Mathematics process

Welcome to free math tutor online,

Is mathematics a process? Is it a collection of facts, or patterns, or
theorems? Would mathematics continue to exist if all conscious beings
were eliminated from the universe? Do the theorems that we haven't yet
worked out already exist, in some implicit form? Or do they come into
being only when they become known?

This is why I think you should read 'A conversation with Einstein's
brain'. It's pretty short, wonderfully written, and it will give you a
_lot_ to think about with respect to this issue. examples on math helper; (That way, regardless
of how the essay comes out, the experience won't have been a complete
waste of your time.) more examples on online math forum.

Get help with Algebra

College algebra problems have different types of topics. The college level math problems we have the following sets, logic, real number systems, functions and their graphs, probability and Statistics and some topics from algebra and geometry. The college math problems give much importance for all topics.Their are various methods to get algebra help online.Online Math problem is expected to be one of the smart trials, as it supplies the part an excellent chance to work out. The event is all about trying the originality and logical skills of a person and making mathematics fun.It is not a very difficult task to get online algebra tutor in today's age of technology.In the coming blogs we will see the methods of getting online algebra tutoring.
Hope you like the above example of get help with algebra,please leave you comments if you have any doubts.

Help with word problems

Let us get help understanding about word problems in this blog.online math word problems To solve online math word problem solving are helps the students to know the details of the given problems easily because here no notes to be taken by the students. It is clearly states about the problems in step by step process. In the growth of technology now days, students are studying their subjects through online methods only because it saves their valuable times.Usually students are asked to solve math word problems for homework. If students face any problem with solving these problems they can get free math tutoring online.Hope you like the above example of Help with word problems,please leave your comments if you have any doubts.

get answers on Pre-Calculus

We can get help on Free precalculus answers,pre calculus, (or Algebra 3 in some areas) an advanced form of secondary school algebra, is a foundational mathematical discipline. It is also called Introduction to Analysis. In many schools, pre calculus is actually two separate courses: Algebra and Trigonometry. Pre calculus does not prepare students for calculus as pre-algebra prepares students for Algebra I.Most of the students face problems while solving the calculus homework.

In the next blog we will learn about online precalculus answers. Hope you like the above example of get answers on pre-calculus,please leave your comments if you have any doubts.

Get help with Calculus

We can get calculus help online, The AP calculus is advanced version of calculus. In high school, AP calculus is widely used. We need learn about general formulas for solving AP calculus problems. AP Calculus is classified as differential calculus and integral calculus. Different problems are used for solving the AP calculus problems.
In recent times it is seen that various online calculus courses are available, The online calculus courses is common and open to everyone around the world. Students from anywhere can enroll in this online calculus courses. There is no need of class meetings in online calculus courses. Online calculus courses include limits, derivatives, applications of derivatives, integrals and application of integrals. In online calculus courses, students can attend final exam at their home or anywhere around the world.In the next blog we will learn about calculus online.

Hope you like the above example of Get help with Calculus,please leave your comments if you have any doubts.

Math Reasoning

Welcome to free math tutors online,
one problem here is that math often _doesn't_ tell the
truth - about the real world, that is. Math is based on reasoning from
stated premises (axioms); as long as those are true, and we don't make
mistakes in our reasoning, the results have to be correct. help in math; But those
axioms deal with an ideal world, not the real one in which lines are
made of atoms with a finite size, "space" may be curved by gravity,
and so on.

So it's easy to find cases where math gives a wrong result
- not because the math itself was wrong, but because it was applied to
an incompletely understood reality, or one that differs in small but
important ways from our assumptions. continue learning on math forum.

Mathematician and physicist

Welcome to math helper,

A mathematician and a physicist were arguing over whose field of
study was better. They decided to settle the argument by posing
questions. The mathematician went first, and posed a complicated
mathematical problem.

With a great deal of effort, math forum; several books
of mathematical tables and techniques, and a few hours, the
physicist gave the solved problem to the mathematician, who was duly
impressed.

More explanations on free math tutor.

Math common factors

Welcome to free math homework help,
Well, the main reason for identifying common factors is to let you see
more deeply into the pattern. In this case, once we get the 4b^2 out
in front, math forum; we can see that we have a standard quadratic form in y,
which we can simplify even more:

4b^2y^2 - 20b^2y + 24b^2 = 4b^2(y^2 - 5y + 6)

= 4b^2(y - 2)(y - 3)

Now, why is _this_ form preferable? Well, for one thing, if the '?'
is a zero, as it is in 'standard' form, then we know that

4b^2(y - 2)(y - 3) = 0

Just by looking at this, we can see that if b is non-zero, there are
only two possible values of y that can make this equation true:
y = 2 and y = 3.
examples available on free math help online.

Math construction

Welcome to free math tutoring,
If you tied a string around the entire earth, and you wanted to add
enough string to lift it one inch off the ground everywhere,online math forum; you would
have to add the same amount of string -- about 6 inches!

On the other hand, does it surprise you that you can construct two
triangles of vastly different size, e.g.,

            |                        |
      5   / |                      / |
        /   |  4                 /   |
      /     |         75,000   /     |
    /_______|                /       |  60,000
                           /         |
        3                /           |
                       /             |
                     /_______________|

                          45,000

that contain exactly the same angles? One answer to your question is
just that scaling doesn't always work the way you expect it to.learn more on math forum.

