WHAT DOES A PERPENDICULAR MEAN?

A Perpendicular is any line which is stands at a right angle to the given line.
The 'perpendicularity' can be with planes or lines.
When one speaks about lines, two lines could be declared as perpendicular in two ways:

• One when the angle between them is 90 degree and so is the congruent angle too.
• Other, when the lines satisfy the condition of the perpendicularity with respect to slope.

In a graph, the condition of 2 lines being perpendicular can be observed in 3 cases:

• One when the line is having an x coordinate value = 0 and some value for the y coordinate ( a line which would be parallel to the x-axis)
• Another when the line is having an y coordinate value = 0 and some value for the x coordinate ( a line which would be parallel to the y-axis)
• Another when the product of the slopes of both the lines result in -1.(minus 1) 

This way under graphical drawings, two lines can be declared perpendicular.

Standard integrals

Integral refers to the notion of antiderivative.In a function F whose derivative is the given function ƒ,it is called an indefinite integral.

See the link given for standard integrals.

The expression of definite integral with lower and upper limit is f(x) dx . The definite integral is called as Riemann integrals. In definite integral, f(x) dx where a, b and x is the complex numbers and path of integration from a to b. The fundamental theory of calculus allows the definite integrals to be computed in terms of indefinite integrals Where F is the indefinite

integral and f(x) is continuous function. The standard form of indefinite integral is f(x) dx.Standard form of the definite integral with an interval a to b is given as : f(x) dx = F(b) - F(a).    

Molecularity

In chemistry, molecularity is the number of colliding molecular entities that are involved in a single reaction step. While the order of a reaction is derived experimentally, the molecularity is a theoretical concept and can only be applied to elementary reaction.The reaction order, the molecularity and the stoichiometric coefficient are the same in elementary reaction although only numerically, because they are different concepts.

Here is provided a link on pure and applied chemistry

Elementary reactions are classified according to their molecularity. The number of reacting species involved in simultaneous collision to bring about a chemical reaction is called the molecularity of the reaction.

Simultaneous equation

In algebra,If a set of linear functions describe a single situation, then it is called as a set of simultaneous equations.

Solving high grade simultaneous equation by elimination method:

A set of simultaneous equations can be solved by different methods - Substitution method, Elimination method, Matrix method, Determinant method and Graphical method.

You can also see the link on How to Graph Set of Linear Functions or Simultaneous Equations

Let us take an example of solving simultaneous equation by elimination method:

Solve the following simultaneous equations by using the elimination method:

Solution:

Label the equations as follows:

Notice that 3y appears on the left-hand side of both equations.  Adding the left-hand side of (1) and (2), and then the right-hand sides, gives:

  

 

Algebra 2

Algebra 2:
Algebra 2 includes quadratic equations, graphing, complex numbers, functions, sequences and series, and exponents and logarithms. Problem solving skills are given importance and time is devoted to advanced topics like telescoping sums and piecewise functions.Need help on Algebra 2? See the link on Free online algebra 2 help

Algebra 2 homework:
In the home work we get different types of problems, solving equation like Addition , subtraction , multiplication , division and like solving polynomials , inequalities, word problems ,exponents graphing equation like etc…

You can avail Algebra 2 help free online. Here you will have the chance to get free session on Algebra 2 . You can experience the teaching and decide to avail online help from tutors according to your satisfaction.

Algebra 1

Algebra 1:

Algebra 1 is an important topic in mathematics. All about algebra 1 is used to understand all the concepts which are in algebra 1 can be learned in a very efficient and effective way of understanding the problems also the definitions for the terms.It is used to solve the different problems and it brings a very good knowledge in algebra 1.You can get to know the basic concepts on algebra 1 online.

Also see the link on online algebra 1 help.

 

Topics on Algebra:

Algebra 1 covers the following topics:

1) Algebra in finance 2) Functions, domain, not graphing 3) Coordinate systems, graph plotting etc. 4)graphs, graphing equations and inequalities 5)real numbers, irrational numbers, etc. 6)Absolute value 7)logarithm 8) system of linear equations 9) square root, cubic root, n-th root 10) negative and fractional exponents 11) expression involving variables, substitution etc.

Solving two step equations

Two steps equations: It is an equation that needs only two steps for solving.

Solving two steps equations: How to solve two step equations need to follow few rules in order to have only variables on one side of the equal sign and numbers on the other side of the equal sign. The another goal is to have the number in front of the variable equal to one. The variable does not always have to be

Solving two step equation activities is used to calculate the equation in a single step. Solving two step equations calculator give out the result instantly without performing complex steps.

Incentre of Triangle

Incenter of triangle: The point of the intersection of any two internal bisectors of the angles of a triangle is called the incentre of the triangle. The incentre of a triangle is denoted by the symbol I.

Theorem on incenter of triangle: The angle bisectors of a triangle pass through the same point.

If you want to know more about triangle see the link on congruent triangles.

You will also find the incentre of a right triangle. For more information on this, visit online websites for help.

Three dimensional geometry

Introduction to three dimensional geometry: Three dimensional shapes have 3 dimensions - length height and depth .They are of solid shapes and have faces , vertex (vertices's) and edges . Face or plane is a flat surface , vertex is the corner of a solid shape.The meeting lines of the faces of a 3 dimensional shape meet is called the edge. 

I will provide you a link on geometry theorems and constructions

Here you can learn the basics of geometry.

Examples of 3 dimensional shapes:cube , prism , pyramid , cone , cylinder and sphere are examples of 3 dimensional shapes.A prism having a triangle base is known as triangular pyramid . 

Scientific notation

Scientific notation: 

Scientific notation is a way of representing a very large number or a very small numbers in the form of shorthand. It is developed for saving time by using less characters. This adjustment is based on the power of base ten.Scientific characters provides a place to hold the zeroes that appear after a whole number or  a fraction.

Examples on how to write scientific notation:

The followings are scientific notation examples.

Fraction = 1/100

Decimal = 0.01

Scientific notation = 10^-2

Fraction = 1/10

Decimal = 0.1

Scientific notation = 10^-1

Number = 1

Scientific notation = 10⁰

Number = 10

Scientific notation =10¹

Number = 100

Scientific notation = 10²

Number = 1000

Scientific notation = 10³

Centroid of a triangle

What is a centroid?

The point through which all the mass of a triangular bowl seems to act is called the centroid. 

In the diagram above, the medians of the triangle are shown.

The following points are facts about centroid.

1)The centroid is consistently inside the triangle.

2)Each median divides the triangle into two triangles of same area.

3)The centroid is absolutely two-thirds the way forth each median. 

Centroid formula of a triangle:

A centroid of a triangle is the point where the medians of the triangle intersect. If the three vertices are a = [x_a, y_a], b = [x_b, y_b] and c= [x_c, y_c] then the centroid is given by

      C = (1 / 3) (a + b + c)

 

                            C = ((1 / 3) (x_a + x_b + x_c), (1 / 3) (y_a + y_b + y_c))