probability examples

In this blog we will learn about probability examples,

Ex 1: What is the probability of getting a sum is 4 or 8 when throwing two dice simultaneously?

Solution:Now we will see how to solve probability examples

Let S = sample space, S = {(1, 1), (1, 2), (1,3)...(6, 5), (6, 6)}, n(S) = 36

A be the event of getting a sum is 4, n(A) = {(1, 3), (2, 2), (3, 1)} = 3

B be the event of getting a sum is 8, n(B) = {(2, 6), (3, 5), (4, 4), (5, 3), (6, 2)} = 5

P(A) = =

P(B) = =

P(A or B) = P(A) + P(B)

P(4 or 8) = + = .

In the next blog we will learn about linear definition and math dictionary algebra.Hope you like the above example of probability examples,please leave your comments if you have any doubts.

square root of 72

In this blog we will learn how to solve square rot of 72,

How to Solve Square Root of 72:

In this given number square root of 72 is written as in the form of .

It can be solve by so many methods and operations like addition, multiplications and etc…

And the number 72 is factored by so many numbers like 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, and 36.

Now we have to solve the given number square root of 72 in all the entire methods of one by one.

If we solve the square root of 72, we get the constant answer or exact value is 8.48. But it is formed by so many ways, now we are find the answer for square root of 72 in so many ways.It is also easy to find square roots of other numbers like say for example we can learn about solving square root of 256 . In the next blog we will learn about percentage change calculator.Hope you like the above example of square root of 72,please leave your comments if you have any doubts.

factor theorem

In this blog let us learn about factor theorem,

Proof of Factor Theorem:In this blog we will learn about factor theorem,

P(x) is divided by x-a,
Using remainder theorem,
R = p (a)
P(x) = (x-a).q(x) + p(a)
But p (a) = 0 is given.
Hence p(x) = (x-a).q(x)
(x-a) is the factor of p(x)
Conversely if x-a is a factor of p(x) then p(a)=0.
P(x) = (x-a).q(x) + R
If (x-a) is a factor then the remainder is zero (x-a divides p(x)
Exactly)
R=0
By remainder theorem, R = p (a) .Next let us learn about area of a circle formula,in the next blog we will learn about math definitions for kids.Hope you like the above example of factor theorem,please leave your comments if you have any doubts.

triangles and angles

In this blog we will learn about triangles and angles, Triangle is one of the basic shape in geometry, and it is a closed figure with three sides. There are different types of triangles available and can be categorized based on their sides and angles.Three types of triangle, it is classified based on their sides and four types of triangles based on their angles.Let us discuss about three basic types of triangle; it is classified based on their sides.

Classifying triangles based on their Sides.

1) Equilateral triangle

2)Isosceles Triangle

3) Scalene Triangle,Normally angle is the shape in the geometry. They are special forms of the angle is obtainable in the mathematic. These special forms of the angle are specified below,right angle,acute,obtuse,straight,reflex and complete angles.In the next blog we will learn about probability definition and equations in algebra.Hope you like the above example of triangles and angles,please leave your comments if you have any doubts.

2nd grade math word problems

In this blog we will learn about 2nd grade math word problems,

Example 1 (Addition):

On a fine morning there were 3 peacocks in the garden and 2 peahens were near it. How many birds were there in the garden in the morning?

Solution:

Number of peacocks- 3,

Number of peahens- 2.

Total no of birds in the garden=

=5 [Birds]

Therefore, there were 5 birds in the garden.

Example 2 (Subtraction):

To Harris’s birthday party 24 boys and 15 girls came. Find how many boys were more than the girls present in the party.

Solution:

Number of boys present in the party -24,

Number of girls present in the party- 15.

The difference of number of boys and girls present in the party are;

=

= 9.

Therefore, there were 9 boys more than the class.This was one simple example of 2nd grade math word problems.When students learn any sum or method its a process and as the class advances and the age of the student increases the problems and sums also become wide ranged.Most of the students fear tests and exams,even I remember having a very scary experience of 7th grade math test.In the next blog we will learn about multiplication tables chart.Hope you like the above example of 2nd grade math word problems.Please leave your comments if you have any doubts.

analytical geometry

In this blog let us learn about analytical geometry,
Find the equation of the parabola if the curve is open upward, vertex is (− 1, − 2) and the length of the latus rectum is 4.
Solution:
Since it is open upward, the equation is of the form

(x − h)² = 4a(y − k)

Length of the latus rectum = 4a = 4 and this gives a = 1

The vertex V (h, k) is (− 1, − 2)

The equation of parabola is [x-(-1)]²=4*1 [y-(-2)]

[x+1]²=4[y+2].In the next blog we will learn about deviation and ratios.Hope your like the above example of analytical geometry,please leave your comments if you have any doubts.

Math is an Invention ?

Welcome to math helper,

Personally, I think that the question 'Is math invented or
discovered?' is meaningless. But thinking about _why_ it's meaningless
can lead you to some very interesting ideas about the nature of
meaning!