Math learning tips

Welcome to free math tutor online,

Now, here's the thing: If you wait until the night before the test to
try to learn the material, it's probably not going to work. A better
way to use your book would be this: If your teacher is going to talk
about section 6.3 tomorrow, you should read that section tonight and
try to answer all the practice questions.

If you can answer them all,
then you can just treat the next day's class as a review session. online math forum; But
if you can't answer them all, then the next day in class you can ask
the teacher to go over the ones you couldn't do - which shouldn't be a
problem, since that's the material he or she is supposed to be
covering anyway. learn more on math forum.

Inverse Operations

-->
Inverse Operations:Let us see what we mean by inverse operations, In mathematics, when an operation do the reverse of another operation we can say the operations are inverse operations. By studying the inverse operations with example problems we can do our exams easily.Let us see what we mean by order of operations.Why do we need order of operations calculator and is there a need for learning this concept?The answer is a big YES. We need to learn the concept since Math is a universal language where everyone should work the same way, this could be done with some predefined rules. The evaluations of an expression could be an easy process but need to follow the order of operations to get the right answer for the given expression.Hope you like the example of Inverse Operations,please leave your comments if you have any douts.

mathematical reality

Welcome to help with math problems,
If you are concerned that there may be no reality beyond your own
perception, I think you can relax. The kind of philosophy you are
struggling with has trouble dealing with the surprising "reality" of
math, among other things.

The fact that this mathematical "language,"
which fits together so beautifully, turns out to fit the reality we
perceive, should encourage us to believe that what we perceive has an
order to it far deeper than our own imagination could build (do your
dreams have such order and consistency?), and therefore has some
reality beyond ourselves. Most of us, because we don't think deeply,
aren't surprised that math "works";

you have recognized that there is
no reason to assume that the "reality" of free math and the "reality" of
perception would fit together at all, so math becomes a surprise that
makes you re-evaluate your philosophy. That's good.
I hope the above explanation was useful, now let us study more example on online math forum.

Math & perceptibility

Hi,
Let me welcome you to our online math tutors page,

Let us study about math & perceptibility in this free math tutoring online,
I think that mathematics cannot give an exact representation of
reality in the sense of perceptibility - even things that I think
myself are perceptible because I can 'see' or 'hear' the things I
think, because if I don't, I don't think.

So there is no reality beyond perceptibility. There is only
perceptibility.

You cannot say 2 + 3 = 5, because 2 is not three is not five. How
can two things (2 and 3), neither of which is identical to 5, be
identical to five if they are united? 5 in itself is also
an independent "being." If it weren't, it indeed could exist as a
collection of at least two other 'entities'. learn more in online math forum.

Math Abstraction

Welcome to Online math tutor,

It is often found that a concept that is first encountered in one part
of our experience turns out to be useful in other areas as well.
Having solved a problem in one context, we don't have to solve it
again, because we solved it abstractly.

For example, a common problem
is to find the number of sides and diagonals of a polygon. It turns
out that the same solution applies also to a question about the number
of handshakes that occur if everyone in a room shakes hands with
everyone else, and also to a problem about the number of different
ways a student could choose two classes to take. you can get more out of math help.

They all look the same when you think of them abstractly. If I know the solution to one
of these problems, I can transform a new problem into the known
problem, and quickly find the answer. That kind of thinking is central
to what math is.

now let take you to math forum,

Math in daily life

We use math in our daily life,
For instance, When you look at a road map and try to figure out how to get from one place to another - you're doing free math tutoring to yourself. The map is an abstract representation of the world that allows you to do certain useful things with it.
Its so funny, We use free math that we don't know ourselves.
When a scientist tries to analyze something about the world, to understand how it works, and describe it in a way that tells us something important about how things behave - they're doing math.
I hope the above examples helped you, get your free online tutoring math problem solver here.

Introduction to what is the greater than sign

Introduction to what is the greater than sign:
In mathematics, the inequality plays the main role. In inequality we have many signs like less than, greater then, less than or equal to, greater than or equal to .In this symbol for What is the greater then sign is “> “.

This what is the greater then sign specifies that the left hand side of the greater then sign is greater then the right side constant or variable.
Symbols and Rules on What is the Greater than Sign:
Symbols - What is the greater then sign:
* > is the greater then sign.
* > = is the greater then or equal to sign.
* >> is the much greater then sign
I hope the above explanation was useful, now let me explain factors of 27

Differential Equation & Indefinite Integrals

Let us study about Differential Equation,

Differential Equation : A differential equation is a relation between the independent, dependent variables and their differential coefficients.
Indefinite Integrals : The expression ∫ f(x) dx is read "the indefinite integral of f(x) with respect to x," and stands for the set of all antiderivatives of f. Thus, ∫ f(x) dx is a collection of functions; it is not a single function, nor a number.

I hope the above explanation was useful.

Coordinate plane

Let us study about Coordinate plane,

The math term plane is a two dimensional flat surfaced with no thickness spanned with two linearly independent vectors and its extends its boundary forever. The generalization of the math term plane with higher dimension is called a hyper plane and the angle between the two intersecting plane is called dihedral angle.

