Online Math Help

Introduction to online math help:

Online math help is a service that provides mathematics help on online. It includes reviewing lessons, homework help, learning aids, games, puzzles and test preparation for kids, teens, schools, home schools. Here all the tutors are well qualified and they explain the topic in detailed.  All grade students are used to get any help from mathematics. For example Grade 1 to Grade 12 and it is also possible for college student. This is a process how we get help in math through online. All the topic doubts are cleared by the experienced tutors (Algebra, calculus, probability, geometry, trigonometry ,Number system etc…).Online math help provides  two different  services such as free and  payment system. Is this topic Half Angle Formula Examples hard for you? Watch out for my coming posts.


Features of online math help:

Online math help provide live and fully interactive one to one tutoring. Master basic, advanced math concepts and also get help with homework, practicing problems, assignment test and etc…In this service parents, students, teachers are interact with the tutors. Different types of sites are available in the online math help. All the sites provide online math help with fully interacting, interesting, and qualified math problem help. Online math help services s are unlimited and get step by step detailed help and take back to back sessions.  Online math help also help in a step by step procedure in different ways so that students can follow the concept and ask any doubt on any particular step.

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Benefits of online math help:

In online math help, all formulas, Practicing problems, home work problems, graphs, geometric diagrams are explained by the well expert teachers. The first requirement is to admit the problem and then it needs to be understood that many student who had math anxiety did manage to overcome it. Success requires guidance and work. Online math help can be viewed from a couple of perspectives that might be helpful. One is that math is a language and students need to learn some examples and their definitions very well before they can start doing the problems.

Binary Relations

Introduction of binary relations:-

In mathematics, a binary relation on a set A is a collection of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2 = A × A. More generally, a binary relation between two sets A and B is a subset of A × B. The terms dyadic relation and 2-place relation are synonyms for binary relations.(Source: Wikipedia).

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Example problems for binary relation:-


Problem 1:-

Find four binary relations from `{a,b}` to `{x,y}` that are not functions from `{a,b}` to `{x,y}`

Solution:-


R = `{(a, x), (a, y), (b, x)} ` is not a function from `{a, b}` to `{x, y}` because two values related to a
R = `{(a, x)} ` is not a function from `{a, b}` to `{x, y}` because there are no values related to b

It able to find another two easily. In fact, of the 16 binary relations from `{a, b}` to `{x, y}` , only 4 are functions, and 12 are not functions.



Problem 2:-

Find four binary relations from `{a,b,c}` to `{x,y,z}` that are not functions from `{a,b,c}` to `{x,y,z}`

Solution:-

R = `{(a,x),(a,y),(a,z),(b,x),(b,y),(b,z),(c,x),(c,y),(c,z)} `  is not a function from` {a,b,c}` to `{x,y,z}` because three values related to a.

R = `{(a, x)}` is not a function from `{a, b, c}` to `{x, y,z}` because there are no values related to b & c.


It able to find another two easily. In fact, of the 36 binary relations from `{a, b, c}` to `{x, y, z}` , only 6 are functions, and 30 are not functions. Please express your views of this topic What is Rational Number by commenting on blog.


More example problems for binary relation:-


Problem 1:-

Do you understand the following calculations?

X = `{1,2,3}`

|x| = 3.

Solution:-

X x X = `{(1,1),(1,2),(1,3),(2,1),(2,2),(2,3),(3,1),(3,2),(3,3)}`

| X x X | = 9

|P(X x X)| = `2^9`
Because a binary relation on X is any subset of pairs in X x X there are `2^9` possible binary relations on X.
(Some authors say` 2^9 -1` because of not liking an empty relation.)



Problem 2:-

Do you understand the following calculations?

X = `{1,2,3,4}`

|x| = 4.

Solution:-

X x X = `{(1,1),(1,2),(1,3),(1,4)(2,1),(2,2),(2,3),(2,4),(3,1),(3,2),(3,3),(3,4),(4,1),(4,2),(4,3),(4,4)}`

| X x X | = 16

|P(X x X)| = `2^16`
Because a binary relation on X is any subset of pairs in X x X there are` 2^16` possible binary relations on X.
(Some authors say `2^16 -1` because of not liking an empty relation.)

What is Statistics in Math

Introduction to statistics in math:

What is statistics in math?

In math, Statistics is the science of making effective use of numerical data relating to groups of individuals or experiments. Mathematical statistics deals with all aspects of this, including not only the collection, analysis and interpretation of such data, but also the planning of the collection of data, in terms of the design of surveys and experiments. I like to share this Data Sets for Statistics with you all through my article.

Statistics is specifically useful in drawing general conclusions about a set of data from a sample of the data. Statistics can either be singular or plural. In the singular form, Statistics is a quantity calculated from a set of data, whereas in plural form statistics is the mathematical science discussed in their article


Statistical definitions in math:

What is statistical inference?