(For example, if you're lucky it might lead you to read Doug
Hofstadter's wonderful essay 'A Conversation with Einstein's Brain',
in his book _The Mind's I_.) examples on math help; So I hope you'll continue to noodle
around with this issue this even after your essay has been completed.
I hope the above explanation was useful, now let us learn more on online math tutors.

math intuition

Welcome to free math tutor online,

One way to train my intuition is to compare the problem with something
I've seen plenty of times in real life. I've painted murals, mixing
the colors I want from poster paint. Often I want a light color, and a
little color goes a long way.

I have learned to be very careful not to
add too much color to the white at first. Why? I If I need 1 part blue
to 100 parts white (which is not unreasonable in my experience), and I
put in 2 dabs of blue instead of 1, meet math tutors online for more examples;
I need to add another 100 parts of
white to get the color to be what I wanted!

I can't tell you how many
times I've ended up with far more paint than I needed, by the time I
got the color right. I've learned that it's better to throw away half
the too-dark mixture, rather than try to save the whole batch by
adding white. learn more on math forum.

Sphere of radius

Welcome to free online math tutoring,

We have a sphere of radius R, with a rope of length 2 pi R around its
circumference; then we add L units to that circumference. What is the
new radius of the rope? The new circumference is (2 pi R + L); the new
radius is that divided by 2 pi, or R + L/(2 pi). This means that the
radius is increased by L/(2 pi), which is independent of R.

This seems a little less surprising, perhaps, than if we solved it with specific
numbers, since we don't have a specific unexpectedly large number to
reject outright; we're forced to look at the algebra. more help on online math forum;
But we can still question the algebra once we see what it tells us.

The next step, of course, is to check the answer: plug in actual numbers for R and L,
solve for the change in R, and then add that to R to find what the new
circumference will be. It will be L more than the original, showing
that as long as we accept 2 pi R, our answer is right. read more on math forum.

Mathematics intuition

Welcome to free math tutoring online,

The first thing we have to recognize is that our intuition can be
wrong. Mathematicians (and the rest of us) need a healthy dose of
humility, because this happens all the time.

I suppose one of the
benefits of studying math beyond mere arithmetic is that it can teach
us not to trust our assumptions, or even what seems like sound
reasoning, but to look closely at the logic behind what we believe.
examples on online math forum; What seems true, not only in math
but in all of life, may not be! That's just part of growing up.

continue learning on our math forum.

Math quadratic formula

Welcome to free math,

The quadratic formula,

-b +/- sqrt(b^2 - 4ac)
x = -----------------------
2a

applies whenever you have an equation like

ax^2 + bx + c = 0

So we can start with either the formula, or the equation. visit online math forum; Frankly, the
equation looks as if it will be less work:

ax^2 + bx + c = 0

bx = -ax^2 - c

b = (-ax^2 - c) / x
more exercise on math forum.

Math Pi

Welcome to free online math tutors,
pi shows up in so many other places in mathematics, this guy
might find himself asking: "Why is the ratio of circumference to
diameter close to pi for small circles, but not for large ones?" And
if he investigated that question deeply enough, get more on math forum;he might eventually be discover that there are other ways of measuring distances than always
going along the surface of the earth.

That is, he might learn to think
in terms of three (or more) dimensions, even if he can't directly
experience those dimensions. continue reading on free math help online.

Reading math material

Greetings from math online tutor,
Read the
relevant part _before_ each lecture, rather than hearing it for the
first time in the lecture.

This _sounds_ like a lot of extra work, but it's not. Suppose you
have lectures A, B, and C that cover reading material a, b, and c.
Most students would do this:

Listen to A; read a; listen to B; read b; listen to C; read c.

I'm suggesting that you do this instead:

Read a; listen to A; read b; listen to B; read c; listen to C.

As you can see, it's the same amount of work. Only the order is
different. And the reason the order is so crucial is the one I've
already mentioned: If you don't understand something in the reading
material, you can ask about it in the lecture where the material is
covered, which is no extra trouble for the teacher. online math forum;
But if you try to ask a question about yesterday's material in today's lecture, the
teacher will be impatient to move on, and it's likely that you won't
get the answer you need, if you get one at all. View more on math forum.

How to remember formulas

Welcome to math online tutor,

One trick you can use when trying to remember patterns or principles
is to encode them as examples. For example, for the life of me I can
never remember whether (a^b)^c is a^(b+c) or a^(bc). So whenever I
need to know, I drag out this example:

(a * a) * (a * a) * (a * a) = a^6, so (a^2)^3 = a^6

which means that it must be (bc), and not (b+c). Does this get
tiresome? You bet. Is it preferable to guessing wrong? You bet!

Two other tricks I can recommend are:

Try teaching what you've learned to someone else. This is probably
the single most effective way of learning anything, especially if the
other person is having difficulty learning it. learn more on math forum; It forces you to think
of new ways to understand the material, in order to avoid presenting
it in the same old way. more examples on online math tutoring.

Remembering formulas

Welcome to free math help online,
I can sympathize with you, because I have a similar problem. I've
_never_ been able to remember formulas, and the way that I've had to
compensate is that whenever I learn a new formula, I have to learn how
to derive it from first principles - by which I mean, the things that
are so basic that I _can't_ forget them.

