Rational Exponents

Rational exponents in the field of mathematics can be defined as a fractional number play a role of exponents for nay number. To understand this concept we need to first understand the definition of rational number and definition of exponents. In mathematics, exponents can be define as a power of any number which shows no. of times a number can multiplied by itself. The mathematical representation of an exponent can be defined by following given notation that is a^b .

The above mathematical notation can be define as exponential representation where ‘a’ and ‘b’ are integer value and the value of a can be consider as base value and value of b can be consider as value of exponent. On the side Rational can be specified as a number which is able to represent two integer values in the form of quotient. Suppose x and y are two different integer value then they can be represented as x / y form.

Now we come to the point that is rational exponent, it can be define as a number where base value has a power of any fractional number. These are also able to for representing an integer and nth root value. Some of the popular rational exponents are square root exponents, cube root exponent and 4th root exponent. Suppose there is a number 5, now it can be represented as 5^1/2 = √5, 5^1/3 = ³√5,

5^1/4 = ⁴√5 and so on. In mathematics, generally these are defined as:

X^y/z = ^z√xy.

In the field of chemistry the Properties of Acids can be define as feature of acids with different chemical in different situations. In India, those school who affiliated from ICSE board then they have to follow icse syllabus 2013 for better result.  In the next session we will discuss about Geometric Progression. 

Geometric Progression

Geometric Progressions in mathematics are the successions which have a particular relation between the numbers in the series like other progressions. Every number is achieved by multiplying the previous number by a constant value. A definite proportion is maintained between the successive terms of the sequence. Suppose we have a geometric sequence given as follows: s, s * p, s * p², s * p³, s * p⁴ and so on. Where, s denotes the first term of the GP and p represents the definite ratio maintained between the terms.

For example, the sequence 8, 16, 32, 64 is a geometric progression with the first term as 8 and the fixed ratio as 16 /8 = 2.

We solve the geometric progression questions as follows: 1^st we have to write down the specified facts or figures given regarding the progression. It can be any combination of data that is available to us, it can either be the 1st term and the relation between the numbers or the 1st term and the succeeding term of the progression.

For instance, if the 1st term is 4 and the successive term is 20. The GP can be written as:

4, 4 * 5, 4 * 5², 4 * 5³, 4 * 5⁴ and so on.

Next we discuss another concept of maths that is related to the product differentiation of a function. The derivative of a function that contains the product can be solved as follows:

Suppose we have a function: y = f (x) * g (x),

D (y) / D (x) = g (x) D (f (x)) / D (x) + f (x) D (g (x)) / D (x).

We solve such problems by differentiating the two functions simultaneously. These concepts are important in maths and we can free download cbse books to refer these topics. In the next session we will discuss about Rational Exponents. 

properties of exponents

Exponents can be defined as the power to the base of any expression. Any mathematical expression is expressed in the form of base and exponents. If there is no exponent then it is said to have 1 as an exponent. There are different properties of exponents that are defined in this section. The first property of exponents is product of power property according to this property if two expressions are multiplied having same base and different exponents then in their resultant the powers are added having base as same. Second property is of Zero exponent according to this property, when two expressions of same base but one of them having 0 as exponent then on adding 0 to any other power will produce the same exponent in the resultant also. Third property is Negative Exponent property in which base are same of both the expressions but one power is negative and since it is negative therefore the exponent in resultant is obtained by subtracting the exponents.

Fourth property is quotient of powers property according to which when two expressions of same base having different exponents are divided then in the resultant their powers are subtracted.
Fifth property that is power of product property says that if two different base having same exponents are multiplied then their resultant can also be determined by first multiplying and then taking power of it. According to power of quotient property, if two expressions are divided having different base but same exponent then their power can be taken after dividing the terms.
Protein purification is termed as the process used for the extraction of single type of protein from a mixture or we can say complex mixture. It is used for the characterization of structure or function and also for the interactions of the proteins. CBSE is termed as Central Board Of Secondary Education which runs all over India in every state. Cbse syllabus for class 11 consists of serial pattern of topics for each and every subject and can be easily checked on internet also.

