Most Common Number System (Nandan Nayak)

Introduction to most common number system:

In this we have most common number system. Most common system in math includes rational system, decimal numbers, fractional number, whole number, and so on. In this topic we will see some example problems for decimal number, fractional numbers, whole numbers, and so on. And also we have practice problems. Let us start to study about most common number system.

Example problems for most common number system:

Example problem 1: There is a population of 30,000 bacteria in a colony. If the number of bacteria doubles every 25 minutes, what will the population be 50 minutes from now?

Solution:

First, find out how many times the population will double. Divide the number of minutes by how long it takes for the population to double.

50 ? 25 = 2

The population will double 2 times.

Now figure out what the population will be after it doubles 2 times. Multiply the population by 2 a total of 2 times.

30,000 ? 2 ? 2 = 120,000

That calculation could also be written with exponents:

30,000 ? 22 = 120,000

After 50 minutes, the population will be 120,000 bacteria.

Answer: After 50 minutes, the population will be 120,000 bacteria.

Example problem 2: Preston bikes 0.4 kilometers each school day. How far in total will Preston bike over 14 school days?

Solution:

Multiply the kilometers biked each school day by the number of school days.

0.4 ?14 +40 = 56

Count the number of decimal places in the factors. There is 1 decimal place in 0.4.

56. => 5.6

Preston will bike 5.6 kilometers.

Answer: Preston will bike 5.6 kilometers.

Practice problems for most common number system:

Practice problem 1: Crystal is creating potpourri bowls using 18 bags of shredded bark and 15 bags of flower petals. If she wants to make all the potpourri bowls identical, containing the same number of bags of shredded bark and the same number of bags of flower petals, what is the greatest number of potpourri bowls Crystal can create?

Practice problem 2: There is a population of 10,000 bacteria in a colony. If the number of bacteria doubles every 19 minutes, what will the population be 38 minutes from now?

Practice problem 3: A restaurant chef made '1 2/3 ' pints of tomato soup. Each bowl of soup holds '5/6' of a pint. How many bowls of soup will the chef be able to fill?

Solutions for most common number system:

Solution 1: The greatest number of potpourri bowls Crystal can create is 3.

Solution 2: After 38 minutes, the population will be 40,000 bacteria.

Solution 3: The chef will be able to fill 2 bowls.

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Function of Cell Membrane (Omkar Nayak)

Introduction to function of cell membrane:

Cell membrane or plasma membrane is one of the most important parts of a cell that encloses and protects the components of a cell. Cell membrane separates the interior of a cell from outside environment. It is like a covering that encloses the different organelles of the cell and the cytoplasm that contains these organelles. In brief cell membrane physically separates the contents of the cell from the outside environment. The major function of cell membrane is the same in plant cell and animal cell. The membrane is made of two layers of phospholipids and each phospholipid molecule has a head and a tail region. The head region is called hydrophilic which shows attraction towards water molecules and the tail ends are known as hydrophobic which repels water molecules. The cell membrane also contains lots of protein molecules, which are embedded in the phospholipid layer. All these constituents of the cell membrane work jointly to carry out the functions of cell mem,brane.The functions of cell membrane are described below.

Functions of membrane:

The following are the major functions of cell membrane

Protection: one of the basic functions of a cell membrane is to act like a protective outer covering for the cell. The following are some of the cell membrane functions.
Support: Cell membrane anchors the cytoskeleton or cellular 'skeleton' made of protein and contained in the cytoplasm and gives shape to the cell.
Cell membrane helps in cell adhesion: Cell membrane is responsible for attaching the cell to the extracellular matrix so that the cells group together to form tissues.

Other functions of cell membrane

Transport of materials: Cell membrane helps in the transportation of materials needed for the functioning of the cell organelles. The semi-permeable cellmembrane of the cells helps in the transferring of those nutrients and chemicals that are required for the cell functioning. Transport may be either active at the expense of cellular energy or passive, without using cellular energy.
The proteins present in the cell membrane receive signals from the outside environment and convert the signals to messages that are passed to the organelles inside the cell.
Receptor for various substances: Proteins present on cell membrane act as a receptors or sites for hormone molecules the signal which cell to start or stop metabolic activity.
Act as barrier: The cell membrane surrounds cell and physically separates the intracellular components from the extracellular environment.
Cell communication: Specific proteins embedded in the cell membrane can act as molecular signals that allow cells to communicate with each other.
Immunity: Protein receptors can function to receive signals from both the environment and other cells. Other proteins on the surface of the cell membrane serve as "markers" that identify a cell to other cells. The interaction of these markers respective receptors forms the basis of cell in the immune system.

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Five Number Summary Tutoring (Nandan Nayak)

Introduction to five number summary tutoring:

Five number summary is one of the important topics in mathematics. Five number summary is a sample from which they are derived from a particular group of individuals. Five number summary has a set of observations. In a single variable, it has a set of observations. Five number summary has a different statistics. Here we study about the different statistics involved in five number summary.The online tutoring for the five number summary will give the explanations to the students very interactively through the definitions, steps and examples problems. Therefore, students can learn from online.

Five number summary tutoring:

Different statistics are involved in five number summary are,

Minimum
Maximum
Median
Lower quartile
Upper quartile

Minimum:
Lowest value in the given set of numbers.

Maximum:
Largest value in the given set of numbers.

Median:
Middle value in the given set of numbers.

Lower quartile:
Number between the minimum and median.

Upper quartile:
Number between the maximum and median.

Five number summary tutoring - Steps to solve:

There are different steps to solve the five number summary are,

Observation can be arranged in the ascending order.
The lowest and largest value in the observation can be determined.
The median can be determined. When the observation has odd number of observation than the median is in middle of the observation. Otherwise it is an even number then the median is calculated by the average of the two middle numbers.
The upper quartile can be determined. When the observation minus one is divided by 4 means it is starting with the median and observations in the right side. Otherwise the observation is not divided by four means upper quartile is the median of the observation to the right of the location of overall median.
The lower quartile can be Determined. When the observation set minus one is divided by 4 then it is starting with the median and its observations in the left side. Otherwise the observation is not divided by four means lower quartile is the median of the observation to the left of the location of overall median

Five number summary tutoring - Example problem:

Example 1:

Find the five number summary for the given set of data

{535, 572, 534, 545, 529, 528, and 577}

Solution:

Given set of data

{535, 572, 534, 545, 529, 528, and 577}

{528, 529, 534, 535, 545, 572, 577} [Arrange the set in ascending order]

Minimum and Maximum values in the given set of data are 528 and 577.