In the term plane, there is only two axis are there,

* X axis (width);
* Y axis(Length)

I hope the above explanation was useful.

What is polygon centroid

Let us study about Polygon Centroid,

Introduction to calculating centroid:
Centroid should be a point over the figure or diagram at which the whole mass of the body acts. It must be the center point of complete figure. The calculating centroid of the straight line must be its middle point. When the diagram is triangle, calculating centroid should be a point which the medians are cross. These are intersecting with the ratio of 2:1.

Finding Centroid of the Triangle:

The co-ordinates of the triangle are (x₁ , y₁), (x₂, y₂) and (x₃, y₃). Therefore, the formula for calculating centroid of that triangle is,

((x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3)

I hope the above explanation was useful.

What is Acute Triangle

Let us study what is Acute Triangle,

Introduction to an acute triangle can have:

An acute triangle article deals with the defintion of acute triangle and the properties of the acute triangles

Acute triangle having all three angles are less than 90 degrees and with different side lengths.This triangle contain three internal angles and these internal angles sum up to 180 degrees.Acute triangle is two-dimensional closed three-sided shape .we have different terms and formulas to find the area and perimeter of the acute scalene triangle.

I hope the above explanation helped you, now let me explain about Perimeter of circle.

Explain Perimeter of a triangle

Let us study what is Perimeter of a triangle,

Triangle is a three sided polygon, the sides are closed three line segments. To calculate perimeter of a triangle in calculator we know three sides of a triangle. The perimeter of a triangle is measured in terms of units. Let we learn about how to find perimeter of a triangle calculator.
Perimeter of a Triangle Calculator:

The formula for perimeter of a triangle used calculator is

Perimeter p = a + b + c units, where a, b and c are the three sides of a triangle.

I hope the above explanation was useful.

How to factor polynomial equations

Let us learn How to factor polynomial equations,
A "quadratic" is a polynomial that looks like "ax²+ bx + c", where "a", "b", and "c" are just numbers. For the easy case of factoring, you will find two numbers that will not only multiply to equal the constant term "c", but also add up to equal "b", the coefficient on the x-term. For instance:

* Factor x² + 5x + 6.

I need to find factors of 6 that add up to 5. Since 6 can be written as the product of 2 and 3, and since 2 + 3 = 5, then I'll use 2 and 3. I know from multiplying polynomials that this quadratic is formed from multiplying two factors of the form "(x + m)(x + n)", for some numbers m and n. So I'll draw my parentheses, with an "x" in the front of each:

(x )(x )

Then I'll write in the two numbers that I found above:

(x + 2)(x + 3)

This is the answer: x² + 5x + 6 = (x + 2)(x + 3)
I hope the above explanation helped you.

circle circumference

Let us study about Circle Circumference,
The circumference of a circle is the actual length around the circle which is equal to 360°. Pi (p) is the number needed to compute the circumference of the circle.
p is equal to 3.14.
Pi is greek and has been around for over 2000 years!

In circles the AREA is equal to 3.14 (p) times the radius (r) to the power of 2.
Thus the formula looks like:
A= pr2.

In circles the circumference is 3.14 (p) times the Diameter.
Thus the formula looks like:
2pr or pd.

Example :

A circular swimming pool has a radius of 14 m. Find the circumference of the pool.

Solution:






So, the circumference of the pool is 88 m.

Note:


I hope the above explanation was useful.

Operations with Algebraic Fractions

Let us study about operations with Algebraic Fractions,

Operations with Algebraic Fractions :


There are many techniques that will simplify
your work as you perform operations with algebraic fractions. As you review these examples, note the steps involved in each operation and any methods that will save you time.

Reducing algebraic fractions

To reduce an algebraic fraction to lowest terms, first factor the numerator and the denominator; then cancel, (or divide out) common factors.

Example : Reduce.
Warning: Do not cancel through an addition or subtraction sign as shown here.
Hope the above explanation was useful.

Conditional Probability

Let us study about conditional probability,
Sometimes you have more information than simply total outcomes and favorable outcomes and, hence, are able to make more informed judgments regarding probabilities. For example, suppose you know the following information: In a particular village, there are 60 women and 40 men. Twenty of those women are 70 years of age or older; 5 of the men are 70 years of age or older. See Table 1 .


What is the probability that a person selected at random in that town will be a woman? Because women constitute 60 percent of the total population, the probability is .60.

What is the probability that a person 70+ years of age selected at random will be a woman? This question is different because the probability of A (being a woman) given B (the person in question is 70+ years of age) is now conditional upon B (being 70+ years of age). Because women number 20 out of the 25 people in the 70+ years-old group, the probability of this latter question is 20/25, or .80.

Conditional probability is found using this formula:
which is read: The probability of A given B equals the proportion of the total of A and B to the total of B. The vertical bar in the expression A| B is read given that or given.
I hope the above explanation was helpful.

