postulates.[3]
Euclidean geometry is the study of geometry that satisfies all of Euclid's axioms, including the parallel postulate.
The postulate was long considered to be obvious or inevitable, but proofs were elusive. Eventually it was discovered that inverting the postulate gave valid, albeit different geometries. A geometry where the parallel postulate does not hold is known as a non-Euclidean geometry. Geometry that is independent of Euclid's fifth postulate (i.e., only assumes the modern equivalent of the first four postulates) is known as absolute geometry (or sometimes "neutral geometry").import java.util.*;
public class Exercise60 {
public static void main(String[] args){
Scanner in = new Scanner(System.in);
System.out.print("Input a Sentence: ");
String line = in.nextLine();
String[] words = line.split("[ ]+");
System.out.println("Penultimate word: "+words[words.length - 2]);
}
}
Write a program to input a sentence and print the penultimate word of this sentence. Penultimate
word is the second last word of a sentence. (Assume that the Sentence is of 2 or more words)
E.g. Input : The quick brown fox jumps over a lazy dog. Output : lazywhat is meant by euclids postulate.and also what are postulatesIn geometry, the parallel postulate, also called Euclid's fifth postulate because it is the fifth postulate in Euclid's Elements, is a distinctive axiom in Euclidean geometry. It states that, in two-dimensional geometry:
If the sum of the interior angles α and β is less than 180°, the two straight lines, produced indefinitely, meet on that side.
If a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles.
This postulate does not specifically talk about parallel lines;[1] it is only a postulate related to parallelism. Euclid gave the definition of parallel lines in Book I, Definition 23[2] just before the five postulates.[3]
Euclidean geometry is the study of geometry that satisfies all of Euclid's axioms, including the parallel postulate.
The postulate was long considered to be obvious or inevitable, but proofs were elusive. Eventually it was discovered that inverting the postulate gave valid, albeit different geometries. A geometry where the parallel postulate does not hold is known as a non-Euclidean geometry. Geometry that is independent of Euclid's fifth postulate (i.e., only assumes the modern equivalent of the first four postulates) is known as absolute geometry (or sometimes "neutral geometry").