(One of the luckiest breaks I ever caught in my life was when I took
second-semester calculus in college. examples on math forum; That's the semester when you
have to memorize about a zillion formulas that all look pretty much
the same - one plus or minus the sine or cosine of plus or minus
something, under or over the square root of something similar - so I
fully expected to fail. But on the first day, the professor said: "I
don't expect you to remember anything that I can't remember, and the
only thing that I can remember is that cos^2 + sin^2 equals 1." So
you're not alone!)

I hope the above explanation was useful, now let us study more on online math forum.

Math Derivations

Welcome to online math tutoring,

Mathematicians can come up with some pretty weird stuff,
but the individual steps in each derivation are built entirely on
processes like the one outlined above.

Additionally, mathematical
publications are very closely scrutinized by several mathematicians
other than the author before being published, and are often criticized
by even more after publication.

All of this amounts to a good
assurance that theorems do in fact follow from assumptions. more explanations on free online math tutor and math forum.

Mathematical realm

Welcome to math online tutor,
mathematical realm, when I say that 2+3 = 5, I am not
saying that any particular 2 and 3 items are the same as any
particular 5 items. I am saying, in an abbreviated form, that whenever
I put together 2 of something and 3 more of them, I will have 5 in
all. Also, I am not somehow "combining" a "2" and a "3" to make
something new that is identical to "5";

I am performing an operation
on two numbers that is the abstract representation of putting together
two sets of things, in order to determine the number of things in the
combined set. math help If you prefer, you can say I am simply stating a
relation among the numbers 2, 3, and 5.
I hope the above explanation was useful, let me take you through free math tutoring.

Arithmetic and Math

Welcome to math help online,

Arithmetic is just one branch of mathematics, namely that involving
basic techniques of calculation with numbers. When you add, subtract,
multiply, divide, take square roots, and so on, you are doing
arithmetic.

When you solve an equation you are doing algebra. When you
determine relations between shapes or find their area, you are doing
free math geometry (though the latter calculation will be done by applying
arithmetic to the geometric formulas).

Most of what young children learn in math is arithmetic.
Hope the above explanation was useful, now let us study online math tutoring.

Math and Art

Welcome to online math tutoring,

There may be much in common between mathematics and art, and since
art is also difficult to define, it is difficult to discuss this
relation. Certainly, there are definitions of art that would allow the
inclusion of mathematics as an art. The creation of mathematics
requires creativity, and I think most mathematicians would agree that
some constructs are more beautiful than others, so that there is an
aesthetic aspect to mathematics.

In any case, mathematics certainly is a human endeavor involving the
exchange of ideas between human beings. math help com It has been around for
millennia, and shows no signs of abatement.

These ideas are debatable and reflect my own personal opinion. Also,
this response is really too short to explore all the aspects your
question addresses math forum.

What is Algebra ?

Let me help you on math help & study what is algebra,

Algebra is a branch of mathematics. Algebra plays an important role in our day to day life.

The algebra executes the four basic operations such as addition, subtraction, multiplication and division. The most important terms involved in algebra expressions, equations and polynomial.

In Algebra, besides numerals we use symbols and alphabets in place of unknown numbers to make a statement. Hence, algebra may be regarded as an extension of Arithmetic.
you get more help in math and online math help in our blog posts.

I hope the above explanation was useful.

Area and Perimeter of a Concave Polygon

Area and Perimeter of a Concave Polygon

Unlike a regular polygon, there is no easy formula for the area of an irregular polygon. Each side could be a different length, and each interior angle could be different.

so we have to split concave polygon as triangles or parallelograms or other shapes that easy to find area . here is the example on how to calculate the area of concave polygon. in this example we could not directly find the formula for finding area but we can split this concave polygon as two parallelogram then we could find area easily by using formula for area of parallelogram .
* The perimeter of any polygon is the total distance around the outside.
* which can be found by adding together the length of each side.

I hope the above explanation was useful, now let us study words with x in them

Explain Ration in math

Let us study How to do ratios,

Definition for ratios:

In mathematics, a ratio expresses the magnitude of quantities relative to each other. Specifically, the ratio of two quantities indicates how many times the first quantity is contained in the second and may be expressed algebraically as their quotient.

Example: For every Spoon of sugar, you need 2 spoons of flour (1:2)
I hope the above explanation was useful.

Math definitions for kids

Math definitions for kids:Addition means sum of two quantities. The sign used to do addition is ‘+ ‘.

If Joe has 2 black pencil and 3 blue pencil means then the total number of pencil is

2+3 that is 5 pencils.
Subtraction:

Subtraction means difference of two quantities. The sign used to do subtraction is ‘– ‘.

If Kayla has 5 rupees and she spent 2 rupees in a store then the amount she has left in a hand is 5-2 that is 3 rupees.
Division:

Division means sharing a number into equal parts. The sign used to do division is ‘/’.

If a mom has 6 chocolates and then if she wants to give those chocolates to 2 children means, then it is 6/2 that is 3 .So she will give 3 chocolates to each child.
Multiplication:

Multiplication means a number is added to itself a number of times. The sign used to do multiplication is ‘x’ or sometimes ‘*’.

