Note on half life equation

Introduction of half-life:

Today let me help you understand on half life equation. The time required for the atoms to disintegrate is considered as infinite. The half-life is considered for the radioactive element. Half-life of a radioactive element is the time required to reduce its size to the half of its initial amount of the radioactive sample. This half-life of radioactive is used for comparing the different radioactive elements and their activities.

Equation of Half-life:

Equation of half-life:

One of the characteristics of the radioactive element is half-life. It is the time taken to reduce its value half of the radioactive element. The equation of half-life is T/2. The range of half-life is from micro changes to billions of years. It is depends on the radioactive element.This could also help us on grams to liters.

Representation of equation of half-life:

Consider a radioactive element has N nuclei at initial. After first half-life time the radioactive element has N/2 nucleus and after next half-life time again it is reduced into N/4 and so on.

Introduction to quantum number

Introduction to quantum number:

In this section let me help you on quantum numbers. Let us discuss the chemistry quantum number. In an atom, the relative distance of electron form the nucleus, type of orbital, direction of spin etc. the type of information is shown by the numbers. This is called the quantum numbers. The quantum numbers n, l and m evolve from Schrodinger sign equation but the fourth quantum number is called the spin quantum number.

Definition of Quantum Number

The chemistry quantum number is also essential for the complete description of an electron and undefined slope. This chemistry quantum number does not appear in solutions of wave functions obtained by solving schordinger equation but it is introduced on the basis of observations. Next we see the principal of quantum number chemistry.

Help on Probability Formula

Introduction to probability formulas help:
Probability formula is one of the most important parts in the mathematics. Consider the example; a card is drawn from the set of cards. Probability is the way for expressing the event.The formula includes the process of finding the probability for the normal event and the mutually exclusive event. The probability theory is used in the field of mathematics and the statistics.

Formula - Probability Formulas Help:

• The formula used to predict the probability for any event A is P (A) = number of favorable cases/ total number of cases.
• P (A’ ) + P (A) = 1
• P(S) =1, where S determines the sample space.
• P( A U B) = P(A) + P( B), A and B are called the mutually exclusive events.
• If A, B are any events then P( A U B) = P(A) + P( B) - P(A ∩ B)
• P (A ∩ B) = P (A) P (B), A and B are called as the independent to each other events that means the independent event. This could also help us on rate of change formula

Example Problems for Probability Formulas Help:
Example 1 for probability formulas help:
The events A and B are mutually exclusive event and P (A) = 0.35 and P (B) = 0.56. Calculate the value for P (A U B).
Solution:
Given that P (A) = 0.35 and P (B) = 0.56. We have to find the value for P (A U B).
The formula used to find P (A U B) if A and B are mutually exclusive event is
P (A U B) = P (A) + P (B)
P (A U B) = 0.35 + 0.56
P (A U B) = 0.91
The value for P (A U B) is 0.91.

Introduction to prime number list

Introduction to prime number list:

List of prime numbers is a number only factors are itself 1.For example, 13 is a prime numbers, since it only factors are 1 and 13 this is the beginning list of the prime numbers as show below.

Prime number list

Here 2 is only the even prime number.The list of all the prime numbers goes on without stopping

Problem 1:

Identify each of the numbers below as either a prime numbers or a composite number. For other that are composite, give two divisor other than the number itself or 1

1. 43

2. 12

This will also help us on permutations and combinations

Solution:

a. Here 43 is a prime numbers because the only number that divide it without a remainder are 43 and 1.

b.12 is a composite number, because it can be written as 12 = 4*3 which means that 4 and 3 are divisor of 12

find least common multiple

Introduction for finding least common multiple:

In this section let me help you on find least common multiple. In arithmetic and number theory, the least common multiple or (LCM) least common multiple or smallest common multiple of two rational numbers a and b is the smallest positive rational number that is an integer multiple of both a and b.

Examples for Finding least Common Multiple:

Example 1:

Find lowest common multiple for the number 24 and 34.

On finding the LCM we have to find the prime factors for the given number. This will also help us on least common multiple lcm

24 : 2 2 2 3

34 : 2 17

---------------------------

LCM : 2 2 2 3 17

Lowest common multiple for the numbers 24 and 34 is 2 * 2 * 2 * 3 * 17 = 408

Introduction to fraction converter

Introduction to fraction converter:

Fraction :

In mathematics , Part of the whole can be expressed as fraction. There are three kinds of fraction

* Proper fraction
* Improper fraction
* Mixed fraction

In this article we are going to see about how to simplify the ration as fraction by using the ratio to fraction converter. This can also help us on similar polygons.
Ratio to Fraction Converter :

Converter:

The electronic or software device that can perform the operations Quickly. The ratio to fraction converter can be used to convert fraction for the given ratio.

Help on how many triangles

Introduction to how many triangles are there:
In math, the triangles are closed figure with three sides. The triangles has different types and each has different size of angles. If we add the angles of triangles, we get the answer as 180 degree. We can count how many triangles are present in some pictures by using formula.Here we can see about how many triangles are there with examples.

Explanation for How many Triangles.

The formula for finding how many triangles are there in pictures:

Step 1: We can add the consecutive odd numbers and get the answer equal to N². That is 1 + 3 + 5 + …. + (2N -1) = N².

Step 2: Using induction, we show the elementary proof and assume N = k. This will also help us on blank unit circle.

Therefore, 1 + 3 + 5 + …+ (2k – 1) = k².

Step 3: Let take N = k + 1.

That is 1 + 3 + 5 +….+( 2k – 1) + [2 (k + 1) – 1] = (k + 1)².

Step 4: Compare the left side of step 3 and step 4 equation.

Get the answer as [ 2(k + 1) – 1] = 2k + 1.

Step 5: The right hand sides are (k + 1)² – k² = 2k + 1.

