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.
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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.

straight line

In the previous section we have discussed about length of an arc calculator and In today's session we are going to discuss about Straight line, It was developed by mathematicians to represent objects which are straight and have insignificant depth and width. They have one dimension that is only length with no depth and width .The straight line definition says it is nothing only flow of points and it is equally extended to the two points
A line was described by Euclid as breathless length and with some provable properties he constructed geometry which is called as Euclidean Geometry in today’s Mathematics .A line is called as shortest path between the points but some mathematicians says that a line is a 2 dimensional Vector space
Equation of a Straight line or slope intercepts form
Y=mx +b
Where
Y=how far
X =how far along
M=slope
B= Y intercept
The equation has variable expression without any exponents
Find the equation of straight line which has slope m = 3
and passes through point (2, –6).
Solu: So in the above problem value of the slope is m=3.And the value of x = 2, and value of y =-6.We don’t have the value of b in the equation
Here we will put the values in the slope equation to get the value of b
 y=mx + b
(-6)=3*(2) + b
-6 = 6+b
-12=b
So equation of the line will be y= 3x-12

Find the equation of straight line which has slope m = 6
and passes through point (-1, –3).
Solution: So in the above problem value of the slope is m=6.And the value of x = -1, and value of y =-3.We don’t have the value of b in the equation
Here we will put the values in the slope equation to get the value of b
 y=mx + b
(-3)=6*(-1) + b
-3 = -6+b
3=b
So equation of the line will be y= 6x+3
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length of an arc calculator

Arc of the circle is from the circumference of the circle, it is a portion from that even we can consider circumference as an arc

Length of an arc is calculated with the help of length of an arc calculator or Arc Length Formula. It is defined as arc length which is formed in a circle with a radius r and an angle θ

Arc length can be either measured in the degrees or unit length. It is dependent on its centre angle
Length of an arc calculator
S = 2πr θ/360⁰

Where S is length of the arc
 r is radius of the circle
θ is the angle in the radians
Calculator is derived from the help of the centre angle and the radius of the circle. Length of the arc is represented with symbol s .We have to use the angle from the total angle of the circle from which we will derive the value θ/360⁰   and then use the circumference of the circle which is 2πr.It is a calculator which makes the calculation simple and fun to solve

Understand the calculator with examples

Example 1
Find the arc length of the arc, if θ = 30⁰ and r = 10
Solution
 Formula for arc length is,
Length of arc = 2πr θ/360⁰
Put the values of angle and the radius in the formula
= 2 × 22/7 × 10 × 30⁰/360⁰
= 440/7 * 1/12
=5.2
Example 2
Find the arc length of the arc, if θ = 20⁰ and r = 5cm
Solution
 Formula for arc length is,
Length of arc = 2πr θ/360⁰
Put the values of angle and the radius in the formula
= 2 × 22/7 × 5 × 20⁰/360⁰
= 0.004

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free online math tutoring

While solving the problems of mathematics, Free online math tutoring,   is available at different sites, which will give time to time guidance to the learners. It is helpful to learn the new concepts and to understand the difficult topics with the ease. It gives you guidance to understand and solve the problems, with the easy methods. It also provides you the tips to understand the different problems of mathematics with step to step guidance in order to understand each and every step. These online tutors can be used even on weekends and at odd hours, whenever you feel to use it. Thus we say that solving the problems of mathematics has become a comfort and you need not to search a tutor visiting your house or to travel long distances to your tutors place to get your problems solved time to time.
 Thus we must get our self registered for the online tutor, which is available either at free or at a very nominal cost which is at your approach.  The charges for the online tutor can be based on  per hour/  per week / or sometimes based on the contract per topics in some cases.
We must get our self registered for on line tutoring in order to make our study of mathematics comfortable, interesting and enjoyable. It will create interest in the subject and remove the terror of studying the subject mathematics, which exist in most of the children. Now a day we have different tools available for learning mathematics by relating the learning method with the real life applications. So the concepts are clearer and the child starts understanding the topics easily.

You can also learn about Area Of A Rectangle Formula with the online math tutor help. Also you can collect details about Andhra Pradesh Board Of Intermediate Education online and In the next session we will discuss about Predictions from data.

Statistical methods to make inferences

Hello students,Previously we have discussed about how to do trigonometry step by step and today we are going to discuss the statistical methods to make inferences which comes under 12 gujarat board syllabus. As we know that statistics is concept by which we organize our data and display that data and this process includes complete process of the data analysis and this process starts from inspecting data to modeling data, it also covers cleaning data as well as transforming data.

Statistical methods to make inferences is a process, that uses the organized information so that it can obtain and make a final decision or conclusion and all the process is done when our system get affected by random variation and due to this some type of datasets is arises and conclusion made from obtained datasets. Statistical inferences are also known as the statistical induction and inferential statistics. Sometimes the result or final outcome of Statistical inferences can be a answer for the next questions.

Methods of statistics are also the basis of statistics type mathematics. They provide the primary research papers, various types of proofs and theorems so that we can complete our research. Descriptive and probability distribution are also assumes the methods of statistics. Lets take an example that will show the use of statistical inferences.

Example: - A card is taken from a shuffled pack of cards and the total trails are 300.

Suit Spades Clubs Hearts Diamond

No. of times drawn 70 50 100 80

Solution: - Find the probability of To got Hearts cards and Except Diamond card

-Total number of events = 300

Number of trial of hearts cards = 100

P (drawn card is heart)

100/300 = 0.33

-Total number of events except diamond card is 70 + 50 + 100 = 220

P(the card is not diamond)

220/300 = 0.73

In the next session we will discuss about free online math tutoring and You can visit our website for getting information about physics homework help.

Predictions from data

Previously we have discussed about integration worksheets and In today's session we are going to discuss about Predictions from data which comes under cbse 10th syllabus, Data prediction is an important concept based on some previous data that helps in decision making, So for data is collected and represented in the way that anyone can easily understand that data for predicting the future decision. It is the only way by which any one can easily and efficiently makes the effective plans or strategies that are totally based on the previously stored data in the specified format. Before making any predictions from data it should be noted that how data stored and collected as well as from where data is collected for future prediction.
Data should collect correctly as well as from the true resources within the specified time means at the time data is needed by someone it can be easily retrieved by them and after collection of the data it should be organized properly. For representing the series as like time related to temperature or rainfall or population growth or birth and death rates line graphs are drawn that also helps in data prediction. Polygraph is also a line graph in that two or more than two variables are shown on a same diagram by different line. These diagrams are also used for show the birth and death rates and also used for showing the growth rate of different crops.
After all the collection and organization of the data there is next important concept is representing the data. It is the only concept through which the user can understand the previously recorded data and makes some decision on that .Collection and representation of data in probability are also helpful to make the future strategies as well as helps in comparison of the data among several years for the same period of time.
There are several methods and various type of data representation like image processing , Global positioning system .The main motive behind display  of the data is to understand the available data and deriving the meaning and also extract the useful in conclusion .So Predicted Probabilities are helpful in growth of the organization.
In the next session we will discuss about Statistical methods to make inferences
and You can visit our website for getting free algebra help.