Data Analysis

In the previous post we have discussed about Associative Property of Addition and In today's session we are going to discuss about Data Analysis. The data analysis as the name suggests is just the analysis of the data. But we will look into the broader meaning of the term data analysis. The data analysis is a type of method which is generally used for enquiring about the data, cleaning the data, for taking the data from one place to another and also for data modeling. The motive of the data analysis that is the need of analyzing any type of the data is to get some vital information, to provide the conclusions and also to help in the process of making any type of the decision. (know more about Data analysis, here)
Let us take an example of the data analysis now. The mining of the data is also a special type of process of the data analysis which generally emphasizes on the modeling and on the discovery of the information for a motive which is predictive and not for any type of the purpose which is completely descriptive.
The term data analysis is also sometimes used in place of the ‘modeling of the data’. The data analysis is just a method under which various types of the phases can be separated. The data analysis is very much related to the visualization of the data.
Now we have seen the various definitions of the data analysis. So let us move on and study some further details of the data analysis. Therefore we will discuss now about the cleaning of the data which is nothing but only a part of the process of the data analysis. The cleaning of the data is a critical process under which the data is being enquired to check whether it is correct or not and finally the data which is found out to be incorrect are corrected if it is required.
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Associative Property of Addition

In the previous post we have discussed about The Unit Circle and In today's session we are going to discuss about Associative Property of Addition, Different properties of addition can be checked for the numbers namely closure property, commutative property and associative property for addition.  By Associative Property Of Addition, we mean that if we have any three natural numbers say a, b and c then we say that the addition of these three numbers is associative, which indicates that even if the order of addition of the three numbers is changed, the sum of the three numbers remains same. So we say that the numbers a and b are added first and then number c is added to it, the sum we get will be the same as when we add the numbers b and c and then the number a is added to it.  Thus it can be mathematically expressed as follows:
 ( a + b )  + c = a + ( b + c )
 The associative property of addition also holds true for the whole numbers, integers and even for the fraction numbers.  If we have 3 fraction numbers say a1/b1, a2/ b2 and a3 / b3, then we say that the associative property of addition also holds true for the fraction numbers which can be indicated numerically as follows:  ( a1/b1 +  a2/ b2 ) + ( a3 / b3) =  ( a1/b1) + (  a2/ b2  + a3 / b3 )
 We also check the associative property of addition for the rational numbers and observe that the associative property of addition also holds true for the addition of the rational numbers too. (know more about Associative property, here)
To understand the concept of how to do fractions, without the help of the teacher, we can take the help of online math tutor and understand the concepts. We can also download CBSE Board Hindi Syllabus to know about the marks distribution of different topics and understand the pattern of the question paper.

The Unit Circle

In the previous post we have discussed about How to Find Altitude and In today's session we are going to discuss about The Unit Circle. The unit circle is a mathematical term used to prove many theorems plus has many other applications also. The unit circle is self defined as the word unit or unity is for 1, so the unit circle is nothing but a circle with radius one. According to Cartesian coordinate system, the unit circle is used quite frequently in trigonometry and according to which the unit circle is the circle with radius one and centered at the origin (0, 0) in the Euclidean plane. The unit circle is denoted by S¹. If we would generalize this term in higher dimensions, then we call it as the unit sphere.
Another simple way of defining a circle with a radius one is that its center is put on the Euclidean graph where both axes x axis and y axis intersect or cross. And it is a very simple and great way to learn and talk about angles and lengths.
As we all are aware with the term Pythagorean theorem, but for those who do not know the actual sense of the theorem, here is the explanation: if we consider a point (x, y) on the unit circle and let x and y are positive, then x and y will be the lengths of the legs of a right angle triangle whose hypotenuse has length 1. Hence x and y satisfy the equation given by the Pythagorean Theorem: which says the sum of the squares of the lengths of the other two sides of right triangle is equal to the square of hypotenuse length.
x² + y² = 1
The above equation says that the reflection of any point (x, y) on the unit circle about x or y axis is also on the unit circle as x² = (- x²) for all x.
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How to Find Altitude

In the previous post we have discussed about Explain Analytic Geometry and In today's session we are going to discuss about How to Find Altitude. Altitude of a triangle is a straight line through the top point or it is generally called vertex and or you can say that altitude is a line which makes right angle or is perpendicular with the line opposite of the triangle or base. This line which consists of the opposite side of any triangle is called the extended base of the altitude. The foot of the altitude is the point where the intersection between the extended base and the altitude takes place. And another term that is the length of the altitude is the distance between the base and the vertex of any triangle. If we want to draw an altitude from the vertex of the triangle to the foot of the triangle, then it can be done by the process known as dropping.
Dropping of an altitude is a special case of the orthogonal projection. An altitude is the shortest distance from the vertex of a triangle to the opposite side or base of that triangle.
Three altitude of a triangle intersect at a single point which is called as an orthocenter.
Altitude can also be used to calculate the area of a triangle by using the formula: ½ bh, where b and h are the lengths of the base and the altitude respectively. The altitudes are related with the sides via many theorems like in radius theorems, equilateral triangle theorem and area theorem etc. , and we have one very important formula called Heron’s formula which relates the sides and altitude of a triangle.
One thing is proved here and which that the longest altitude of a triangle is always perpendicular to the shortest side of the same triangle.
The foot of the altitude is the midpoint of the base of the triangle in case of an isosceles triangle. And the altitude also divides the angle of vertex or form the angle bisector of the vertex.
In order to get help on the topics altitude, integral table and icse board sample papers for class 12, you can visit our next article.

Explain Analytic Geometry

Analytic geometry is deals with the algebra, and it is used to form the geometric objects, and some of the geometric objects contain points, straight line, and circle. In the geometry the representation of a point is ordered pair in the plane analytic geometric objects and in case of straight line in analytic geometry, straight line is represented by set of points which assure the linear equation and the part of analytic geometry which is related with the linear equation is also said to be linear algebra. There are some other names of analytic geometry which are Coordinate geometry, Cartesian geometry. Plane analytic geometry is based on the coordinate system and the principal of algebra and analysis.
Now we will see the basic principal of analytic geometry which is given below:
Each point has a pair of real number coordinates in the analytic geometry. Cartesian coordinates system is one of the most important coordinate system in the plane analytic geometry, in which all the x- coordinates are plotted along the horizontal position in the graph and y- coordinates are plotted along the vertical direction in the graph. And the general forms of these coordinates are of order pair (x, y). It is also used in the three dimensional geometry, where all the points are denoted by an ordered pair of coordinates like (x, y, z);
Now we will see how to find the distance and angle of analytic geometry:
Suppose we have coordinates s₁, s₂ and t₁, t₂ for the plane of geometry:
Then we see how to find the distance of analytic geometry by using above coordinates:
d = √ (s₂ - s₁)² + (t₂ - t₁)²;
Where’d’ is distance.
By using the Pythagoras theorem we can find the distance of analytic geometry.
Now we will find the angle of plane of geometry:
The angle of analytic geometry is:
∅= arc tan (m);
Where ‘m’ represents the slope of line;
By this formula we can find the distance of analytic geometric.
Compound interest calculator is a mathematical tool which solves the equation easily; we have also found the compound interest in CBSE class 9 books.