Help on Geometric Progression

Introduction:

In this section let me help you on geometric progression. Solving online progression is very interesting since we can find the nth term of the particular sequence in much easier way. In this article we shall learn about steps involved in progressions solving. Moreover we will see in detail about different types involved in progression.

There are three types of Progression in math,

* Arithmetic progression
* Geometric progression
* Harmonic progression

Let us see these progression and their properties in the following section.
Arithmetic Progression. This can also help us on linear programming

Definition:

It is a sequence of numbers in which each term except the first term can be calculated by adding constant number (common difference) to the immediately preceding number.

The General form of the arithmetic sequence is,

a, a+d, a+2d, a+3d………..

Here a is the first number and d is the common difference.

To find the nth term of an arithmetic progression we can use the following formula,

an=a+ (n-1) d

Properties of Arithmetic Progression:

* When we add or subtract any constant number with all the terms of the sequence, the arithmetic sequence remains an arithmetic sequence.

Keep reading may be in the next session let me help you on Polynomial Function

Note on Frequency Polygon

Introduction to Frequency Polygon:

A frequency polygon is a graphical display of a frequency table. The intervals are shown on the X-axis and the number of scores in each interval is represented by the height of a point located above the middle of the interval. The points are connected so that together with the X-axis they form a polygon

Frequency polygons are useful for comparing distributions.This is achieved by overlaying the frequency polygons drawn for different data sets. The figure below provides an example. This will also help us on kinematics equations. The data come from a task in which the goal is to move a computer mouse to a target on the screen as fast as possible. On 20 of the trials, the target was a small rectangle; on the other 20, the target

was a large rectangle. Time to reach the target was recorded on each trial.

I hope you liked my information on this. Keep reading may be in the next session let me help you on Polygon Centroid

Fundamental Theorem of Calculus

Introduction to Fundamental Theorem of Calculus :

In this section let me try to help you on fundamental theorem of calculus. Calculus originated to solve mainly two geometric problems : the first is studied by a limit process known as differentiation and the second by another limit process known as integration.

Integral calculus is the study of the definition, properties and applications of two real concepts: the indefinite integral and definite integral.

The indefinite integral is the antiderivative. the definite integral inputs a function and outputs a function a number. The technical definition of the definite integral is the limit of a sum of areas of rectangles, called Riemann sum, as propounded by Riemann. This will also help us on normal distribution table

The fundamental theorem of calculus is the statement that the two central operations of calculus, differentiation and integration, are inverse operations: if a continuous function is first integrated and then differentiated, the original function is retrieved.

Keep reading may be in the next session let me help you on Polynomial Function.

Definite Integral Calculator

Definite integral calculus:

Definite integral calculator is same as the integral calculus calculator but it is mainly for finding the integral which is covered by a specific intervals. That is it has upper limit value and lower limit value.

For this definite integral calculus calculator first the given expression should be integrated as integral calculator and then the limits should be applied. The final output can be derived by substituting the upper limit – lower limit.

Integral calculator:

Integral calculus calculator is mainly for finding the indefinite integral of the given expression by getting an input value.

Consider an expression x then the integral calculus gives the calculator is, This will also help us on integral table

Example:

Find the integral calculus calculator of the function f=10x3.

Solution:

Given,

Function f=10x3

We know the integration of xn is

Therefore [int 10x^3] =10 [intx^3] =10 [x^4/4]

= [5/2x^4]

Keep reading may be in the next session let me help you on Linear Definition

what is measurement

In this lesson let me help you understand more on what is measurement and how it is measured in our day today life. keep reading
Everything that we use in our daily life is ultimately governed by principles of physics. All gadgets we use everyday at home, bicycles and cars, all different types of machinery and instruments, work on principles of physics. Hence to understand even the elementary working of these things, the study of physics is essential.
For understanding the relationships between matter and energy, measuring them is very essential. There are thousands and thousands of different things around us. There are different kinds of forces around us and there are different kinds of energies that we come across every day. Thus there would be millions and millions of physical quantities and energies that could be measured. Yet you would be surprised to know that there are only six basic units from which all other units are derived. This also helps us on water pollution statistics. These basic units are the units of length, mass, time, electric current, temperature and luminous intensity. Out of these only three fundamental or basic units of measurements are used in mechanics.
keep reading may be in the next session let me help you on newtons first law of motion

Note on Continuous Function

Definition of Continuous Function:

In study of probability, a Random Variable X is assumed as a continuous variable, if it can take all possible values within certain given limits. That is X is a continuous its values cannot be put in one to one associated with N.

A nonstop probability function f(x) is a function that satisfies the following properties:

• It is non-negative for all real X.
• The probability function of integral is one.
• Constant continuous probability functions are known as probability definition function (pdf).
• Since regular probability function are defined for uncountable number of
  points over an interval, the probability at a single point is always zero.