2+2+2=6 which is same as 3 times 2 which is equal to 6.In maths we also learn multiplication with the help of time table chart.Hope you like the above example of Math definitions for Kids.Please leave your comments, if you have any doubts.

Percentage Change Calculator

Percentage Change Calculator:A percentage change is a way to express a change in a variable. It represents the relative change between the old value and the new one.

The formula used to calculate the percentage change is Percentage change = [((V2 - V1) / (V1)) * 100] .

V1- represents the old value

V2 - the new one.There are many online calculators available for calculating percentage change.
Percentage Change Calculator - Example Problems:

Let us understand the meaning and example problems related to Percentage change calculator - Problem 1:-

Ram scored 86 runs in the cricket match on Monday. On Friday he scored 95 runs. Calculate the Percentage of change?

Solution:-

Given

V2 = new value = 95 runs.

V1 = old value = 86 runs.

Percentage of change = ?.

The formula used to calculate the percentage change is

Percentage change = [((V2 - V1) / (V1)) * 100] .

By plugging in the given values in to the formula we get

Percentage change = [ (95 - 86) / (86) * 100] .

The difference between 95 and 86 is 9.

By plugging in it to the formula we get the answer as

= [9 / 86] * 100.

The fraction 9/ 86 gives us 0.1046.

=0.1046 * 100

=10.46

The percentage of change is 10.46.In the next Blog we will discuss about Radical calculator.Hope you like the above example of Percentage change calculator.Please leave your comments, if you have any doubts.

Factoring Trinomials Calculator

The equation or a function is in the structure of ax2+bx+c =0 (where a≠0, b, c are constants ) called as trinomials.We can also refer it as a quadratic function. An algebraic expressions which has 3 terms known as trinomials.The trinomials having highest power 2.The trinomials have the two roots. There are two ways to factor the trinomial according to the co-efficient of x2 . In the following section we are going to learn how to factor the trinomials by using trinomials calculator.Factor Trinomials Calculator Method 1:For factoring the trinomials we must know the below two methods.

Factor trinomial calculator Method 1:

If the coefficient of x2 is one. That is a=1.

x2+bx+c=(x-r1)(x-r2), In this r1 and r2 are the roots of the trinomial equation

(x - r1) and (x - r2) are the factors of the trinomial.In the Blogs to come we can learn about factoring polynomials calculator.Hope you like the above example of Factor Trinomial Calculator.Please leave your comments, if you have any doubts.

Factoring Quadratics

Factoring Quadratics:The explanation for factoring quadratics expressions,

Step 1: In the first step, the constant term must be identified.

Step 2: In the next step, the product term for the constant terms must be identified.

Step 3: Check whether the obtained product is equal to the sum of the co-efficient if x.

Step 4: Write the product of the obtained terms.Factors of 28 is one of the most commonly asked question under this topic.Hope you like the above example of factoring quadratic.Please leave your comments, if you have any doubts.

Parallelogram Definition

Let us learn about the Parallelogram Definition:Two diagonals in the figure which intersects at a particular point and lie in the interior part of parallelogram.When two pairs of the sides are opposite and they are parallel to each other.Then it is called as parallelogram .Now let us see about the parallelograms sides introduction.In parallelograms introduction, we can draw a pair of parallel lines. Draw another pair of parallel lines intersecting the former.Thus the parallelogram can be formed.Thus we can say that the pair of opposite sides of parallelogram is of equal length.Similarly we can also learn about other topics such as types of lines.Hope you like the above example of Parallelogram Definition.Please leave your comments, if you have any doubts.

How to find standard deviation

Let us learn how to find standard deviation.The variance is the measure of variability about the mean. To find standard deviation is the square root of average squared deviation from the mean.In the determination of variance, we find that the units of individual observations xi and the unit of their mean or [barx] are different from that of variance, since variance involves the sum of squares of (xi– [barx] ). The mean of a set of examination is expressed as positive (+ve) square-root of the variance and is called standard deviation. In order to find standard deviation the following formula is to be used.The formula for standard deviation is
σ = [sqrt((1/n)sum_(i=1)^n (x i - barx )^2)] . In find standard deviation usually denoted by σ.Hope you like the above example of how to find standard deviation.Please leave your comments, if you have any doubts.

Properties of exponents

Properties of Exponents:
The following properties are very essential in solving exponents,
1. Property for the product exponents with same base,

a^m * aⁿ = a^m+n, provided a b

2. Property of exponents with zero superscript,

a⁰ = 1, provided a 0

3. Property for exponemts in fraction form,

= a^m * a^-n , provided a 0

4. Property for exponents with whole superscript,
(ab)^m = a^m * b^m , provided a b
5. Property for exponents with negative superscript,

a^-m = provided a 0

6. Property for exponents with common superscript when the terms are in product,

(a^mb^mc^m) = (a*b*c)^m ,

(a^m/b^m) = ( )^m , provided a b

7. Property for exponents with radicals,

= x

(a^m)ⁿ= a^{mn
I hope the above explanation was useful, now let me explain about dividing radicals.}

Multiplying Radicals

Multiplying Radicals:The explanation to multiplying radicals is given below.There are mainly two laws are used. They are given below,Product law:

* Product law are also used in the radical expressions.
* By using the product law, if the given radical expressions are having the same index value means, then it can be multiplied.

