Identity Definition

An identity is a relation which is tautologically true. This is usually taken to mean something that is true by definition, either directly by the definition, or as a consequence of it. An equation which is true for every value of the variable is called an identity equation. An inequality which is true for every value of the variable is called an identity inequality.

Identity definition: Identity definition is *An identity is an equality that remains true regardless of the values of any variable that appear within it, to distinguish it from an equality which is true under more particular conditions. ... The basic Number Properties (or laws) that apply to arithmetic operations are Commutative Property, Associative Property, Identity Property and Distributive Property. When a set possesses an identity element for a given operation, the mathematical system of the set and operation is said to possess the identity property for that operation.

To know more about what are pythagorean identities click here.

EQUATION OF LINE

The general equation of a line is given by: Ax +By = C

where A, B and C are constants and A and B cannot be both zero. Any straight line in a rectangular system has an equation of this form

The slope equation of a line m can also be written as follows: Y = mx + b where m is the slope of the line and b is the y intercept of the graph of the line.

The above form is called the slope intercept form of a line.
Given below is one solved example on equation of straight line.
1) Find equation of a line that has slope m = 4 and passes through the point (–1, –6). O

Here the value of slope is given; in this case, m = 4. Also, giving a point on the line, an x-value and a y-value for this line is being provided which is x = –1 and y = –6.

In the slope-intercept form of a straight line, We have y, m, x, and b. So the only thing that we don't have so far is a value for is b (which gives me the y-intercept). Then all we need to do is plug in what is being provided for the slope and the x and y from this particular point, and then solve for b:

y = mx + b (–6) = (4)(–1) + b –6 = –4 + b –2 = b

Then the line equation must be "y = 4x – 2".

There are different types of equations like Linear Equation, Quadratic equation etc.. I will be back on detail write on these shortly....

Linear programming

Here I come with another complex topic in math. I know that sounds boring but let us try to make it simpler so that we can understand the same.

Linear programming, sometimes known as linear optimization, is the problem of maximizing or minimizing a linear function over a convex polyhedron specified by linear and non-negativity constraints. Simplistically, linear programming is the optimization of an outcome based on some set of constraints using a linear mathematical model. Linear programming in which variables may take on integer values only is known as integer programming.

The Linear Programming plan helps to maximize the profit or else minimize the cost subject to the limitations. The profit or the cost is made up of unknown quantities. These unknowns are variables of the degree; one and they are called decision variables. The profit or else the cost are a linear function of these variables. These in equations are called constraints. The linear programming simplex (LPX) is to maximize or minimize the aim function subjected to the Linear Programming constraints.

This does not end here. Lot more to come so keep in touch…. Thank you for reading this post.

Prime Factorization

In our 6th class we all must have learnt about Prime Factors, Whole number, Prime numbers etc….

Today let us discuss about Prime Factorization:

Fist let us understand what is a Prime Number?

A Prime Number is a whole number, greater than 1, that can be evenly divided only by 1 or itself.

PRIME FACTORIZATION:-

Converting the composite numbers in to multiplication of numbers is known as factorization, simplifying till the prime numbers is known as prime factorization.

See the Image below:-


"Prime Factorization" is finding which prime numbers you need to multiply together to get the original number. Converting the composite numbers in to multiplication of numbers is known as factorization, simplifying till the prime numbers is known as prime factorization.
For e.g. the Prime factors of 6 are 2 and 3 (6 = 2*3). Here both have multiplicity 1.

Integers and Properties of Integers

I am sure we all are aware about integers; Let us recollect it again...

Integers: Integers are possitive and negative numbers. E.g. ...., -6, -5, -4, -3, -2, -1, 0, +1, +2, +3, +4, +5, +6,..... Here each negative number is paired with a positive number the same distance from 0 on a number line.

Properties of Integers:

Below are some properties of Integers:

1. The sum of two integers is a integer
2. Addition on integers is cummutative, i.e a+b = b+a for all integers a,b
3. Addition of integers is associative, i.e. (a+b)+c = a+(b+c) for all integers a,b,c.
4. The integer zero, (0), is such that a+0 = a = 0+a for any integer a.
5. For any integer a, there correcponds an integer -a such that a+(-a) = 0 =(-a) +a
6. The product of any two integers is an integer.
7. Multiplication of integer is commutative i.e. a.b = b.a for any two integers a, b.
8. Multiplication of integers is distributive over addition i.e.
9. Multiplication of integers is associative, i.e. (a.b).c = a.(b.c) for all integers a,b,c.

a.(b+c) = a.b+a.c
(b+c) . a =b.a+c.a
for all integers a,b,c

10. The integer 1 is such that a.1 = a= 1.a for any integer a.


LIKE IT??????????? Leave a Comment...... Will get back to you with more of such interesting topics........

Empirical Probability

Empirical probability, also known as relative frequency or experimental probability, is the ratio of the number favorable outcomes to the total number of trials, not in a sample space but in an actual sequence of experiments. In a more general sense, empirical probability estimates probabilities from experience and observation.

An advantage of estimating probabilities using empirical probabilities is that this procedure is relatively free of assumptions. For example, consider estimating the probability among a population of men that they satisfy two conditions:

1. they are over 6 feet in height;
2. that they prefer strawberry jam to raspberry jam.

A direct estimate could be found by counting the number of men who satisfy both conditions to give the empirical probability the combined condition. An alternative estimate could be found by multiplying the proportion of men who are over 6 feet in height with the proportion of men who prefer strawberry jam to raspberry jam, but this estimate relies on the assumption that the two conditions are statistically independent.

Subtraction

Subtraction is inverse function of addition. If any number that is added with its own inverse the result will be zero. If the number is subtracting with the lesser number then the result is positive. If the number is subtracting with the larger value then the result is negative value.

Subtraction is used to model four related processes:

1. From a given collection, take away (subtract) a given number of objects. For example, 5 apples minus 2 apples leaves 3 apples.

2. From a given measurement, take away a quantity measured in the same units. If I weigh 200 pounds, and lose 10 pounds, then I weigh 200 − 10 = 190 pounds.

3. Compare two like quantities to find the difference between them. For example, the difference between $800 and $600 is $800 − $600 = $200. Also known as comparative subtraction.

4. To find the distance between two locations at a fixed distance from starting point. For example if, on a given highway, you see a mileage marker that says 150 miles and later see a mileage marker that says 160 miles, you have traveled 160 − 150 = 10 miles.