The probabilities are measured between intervals। That Is, the area under the curve stuck between two distinct points define the probability for that interval.This can also help us on how to simplify radicals.

P(a ≤ x ≤ b) = P(a ≤ X < b) = P(a < x ≤ b) = P(a < x < b)

Discrete Probability function is referred to as probability mass function.

Continuous probability functions are known as probability density function

keep reading may be in the next session let me help you on Volume of Cube.

Sample Problems on Radicals

Introduction for radical:

The opposite operation to the exponent is known as radical. A radical is an expression which contains the square roots, cube roots etc. For example the expression √49 can also be called as square root of 49 or root of 49. Radicals have the same property of the numbers.

Examples for Radical:

Following are the examples of radicals.

Example 1 for radical problem:

Simplify the radical: √ (49) / (√36)

Step 1: Factors of 49 = 7 × 7

√ (49) = √ (7 × 7)

= √7²

Step 2: Square root of 7² = 49

Step 3: Factors of 36 = 6 × 6

√ (36) = √ (6 × 6) = √6²

Step 4: √6² = 6

Step 5: so, √ (49) / √36) = 7 / 6

The answer of the given radical is 7 / 6

Even Rules of Radicals helps us understand better in doing all the problems.

Example 2 for Radical Problem:

Simplify the radical: 3√8 × √12

Step 1: Find the factor of 8 = 2 × 2 × 2

Step 2: Take cubic root of 8 = 2

Step 3: Find the factor for 12 = 2 × 2 × 3

Step 4: Take square root of 12 = 2 √3

Step 5: so, 3√8 × √12 = 2 × 2 √3

The answer for the given radical is = 4√3

This was just a sample examples on this topic. keep reading and leaver your comments. if you like this. May be in the next session lets study on dividing radicals

Help on Probability

In this lesson let me share with you on what is probability and its importance to mathematics.

Introduction to Probability:

In our day to day life, we come across many uncertainties of events. We wake up in the morning and check the weather report. The statement could be 'there is 60% chance of rain today'. This statement infers that the chance of rain is more than that having a dry weather. We decide upon our breakfast from a statement that "corn flakes might reduce cholesterol". What is the chance of getting a flat type on the way to an important apartment? And so on.

How probable an event is? We generally infer by repeated observation of such events in long term patterns.

Probability is the branch of mathematics devoted to the study of such events and this study also will help us on probability problems.

I hope you enjoyed reading this. Keep reading and leave your comments. May be in the next lesson let us study on Probability Calculator.

Note on Closure property of integers under addition

In this lesson let me help you go through on closure property of integers under addition. Before i go more deep on this let me help you understand on what is all about integers.

What is integers?
The negative numbers, zero and the natural numbers together are called integers.
For example -8, -2, 0,2,8

Now we will discuss about the closure property of integers:

If a and b are two integers, then a+ b is also an integer. In other words, the sum of any two integers is also an integer or, integers are closed for addition.

Verification : In order to verify this property, lets us take any two integers and add them. We find the sum is always an integer.

Consider the following :

Integer(a) Integer(b) Sum(a+b)

5 7 (5+7)=12

[Here we observe that 5 is an integer as well 7 is also another integer and now if we add these two integers then the sum 12 is also an integer].

Integer(a) Integer(b) Sum(a+b)

-8 5 {(-8+5)}=-3

[Here we observe that -8 is an integer as well 5 is also another integer and now if we add these two integers then the sum -3 is also an integer].

Integer(a) Integer(b) Sum(a+b)

8 -10 {8+(-10)}=8-10=-2

[Here we observe that 8 is an integer as well -10 is also another integer and now if we add these two integers then the sum -2 is also an integer].

This was just a brief introduction to the topic . Keep reading and leave your comments. May be in the next lesson let me help you go through more on properties of logarithms.

Solved Problem on Cyclic Quadrilateral.

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Introduction to Cyclic Quadrilateral.

A Quadrilateral whose all four vertices lie on the circumference of the same circle is called a Cyclic Quadrilateral. As all the vertices are on same circle, so they are called Concyclic. Thus, a Cyclic Quadrilateral can be circumscribed. The circumcenter may or may not lie in the interior of the Quadrilateral

Sample problems on cyclic Quadrilateral.

Let me help you go through few solved problems on Cyclic Quadrilateral.

Problem: 1

The Cyclic Quadrilateral ABCD,

Solution

In the Cyclic Quadrilateral ABCD,

80 +

Similarly,

120° +

Hence,

Problem: 2

ABCD is a Quadrilateral circumscribed by a circle with center O. The diagonal AC is also the diameter of the circle. Find

Solution:

Since AC is the diameter

therefore,

Now,

90° +

Hence,

I hope you enjoyed reading this. Keep reading and leave your comments.May be in the next lesson .. let me help you go through on Rational expressions.