Example: [root(4)(2)] [xx] [root(4)(3)] = [root(4)(6)]

Distributive law:

* Distributive law are also used in the radical expressions.
By using the distributive law, we have to multiply each and every terms.

Example: a (b + c) = ab +ac.The other key area of study is dividing radicals.Hope you like the above example of Multiplying Radicals.Please leave your comments, if you have any doubts.

Want to know about Basic Points Calculator

How many Triangles

How many triangles:A triangle is a geometrical figure formed by three lines, which intersect each other and which are not all concurrent.Let us now learn how many triangles are their altogether,Types of Triangle.There are three types of triangles they are: Equilateral triangle,Isosceles triangle and Scalene triangle.In equilateral triangle all the three sides are equal and all the angles are equal,in isosceles triangle two sides and their opposite angles are equal,in scalene all the three sides are not equal.While studying Triangles we usually come across congruent triangles too.Hope you like the above example of How many Triangles.Please leave your comments, if you have any doubts.

How to Measure Circumference of a Circle

Searching for circumference of a circle formula ? let me explain you how to find the circumference of a circle,

* Measure diameter. The diameter of a circle is the distance across a circle, through its center. It can be visualized as a straight line cutting the circle in half. For large circles like running paths, the diameter can be estimated.

* Consider radius. Radius is the distance from the center of a circle to any point on the circle. The radius of a circle is half its diameter. When diameter is too large to determine, estimate the radius. Then use simple math and multiply the radius by 2.

* Grasp pi. Pi is the ratio of the circumference of a circle to its diameter. Pi is called a constant in math. It is a number that does not change, no matter the size of the circle. The value of pi is usually rounded to 3.14.* Calculate circumference. Use simple math to multiply the diameter of the circle by pi. If a jogger estimated diameter of a circular path as 200 meters across, then circumference would be 200 times 3.14 or 628 meters.

* Verify units of measurement. The units for circumference are the same as the units for diameter. If diameter is measured in meters, report circumference in meters.

I hope the above explanation was useful.

TRINOMIAL SQUARES

Let us study about TRINOMIAL SQUARES,

A trinomial that is the the square of a Binomial is called a TRINOMIAL SQUARE. Trinomials that are perfect squares factor into either the square of a sum or the square of a difference. Recalling that (x + y)² = x² + 2xy + y² and (x - y)² = x² - 2xy + y², the form of a trinomial square is apparent. The first term and the last term are perfect squares and their signs are positive. The middle term is twice the product of the square roots of these two numbers. The sign of the middle term is plus if a sum has been squared; it is minus if a difference has been squared.

The polynomial 16x² - 8xy + x² is a trinomial in which the first term, 16x , and the last term, y², are perfect squares with positive signs. The square roots are 4x and y. Twice the product of these square roots is 2(4x)(y) = 8xy. The middle term is preceded by a minus sign indicating that a difference has been squared.

I hope the above explanation helped you.

Explain Concentric circles

Let us study about concentric circles,
In a large circle, two or more small circles inside a large circle and the center for all the circle inside is same. Other wise circle which have common center are known as concentric circle.

Wher R is the radius of the large circle, and r is the radius of the small circle.

In the figure we see that the center is same for both the circle.

For concentric circle we can find the area of ring inside large circle and small circle is given by.

Area of a ring = Area of large circle - area of small circle

= πR2 - πr2

= π(R+r)(R-r) Square units

Let us example for area of a ring in a concentric circle.

I hope the above explanation was useful, now let me explain how to find area of circle.

Statistics

Statistics:

The common question that is asked about any new topic is what is the meaning of that topic,similarly let us learn about what is Statistics??Statistics deals mainly in communicating facts and figures in terms of a method called statistical method. Collection, classification, tabulation, representation, reasoning, testing and drawing inferences are part of statistical methods.Rainfall patterns of a particular city over a period of time can be analyzed and a fair estimate about next season can be arrived at, with the help of figures (data) collected over a period of time.

The statistical method of studying a problem broadly consists of the following steps,basically we can get help on the statistical methods by following the steps given below:

* to collect numerical data about the problem,
* to present the collected data systematically,
* to analyze the data and
* to interpret the data and draw conclusions from it.

We have already learnt about the measures of central tendency, the mean, median and mode. Each of these gives a representative value of the data. If we say "the mean of a data is 15", we expect most of the values to be centered around 15. But measures of central tendency don't give us the complete picture. We would want to know how the values are scattered around the mean or the median. In other words, we want to study the variability and define a single number to describe the variability. This number is called the "measure of dispersion". Two of the measures of dispersion are Mean Deviation and Standard Deviation.We can also get help on statistics and probability by learning the statistics formulas.

