Saturday 16 June 2012

Multiplying Polynomials

In the previous post we have discussed about Use Greatest Common Factor Calculator and In today's session we are going to discuss about Multiplying Polynomials. We will learn about Multiplying Polynomials in this unit. To understand the concept of multiplying polynomial we come across different types of polynomials. In case we have to multiply a monomial with the monomial, we will simply multiply the coefficient of both the terms and then the powers of the variables are added up. Suppose we are multiplying 3x with 5xy>2, here we have the coefficient of the terms as 3 and 5, so we write
3x   * 5xy>2 = 15 * x>2 * y>2
Thus we say that constants are multiplied separately and then the variables are multiplied separately to get the product of two monomials. (know more about Polynomial, here)
Now proceeding further, let us consider the two   polynomials, where one of them is a monomial and the other one is a binomial, (it means a single term is to be multiplied with the two terms) In such a situation, we will multiply the single term of the monomial with both the terms of the binomial separately and thus the result we will get will be the binomial.
Let us consider the following example: Multiply 2x>2 with ( 3x + 5y)
 Here 2x>2 is a monomial and the expression 3x + 5y is the binomial. So we will first multiply the term 2x>2 with 3x and then the same term is multiplied with the term 5y. Thus we get the product as follows:
 ( 2x>2 * 3x) + ( 2x>2 * 5y)
= 6 x>3 + 10x>2 Y Ans
 Thus we observe that the resultant polynomial is the binomial. In the same way if a trinomial is multiplied with the monomial, we get the polynomial as the trinomial only.

  To learn about the Positive Correlation, we can make use of math online tutors. cbse board books are also available online which the students can use to consult the specific topics.

Friday 15 June 2012

Use Greatest Common Factor Calculator

In the previous post we have discussed about How to use Matrix Multiplication Calculator and In today's session we are going to discuss about Use Greatest Common Factor Calculator. In mathematics, GCF stands for greatest common factor which is used for solve the various kind of problem. The greatest common factor is the numbers which can be define as a common factor for two or more numbers. The GCF is most popularly known as a highest common factor which is able to divide the two or more positive integer without any remainder. In mathematics, Greatest common factor calculator mostly deals with the integer values and fractional values to reduce the complexity for performing the various tasks.
In the term Greatest common factor calculator we generally deal with the three words, (a) Greatest (b) common (c) factor. Here factor can be defined as a number which are used for performing the multiplication of two or more numbers. In the same aspect ‘common factor’ refers to the number which works as a common number for groups of numbers. Now the question arises in our mind that how to we calculate the greatest common factor for positive integer value. Lets we show you below:
Suppose we want to get the greatest common factor of two or more numbers then we need to follow the following given steps of greatest common factor calculator.
A)      First of all perform the prime factorization of each number that is given.
Suppose we have a number 15 then there prime factor will:
      15 = 3 * 5
B) After performing the prime factorization we can easily perform the multiplication of those factors that are common factors in all given numbers. If in any case there is no prime factor exists in between the prime factors of numbers then GCF can be consider as 1 for all positive number values. (know more about Factorization, here)
From the process of prime factorization we can get either single common factor or multiple numbers of common factors. During the processing of Greatest common factor calculator, prime factorization plays an important role in solving various kinds of problem that are related to mathematics.  Volume of a Sphere Formula can be described as a calculation of three dimensional spaces that are occupied by the sphere. Sphere is a three dimensional rounded shaped figure which are enclosed by some boundary. Education board in any state works as a board for secondary and senior secondary education. They manage the flow of education and their examination every year.