The Nullspace of a Matrix

Let us study the Nullspace of a Matrix,

The solution sets of homogeneous linear systems provide an important source of vector spaces. Let A be an m by n matrix, and consider the homogeneous system

Ax = 0

Since A is m by n, the set of all vectors x which satisfy this equation forms a subset of R n . (This subset is nonempty, since it clearly contains the zero vector: x = 0 always satisfies A x = 0.) This subset actually forms a subspace of R n , called the nullspace of the matrix A and denoted N(A). To prove that N(A) is a subspace of R n , closure under both addition and scalar multiplication must be established. If x1 and x2 are in N(A), then, by definition, A x1 = 0 and A x2 = 0. Adding these equations yields
which verifies closure under addition. Next, if x is in N(A), then A x = 0, so if k is any scalar,
verifying closure under scalar multiplication. Thus, the solution set of a homogeneous linear system forms a vector space. Note carefully that if the system is not homogeneous, then the set of solutions is not a vector space since the set will not contain the zero vector.
Hope the above explanation helped you to know about Nullspace of a matrix, now let me explain you about matrices and determinants.

Right Circular Cylinders

Let us study about Right Circular Cylinders,
A prism shaped solid whose bases are circles is a cylinder. If the segment joining the centers of the circles of a cylinder is perpendicular to the planes of the bases, the cylinder is a right circular cylinder. In Figure 1, cylinder (a) is a right circular cylinder and cylinder (b) is an oblique circular cylinder.

Figure 1 Different types of circular cylinders.

Lateral area, total area, and volume for right circular cylinders are found in the same way as they are for right prisms.

If a cylinder is pictured as a soup can, its lateral area is the area of the label. If the label is carefully peeled off, the label becomes a rectangle, as shown in Figure 2

Figure 2 The lateral area of a cylinder.

The area of the label is the area of a rectangle with a height the same as the altitude of the can and a base the same as the circumference of the lid of the can.

Theorem: The lateral area, LA, of a right circular cylinder with a base circumference C and an altitude h is given by the following equation.




Theorem: The total area, TA, of a right circular cylinder with lateral area LA and a base area B is given by the following equation.

Theorem: The volume of a right circular cylinder, V, with a base area B and altitude h is given by the following equation.

Example 1: Figure 3 is a right circular cylinder; find (a) LA (b) TA and (c) V.

Figure 3

Finding the lateral area, total area, and volume of a right circular cylinder.

Hope the above explanation helped you.

Rectangle

Introduction:
It is very easy to identify a Rectangle,it is a square figure we can find many objects around us of this shape.
A rectangle is a four-sided polygon and a flat shape with straight sides. Here every angle is a right angle (90 degree). And also opposite sides of rectangles are equal length and parallel.

A crossed rectangle is a complex rectangles, also called a butterfly rectangle or bow-tie rectangle .The rectangles are used to many episodic tessellation patterns, in stonework.



Properties and Formula of rectangles:

A simple rectangle has the following Properties:

* Rectangle is an isogonal..
* In rectangles, the two diagonals are equal in length.
* And also opposite sides are equal in length.
* Rectangle has two lines of rotating symmetry and reflection symmetry of order two.
* The double polygon of a rectangle is a rhombus. It is cyclic and convex.
* All angles are 90 degrees.
* The two diagonals bisect each other.
* Opposite sides are parallel.

Formula:

If a simple rectangle has length l and width w,

* Area A = lw,
* Perimeter P = 2l + 2w = 2(l + w),
* Each diagonal has length √l2+w2
* And when l = w, the rectangle is a square.

Examples of rectangles:

Example 1:

Find the area of rectangles with the given length 5 cm and width 6cm.

Solution:

Area = l * w

= 5 * 6

= 30 cm2

Answer: 30 cm2

Example 2:

Find the Perimeter and Area of rectangles with the given length 8 cm and width 10 cm.

Solution:

Perimeter P = 2(l + w)

Here we can add the values of length and width and multiplied by 2.

=2(8+10)

=2(18)

=36 cm

Area A = l * w

= 8 * 10

= 80 cm2

Answer: 80 cm2

Hope you like the above example of Rectangle.Please leave your comments, if you have any doubts.

Grouped Frequency

Grouped Frequency:

Before we get into the details of what is grouped frequency,let us first learn about the meaning of frequency.

What is the meaning of Frequency??

A frequency distribution is a tabular collection of data showing the frequency of each observation.

Frequency distributions are two types:

* Discrete frequency distribution
* Grouped frequency distribution

Grouped Frequency:


The grouped frequency table is the frequency data value that occur the number of times in the frequency table. It is the particular value that occur number of times in the grouped frequency table.

For example if five students have scored 90 marks in mathematics in a test

Then the mark scored 90 is the frequency of 5 members. Here f can be represented as frequency of grouped frequency table.

The frequency table can be constructed by arranging collected data value. The frequency tables are arranged in ascending order by magnitude with their corresponding frequencies.Now let us look at few examples of Grouped Frequency.

Example of Grouped Frequency Table:

Grouped frequency distribution

If the number of observation is large and the difference between the greatest and the smallest observations is large, then condense the data into classes or groups

There are two methods classifying the data according to the class interval:

* Exclusive method
* Inclusive method

Methods of Classifying Data:

Exclusive method:

when the class intervals are so fixed that the upper limit of one class is the lower limit of the next class, it is called Exclusive Method of classification. In this method upper limit of the class is not included in the class.

Inclusive Method:

In this method the classes are so formed that the upper limit of a class is included in that class.
Hope you like the above example of Grouped Frequency.Please leave your comments, if you have any doubts.