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

Area of Circle

Area of a Circle:

Draw a circle. Divide it into equal (even) sectors and arrange them in line as shown below.

This shape looks like a rectangle of length 'pr' and breath 'r' units
Let us now learn about the area of a circle in detail.
Area of the circle = Area of the rectangle

= length x breadth

= ∏ r x r

= ∏ r2 Sq. units
Next in this Blog let us look at the formula of the Areas of a circle.
Area of a circle Formula is ∏ r2 Sq. units

Area of a semicircle = 21 ∏ r2 Sq. units

Area of a quadrant = 41 ∏ r2 Sq. units.
The last topic that we will learn about in this area of the Circles Problems,and we will also see the various how we can solve these problems.
Problems related to area of A Circle:If the area of the sector of a circle is 60 sq. cm and the length of the arc of the sector is 12 cm, what is the radius of the circle?

Solution:
Area of the sector = 1 lr = 60 cm2
2

l = 12cm.
A = 1 x 12 x r = 60
2

6r = 60

r = 10 cm.

The radius of the circle is 10 cm.

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

Symmetry

Definition:-

Symmetry generally conveys two primary meanings. The first is an imprecise sense of harmonious or aesthetically pleasing proportionality and balance; such that it reflects beauty or perfection. The second meaning of Symmetry is a precise and well-defined concept of balance or "patterned self-similarity" that can be demonstrated or proved according to the rules of a formal system: by geometry, through physics or otherwise.

In formal terms, we say that a mathematical object is symmetric with respect to a given mathematical operation, if, when applied to the object, this operation preserves some property of the object. The set of operations that preserve a given property of the object form a group. Two objects are symmetric to each other with respect to a given group of operations if one is obtained from the other by some of the operations (and vice versa).

Types of Symmetry:

In this Blog I will also share with you the information on the different types of Symmetry.In the following two different types of symmetry are given:

1. Symmetry in geometry
2. Symmetry in mathematics


Symmetry in geometry:

Symmetry definition in geometry it means a sub-group.Our next concern is the very important topic on Isometrics,the most common question here is-What does Isometrics consists of?? Isometrics consists of three or two dimensional space. In following operations:

1. Reflectional Symmetry(FLIP)
2. Rotational Symmetry (TURN)
3. Translational Symmetry (SLIDE)

Reflectional symmetry (FLIP):

Splits the image into one side of the half side of mirror image. It is also called line or mirror symmetry. A Reflectional symmetry is called FLIP.

Rotational symmetry (TURN):

To turn the center point of an object into degress. A Rotational symmetry is called TURN.

Translational symmetry (SLIDE):

In straight line is divided into sequence line. A Translational symmetry is called SLIDE.

Symmetry in Mathematics

In mathematical operation, to apply the object into operation. The set of operations to form a group. Two object form a group of operations. To apply the objects into symmetry. So it is called a symmetry definition in mathematics.

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

Fractions

In this Blog I will help you understand the concept of Fractions and also we we see how to solve the fractions.Fraction is an equal part of one whole object.The most common question is how do you denote a fraction???Fraction can be represented as " p/q " where 'p' denotes the value called numerator and 'q' denotes the value called denominator and q not equal to zero.

Introduction to fraction:

A fraction is a number that can represent part of a whole. The earliest fractions were reciprocals of integers: ancient symbols representing one part of two, one part of three, one part of four, and so on. A much later development were the common or "vulgar" fractions which are still used today (½, ⅝, ¾, etc.) and which consist of a numerator and a denominator.

In this Blog we are going to see how to change 385 to fraction and 385 into decimal,what is mean by improper fraction and some other examples based on fraction.

385 to Fraction:

385 to Fraction:

In this Blog we are going to see how to convert 385 to fraction and what is mean by improper fraction and how to convert 385 into decimal.Let us now solve few problems related to Fractions to understand the concept even better.

Problem 1:

Convert 385 to fraction.

Solution:

Given integer 385.

To convert the 385 to fraction we need to multiply and divide by the same number.We get only the improper fraction.

Improper fraction:

If [a/b] is improper fraction means, b < 10 =" [3850"> 38.5 × 10

(ii) 385 × (100/100)

=> 3.85 × 100

=> 3.85 × 102

(iii) 385 × (1000/1000)

=> 0.385 × 1000

=> 0.385 × 103

Problems on Fraction:

Problem1:

Add two fraction [3/4] and [2/5]

Solution:

Given , [3/4] and [2/5]

= [3/4] + [2/5]

To add fraction ,we need common denominator,

To make a common denominator , multiply 3/4 by 5 on both numerator and denominator and multiply 2/5 by 4 on both numerator and denominator.