Median:

Given observation is odd. So the median is middle of the observation then the median is 535.

Lower quartile:

Given observation is not divisible by four. So the lower quartile is {528, 529, and 534}

Upper quartile:

Given observation is not divisible by four. So the upper quartile is {545, 572, and 577}.

Answer:

Minimum: 528

Maximum: 577

Median: 535

Lower quartile: {528, 529 and 534}

Upper quartile: {545, 572 and 577}

Example 2:

Find the five number summary for the given set of data

{36, 71, 33, 44, 22, 27, 55 and 76}

Solution:

Given set of data

{36, 71, 33, 44, 22, 27, 55 and 76}

{22, 27, 33, 36, 44, 55, 71, 76} [Arrange the set in ascending order]

Minimum and Maximum values in the given set of data are 22 and 76.

Median:

Given observation is even. So the median is median is calculated by the average of the two middle numbers

Median = (36 + 44)/2

= 80/2

Median = 40

Lower quartile:

Given observation is not divisible by four. So the lower quartile is {22, 27, 33 and 36}

Upper quartile:

Given observation is not divisible by four. So the upper quartile is {44, 55, 71 and 76}.

Answer:

Minimum: 22

Maximum: 76

Median: 40

Lower quartile: {22, 27, 33 and 36}

Upper quartile: {44, 55, 71 and 76}

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Star Formation (Omkar Nayak)

Introduction on star formation:

The process of star formation involves collapse of dense molecular clouds into a denser ball of plasma to form a star. Star Formation as a subject includes a study of interstellar medium and giant molecular clouds that precede star formation along with a study of young stellar objects including planets of stars.

Precursors to Star Formation

Empty Space, Interstellar Clouds and Cloud Collapse

Typically the space between interstellar objects, both within galaxies like our Milky Way and between galaxies situated far apart, is not an absolute void or vacuum and contains a diffused interstellar medium (ISM) of gas and dust. ISM has a very low density and about one hundred thousand to one million particles per cubic meter. Its composition by mass is approximately 70% hydrogen and the rest being made up mainly by helium with traces of heavier molecules. Higher density parts of ISM form interstellar clouds whose collapse leads to formation of stars.

Interstellar clouds contain a major part of Hydrogen in the molecular form and are hence referred to as molecular clouds too. Dense giant molecular clouds can often have densities of 100 million particles per cubic meter with very large diameters of 100 light-years (a million trillion km) and a total mass of up to a million times that of our Sun. The process of cloud collapse leads to a rise in temperature.

This internal cloud of gas remains in a stable equilibrium with the two forces of gravitational attraction and kinetic energy of particles working against each other. When the cloud gets sufficiently large and massive and the forces of gravity overcome the kinetic energy, then the process of cloud collapse begins. This may happen on its own or sometimes may be triggered by other stellar events such as collision of molecular clouds, a nearby supernova explosion and galactic collisions. Sometimes, an extremely heavy black hole at the core of a galaxy may also play a role in triggering or preventing star formation.

During the process of collapse Interstellar Cloud breaks into smaller pieces until its fragments reach stellar mass with each fragment radiating energy gained by the release of gravitational potential energy. The process of collapse leads to an increase in density restricting energy radiation and causing a rise in the temperature of the cloud. Rising gravitational force also acts to limit further fragmentation leading to formation of rotating spheres of gas called stellar embryos.

History of Protostar:

A wide range of forces caused by turbulence, spin, magnetic fields formed due to spinning and macroscopic flows come into play and are affected by and also affect the cloud geometry. These influences can hinder or accelerate the process of collapse. If the process of collapse continues the dust within the cloud becomes heated leading to a rise in temperature to around 60,000 -100,000 degrees Celsius with its particles emitting radiations of far infrared wavelengths promoting further collapse of the cloud and rise of temperature in the core.

Rising core temperature and declining density of the surrounding gases create conditions congenial to let the energy escape. This allows the core temperature to rise further causing dissociation of hydrogen molecules. Resulting ionization of hydrogen and helium atoms absorbs energy of contraction. The process of collapse continues until a new equilibrium is reached between the internal pressure of hot gases and gravitational forces. The object so formed is called a protostar.

Star Formation

Protostar continues to grow by attracting material and finally when the conditions are just right the process of fusion begins. Resulting radiation further slows the process of collapse. Finally the surrounding gas and dust envelope is eliminated through absorption into protostar or dispersal and further accretion of mass stops though the process of collapse continues.

At this stage the main source of energy continues to be gravitational contraction and the object is called a pre-main sequence (PMS) star. Further collapse stops at a point and fusion process begins in the core replacing gravity as the main source of energy. The object then begins a main sequence star. Further life cycle of the star thus formed depends on its size.

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Non Conventional Energy Resources (Omkar Nayak)

Introduction to non conventional energy resources:

With increasing demand for energy and with fast depleting conventional sources of energy such as coal, petroleum, natural gas etc. the non-conventional sources of energy such as energy from sun, wind, biomass, tidal energy, geothermal energy and even energy from waste material are gaining importance. This energy is abundant, renewable, pollution free and Eco-friendly. It can be more conveniently supplied to urban, rural and even remote areas. Thus it is capable of solving the twin problems of energy supply in a decentralized manner and helping in sustaining cleaner environment.

non conventional energy resources : Types of non conventional energy resources

The different types of non-conventional sources of energy:

1. Wind energy - Wind is another important source of non-conventional energy. The sun heats up the earth unevenly, winds are formed. The kinetic energy of winds can be used to run wind turbines to produce electricity.

2. Hydro power - Generation of electricity from hydro power sources is a low cost, environment friendly and renewable source of energy.