Pie Chart:

Pie Chart:

A circle is divided by several radii into sectors whose relative areas represent the relative magnitudes of quantities or the relative frequencies of items in a frequency distribution.The basic understanding of a Pie Chart is A pie chart (or a circle graph) is a circular chart divided into sectors, illustrating proportion. In a pie chart, the arc length of each sector (and consequently its central angle and area), is proportional to the quantity it represents. When angles are measured with 1 turn as unit then a number of percent is identified with the same number of centiturns. Together, the sectors create a full disk. It is named for its resemblance to a pie which has been sliced.


A pie chart is a tool that helps you visualized the relative importance of several diagrams... A histogram is a diagram which graphically depicts the variability in a process

These are best used with categorical data to help us see what percentage of the whole each category constitutes. These Pie charts require all categories to be included in a graph. Every graph always represents their entire segments.

Draw a pie chart to display the information.

Solution:

Total weekly expenditure in house = 250 + 300 + $85

= $635

Find the percentage of total expenditure of each item

Percentage:

Fruits = (250 / 600)100% = 41.6%

Vegetable = (300 / 600) 100 = 50%

Oils = (85 / 600) 100 = 14.1%

If we draw the pie chart, divide the circle into hundred parts. Allocate the percentage parts require for each item.

Uses:

A pie diagram can be used in various applications. For instance, this is mostly used in government to represent cities and the statistical information that relates to income, age, gender and race. A pie chart makes the information more easily and understood as a graphical representation of the statistics.

Hope you like the above example of Pie Chart.Please leave your comments, if you have any doubts.

Binomial Distribution

Binomial Distribution:

Introduction to Binomial Distribution:

The general meaning of a Binomial Distribution is if two mutually exclusive possible outcomes are available means binomial distribution happen.Discrete probability distribution concept is used..It sequence of success in numbers.In binomial distribution,two outcomes are referred.One outcome is success and another one is failure.Probability f success in trials with probability of success on single trial is determined by binomial distribution.p is denote the binomial distribution.


Binomial Distribution is a statistical experiment which means the number of successes in n repeated trials of a binomial experiment. It is also called as Bernoulli distribution or Bernoulli trial.To understand any concept an example is required,now let us look at an example of Binomial Distribution.

For example:

For a clinical trial, a patient may live or die. Here the researcher faces the number of survivors and not how much time the patient lives after treatment.


Properties and Formula for binomial distribution:


For example:

For a clinical trial, a patient may live or die. Here the researcher faces the number of survivors and not how much time the patient lives after treatment.

We take a coin and flipped two times. Here we calculate the count of number of heads(successes). So the binomial distribution is

Number of heads Probability

No head 0.25

One head 0.5

Two head 0.25


Properties of Binomial Distribution:

1. The experiment has n repeated trials.
2. Each trial can have two possible outcomes. One is success and another one is failure.
3. Here the trials are independent.
4. Mean = n * P.
5. Variance = n * P * (1 – P).
6. Standard Deviation = sqrt[ n * P * ( 1 – P ) ].

Binomial distribution Formula:

b(x; n, P) = nCx * Px * (1 - P)n – x

Here the Notation are,

B(x; n, P) = Binomial Probability.

X = successes

N = number of trials

P = Probability of success

nCx = Number of combinations of n trials, x is success.


Example Problem(the binomial distribution):

A die is tossed 6 times. What is the Probability of getting exactly 2 fours?

Solution

Here n = 6, x = 2, probability of success on a single trial = 1/ 6 or 01.167.

Therefore, The binomial probability is,

b( 2; 6, 0.167 ) = 6C2 * ( 0.167 )2 * ( 1 – 0.167)6 – 2

= ( 6! / 2! * (6-2)!) * 0.0279 * ( 0.833)4

= (6! / 2! * 4!) * 0.0279 * 0.481

= 15 * 0.0279 * 0.481

b( 2; 6, 0.167 ) = 0.201. Answer.


Hope you like the above example of Binomial Distribution.Please leave your comments, if you have any doubts.

Poisson Distribution definition:

Poisson distribution definition:
The Poisson distribution theory is explained in detail below:
In statistics,the cases of probability theory consists of the Poisson distribution of large numbers are discrete probability distribution that relates the probability of a many cases done in a fixed time period. When the event occurs with an average rate & independently of the time.Also be used for the some events in other specified intervals such as distance,volume or area .

Formula for Poisson Distribution:

If the expected case of the number of cases in this interval is λ, that the probability there are exactly n occurrences(n being a non-negative integer, n = 0, 1, 2 ...)is equal to

f (n:ג)=(גn* e-ג)/n!

where,

* e is the base of natural logarithm(e = 2.71828...).
* n is the some occurrences of an event happens mutually the probability of which is given by the function in study poison distribution.
* n! is the factorial of n.
* λ is the positive real number is equal to the expected number of occurrences that may occur during the given interval.If the events occurs on average four times per minute, and are interested in the number of events occurring in a ten minutes interval, would use as the model a Poisson distribution with λ = 10×4 = 40.

The study of Poisson distribution can applying to various systems with a large number of possible events, each of rare. A classic example is the nuclear decay of atoms.

