help with calculus

Calculus or can be named as mathematical analysis it is the branch of mathematics which deals in the study of change. It sometimes divided into two major concerns i.e. in differential calculus and in integral calculus which are related by the fundamental theorem of calculus. It has widespread applications in engineering, economics and science. We can help with calculus in solving the problems related to algebra where algebra alone is insufficient. The well known examples of calculus are joining calculus, lambda calculus, pi calculus, propositional calculus.

Now let’s have a brief theory about its two major concerns that is about the differential calculus and integral calculus. Differential calculus is the study of the properties and definition of the derivative of the function. Its major object of differential calculus is the derivative of the function. The procedure to find the derivative is known as differentiation. Derivative mainly works in the field of maxima and minima of the function. Those derivative functions which involve equation are called as differential equation. The derivatives and generalization appear in the many fields of mathematics like in differential geometry, measure theory, complex analysis, functional analysis, and abstract algebra.

Among its two main operations of calculus the integral calculus is its other major concept. In simple terms we can say that it is the inverse of differentiation. It is further bifurcated in definite integral and indefinite integral. The procedure of finding the value of integral is called as integration. We can also say that indefinite integral is the inverse operation of derivative which sometimes termed as antiderivative. While the definite integral inputs the function and its output is in definite numerical terms. Sometimes it is quite difficult to get answers to math problems; free online tutors are available which help you to get confidence. To get information on school boards in India, you can visit official sites of Indian education system and In the next session we will discuss about Understand Pythagorean triples.

substitution method calculator

When we study about Substitution Method Calculator, we need to know what all is the substitution method of solving the linear pair of the equations. While using the substitution method we will first convert one variable in the form of another variable and then the value of the variable is substituted.  We use the following sets of procedures to get the solution of the linear pair of equations by substitution method of solving the equations.  The steps are as follows :
1.       We will first express the variable y in terms of x in one of the given equation.
2.      Now we will substitute this value of y , which we have taken in the terms of x in other equation. This helps us to get the linear equation in form of x variable. You can also read about linear equations to sharpen your skills.
3.       Now we will solve the linear equation in form of x, which we have obtained in step 2.
4.       In next step, we will substitute the value of x, which we have just calculated in the relation which we have taken in step 1, which will help us to get the linear equation in form of y.
5.       At last, we will solve the above linear equation in form of y, to get the value of y.
Thus we observe that the result of the solution of the pair of the liner equation is the  answer of x and y, thus we find that  the value of both unknown variables is calculated with the help of substituting one variable in the equation.
 We can solve any pair of linear equations by using this method of finding the solution.

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Understand Pythagorean triples

In Geometry Tutoring we know that a natural number, n , is said to be the perfect square of the natural number, a, if n = a*a . In other words, we can say that a natural number is called a perfect square if it is the square of some other natural number. By the term square of a number, we mean that the product of a number multiplied by itself.
Then we have also learnt some properties of perfect squares. Adding to such list of properties, we will learn one important property of perfect squares here. This property of perfect squares is called the Pythagorean triples. Let’s define the term first.
Three natural numbers m, n, p are said to to form a Pythagorean triples if m  Ì‚2 + n  Ì‚2 = p  Ì‚2
The Pythagorean triples formula comes from the Phythagorean Theorem of right triangles in which the square of the length of hypotenuse is equal to the sum of the squares of the other two sides. In Pythagoras theorem, given a, b to be the two sides of a right triangle & h as the hypotenuse of the triangle, we have the relation h  Ì‚2 = a Ì‚2 + b Ì‚2. According to Pythagorean triples formula , if m is a natural  number greater than 1 , i.e., m>1, we can find a Pythagorean triples using the formula ,
( 2m , m  Ì‚2 – 1 , m  Ì‚2 +1 )
Lets take an example from Andhra Pradesh Board sample papers

Putting m = 4 , we get the Pythagorean triples as
2m = 2 * 4 = 8
m  Ì‚2 – 1 = 16 – 1 = 15
m  Ì‚2 + 1 = 16 + 1 = 17
Thus , the numbers 8, 15, 17 form the Pythagorean triples. For more information read here

This was all about Pythagorean triples. Visit our blogs for more information on Perpendicular Linesplanes and pythagorean theorem in grade vii

Properties of inscribed and circumscribed polygons of circles

Hello students, in this blog we are going to discuss about the inscribed polygon and circumscribed polygon of circle. First of all we define about the inscribed polygon that is define as polygon (also see What is a Regular Polygon) that is inscribed in a circle if all the vertices of polygon are points on the circle and circle included all the sides of polygon then it is known as inscribed circle .We can define some Properties of inscribed polygons of circles that are as follows:
Property no (1) : All regular polygons inscribed in the circle .
Property no (2) : Both inscribed polygon and circumscribed circle have the center .
Property no (3) : If we talk about the radius of inscribed circle it is also same as the radius of circumscribed circle .
When we talk about the circumscribed circle of a polygon it is define as a circle that passes through all the vertices of the polygon .We can define some Properties of circumscribed polygons of circles as follows:
Property no (1) : Center of the circle is known as circumcenter .
Property no (2) : The radius of the circle is known as circumradius .
Property no (3) : When a polygon has circumscribed circle mean that polygon is a cyclic polygon also defined as co-cyclic polygon .
When there is triangle that is also a polygon have the sides a, b and c then for inscribed circle radius r will be define as r = Ö (p – a) ( p – b) ( p – c) / p .
here p = (a + b + c) / 2 .
And also for circumscribed circle radius R is defined as
R = a * b * c / 4 Ö p ( p- a) ( p – b) ( p -c ) .