3. Solar energy - Sun is the source of all energy on the earth. It is the inexhaustible source of energy and zero emissions of greenhouse gas and air pollutants. Solar energy can be applied in many ways, including:

i. To generate electricity using photovoltaic solar cells, space solar power satellite.

ii. To heat foodstuffs, through solar ovens.

iii. To heat water for domestic consumption and heating using rooftop solar panels.

iv. To heat and cool air through use of solar chimneys.

4. Energy from wastes - Generation of waste is inevitable in many human activities. In nature, a balance is maintained as the waste generated by animals and human beings serve as nourishment for the plant life. This waste is processed and treated further to produce electricity.

5. Geothermal energy - It is the energy obtained by tapping the heat of the earth itself, usually from kilometers deep into the earth's crust. This energy is derived from the radioactive decay in the core of the earth, which heats the earth from the inside out.

6. Energy from bio gas - Bio gas is based upon the use of dung to produce gas which is used as domestic fuel especially in rural areas. This technique is based on the decomposition of organic matter in the absence of air to yield gas consisting of methane (55%) and carbon dioxide (45%) which can be used as a source of energy.

7. Tidal energy - It is the energy derived from the tides developed in the oceans and seas, which is used for generating power.

non conventional energy resources : Advantages of non conventional energy resources

They are inexhaustible source of energy.
They are pollution free. Therefore considered to be environment friendly.
They are very inexpensive.

Comprehend more on about Ohm's Law Formula and its Circumstances. Between, if you have problem on these topics heat equation Please share your views here by commenting.

Neutron Star Black Hole (Nandan Nayak)

The birth, life and death of a star is determined by interplay of nuclear reactions and the gravitational forces. The nuclear reactions that take place in the interior of the star will create a radiation pressure which in turn tries to push the star outward. However the gravitational forces between the particles of the star will try to pull it inward towards the center.When there is a balance between the outward radiation pressure and the inward gravitational pressure the star attains stability. However, when the nuclear fuel inside the core of a massive star gets exhausted, the star collapses under its own enormous gravitational force., As a result the star shrinks to a smallest size. This collapsed star will be so dense that even light cannot escape from it. Such an entity in the cosmos is called 'Black hole'

Introduction to Neutron Star Black Hole

A star is formed when a large amount of interstellar gas, mostly H2 and He starts to collapse on itself due to the gravitational attraction between the gas atoms or molecules . As the gas contracts it heats up due to atomic collisions. As the gas continues to contract, the collision rate increases to such an extent, that the gas becomes very hot, and the gas atoms are stripped off their electrons, and the matter is in a completely ionized state, containing bare nuclei and electrons. Such a state of matter is called plasma state. Under these conditions, the bare nuclei have enough energy to fuse with each other. Thus hydrogen nuclei fuse in such a manner to form helium with the release of large amount of energy in the form of radiation. The radiation emitted in this process is mostly emitted in the form of visible light, UV light, IR light etc., from its outer surface. This radiation is what causes the star to shine, which makes them visible (Ex : Sun and other visible stars).

Neutron star black hole : Process

The star at the stage is halted from gravitational collapse( contraction) since the gravitational attraction of matter towards the centre of the star is balanced by the out ward radiation pressure. A star will remain stable like this for millions of years, until it runs out of nuclear fuel such as H_ and He. The more massive a star is , faster will be the rate at which it will use its fuel because greater energy is required to balance the greater gravitational attraction owing to greater mass i.e., massive stars burn out quickly. When the nuclear fuel is over, i.e., when the star cools off, the radiation pressure is not sufficient to halt the gravitational collapse. The star then begins to shrink with tremendous increase in the density. The star eventually settles into a white dwarf, Neutron star or Black hole depending upon its initial mass

Neutron Star and Black Hole : Conditions

For a star to become a neutron star, its initial mass must be greater than ten solar masses. (M> 10Ms ). As a star with initial mass M > 10 Ms cools off the large mass of the star causes it to contract abruptly, and when it runs out of fuel it springs back and explodes violently. This explosion flings most of the star matter into space and such a state of star is called a Supernova. A supernova explosion is very bright and outshines the light of an entire galaxy. The mass of the matter left behind is greater than 1.4 Ms . If the mass of the left over matter is between 1.4 Ms and 3 Ms Neutron stars evolve. At this stage the repulsion between electrons will not be able to halt further gravitational collapse. Under such conditions, the protons and electrons present in the star combine to form neutrons. After the formation of neutrons, the outward degeneracy pressure between neutrons prevents further gravitational collapse, and the matter left over is called the Neutron Star.

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Most Common Number System (Nandan Nayak)

Introduction to most common number system:

In this we have most common number system. Most common system in math includes rational system, decimal numbers, fractional number, whole number, and so on. In this topic we will see some example problems for decimal number, fractional numbers, whole numbers, and so on. And also we have practice problems. Let us start to study about most common number system.

Example problems for most common number system:

Example problem 1: There is a population of 30,000 bacteria in a colony. If the number of bacteria doubles every 25 minutes, what will the population be 50 minutes from now?

Solution:

First, find out how many times the population will double. Divide the number of minutes by how long it takes for the population to double.

50 ? 25 = 2

The population will double 2 times.

Now figure out what the population will be after it doubles 2 times. Multiply the population by 2 a total of 2 times.

30,000 ? 2 ? 2 = 120,000

That calculation could also be written with exponents:

30,000 ? 22 = 120,000

After 50 minutes, the population will be 120,000 bacteria.

Answer: After 50 minutes, the population will be 120,000 bacteria.

Example problem 2: Preston bikes 0.4 kilometers each school day. How far in total will Preston bike over 14 school days?

Solution:

Multiply the kilometers biked each school day by the number of school days.

0.4 ?14 +40 = 56

Count the number of decimal places in the factors. There is 1 decimal place in 0.4.

56. => 5.6

Preston will bike 5.6 kilometers.

Answer: Preston will bike 5.6 kilometers.

Practice problems for most common number system:

Practice problem 1: Crystal is creating potpourri bowls using 18 bags of shredded bark and 15 bags of flower petals. If she wants to make all the potpourri bowls identical, containing the same number of bags of shredded bark and the same number of bags of flower petals, what is the greatest number of potpourri bowls Crystal can create?