Algorithm for poisson distribution

Algorithm:

algorithm :Poisson random number:

init:

Let L ← e−λ, k ← 0 and p ← 1.

do:

Generate uniform random number u in [0,1] and let p ← p × u.

while p > L.

return k − 1.

Hope you like the above example of Poisson Distribution.Please leave your comments, if you have any doubts.

Permutations and combinations:

Permutations and Combinations:
When we talk about the concept of Permutation and Combination,the basic meaning of permutation is rearranging in an ordered fashion,and the combination means the selection of a number of things taking some or all of them at a time.The permutation and combination takes place on different types of objects. The permutation of a different object is the number of different ways they can be ordered i.e. which is first, second, third, etc. If you desire to choose some objects from a larger number of objects, the way you place the chosen objects is also important. When comes to combination, on the other hand, one does not consider the order in which objects were selected or placed, just which objects were selected.

Permutation:

Permutation has two types:

* Permutation with Repetition.
* Permutation without Repetition.

Permutation with Repetition:

When we have n different objects then we have n choices each time. And if we are in a position to choose object r from n objects, the permutations are

n * n * n…..(r times) = n r

P (n, r) = n r

Permutation without Repetition:

In permutation without Repetition, we have to reduce the number of available choices each time. When we have n different objects then we have to reduce 1 from the previous term for each time.

This is like n * (n-1) * (n-2)….

And if we are in a position to choose r objects from n objects, the combination is

P (n, r) = [(n!)/((n-r)!)]

Example:

In how many ways a man can put 4 balls in 3 bags.

Solution:

First ball can put in 3 ways.

Second ball can put in 3 ways.

Third ball can put in 3 ways.

Fourth ball can put in 3 ways.

So the 4 ball can put in 3 * 3* 3* 3 =34 = 81 ways.

Combination:

Combination has two types:

* Combination with Repetition.
* Combination without Repetition.

Combination with Repetition:

We need to do is alter our permutations formula to reduce it by how many ways the objects could be in order but the order is not important here.

C (n, r) = [(n!)/(r!(n-r)!)]

Combination without Repetition:

When we have n different objects and to select r objects with repetition we have a formula

C (n, r) = [(n+r-1)/(r!(n-r)!)]


Example:

Write all the combination of four balls taken one at a time.

Solution:

Here n=4 and r=1

4C1= [(4!)/(1!(4-1)!)]

4C1= [(4 * 3 * 2 *1)/(1 * 3!)]

4C1= [(4*3*2*1)/(1*3*2*1)]

4C1 = 4.

Hope you like the above example of Permutations and Combinations.Please leave your comments, if you have any doubts.

Parabola

Parabola:




Parabola:

Let us learn about the meaning of a Parabola,and also let us learn to solve the equation of a Parabola.

The locus of a point whose distance from a fixed point is equal to its distance from a fixed line is called a parabola. That is a parabola is a conic whose eccentricity is 1.

Standard equation of a parabola :


Given :
Fixed point (F)
Fixed line (l)
Eccentricity (e = 1)
Moving point P(x, y)
Construction :
Plot the fixed point F and draw the fixed line ‘l’.
Drop a perpendicular (FZ) from F to l.
Take FZ = 2a and treat it as x-axis.
Draw a perpendicular bisector to FZ and treat it as y-axis.
Let V(0, 0) be the origin.
Drop a perpendicular (PM) from P to l.
The known points are F(a, 0), Z(− a, 0) and hence M is (− a, y).
By the definition of a conic,
FP / PM = e = 1 ⇒ FP2 = PM2
(x − a)2 + (y − 0)2 = (x + a)2 + (y − y)2
x2 − 2ax + a2 + y2 = x2 + 2ax + a2 which simplifies to y2 = 4ax.
This is the standard equation of the parabola.


Ellipse:

An ellipse is a conic obtained on slicing across obliquely one nappe of a cone.If P is any point on the ellipse and
F1and F2 its foci, the angle subtended by F1P and F2P with the tangent at P are equal and if a source of light or sound is
placed at one focus of an ellipsoidal reflector (surface generated by revolving an ellipse about its major axis) all the
waves will be reflected so as to pass through the other focus



Hyperbola:

A hyperbola is a conic obtained on slicing a double napped cone by a plane parallel to the axis of the cone. The lines from the foci to any point of a hyperbola make equal angles with the tangent at that point. Hence if the surface of a reflector is generated by revolving a hyperbola about its transverse axis, all rays of light converging on one focus are reflected to the other.

Hope you like the above example of Parabola.Please leave your comments, if you have any doubts.

Conditional Probability:

Conditional Probability:

What do we understand by the term Conditional Probability??? And what is the meaning of the term Conditional Probability??? Let us now find answers to these frequently asked questions.Suppose the two events are not independent, that is the occurrence of one depends on the occurrence of other, then how do we compute This can be explained by conditional probability.

Baye's theorem is named after the British mathematician Thomas Bayes who published it in a research paper in 1763. It gives one of the important applications of the conditional probabilities by using the additional information supplied by the experiment or the past records.

Conditional Probability

Let A and B be any two events associated with a random experiment. The probability of occurrence of event A when the event B has already occurred is called the conditional probability of A when B is given and is denoted as P(A/B).

Solving Coin problems

In algebra we deal with the word problems involve pennies, nickels , dimes and half quarters. To solve such type of problems we need prepare tables.