How to use Matrix Multiplication Calculator

In the previous post we have discussed about Side angle Side Theorem and In today's session we are going to discuss aboutIn this blog we are going to discuss about the matrix multiplication calculator. It is a online tool for performing the multiplication operation on the given two matrixes that are define in the given text box of the calculator. The main concepts of calculating the multiplication of matrixes are not same as the general multiplication method. As we know if there are simple two numbers as a and b then a * b is equal to
b * a or a * b = b * a. That shows the commutative property of the Multiplication. But one thing you should keep in your mind that multiplication of the matrixes are not commutative. If we have two matrix p [] and q [] then p [] * q [] not equal to q [] * p [] . The most commonly used matrix multiplication dimension is 2 dimensional matrixes.  (know more about Matrix Multiplication Calculator, here)
When in the matrix multiplication both of the matrixes are of different dimensions then one thing must be noted that the number of columns of first matrix is equal to the number of rows of second matrix. It is define as if there are two matrix x [2] [3] then in the second matrix y the number of rows are equal to the 3 that is the number of columns of first matrix so y [3] [4] or y [3] [2] or…. Y [3] [n] where n is any number for defining the columns in the second matrix y.
We define the matrix multiplication as
  [ a11 a12    [ b11 b12      =  [a11 b11 + a12 b12    a11 b12 + a12 b22
    a21  a22 ]      b21  b22]       a21 b11 + a22 b21     a21 b12 + a22 b22]
Matrix multiplication calculator helps the students to multiply the entered matrix in short period of time and accurately. Formula for circumference of a circle helps in calculating the circumference of a circle. CBSE syllabus provide  the guidelines about the topics to their related subjects that helps the students for proper study.  

Monday 4 June 2012

Side angle Side Theorem

In the previous post we have discussed about How to find sector of a circle and In today's session we are going to discuss about, Side angle Side Theorem SAS is one of rules of congruency. Before we know about it, let us quickly revise congruency of triangles. We are very much familiar with the smallest member of our polygon family, yes the triangles. They are the youngest member being formed with the minimum number of line segment. Now, as in a family there may be a number of members, and some of them may be alike in all aspects, so is with this member of polygon family. There may be an endless number of triangles that can be drawn in a plane. Of all the triangles so drawn, the triangles that are the same in all aspects are called congruent triangles. In simpler words, the triangles are said to be congruent to each other if all of their corresponding sides & angles are equal. Thus, to say in an easier way, the triangles, if fix one over the other exactly to give the appearance of being one, are termed as congruent triangles.
There are a few criterions to check whether the given triangles are congruent or not. One of these criterions is called the SAS criterion or rule of congruency of triangles. This rule states that given the sides & angles of any two triangles, if any two corresponding sides & the corresponding angles included between these equal sides are equal, then the two triangles are said to be congruent. The rule SAS is read in the same sequence to know the congruency; which means the corresponding side, then the corresponding angle carried by such side & finally the other side of such angle must be correspondingly equal. The easier way is to find out any one pair of corresponding angles in the two triangles that are equal & then find out whether their corresponding sides are also equal. If yes, the triangles are congruent else not.
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How to find sector of a circle

The sector of a circle is just like a piece of a circle which is covered by a curve (arc) and two straight lines (radii). The curve or an arc is a part of the circumference of the circle. The important and necessary condition for the sector of the circle is that these two lines must be the radius of a circle r. The jointing point of these two radii is the centre of the circle and they make a angle β, β is called by central angle. When we make a sector of a circle then another one is automatically observed. The circle is divided in two sectors and these are minor sector and major sector. M is the length of the arc of the minor sector.
When the value of the β or central angle is 180 degree the circle is called semicircle.
When the value of the β or central angle is 90 degree the sector is called quadrants.
When the value of the β or central angle is 60 degree the sector is called sextants.
When the value of the β or central angle is 45 degree the sector is called octants.
When we form an angle connecting the end point of the arc to any point in circumference except in sector is half of the angle made by the sector at the center.
To find parameter (P) of the sector is adding length (L) of arc plus two times radii.
P = L + 2r
For finding the total surface area of the sector we have to know first area of circle so area of circle is pie r2 so, we multiply the area of circle by the ratio of sector angle by circle angle therefore area of a sector will be r2β/2 where β is a central angle.  The sector of a circle and the product rule are described in the CBSE class 9 previous year question papers.