Practice problem 2: There is a population of 10,000 bacteria in a colony. If the number of bacteria doubles every 19 minutes, what will the population be 38 minutes from now?

Practice problem 3: A restaurant chef made '1 2/3 ' pints of tomato soup. Each bowl of soup holds '5/6' of a pint. How many bowls of soup will the chef be able to fill?

Solutions for most common number system:

Solution 1: The greatest number of potpourri bowls Crystal can create is 3.

Solution 2: After 38 minutes, the population will be 40,000 bacteria.

Solution 3: The chef will be able to fill 2 bowls.

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Five Number Summary Tutoring (Nandan Nayak)

Introduction to five number summary tutoring:

Five number summary is one of the important topics in mathematics. Five number summary is a sample from which they are derived from a particular group of individuals. Five number summary has a set of observations. In a single variable, it has a set of observations. Five number summary has a different statistics. Here we study about the different statistics involved in five number summary.The online tutoring for the five number summary will give the explanations to the students very interactively through the definitions, steps and examples problems. Therefore, students can learn from online.

Five number summary tutoring:

Different statistics are involved in five number summary are,

Minimum
Maximum
Median
Lower quartile
Upper quartile

Minimum:
Lowest value in the given set of numbers.

Maximum:
Largest value in the given set of numbers.

Median:
Middle value in the given set of numbers.

Lower quartile:
Number between the minimum and median.

Upper quartile:
Number between the maximum and median.

Five number summary tutoring - Steps to solve:

There are different steps to solve the five number summary are,

Observation can be arranged in the ascending order.
The lowest and largest value in the observation can be determined.
The median can be determined. When the observation has odd number of observation than the median is in middle of the observation. Otherwise it is an even number then the median is calculated by the average of the two middle numbers.
The upper quartile can be determined. When the observation minus one is divided by 4 means it is starting with the median and observations in the right side. Otherwise the observation is not divided by four means upper quartile is the median of the observation to the right of the location of overall median.
The lower quartile can be Determined. When the observation set minus one is divided by 4 then it is starting with the median and its observations in the left side. Otherwise the observation is not divided by four means lower quartile is the median of the observation to the left of the location of overall median

Five number summary tutoring - Example problem:

Example 1:

Find the five number summary for the given set of data

{535, 572, 534, 545, 529, 528, and 577}

Solution:

Given set of data

{535, 572, 534, 545, 529, 528, and 577}

{528, 529, 534, 535, 545, 572, 577} [Arrange the set in ascending order]

Minimum and Maximum values in the given set of data are 528 and 577.

Median:

Given observation is odd. So the median is middle of the observation then the median is 535.

Lower quartile:

Given observation is not divisible by four. So the lower quartile is {528, 529, and 534}

Upper quartile:

Given observation is not divisible by four. So the upper quartile is {545, 572, and 577}.

Answer:

Minimum: 528

Maximum: 577

Median: 535

Lower quartile: {528, 529 and 534}

Upper quartile: {545, 572 and 577}

Example 2:

Find the five number summary for the given set of data

{36, 71, 33, 44, 22, 27, 55 and 76}

Solution:

Given set of data

{36, 71, 33, 44, 22, 27, 55 and 76}

{22, 27, 33, 36, 44, 55, 71, 76} [Arrange the set in ascending order]

Minimum and Maximum values in the given set of data are 22 and 76.

Median:

Given observation is even. So the median is median is calculated by the average of the two middle numbers

Median = (36 + 44)/2

= 80/2

Median = 40

Lower quartile:

Given observation is not divisible by four. So the lower quartile is {22, 27, 33 and 36}

Upper quartile:

Given observation is not divisible by four. So the upper quartile is {44, 55, 71 and 76}.

Answer:

Minimum: 22

Maximum: 76

Median: 40

Lower quartile: {22, 27, 33 and 36}

Upper quartile: {44, 55, 71 and 76}

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Non Conventional Energy Resources (Omkar Nayak)

Introduction to non conventional energy resources:

With increasing demand for energy and with fast depleting conventional sources of energy such as coal, petroleum, natural gas etc. the non-conventional sources of energy such as energy from sun, wind, biomass, tidal energy, geothermal energy and even energy from waste material are gaining importance. This energy is abundant, renewable, pollution free and Eco-friendly. It can be more conveniently supplied to urban, rural and even remote areas. Thus it is capable of solving the twin problems of energy supply in a decentralized manner and helping in sustaining cleaner environment.

non conventional energy resources : Types of non conventional energy resources

The different types of non-conventional sources of energy:

1. Wind energy - Wind is another important source of non-conventional energy. The sun heats up the earth unevenly, winds are formed. The kinetic energy of winds can be used to run wind turbines to produce electricity.

2. Hydro power - Generation of electricity from hydro power sources is a low cost, environment friendly and renewable source of energy.

3. Solar energy - Sun is the source of all energy on the earth. It is the inexhaustible source of energy and zero emissions of greenhouse gas and air pollutants. Solar energy can be applied in many ways, including:

i. To generate electricity using photovoltaic solar cells, space solar power satellite.

ii. To heat foodstuffs, through solar ovens.

iii. To heat water for domestic consumption and heating using rooftop solar panels.

iv. To heat and cool air through use of solar chimneys.

4. Energy from wastes - Generation of waste is inevitable in many human activities. In nature, a balance is maintained as the waste generated by animals and human beings serve as nourishment for the plant life. This waste is processed and treated further to produce electricity.

5. Geothermal energy - It is the energy obtained by tapping the heat of the earth itself, usually from kilometers deep into the earth's crust. This energy is derived from the radioactive decay in the core of the earth, which heats the earth from the inside out.

6. Energy from bio gas - Bio gas is based upon the use of dung to produce gas which is used as domestic fuel especially in rural areas. This technique is based on the decomposition of organic matter in the absence of air to yield gas consisting of methane (55%) and carbon dioxide (45%) which can be used as a source of energy.

7. Tidal energy - It is the energy derived from the tides developed in the oceans and seas, which is used for generating power.

non conventional energy resources : Advantages of non conventional energy resources

They are inexhaustible source of energy.
They are pollution free. Therefore considered to be environment friendly.
They are very inexpensive.