Probability using Z score

By using Z-scores, normal distribution is standardized. We can find probability for standard normal distribution using Z-scores. Using random variable, mean and standard deviation, Z-scores are calculated.

Hope you like the above example of Conditional Probability.Please leave your comments, if you have any doubts.

Properties of Proportions

Learn us study properties of proportions,
The four properties that follow are not difficult to justify algebraically, but the details will not be presented here.
Property 1 (Means-Extremes Property, or Cross-Products Property): If a/b = c/d, then ad =bc. Conversely, if ad = bc ≠ 0, then and .


Example 1: Find a if a/12 = 3/4.
By Property 1:

Example 2: Is 3 : 4 = 7 : 8 a proportion?
No. If this were a proportion, Property 1 would produce


Property 2 (Means or Extremes Switching Property): If a/ b = c/ d and is a proportion, then both d/ b = c/ a and a/ c = b/ d are proportions.
Example 3: 8/10 = 4/5 is a proportion. Property 2 says that if you were to switch the 8 and 5 or switch the 4 and 10, then the new statement is still a proportion.
If 8/10 = 4/5, then 5/10 = 4/8, or if 8/10 = 4/5, then 8/4 = 10/5.
Hope the above explanation helped you.

Orthocentre

Orthocentre:
Let us firstly learn about the definition of Orthocentre.
Definition of Orthocentre of Triangle:

The point of concurrency of the three altitudes of a triangle is called its "Orthocentre". It is generally abbreviated as 'O'.

To locate orthocentre it is sufficient to draw altitudes of any two sides of a triangle. The third altitude will then automatically pass through it.


Theorem on Orthocentre of Triangle:

The Theorem of Orthocentre of Triangle says that in a triangle, the three altitudes pass through the same point.

Given:

In DABC, AD, BE and CF are the altitudes.
To prove Theorem on Orthocentre of Triangle:

AD, BE and CF are concurrent (or pass through the same point)
Construction:

Through A, B and C draw lines parallel to BC, AB and AC respectively. Let these lines meet at P, Q and R forming DPQR.
Proof:

QA || BC and QC || AB by construction.
ABCQ is a parallelogram.

AQ = BC . . . (1)
Similarly BCAR is a parallelogram.

AR = BC . . . (2)
From (1) and (2),

AQ = AR . . . (3)

AD is the perpendicular bisector of RQ.
Similarly we can prove that BE is the perpendicular bisector of PR and CF is the perpendicular bisector of PQ. Thus AD, BE and CF are the perpendicular bisectors of the sides of DPQR. Hence AD, BE and CF pass through the same point. (by theorem 2)

Hope you like the above example of Theorem on Orthocentre of Triangle.Please leave your comments, if you have any doubts.

Properties of whole numbers

Properties of whole numbers:



Whole Numbers:While solving problems we usually come across questions like what do we mean by whole numbers,how can we identify whole numbers.Below is the explanation for these type of frequently asked questions

Meaning of whole numbers:

The set of whole numbers is the set of natural numbers along with zero. so W = the set of whole numbers = 0,1,2,3,............

so Zero is the least number of the set of Whole numbers.

As the whole numbers is an infinite set we cant determine the highest number of this set.

The set of Whole numbers is a subset of Rational numbers.
Let us now learn about the Properties of whole numbers
Properties of Whole numbers:

t is advisable to use a number line inorder to understand the properties of whole numbers.

1. Number 3 < 5 and the number 3 is to the left of the number 5.Hence of an two numbers on a number line, the smaller number is to the left of the greater number.So too,of any two numbers on a number line the number to the left of the other number, is the smaller of the two.

2. There is no whole number to the left of zero on the number line.So zero is the smaller number than each of the numbers to its right on the number line.That means 0 is the smallest or least of the whole numbers.

3. A whole number which is greater than a given whole number by 1 is said to be a successive whole number. 1 is the successive whole number to 0.Every whole number has one successor.

4. There is no whole number left to zero.hence 0 is not a successive whole number of any whole.

Hope you like the above example of Whole Numbers.Please leave your comments, if you have any doubts.

Circumference Of A Circle

Circumference Of A Circle:

Circumference of a Circle:
When we study about a circle the most common question that we come across is what is the circumference of a circle.The answer to this question is very simple,the distance around the circle is Circumference. In a circle, the distance from center to any point of a circle is called radius. And the line which touches two points of the circle and passes through the center is known as Diameter of a circle.

The formula to find the Circumference of a circle C is C = 2 × Pi × r

Which means Circumference of a circle is 2 times the value of pi times r

Where, r = radius of a circle and

Pi=3.142 which is a constant value.

The formula to find the Circumference of a Circle with Diameter is

C=Pi*d

Which means the circumference of a circle is pi times the diameter.

where, d=Diameter of a circle and

Pi=3.142 which is a constant value.

As we know Diameter is equal to radius divided by 2, we can use the first formula when we have the Diameter in a given problem.

D = r / /2

Which means diameter d is radius r divided by 2.