In upcoming posts we will discuss about Understand Pythagorean triples and Learn Parabolic Functions and Axis of Symmetry. Visit our website for information on syllabus of West Bengal board of higher secondary education

perpendicular lines/planes

Hello students, in this blog we are going to discuss the Perpendicular Lines Definition and planes. But before starting you should be known to the means of perpendicular. Perpendicular means anything at right angles or 90 degree.
The perpendicular lines are intersecting to each other at the right angle or 90 degree. A line has no ends and no thickness.
Another definition of perpendicular lines are, if any two line intersecting each other and forming four equal angles than it is also said to be perpendicular lines and all four angles will be equal to 90 degrees in the case of two perpendicular lines.
Some examples of perpendicular lines are : -
-We draw the graph paper, so on the graph paper, the x axis and y axis are the perpendicular lines.
-The lowest and larger axis of ellipse is also perpendicular.
Note : - In a plane, the perpendicular lines are opposite reciprocal slopes that means the slopes' products is -1. And two perpendicular lines (get more detail here) can be shown by the symbol that is reverse of T. we can make the perpendicular lines by using compass and straightedge. If any line is perpendicular to two or more lines then it will also be perpendicular to the plane. If any line is perpendicular to a plane, than every plane that having the same line will also perpendicular to that plane. We can also find the length of Perpendicular lines.
Whereas the perpendicular planes are the planes in which a plane have a perpendicular line to the other plane and a plane is a flat surface and it also has no thickness.

The perpendicular lines and perpendicular planes can be understand more, if we will see them graphically.

In upcoming posts we will discuss about Properties of inscribed and circumscribed polygons of circles and Learn Cross Sections and Planes. Visit our website for information on West Bengal board of primary education

translations

Hi friends, today in free math answers session I am going to tell you about the transformations of coordinates in which translation is one of the process of transformation that is used for change the shape or size or orientation of the given figure but first of all we have to know about the meaning of transformation that is defined as in terms of the definition of transformation that it is the way of changing the shape or appearance of the figure that is given.So when we talk about the translation that is also the part of the transformation is defined as follows:
Translations is one more method of transformation in which thing or figure that is given for transforming will only move without rotation or resizing .If we translate the thing that means all point of the figure will be on same distance and in same direction when we move a thing on its own place then it will not change its position and size .Translation transformation process is that all the points of an object will move only in a straight line and also the direction of moving is same that means the shape or size and also orientation of the object are same as the original object or thing .If we talk about the same orientation that means object and image of object are facing the same direction .
If we want to understand the translation in simple words then it will be defined as thing or object will move from one location to new location without any changes in the shape, size and orientation. If we talk about the translations in geometry it is simply define as the figure slide somewhere else means location of the figure will change only but during the movement do not change the figure in any other way means do not resize and rotate or flip it over.

In upcoming posts we will discuss about perpendicular lines/planes and Probability and Statistics in Grade XI. Visit our website for information on Andhra Pradesh school textbooks online

isosceles triangle theorem

Today in our free geometry help session we are going to discuss about isosceles triangle theorem.  Before it we have to define the isosceles triangle that is a triangle with two congruent sides.
There are several theorems based on the isosceles triangle that are as follows:
Theorem 1 : When two sides of the triangle are congruent then angles that are opposite to each other are also congruent .We can define the isosceles triangle theorem proof as follows :
As if there is a triangle XYZ then according to the theorem if XY ≅ XZ then angle Y ≅ angle z .
Theorem 2 : If in a triangle two angles are congruent then the sides of the triangle that are opposite are also congruent .It is also known as the converse theorem .we can also define the isosceles triangle theorem proof as follows :
As if there is a triangle XYZ then according to the theorem if angle Y ≅ angle z then XY ≅ XZ .
We can also create two congruent triangles by drawing the altitude in an isosceles triangle it is also proved by Hypotenuse – leg .
When we create two isosceles triangle then congruent legs of isosceles triangle change into the congruent hypotenuse and the altitude change into the shared leg.
It have some true statements regarding to a isosceles triangle as follows (find more details here):

1.     : If we create an altitude to the base of an isosceles triangle then it will bisects the vertex .it

is shown as If there is an isosceles triangle XYZ and an altitude ZA then

angle XZA ≅angle YZA

2.     : In an isosceles triangle altitude to base bisects the base .In this statement if triangle XYZ isosceles and an altitude is ZA then side XA ≅ZA .

 In upcoming posts we will discuss about translations and Math Blog on Types of events. Visit our website for information on Andhra Pradesh geography questions

Planar cross-sections

In this free algebra problem solver session we are going to discuss about the term Planar cross-sections that is used in geometry when a figure is intersected by some plane and that figure must be a solid figure and the result of intersection may be a point or line or line segment or also a plane that is such for circle or a polygon .
A planner cross section is drawn interactively that is interpolate the data along a single line usually .Planar cross-sections is usually done with the gridded data but sometimes it is also possible to do it (Planar cross-sections) with the irregularly-spaced data .If we define the gridded data it will be a model output or gridded radar volumes .
For control of the planar cross sections, configurations containing the planner cross section always contain a horizontal window. So for generate the Planar cross-sections we have to do some steps as defined:
Step no (1) : First of all move the pointer into the horizontal window and end to where you would like to be cross sections plane .
Step no (2) : When Planar cross-sections is done with the help of the computer then push and hold the middle button of mouse and pointer will move gradually and connect the line with its original location .
Step no (3) : until the desired cross section plane will not obtained drag it .
Step no (4): At last release the mouse button.
There are several planes define into the geometry ,So if a plane is parallel to the base of the solid , then plane figure is formed similar to the original or congruent to the solid base .For defining the Planar cross-sections you have to be analyze the shape and size of every geometric figure .

In upcoming posts we will discuss about isosceles triangle theorem and Measures of dispersions in Grade XI. Visit our website for information on CBSE class 12 chemistry previous years question papers