Comprehend more on about Ohm's Law Formula and its Circumstances. Between, if you have problem on these topics heat equation Please share your views here by commenting.

Hydroelectric Energy Production (Omkar Nayak)

Hydroelectric energy production

What is Hydro electricity?

Hydro electrical energy is the term referring to electricity generated by hydro power; the production of electrical power through the use of the gravitational force of falling or flowing water. It is the most widely used form of renewable energy. Once a hydroelectric complex is constructed, the project produces no direct waste, and has a considerably lower output level of the carbon dioxide (CO2) than fossil fuel powered energy plants.

History of hydro electricity :

History of hydro electricity Hydro power has been used since ancient times to grind flour and perform others tasks. In the mid-1770s, a French engineer Bernard Forest de Belabor published Architecture Hydraulique which described vertical- and horizontal-axis hydraulic machines. In the late 1800s, the electrical generator was developed and could now be coupled with hydraulics. The growing demand for the Industrial Revolution would drive development as well. In 1878, the world's first house to be powered with hydroelectricity was Cragside in Norththumberland England. The old Schoelkopf power station No 1 near Niagara falls in the U.S. side began to produce electricity in 1881.

Methods to generate Hydro electricity :

Methods to generate Hydro electricity There are four methods to generate Hydro electricity :- Tide Pumped-storage Run-of-the-river Conventional

Conventional method :

Most hydroelectric power comes from the potential energy of dam water driving water turbine and generator. The power extracted from the water depends on the volume and on the difference in height between the source and the water's outflow. The amount of potential energy in water is proportional to the head. To deliver water to a turbine while maintaining pressure arising from the head, a large pipe called a penstock may be used . Conventional method

hydroelectric energy production-Advantages and disadvantages

Pumped storage method :

Pumped storage method This method produces electricity to supply high peak demands by moving water between reservoirs at different elevations. At times of low electrical demand, excess generation capacity is used to pump water into the higher reservoir. When there is higher demand, water is released back into the lower reservoir through a turbine. Pumped-storage schemes currently provide the most commercially important means of large-scale grid energy storage and improve the daily capacity factor of the generation system.

Tide method :

Tide method A tidal power plant makes use of the daily rise and fall of water due to tides; such sources are highly predictable, and if conditions permit construction of reservoirs, can also be dispatched to generate power during high demand periods. Less common types of hydro schemes use water's kinetic energy or undammed sources such as undershot waterwheels.

How to calculate the amount of available power :

How to calculate the amount of available power A simple formula for approximating electric power production at a hydroelectric plant is :- P= ?hrgk where P is Power in watts, ? is the density of water (~1000 kg/m3), h is height in meters, r is flow rate in cubic meters per second, g is acceleration due to gravity of 9.8 m/s2 k is a coefficient of efficiency ranging from 0 to 1. Efficiency is often higher (that is, closer to 1) with larger and more modern turbines.

Advantages :

The major advantage of hydroelectricity is elimination of the cost of fuel. The cost of operating a hydroelectric plant is nearly immune to increases in the cost of fossil fuels such as oil , natural gas or coal and no imports are needed. Since hydroelectric dams do not burn fossil fuels, they do not directly produce carbon dioxide. A hydroelectric plant may be added with relatively low construction cost, providing a useful revenue stream to offset the costs of dam operation. Advantages

Disadvantages :

Disadvantages Hydroelectric power stations that uses dams would submerge large areas of land due to the requirement of a reservoir. Changes in the amount of river flow will correlate with the amount of energy produced by a dam. Generation of hydroelectric power changes the downstream river environment. Large reservoirs required for the operation of hydroelectric power stations result in submersion of extensive areas upstream of the dams, destroying biologically rich and productive lowland and valley forests, marshland and grasslands.

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Number Sense Tutorial (Nandan Nayak)

Introduction to number sense tutorial:

In mathematics, number system is called as system of numeration. Number systems are used to express the quantities for counting, defining order, comparing the quantities, calculating numbers and denoting values. Number system includes natural numbers, integers, rational numbers, algebraic numbers, real numbers, complex numbers, p-adic numbers, surreal numbers and hyper real numbers.

Number sense is explained with examples and practice problems very interactively by tutorial. So students are getting number sense help by tutorial for their studies.

Examples to number sense tutorial:

Example 1:

Add the following decimal numbers 65.45 + 6.892

Solution:

Addition operation for decimal numbers is just like the integers addition. In this problem

65. 45 has two decimal place but 6.892 has three decimal place. Hence, we have to add 0 with the number 65.45, so we get 65.450

That is, 65.45+6.892 = 65.450+6.892

11 1
65.450
+ 6.892
72.342

Example 2:

Find the square root of the following numbers 'sqrt(289)' .

Solution:

'sqrt(189) ' = 'sqrt(17 xx 17)' = 17

Example 3:

Write the standard for the following number 69.089 'xx' '10^3'

Solution:

69.089 'xx' '10^3' which can be written as

69.089 'xx' 10 'xx' 10 'xx' 10

69.089 'xx' 1000 now we have to shift the decimal point to three decimal point. So that we will get

69089

Example 4:

Add the following mixed numbers '8 1/3' and '8 1/4' .

Solution:

We have to convert the following mixed numbers in to improper fraction. For this, denominators are multiplied with the whole number and then add the result of the product with numerator. So that, we will get the improper fraction.

'8 1/3' => '((8 xx 3) + 1)/3' => '(24 + 1)/3' => '25/3'

'8 1/4' => '((8 xx 4) + 1)' => '(32 + 1)/4' = '33/4'

Now we can add both improper fraction

'25/3' + '33/4' here, denominators are not same. So that, we have to find LCM. The LCM is 12

The denominator 3 from the fraction '25/3' is 4 times in the LCM. So we have to multiply the numerator 25 by 4. So we get '100/12'

The denominator 4 from the fraction '33/4' is 3 times in the LCM. So we have to multiply the numerator 33 by 3. So we get '99/12'

'(100 + 99)/12'

'199/12'

Practice Problems to number sense tutorial:

Problem 1:

Add the following decimal numbers 6.45 + 6.82

The answer is 13.27

Problem 2:

Find the square root of the following numbers 'sqrt(324)' .