Now, we can write the equivalent formula for the diameter which is radius is 2 times the diameter.

r=2 × D

The circumference of circle units can be measured in linear units, like inches, centimeter etc,


Example of Cicumference of the Circle:


Consider the wheel of a cycle and whose one of the length of the sting is 100cm. Since, in a cycle all the stings are passing thorough the center of cycle’s wheel, all the stings are equal to the diameter. So, now we have the diameter of the wheel. With this we can find the circumference of a wheel with the formula circumference is equal to pi times the diameter.

So the circumference of a cycle’s wheel is, C=pi*D

Here we have diameter d=100cm and pi=3.142

Now C = 3.142 × 100cm

C = 314.2cm

The Circumference of cycle’s wheel whose one of the sting’s length 100cm is 314.2cm.

Hope you like the above example of Circumference Of A Circle.Please leave your comments, if you have any doubts.

Isoceles Triangle

Isoceles Triangle:

Introduction to triangles:Let me first brief you up about Triangles in general,a triangle is a three sided figure,and an isosceles triangle has two congruent faces called legs and a third side called the base. The vertex angle is the angle included by the legs. The other two angles are called base angles. The base angles are congruent.
Isosceles Triangle:

The easiest way to learn about the isosceles triangle is to first identify its properties.

• The unequal face of an isoceles triangle is usually referred to as the 'base' of the triangle.
• The base angles (congruent) of an isosceles triangle are always equal. In the figure above, the angles
• When the 3rd angle is a right angle, it is called a "right isoceles triangle".
• The altitude is a perpendicular length from the base to the topmost vertex.

All isoceles triangles:
- Have angles that add up to 180 degrees
- Have two equivalent sides. The irregular side is called the base.
- Have alike base angles.
- Have areas and perimeters that can be establish using the formulas Area=1/2 X (base X height) and Perimeter=side+side+side
A shape triangle with a right angle is called a right isoceles triangle. Also, all equilateral triangles are isoceles triangles, but not all isoceles triangles are right triangles.

Hope you like the above example of Isoceles Triangle.Please leave your comments, if you have any doubts.

Theorem

Theorem:

Introduction:

A Statement that requires a proof is called a theorem.
A theorem is a generalised statement, which can be proved logically. A theorem has two parts, a hypothesis, which states the given facts and a conclusion which states the property to be proved. The two statements given above are examples of theorems.
Theorems are proved using undefined terms, definitions, postulates and occasionally some axioms from algebra.
A theorem is a generalised statement because it is always true. For example the statement or the proposition “If two straight lines intersect, then the vertically opposite angles are equal” is true for any two straight lines intersecting at a point. Such a statement is called the general enunciation.
We can understand Theorems better with the help of an example:
As we can see the above figure,which says that,

Congruent angles are the one that have have the same angle measures. The theorem based on congruent angles is mentioned below

Statement

If two lines intersect, then the vertically opposite angles are congruent.

To Prove

Proof:

Similarly it can be proved that

Hence the theorem is proved.

Hope you like the above example of Theorems.Please leave your comments, if you have any doubts.

Arithmetic progression:

Arithmetic progression:

There are two types of progressions .They are arithmetic and geometric progression. An Arithmetic progression which consists of the sequence of numbers and the terms except the first can be obtained by adding one number to its preceding number. Arithmetic progression is denoted as two consecutive numbers arrangement of progression which is constant.
Let us now learn about the use of arithmetic progression,

• An arithmetic succession is a sequence of numbers such that the difference of some two successive members of the series is a constant.

• Arithmetic progression is used to work out the calculation of the succession and the product of the sequences in the problem.
• S_n= (a+l) (or) {2a+ (n-1) d} Here,
  a-first term of the sequence
  n -total number of sequence
  d - Difference between any two numbers in series
  Here l is the last term
• Let us also learn about properties of arithmetic progression:

• When we add or subtract any constant number with all the terms of the sequence, the arithmetic sequence remains an arithmetic sequence.

Example:
5, 7, 9, 11, 13, 15, 17….. is an A.P with common difference 2.
Add 3 with all the terms,
8, 10, 12, 14, 16, 18, 20…. Is also an A.P with common difference 2.

• When we multiply or divide by a non-zero constant with all the terms of the sequence, the arithmetic progression sequence remains an arithmetic progression.

• Hope you like the above example of Arithmetic progression:.Please leave your comments, if you have any doubts.

Congruent Triangles

We will learn about Congruent triangles,
Three noncolinear points determine a triangle. Draw the three segments connecting the three pairs of points and find three sides, and 3 interior angles, hence the name triangle.

Two triangles are congruent if one can be moved on top of the other, so that edges and vertices coincide. The corresponding sides have the same lengths, and corresponding angles are congruent.


Assume the edges of one triangle are the same lengths as the corresponding edges of another triangle. Move the first triangle onto the second so that the bases coincide. Do the apexes also coincide? Both apexes are x units away from the left end of the base, and y units from the right end of the base. Since the triangles are oriented the same way, both apexes lie above the base. Draw a circle of radius x centered at the left end of the base, and a circle of radius y centered at the right end of the base. These circles intersect in precisely two points, one above the base and one below. Thus there is only one possible location for the apex. Both apexes coincide, and the first triangle lies directly on top of the second. Corresponding angles coincide, and are congruent. This method of proving triangle congruence is called SSS, for side side side.

Hope the above explanation helped you, now let us study about types of triangles.