How to Make a Bar Graph

In mathematics, we will see different types of graph such as histogram graph, function graph. Here we will understand that How to Make a Bar Graph. Generally bar graph are used to categorized the different information, situations by taking bars in the graph. Bar graph is also called as bar charts. Here we need to follow some steps while constructing bar graph are given below:
Step 1: To plot a bar graph first of all we have to plot the axis in the graph. As we discuss above that two axis are there in a graph that is named as x – axis and y -  axis.
Step 2: Then after we have to select an appropriate scale and construct equal intervals.
Step 3: Now using the information of given data items label the horizontal axis.
Step 4: According to data items plot the bars.
Step 5: At last named the title of a graph.
Now we have to apply these steps in example.
 For example: Using the table mention below plot a bar chart.
Scores on the practice Test and the Test

Scores on the practice Test and the Test Student Practice Test Test
Hussen	60	70
Tomer	75	90
Marrine	55	55
Jiff	80

 Solution:
  First of all select or named the title from above mention table. As we see in the table that the title of above table is 'Score on practice Test and Test'. After that choose vertical bars. Here scores are different from one another mostly by 5, 10, 15 or 20. It means select a scale of 10.
 If we find any variation between scores then scores are like 1, 2, 3, 4, or 5, then it is better to select a scale of 1 or 2.
 After marking names on x – axis and scores on y – axis. Suppose if we decide to plot horizontal bars then put names on y – axis and scores on x – axis. At last plot the bars. Bar graph is shown below:

This is how we plot double bar graph using above steps. Now we will see Properties of Real Numbers.Commutative property of addition and commutative property of multiplication. for the prepration of 2013 board exam please prefer icse 2013 board papers.

equiangular triangle

In the previous post we have discussed about Define Equilateral Triangle and In today's session we are going to discuss about equiangular triangle. Hi friends, we will study different types of triangle such as equilateral triangle, isosceles triangle and so on. Here we will discuss one of the important triangle that is equiangular triangle. An equiangular triangle can be defined as a triangle such that the entire interior angles are of equal length and angle are of 60 degree.

The interior angles of an equiangular triangle always reach to 180 degree, and each angle of equilateral triangle is always third part of it. It means we can say that all the angles are of 60 degree. Let’s discuss some properties related to equiangular triangular.

Area – The area of equiangular triangle is given by:

Area = √3 / 4 s², here‘s’ denotes the length of any one side.

In case of equiangular triangle, the radius of a circle is just half of the radius of the circumference. Interior angles – 60 degree is the interior angles of an equiangular triangle. Perimeter – addition of the  entire sides of an equiangular triangle is perimeter.

Perimeter = s + t + u, here ‘s’, ‘t’, ‘u’ are the lengths of three sides of an equiangular triangle. Now we will discuss that how to find the area of equiangular triangle with the help of example: (know more about equiangular triangle, here)

Example: Find the area of equiangular triangle where the length of sides are 16, 16, 16 inch?

Solution: We know that the formula for finding the area of equiangular triangle is:

Area = √3 / 4 s²,

Given, length = 16 inch, put the value of all sides in a given formula:

 Area = √3 / 4 s²

Area = √3 / 4 (16)²,

Area = √3 / 4 (256),

Area = 256 √3 / 4,

So, the area of an equiangular triangle is 256 √3 / 4.

Same side Interior Angles can be defined as the angle pairs which are on inside of two lines and also on same side of traversal. icse guess papers 2013 is very helpful for exam point of view.

Define Equilateral Triangle

An equilateral triangle in the mathematics can be defined as the triangle which has all the 3 sides of the equal length. This is the general definition but in the traditional or we can say the Euclidean type of the geometry, the equilateral triangles are also those triangles which are equiangular which means that all the 3 internal angles of the triangle are congruent to each other like the 3 sides and each angle is equal to 60 degrees. The equilateral triangles are the regular polygons and thus they can also be known as the regular triangles.
According to the definition of the equilateral triangles we can derive many results. Suppose the length of each side of any equilateral triangle is l then we can derive various results for this triangle with the help of the Pythagorean theorem which may be given as follows. (know more about Equilateral Triangle, here)
The area of any triangle which is equilateral may be calculated by the formula A = ( √3/4 ) * l². The perimeter of any such triangle which is equilateral is equal to thrice the length of any side of the triangle that is P = 3l. Also the height or we can say the altitude from any side of the equilateral triangle is given by h = ( √3/2 ) * l. 
We can also derive some of the results for the inscribed and the circumscribed circles of the equilateral triangles. For example the radius of the circumscribed circle of any triangle which is equilateral may be given as R = ( √3/3 ) * l. Then the radius of the inscribed circle of any triangle which is equilateral may be given as r = ( √3/6 ) * l.
In order to get more help on the topics: Equilateral Triangle and Rutherford Atomic Theory you can visit our next article. CBSE Syllabus 2013 is designed in a manner to help students in learning important topics in a very simpler way.