The answer is 18

Problem 3:

Write the standard for the following number 675.89 'xx' ' 10^3'

The answer is 675890

Problem 4:

Add the following mixed numbers '1 5/3' and '2 6/4' .

The answer is '22/12'

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Identify the Correct Statement (Omkar Nayak)

Introduction to identify the correct statement

In this lesson we will see how to handle multiple choice questions effectively. These questions differ from other detailed problem solving as the student is provided with choices of various answers and the student is required to identify the correct answer. Normally four to five alternatives are provided, out of which usually one is correct but occasionally some multiple choice questions will have more than one correct answer. Normally, examinations with only multiple choice questions come with time constraints and in some cases a penalty is imposed for wrong answers to avoid wild guessing. It is therefore important that this section is attempted quickly and accurately.

As said above, the success in attempting these questions will depend on the ability to identify the correct answer quickly. It might not be required to solve the problem from beginning to end. The student might have enough hints to identify the wrong choice. Some of the problems will require solving up to a stage and then eliminating the wrong answers. In some cases it will be good to try working from the alternatives given into the questions and eliminate the wrong ones.

Approaches to identify the correct statement

Main approaches

Identify and eliminate wrong alternatives
Find the range of values for the possible answer or the sign of the number etc and eliminate the alternatives that are outside the range
Try plugging the alternatives in the conditions mentioned in the problem statement and see if all the conditions are met. This will help in eliminating the wrong alternatives quickly
Let us analyze the various approaches to identify the correct statement without actually spending time to solve the problem and arrive at the final answer

Ex 1: What is the value of 'sqrt(52.4176)'

A) 6.94

B) 3,88

C) 7.86

D) 7.92

Sol: It will be extremely time consuming to actually find the square root of the number 52.4176 without a calculating device. Moreover, the chances of making a mistake in calculations are also high.

Step 1: Let us first take the integer part and then identify the perfect squares near by.

The integer part of 52.4176 is 52 and the perfect squares near by are 49 and 64.

'sqrt(49)' = 7 and 'sqrt(64)' = 8.

So 'sqrt(52.4176)' lies between 7 and 8.

Step 2: This will eliminate the first two choices. We are now left with choices 7.86 and 7.92. One of these numbers if multiplied by itself should get 52.4176.

Note, that 52.4176 ends with 6.

Step 3: So the if we try multiplying 7.92 by 7.92, the end digit will have 4 ( as 2 x 2 = 4) and not 6. So 7.92 is not the right answer. The only alternative left is 7.86 and when multiplied by itself will get a number ending with 6. This is the correct choice

Ans: (C) 7.92

The above approach will considerably save time and effort to identify the answer. Note, we identified the answer, we did not work out the answer. In multiple choice questions this approach is very important

Another approach is to work from the alternatives that satisfy the conditions in the question. This approach will be faster in many cases

Let us now try another example

Ex 2: Given b = 2a, Find the values of a,b and c if, '(21a)/(c) = (b+c+1)/(a)= (2c+5a)/(b)'

A) a= 3,b= 6,c= 7

B) a= 2,b= 4,c= 7

C) a=4,b=8, c=2

D) a=1,b=7,c=6

Sol: It will be too time consuming to solve the equations and to arrive at the values for a, b and c. It will be easier if we plug in each alternative into the conditions of the question and eliminate the ones that does not satisfy.

Step 1: First condition is b = 2a, we can easily see that alternative (D) does not satisfy this condition and can be eliminated. We are now left with (A), (B) and (C) only.

Step 2: Let us try the alternative A: '(21a)/(c) = 21*3/7' = 9 and '(b+c+1)/(a) = (6 +7+1)/(3)' = 4.67. These are not equal and hence alternate (A) is not correct

Step 3: Let us try the alternative B: '(21a)/(c) = 21 * 2/7' = 6 and '(b+c+1)/(a) = (4+7+1)/(2)' = 6 and

Step 4: '(2c+5a)/(b)= (2*7 + 5*2)/(4) = 24/4' = 6.These are all equal to 6 and hence alternate (B) is correct

Step 5: To complete let us try alternate C as well

'(21a)/(c) = 21 * 4/2' = 42 and '(b+c+1)/(a) = (8+2+1)/(4)' = 2.75. These are not equal and hence alternate (C) is not correct

Ans: (B) a= 2,b= 4,c= 7

We will look at one more approach to identify the correct statement

Let us consider another example

Ex 3 : What are the roots of the quadratic equation, 3.1x2 -2.1x - 6.9 = 0

A) 1.47, 3.30

B) 2.1, -3.6

C) -3.2, -1.8

D) 1.87, -1.19

Sol: If we solve the problem using the quadratic formula, it will take a long time as it will involve find the square root of fractional numbers etc. To identify the correct statement among the above four, this is not required either. If we use the formula connecting the roots of the quadratic equation, we can eliminate the alternatives easily

Step 1: We know Sum of roots is '-b/a'

Product of roots is 'c/a'

Step 2: If we apply this for the above equation we get

Sum of root of the equation 3.1 x2-2.1 x - 6.9 = 0 is '2.1/3.1' an dpreoduct of the root is -6.9/3.1

Step 3: The product of roots is negative. This means that we will have one root with positive sign and another with negative sign. This will eliminate alternatives (A) and (C). We now need to pick from alternatives (B) and (D)

Step 4: Sum of the roots is positive, this means that the absolute value of the positive root is higher than the negative root. This will eliminate alternative (B)

The only alternative left is (D)

Ans: (D) 1.87, -1.19

Thus we could identify the correct statement without doing any calculation

Exercise on correcting statements

Pro 1: What is the value of Sin 470?

A) 0.31

B) 0.94

C) 0.731

D) 0.26

Hint: Value of Sin 0 increases from 0 to 1 as theta moves from 0 to 90

Ans: C

Pro 2: Which of the following triplets that best forms the sides of a right angled triangle?

A) 13.1,16.7, 28.51

B) 15.2,16.7, 30.4

C) 17.8,19.6,35.7

D) 24.3,15.2,28.66

Hint: Use the principle that sum of any two sides of a triangle is greater than the third side. This will help in eliminating the alternatives

Ans: D

Pro 3 : what is the value of 6.812-3.922?