It makes use of information from a sample data to formulate conclusions about the population from which the sample was taken.

What is experiment in statistics?

Experiment is a process which results in the collection of data, the outcome of which is unknown

What is Sampling unit in statistics?

Sampling unit is a unit in which an aggregate is divided for the purpose of sampling, each unit being regarded as individual and indivisible when the selection is made.

What is population in statistics?

Population represents the collection of people, plants, animals or thing from which we may collect data.

Sample:

A group of units selected from a larger group is called sample.

Parameter:

Parameter is an unknown value which has to be estimated used to represent a certain population characteristic

Sampling distribution:

Sampling Distribution explains the probabilities associated with a statistic when a random sample is drawn from a population .Understanding Double Box and Whisker Plot is always challenging for me but thanks to all math help websites to help me out.


What are the benefits and applications of statistics in math

Benefits:

Statistics provides a presentation of collected and organized data through the figures, charts, diagrams and graph.

Statistics also provides more critical analyses of information

Application:

Bio statistics
Chemo metrics
Demography
Actuarial science
Econometrics
Epidemiology
Geo statistics
Population ecology
Statistical finance
Statistical mechanics
Statistical physics

Volume calculation formula

Introduction

Volume is how much three-dimensional space a substance (solid, liquid, gas, or plasma) or shape occupies or contains, often quantified numerically using the SI derived unit, the cubic meter.

There are arithmetic formulas to find the volume of simple solid shapes, like regular straight edged or circular shapes. One-dimensional figures (such as lines) and two-dimensional shapes (such as squares) are assigned zero volume in the three-dimensional space. (Source: From Wikipedia).


Different types of shapes and formulas for calculating volume


1. Cube = a^3 cubic units, Where a = side of the cube

2. Cuboids = lbh cubic units, where l, b, h are the length, breadth, and height respectively

3. Cylinder = `pi` r^2 h cubic units, where r, h are the radius and height of the cylinder.

4. Pyramid = `(1/3)` bh  cubic units, where b = base area of the pyramid, and h is the height.

5. Cone = `(1/3)`  `pi` r^2h cubic units, where r and h are radius and height of the cone.

6. Sphere = `(4/3)` `pi` r^3 cubic units, where r = radius of the sphere

7. Ellipsoid = `(4/3)` `pi` r1 r2 r3 cubic units, where r1, r2, r3 are the radii of the ellipsoid.


Example for Calculation of the Volumes:


Example 1: Find the volume of a cylindrical canister with radius 10 cm and height 18 cm.

Solution:

Formula for volume calculation: V= ?r^2h

= 3.14 x 102 x 18

= 5652

So, the volume of the canister is 5652 cm^3.


Example 3: Find the volume of a brick 50 cm by 40 cm by 30 cm.

Solution:

Formula for volume calculation: V = lbh

= 50 x 40 x 30

= 60000

So, the volume of the brick is 60000 cm^3

Million Dollars

Introduction  :

Million dollars are nothing but the quantity. we can express the million dollars in numerical form. Numerical form is nothing but the conversion of words into numbers. For example, one million dollar can be expanded in numerical form as 1,000,000 or 106 dollars. In this article million dollars, we are going to discuss about conversion of various values of million dollars into numerical form through example problems and practice problems.

Example Problems on Numerical Form for Million Dollars:

Example 1:

Write thousand nine hundred million dollars in numerical form.

Solution:

Step 1: one million dollar is equal to $ 1000,000.

Step 2: Thousand nine hundred million dollars will be equal to $ 1,900,000,000.

Step 3: Hence, the numerical form is $ 1,900,000,000

Example 2:

Write two thousand five hundred million dollars in numerical form.

Solution:

Step 1: one million dollar is equal to $ 1000,000.

Step 2: two thousand five hundred million dollars will be equal to $ 2,500,000,000.

Step 3: Hence, the numerical form is $ 2,500,000,000

Example 3:

Write four thousand three hundred million dollars in numerical form.

Solution:

Step 1: one million dollar is equal to $ 1000,000.

Step 2: four thousand three hundred million dollars will be equal to $ 4,300,000,000.

Step 3: Hence, the numerical form is $ 4,300,000,000

Example 4:

Write six thousand two hundred million dollars in numerical form.

Solution:

Step 1: one million dollar is equal to $ 1000,000.

Step 2: six thousand two hundred million dollars will be equal to $ 6,200,000,000.

Step 3: Hence, the numerical form is $ 6,200,000,000

Example 5:

Write two thousand seven hundred million dollars in numerical form.

Solution:

Step 1: one million dollar is equal to $ 1000,000.