This is denote induction proof

Norte on Modern Number System

Introduction of modern number systems: The modern number systems deal with the numerical values and their operations on math. This system involves natural numbers, integers, rational numbers, algebraic numbers, real numbers, complex numbers and etc. The arithmetic operations which deals with positive numbers and negative numbers. The natural numbers which includes all the whole numbers. The natural numbers sets are denoted as N. The number systems have the ability to count. The collections of some features are termed with number systems.Modern Number Systems - The positive number systems are which are larger than zero. It is the most used number systems found in our day to day life. The negative number systems are the one which is lesser than the zero. The negative numbers are followed by the sign (-). The negative number systems are also denoted as the inverse of the number.
Example for Modern Number Systems:-
Example: Multiplying the two rational numbers of (-4), (-5/2) Here (-4) is also represented as -4/1.Therefore -4/1 is multiplying with-5/2. (-4)(-5/2)= [(-5/2) (-4/1)] = [(-4) (-5/2) Negative *negative =positive =20/2 If x, y are rational numbers, then (x) (y) is also a rational number.Answer: 10.
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Fundamental Law of Trigonometry

Introduction to Fundamental Law of Trigonometry:-

When we talk about the fundamental law of trigonometry or the very word trigonometry the very first impression that comes in to our minds is right angled triangles. A special branch of geometry dealing with right angled triangles is the basis of trigonometry . When we consider a right angled triangle the first thing that comes to our mind is the hypotenuse which is the longest side of the triangle.The other two sides are the base and the perpendicular ;of course the triangle should have ONE RIGHT ANGLE.

We first determine the ratios of the sides . These are all very special ratios. The ratio between perpendicular and the hypotenuse is called the sine ratio and its inverse is called cosec ratio . The ratio of the base and the hypotenuse is called the cosine or cos ratio and its inverse is called the sec or secant ratio. The ratio between perpendicular and the base is known as the tan ratio and its inverse is known as the cot ratio. Of course all these ratios are in respect to angle theta which is one of the angles in the triangle apart from the right angled triangle.

The Sine Law - Fundamental Law of Trigonometry:

The sine law is such a law in trigonometry that even if we consider a scalene triangle with sides a,b ,c and angles respectively opposite to the sides as A,B,C then a / sinA = b / sinB = c / sinC or even the inverse is true. So if we happen to know any 3 of the data we can find the fourth. So with the help of this wonderful law of trigonometry we can find lots of information regarding the sides and angles of a scalene triangle where there is not necessarily a right angled triangle.

The Cosine Law - Fundamental Law of Trigonometric: -

The cosine law is another wonderful and fundamental law of trigonometry. It states that the square of any one side of a triangle equals the sum of the squares of the other two, less two times their product times the cosine of the angle of the opposite to the first side. That is b^2= a^2+c^2-2ac cos B and a^2= b^2+c^2-2bc cosA and c^2= b^2 + c^2-2ab cos C.

Help in Solving Square Root Problem

Introduction to solve square root problems:
The Square root problems of numbers are done when the number is multiplied through itself. In the same way for polynomial the square root is obtained when the polynomials are multiplied by it.
It is credible for solve together positive and negative numbers but when a negative number is taken out of root the value will become invented. There are two types of square problems such as ideal squares and non perfect square. It is simple to solve square root for perfect square.
Methods for Solving Square Root Problems:
The easiest method to define Square root problems in the method by using Prime Factorization:
(i) Write down the prime factorization of n from the given problems. Pair the factors such that primes in each pairs are equal.
(ii) Select one prime from every one couple and resolve multiplication of all such primes.
(iii) The multiplication obtained in (ii) is the square root of n problems.
These methods are used to solve the square root problems as easiest way.

Solve the square root of the following problems:
(a).√1600 = √2*√2*√5*√5*√4*√4.
According to the method, choose one prime from each pair
= 2*5*4.
= 40
So the perfect square root is 40.
(b).√900 = √3*√3*√5*√5*√2*√2.
According to the method, choose one prime from each pair,
= 3*5*2.
So the perfect square root is 30.
(c).√144 = √2*√2*√2*√2*√3*√3
According to the method, choose one prime from each pair,
= √4*√4*√3
=12.
So the solution is 12.
Non Perfect Squares:
Solve the square root of the following:
(a).√2352 = √2*√2*√2*√2*√3*√7*√7
According to the method, choose prime from each pair
= √4*√4*7*√3
According to the method, choose 4 as a prime from each pair
= 4*7*√3
=28*√3
So the square root of √2352 = 28*√3.
(b).√603 = √3*√3*√67
=3*√67
So, the square root of √603 = 3*√67.
(c).√9408 =√ 2*√2*√2*√2*√2*√2*√3*√7*√7
=2*2*2*7*√3.
=4*2*7*√3
=56*3.
So the square root of √9408= 56*3.

Note on Integers and rational numbers

Introduction to integers and rational numbers:
In the development of science, first we should know about the properties and operations on number which are very important in our daily life. In the earlier classes we have studied about number system and the fundamental operations on them. Now we extend our study on the number system in this subject. We have studied about natural numbers, whole number, integers and fractions and the four fundamental operations on them.

Definition of Natural number:
Counting numbers are called the natural numbers
N={1,2,3,……….} is the set of all natural number.
Definition of Whole numbers:
Natural numbers together with zero are called whole numbers
W={0,1,2,3……} is the set of all whole numbers.
Definitions of Integers:
Positive numbers, zero and negative numbers jointly form integers. We represent the set of integers by Z.
Therefore,
Z={ … – 3, – 2, – 1, 0, + 1, + 2, + 3, ….}
+ 1, + 2, + 3, … are called positive integers.
– 1, – 2, – 3, … are called negative integers.