A) 28.635

B) 31.097

C) 15.637

D) 38.927

Ans: B

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Renaming Mixed Numbers (Omkar Nayak)

Introduction of Renaming Mixed Number

Mixed numbers is the combination of whole number and the fraction. This renaming mixed number can convert the improper fraction which the numerator is greater than the denominator of the fraction, but not completely divisible. Hence the renaming of the mixed numbers is the mixed fractions. Here we see about the example problem of mixed fraction and how it can covert the improper fraction.

Example of renaming mixed numbers:

Example: 4 '(1 /5)'

Here 4 is the whole number and '4 /5 ' is the fraction which 1 is numerator of the fraction '1 / 5 ' and 5 is the denominator of the fraction '1 / 5' . Here we see about the conversion of mixed numbers to improper fraction and viceversa

Example Problems - Renaming Mixed Fraction:

Example 1:

Convert the mixed numbers into improper fraction 3 '(4 / 5)' .

Solution:

Step 1: Multiply the whole number to the denominator of the fraction.

3 * 5 = 15

Step 2: Add the answer to the numerator of the fraction.

15 + 4 = 19

Step 3: Make the fraction as added number as the numerator and denominator as it is.

'19 /5'

This is the procedure for the conversion of renaming numbers to the improper fraction.

Answer: 3 '(4 /5)' = '19 / 5'

Example 2:

Convert the mixed numbers into improper fraction 5 ('4 / 5)' .

Solution:

Step 1: Multiply the whole number to the denominator of the fraction.

5 * 5 = 25

Step 2: Add the answer to the numerator of the fraction.

25 + 4 = 29

Step 3: Make the fraction as added number as the numerator and denominator as it is.

'29 /5'

This is the procedure for the conversion of renaming numbers to the improper fraction.

Answer: 5 '(4 /5) ' = '29 / 5'

Example 3:

Convert the '17 / 9' to mixed number.

Solution:

9) 17 (1

9

...........

8

Step 1: Divide the given fraction as much as possible.

Step 2: Keep the quotient as whole number and remainder as the numerator of the fraction and divisible number as the denominator of the fraction to for mixed numbers.

Answer: 1 '(8 / 9)'

Pick 3 winning numbers is a game of chance where probability comes into picture.One must be lucky enough to become a one-time millionaire for the reason that the game is not manipulated by the authorized people. There are millions of possibilities for getting numbers that will make you win, equivalent to the total winnings that are at stake every game. Play with your instincts and trust them. These numbers are drawn randomly, hence any number can be perfect combination to pick 3 winning numbers.

picking 3 winning numbers

We have to admit that this game revolves around pure coincidence or we say probability. No one can tell which will be the perfect combination of the winning 3 numbers. Hence you just have to believe that your number is the pick three winning number. Who know may be that is the winning number. That is why this is a game of chance where people are given chances every time they play. Also we can say that this game is pure luck. Some numbers may be just too lucky that they are the most likely numbers to be drawn. But there is no guarantee always. Also we may have to take into consideration some factors from the history of th epick 3 winning numbers events. Such as "Are the double numbers all automatic losers?" ,"Did the system using filters allow for double pick 3 numbers?"

Never stick :

Never stick to your own lucky numbers which you might think are lucky for you as there are tons of numbers that can be the luckiest ones. But if you think your instincts are telling that the numbers you chose are the pick 3 winning numbers , then stick to them as your future lies with it . Also you can try jumbling your chosen numbers, resulting to more possible winning numbers.

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Approximation Ratio (Nandan Nayak)

Introduction to approximation ratio:

Ratio is processes that are used to define in the form of word to differentiate the word problems in the given question. The ratio is the numerical expression representing a part of a larger whole or proportion. A ratio consists of two numbers separated by a colon. Ratio is numbers can be compared as multiples of one another. The word approximation radio defines the number that is not exact, but closes enough to be used.

Representation of approximation ratio:

The given two numbers is done by a colon. Then they are said to be ratio

Colon is represented as :

Rules to be followed for calculation approximation ratio:

Rule 1: If the value specified after decimal point is five or more than five we can add one to the previous number of the point by rounding the value.

Examples based on approximation ratio definition:

Example 1: Problems based on approximate ratio.

In a pet shop they are puppies and pussy cats, the ratio of puppies and pussy cats are 2:4. If the shop contains 85 pussy cats, how many puppies will be there .Find the approximation ratio?

Solution:

Given: The pet shop contains 80 pussy cats,

Now, we are going to assign the variable:

Let x = puppies

The item is now found to be written in ratio fraction,

Puppies / pussy cats = '2/4 = x/ 85'

Cross multiplication is to be done.

So, '2 * 85= 4x'

' x= 170/4'

' x = 42.5'

' x=43.'

The value is five after the decimal point we are adding one to the previous number and rounding the value.

Hence the approximation ratio of 43 puppies is present.

Example 2: Problems based on approximation ratio.

In an pond they are fishes and snakes , the ratio of fishes and snakes are found is 6:9 .If the tank contains 25 snakes , how many fishes are there in pond find its approximation ratio?

Solution:

Given: The pond contains 25 snakes,

Now, we are going to assign the variable:

Let x = fishes

The item is now found to be written in ratio fraction,

Fishes / snakes ='6/9=x/25'

Cross multiplication is to be done.

So, '6*25 =9x'

' 150=9x'

'x=150/9'

' x = 16.66'

' x = 17.'

The value is more than five after the decimal point we are adding one to the number before the decimal point.

Hence approximation ratio of 17 fishes is there inside the tank.

Problems to solve based on approximation ratio:

In a zoo they are elephants and horses, the ratio of elephants and horses are found in ratio of 4: 6 .If the zoo contains 25 horses, how many elephants are there find the approximation ratio?
Answer: 17 elephants.

In a forest they are monkeys and lions, the ratio of monkeys and lions, are found in ratio of 2:4.If the circus contains 225 lions, how many monkeys are there?
Answer: 113 monkeys.