Step 2: two thousand seven hundred million dollars will be equal to $ 2,700,000,000.

Step 3: Hence, the numerical form is $ 2,700,000,000

Example 6:

Write eight thousand four hundred million dollars in numerical form.

Solution:

Step 1: one million dollar is equal to $ 1000,000.

Step 2: eight thousand four hundred million dollars will be equal to $ 8,400,000,000.

Step 3: Hence, the numerical form is $ 8,400,000,000




Practice Problems on Numerical Form for Million Dollars:

1) Write four thousand five hundred million dollars in numerical form.

Answer: Numerical form is $ 4,500,000,000

2) Write seven thousand six hundred million dollars in numerical form.

Answer: Numerical form is $ 7,600,000,000

Formula to Figure Slant Height

Introduction about cone:

The slant height of a circular cone is the distance from any point on the circle to the apex of the cone. The slant height of a cone is given by the formula sqrt(r^2+h^2)  where r is the radius of the circle and h is the height from the center of the circle to the apex of the cone. If we know the value of radius and height of the circle, the slant height of cone can be finding using that formula. In this article we shall see how to calculate the slant of the cone .some example problems and practice problems. I like to share this Acute Angled Triangle with you all through my article.

(Source-Wikipedia)

Formula to Figure Slant Height of the Cone with Example Problems:

Slant height of the cone =  `sqrt (r^2+h^2) `

Where r - the radius of the circle

h - the height from the center of the circle to the apex of the cone

Problem 1:

Find the slant height of cone, which has the radius 6 cm and altitude14 cm.

Solution:

Given:

Radius (r) =6 cm.

Altitude (h) =14cm

Formula to figure slant height:

Slant height of the cone = `sqrt (r^2+h^2)` units

=`sqrt(6^2+14^2)`

=`sqrt(36 + 196)`

=`sqrt(232)`

= 15.23

Slant height of the cone = 15.23 cm

Problem 2:

Find the slant height of cone, which has the radius 7 cm and altitude15 cm .

Solution:

Given:

Radius (r) =7 cm.

Altitude (h) =15cm

Formula to figure slant height:

Slant height of the cone = `sqrt (r^2+h^2)`  units

=`sqrt(7^2+15^2)`

=`sqrt(49+ 225)`

=`sqrt(274)`

= 16.55

Slant height of the cone = 16.55 cm

Problem 3:

Find the slant height of cone, which has the radius 8 cm and altitude 16 cm.

Solution:

Given:

Radius (r) = 8 cm.

Altitude (h) =16 cm

Formula to figure slant height:

Slant height of the cone = `sqrt (r^2+h^2)` units

=`sqrt(8^2+16^2)`

=`sqrt(64+ 256)`

=`sqrt(320)`

=17.88

Slant height of the cone = 17.88 cm


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Practice Problems to Find the Slant Height:

1. Find the slant height of cone, which has the radius 9 m and altitude 17 m.

Answer: Slant height of the cone = 19.23 cm

2. Find the slant height of cone, which has the radius 10 cm and altitude 18 cm.

Answer: Slant height of the cone = 20.59 cm

3. Find the slant height of cone, which has the radius 11 m and altitude 19 cm.

Answer: Slant height of the cone = 21.954 cm

Loci Locus

Introduction to locus :

The word loci is the plural of the word locus.  This is a Latin word meaning "place". Though it has several meanings let us discuss the  mathematical meaning of locus or loci in this article. In mathematics, locus is the set of points satisfying a particular condition forming a geometrical figure. Let us discuss locus in detail.

Definition of locus

Locus of a point is the path traced by the point which moves under certain geometrical conditions. More precisely, locus is the set f all points which satisfy a given geometrical conditions or conditions.

Locus - Loci - Examples
The set of all points in a plane such that the distance of each point from a fixed point in the plane is a constant is a locus. We know that this locus is a circle whose centre is the fixed point and whose radius is the constant distance.

Consider the locus of a point which moves so that it is equidistant from two given points A and B. It is the perpendicular bisector of the line AB.

Consider two lines AOB and COD intersecting at O. A point moves so that it is equidistant from those of the two lines. Clearly the path traced by the point is either the internal or external bisector of the angle between AOB , COD.  So, here the locus consists of two straight lines bisecting the angles between the lines AOB ,  COD.

How to Find the Equation of a Locus ( Loci)

Any geometrical condition satisfied by a point ( a , b ) on a locus can be expressed algebraically as a relation between a and b. The relation thus obtained is called the equation of the locus. To find the equation of a locus, we take a point ( a , b ) on the locus and use the given conditions to obtain the relation between a and b . The equation of the locus thus obtained is satisfied by the co-ordinates of every point on the locus and by the coordinates of no other point.