= [3/4] × [5/5] + [2/5] × [4/4]

= [15/20 ] + [8/20]

= [(15+8) / 20]

= [23 /20]

Answer: [3/4] + [2/5] = [23 /20]

Problem 2:

Multiply the fractions 5/6 and 2/8

Solution:

Given, [5/6] and [2/8]

= [ 5/6] × [2/8]

= [ ((5)(2)) / ((6)(8))]

= [10/48]

= [5 / 24]

Answer: [5 / 24]

Problem 3:

[Divide the fraction 16/25 by 10/24]

Solution:

Given, [16/25] ÷ [10 /24]

We can divide by,

(i) Take the reciprocal for [10/24]

(ii) Multiply it with [16/25]

[16/25] ÷ [10 /24] = [16 /25] × [ 24 /10]

= [((16)(24)) / (( 25)(10))]

= [ 384 / 250 ]

= [192 / 125]

Answer: [192 / 125]

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

Volume of Cone

Volume of Cone:
In general terms when we speak about a cone the first thing that comes to our mind is an ice-cream cone as depicted in the picture on the right hand side.

But to be more specific the meaning of a cone is given below "A cone is a three-dimensional geometric shape that tapers smoothly from a flat, usually circular base to a point called the apex or vertex.n geometry, there are two types of shapes." They are two dimensional and three dimensional.

Two dimensional shapes are rectangle, square, parallelogram, rhombus etc.

Three dimensional shapes are cone, sphere, pyramid, cube, prism.


Properties of cone:

There are two properties of cone . They are volume of cone, surface area of cone. By using the properties of cone, we can calculate volume and surface area.

A cone has radius (r) and height (h) , slant height (s).

Volume of cone V = 1/3 * π * radius2 * height where π = 3.14

Volume of cone V = 1/3 * Volume of cylinder

Surface area of cone SA = π*radius* [sqrt(radius^2+height^2)]

Total surface area of cone = Surface area + π*radius2.

In this blog we will also see some example problems related to Volume of a cone.By solving few problems we can understand how to calculate the surface of a cone.
Problem 1:

Find the volume of cone for the radius = 1 meter and height = 1 meter.

Solution:

Given radius = 1 meter

Height = 1 meter

Volume of cone = [1/3] * π * radius2 * height

= [1/3 ] * 3.14 * (1)2 * (1)

= [1/3] * 3.14 * 1 * 1

= [3.14/3]

= 1.05 m3.

Problem 2:

Find the Total Surface area of cone for the radius is 3 meter and height is 4 meter.

Solution:

Given: Radius = 3 m

Height = 4 m

Surface area of cone = π*radius* [sqrt(radius^2+height^2)]

= 3.14 * 3 * [sqrt(3^2+4^2)]

= 3.14 * 3 * [sqrt(9+16)]

= 3.14 * 3 * [sqrt(25)]

= 3.14 * 3 * 5

= 47.1 m2.

Total surface area of cone = Surface area + π*radius2.

= 47.1 + 3.14*32

= 47.1 + 3.14 * 9

= 47.1 + 28.26

= 75.36 m2.

Problem 3:

Find the height of a cone for the volume of cone is 100 cubic inches and radius of a cone is 5 inches.

Solution:

Given: Volume of cone V = 100 cubic inches

Radius of cone = 5 inches

Volume of cone = [1/3 ] * π * radius2 * height

100 = [ 1/3 ] * π * 52 * height

100 = [1/3] * 3.14 * 25 * height

100 = [1/3] * 3.14 * 25 * height

100 = [(3.14*25)/3] *height

100 = [78.5/3] *height

100 = 26.17 * height

Height = [100/26.17]

Height = 3.82 inches

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

Coordinate Planes

Coordinate Plane:

In this Blog before we get into the details of coordinate planes,let us first understand the definition of a coordinate plane.The basic meaning of a coordinate plane is Coordinate plane is a plane formed by the intersection of a horizontal number line.

Definition of Coordinate Plane:

Coordinate plane is a plane formed by the intersection of a horizontal number line with a vertical number line. They intersect at their zero points. This point of intersection is called the origin and written as (0, 0).

On a coordinate plane, the horizontal number line is called the x-axis and the vertical number line is called the y-axis.

This is a coordinate plane. It has two axes and four quadrants. The two number lines form the axes. The horizontal number line is called the x-axis and the vertical number line is called the y-axis. The center of the coordinate plane is called the origin. It has the coordinates of (0,0). Locations of points on the plane can be plotted when one coordinate from each of the axes are used. This set of x and y values are called ordered pairs.




















With the help of another example we can get a clear understanding about the coordinate Planes.


In the coordinate plane there are four quadrants.

Quadrant 1.

In quadrant 1 both X axis and Y axis values are positive. [( +x, +y )]

Quadrant 2

In quadrant 2 X axis values are negative and Y axis values are positive. [( - x, +y )]

Quadrant 3

In quadrant 3 X axis values are positive and Y axis values are negative. [( + x, - y )]

Quadrant 4

In quadrant 4 both X axis and Y axis values are negative. [( - x, - y )]
Hope you like the above example of Coordinate Planes.Please leave your comments, if you have any doubts.

Prime Numbers

Prime Numbers:

Introduction to meaning of Prime Numbers:
We are often faced with the questions like-What is the meaning of Prime numbers??In mathematics, a prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself. The first twenty-five prime numbers are: Prime Numbers:2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.Condition: - If x is the prime number then the next factors of the number x is 1 and X. Let us now see the meaning of prime numbers.A prime number is one that has only two factors namely 1 and itself and a composite number has factors besides 1 and itself.



In this blog we can get a clear understanding of Prime Numbers.A natural number greater than 1 that has no divisor between 1 and itself is said to be prime, hence called a prime number or simply a prime. Every natural number greater than 1 has at least the two distinct divisors 1 and itself; a prime has no others.

The number 2 is a prime, there being no candidate divisors between 1 and itself; from it, all even numbers thereafter are non-prime, i.e. 50% of all subsequent numbers. The numbers 3, 5, and 7 are all prime, meaning that, of the first six such subsequent numbers, precisely half are prime, half non-prime. However, of any subsequent six consecutive numbers, at least one of the odd values must be divisible by 3; including the three even numbers this means that at least 66% must be non-prime.So the trend goes; as we look further afield, with an accumulating collection of primes to be divisors, the density of primes declines progressively. But, no matter how far up the numbers we travel, we never exhaust the primes, nor is there any known point above which all further primes are spaced by more than the minimal value of 2 .

Example Problems - Meaning of Prime Numbers:

The easiest way to understand the prime numbers is by solving problems related to Prime numbers.

Problem 1:

Find out the number 29 is prime number or not?

Solution:

Here the number 29 is divisible by one and itself only. It has no more factors other than this. So 29 is considered as a prime number.

Problem 2:

Find out the number 53 is prime number or not?

Solution:

The getting number 53 is not divisible by two. 53 has only two factors. Those factors are one and itself only. So we can say the given number is prime number.

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

Introduction to Algebraic Fractions

Let us study about Algebraic Fractions,
Introduction to Algebraic Fractions :

Algebraic fractions are fractions using a variable in the numerator or denominator, such as 3/ x. Because division by 0 is impossible, variables in the denominator have certain restrictions. The denominator can never equal 0. Therefore, in the fractions
Be aware of these types of restrictions.
I hope the above explanation was useful.

The Binomial

The Binomial

A discrete variable that can result in only one of two outcomes is called binomial. For example, a coin flip is a binomial variable; but drawing a card from a standard deck of 52 is not. Whether a drug is either successful or unsuccessful in producing results is a binomial variable, as is whether a machine produces perfect or imperfect widgets.

Binomial experiments

Binomial experiments require the following elements:

* The experiment consists of a number of identical events ( n).
* Each event has only one of two mutually exclusive outcomes. (These outcomes are called successes and failures.)
* The probability of a success outcome is equal to some percentage, which is identified as a proportion, π.
* This proportion, π, remains constant throughout all events and is defined as the ratio of number of successes to number of trials.
* The events are independent.
* Given all of the above, the binomial formula can be applied ( x = number of favorable outcomes; n = number of events):
I hope the above explanation was useful.

Gaussian Elimination

Gaussian Elimination :

The purpose of this article is to describe how the solutions to a linear system are actually found. The fundamental idea is to add multiples of one equation to the others in order to eliminate a variable and to continue this process until only one variable is left. Once this final variable is determined, its value is substituted back into the other equations in order to evaluate the remaining unknowns. This method, characterized by step-by-step elimination of the variables, is called Gaussian elimination.

Example 1: Solve this system:


Multiplying the first equation by −3 and adding the result to the second equation eliminates the variable x:


This final equation, −5 y = −5, immediately implies y = 1. Back-substitution of y = 1 into the original first equation, x + y = 3, yields x = 2. (Back-substitution of y = 1 into the original second equation, 3 x − 2 y = 4, would also yeild x = 2.) The solution of this system is therefore ( x, y) = (2, 1), as noted in Example 1.

Gaussian elimination is usually carried out using matrices. This method reduces the effort in finding the solutions by eliminating the need to explicitly write the variables at each step. The previous example will be redone using matrices.
Hope the above explanation was useful, now let me explain about matrices.

Regular Polygons

Let us learn about Regular Polygons,
There is really no limit to the number of sides a polygon may have. The only practical limit is that unless you draw them on a very large sheet of paper, after about 20 sides or so, the polygon begins to look very much like a circle.

Parts of a regular polygon
In a regular polygon, there is one point in its interior that is equidistant from its vertices. This point is called the center of the regular polygon. In Figure 1, O is the center of the regular polygon.

Figure 1 Center, radius, and apothem of a regular polygon.

The radius of a regular polygon is a segment that goes from the center to any vertex of the regular polygon.

The apothem of a regular polygon is any segment that goes from the center and is perpendicular to one of the polygon's sides. In Figure 1 , OC is a radius and OX is an apothem.

Finding the Perimeter

Because a regular polygon is equilateral, to find its perimeter you need to know only the length of one of its sides and multiply that by the number of sides. Using n-gon to represent a polygon with n sides, and s as the length of each side, produces the following formula.

Finding the Area

If p represents the perimeter of the regular polygon and a represents the length of its apothem, the following formula can eventually be shown to represent its area.

Example 1: Find the perimeter and area of the regular pentagon in figure 2 , with apothem approximately 5.5 in.

Figure 2

Finding the perimeter and area of a regular pentagon.

Hope the above explanation helped you.