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Star Formation (Omkar Nayak)

Introduction on star formation:

The process of star formation involves collapse of dense molecular clouds into a denser ball of plasma to form a star. Star Formation as a subject includes a study of interstellar medium and giant molecular clouds that precede star formation along with a study of young stellar objects including planets of stars.

Precursors to Star Formation

Empty Space, Interstellar Clouds and Cloud Collapse

Typically the space between interstellar objects, both within galaxies like our Milky Way and between galaxies situated far apart, is not an absolute void or vacuum and contains a diffused interstellar medium (ISM) of gas and dust. ISM has a very low density and about one hundred thousand to one million particles per cubic meter. Its composition by mass is approximately 70% hydrogen and the rest being made up mainly by helium with traces of heavier molecules. Higher density parts of ISM form interstellar clouds whose collapse leads to formation of stars.

Interstellar clouds contain a major part of Hydrogen in the molecular form and are hence referred to as molecular clouds too. Dense giant molecular clouds can often have densities of 100 million particles per cubic meter with very large diameters of 100 light-years (a million trillion km) and a total mass of up to a million times that of our Sun. The process of cloud collapse leads to a rise in temperature.

This internal cloud of gas remains in a stable equilibrium with the two forces of gravitational attraction and kinetic energy of particles working against each other. When the cloud gets sufficiently large and massive and the forces of gravity overcome the kinetic energy, then the process of cloud collapse begins. This may happen on its own or sometimes may be triggered by other stellar events such as collision of molecular clouds, a nearby supernova explosion and galactic collisions. Sometimes, an extremely heavy black hole at the core of a galaxy may also play a role in triggering or preventing star formation.

During the process of collapse Interstellar Cloud breaks into smaller pieces until its fragments reach stellar mass with each fragment radiating energy gained by the release of gravitational potential energy. The process of collapse leads to an increase in density restricting energy radiation and causing a rise in the temperature of the cloud. Rising gravitational force also acts to limit further fragmentation leading to formation of rotating spheres of gas called stellar embryos.

History of Protostar:

A wide range of forces caused by turbulence, spin, magnetic fields formed due to spinning and macroscopic flows come into play and are affected by and also affect the cloud geometry. These influences can hinder or accelerate the process of collapse. If the process of collapse continues the dust within the cloud becomes heated leading to a rise in temperature to around 60,000 -100,000 degrees Celsius with its particles emitting radiations of far infrared wavelengths promoting further collapse of the cloud and rise of temperature in the core.

Rising core temperature and declining density of the surrounding gases create conditions congenial to let the energy escape. This allows the core temperature to rise further causing dissociation of hydrogen molecules. Resulting ionization of hydrogen and helium atoms absorbs energy of contraction. The process of collapse continues until a new equilibrium is reached between the internal pressure of hot gases and gravitational forces. The object so formed is called a protostar.

Star Formation

Protostar continues to grow by attracting material and finally when the conditions are just right the process of fusion begins. Resulting radiation further slows the process of collapse. Finally the surrounding gas and dust envelope is eliminated through absorption into protostar or dispersal and further accretion of mass stops though the process of collapse continues.

At this stage the main source of energy continues to be gravitational contraction and the object is called a pre-main sequence (PMS) star. Further collapse stops at a point and fusion process begins in the core replacing gravity as the main source of energy. The object then begins a main sequence star. Further life cycle of the star thus formed depends on its size.

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Function of Cell Membrane (Omkar Nayak)

Introduction to function of cell membrane:

Cell membrane or plasma membrane is one of the most important parts of a cell that encloses and protects the components of a cell. Cell membrane separates the interior of a cell from outside environment. It is like a covering that encloses the different organelles of the cell and the cytoplasm that contains these organelles. In brief cell membrane physically separates the contents of the cell from the outside environment. The major function of cell membrane is the same in plant cell and animal cell. The membrane is made of two layers of phospholipids and each phospholipid molecule has a head and a tail region. The head region is called hydrophilic which shows attraction towards water molecules and the tail ends are known as hydrophobic which repels water molecules. The cell membrane also contains lots of protein molecules, which are embedded in the phospholipid layer. All these constituents of the cell membrane work jointly to carry out the functions of cell mem,brane.The functions of cell membrane are described below.

Functions of membrane:

The following are the major functions of cell membrane

Protection: one of the basic functions of a cell membrane is to act like a protective outer covering for the cell. The following are some of the cell membrane functions.
Support: Cell membrane anchors the cytoskeleton or cellular 'skeleton' made of protein and contained in the cytoplasm and gives shape to the cell.
Cell membrane helps in cell adhesion: Cell membrane is responsible for attaching the cell to the extracellular matrix so that the cells group together to form tissues.

Other functions of cell membrane

Transport of materials: Cell membrane helps in the transportation of materials needed for the functioning of the cell organelles. The semi-permeable cellmembrane of the cells helps in the transferring of those nutrients and chemicals that are required for the cell functioning. Transport may be either active at the expense of cellular energy or passive, without using cellular energy.
The proteins present in the cell membrane receive signals from the outside environment and convert the signals to messages that are passed to the organelles inside the cell.
Receptor for various substances: Proteins present on cell membrane act as a receptors or sites for hormone molecules the signal which cell to start or stop metabolic activity.
Act as barrier: The cell membrane surrounds cell and physically separates the intracellular components from the extracellular environment.
Cell communication: Specific proteins embedded in the cell membrane can act as molecular signals that allow cells to communicate with each other.
Immunity: Protein receptors can function to receive signals from both the environment and other cells. Other proteins on the surface of the cell membrane serve as "markers" that identify a cell to other cells. The interaction of these markers respective receptors forms the basis of cell in the immune system.

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Number Theory Homework Tutoring (Nandan Nayak)

Introduction to number theory homework tutoring:

In this article we will see about number theory homework tutoring. Number theory homework tutoring is nothing but it is also the basic chapters of mathematics. The number theory problems will be simple and easier. Number theory homework tutoring is done by the tutors in online process. Below are some of the solved example problems under this topic of number theory. Number theory homework tutoring will include the problems on the topics like scientific notation, prime factorization etc.

Number theory homework tutoring

Homework tutoring is done by the tutors of tutor vista. There are many tutors of high qualification are always ready to provide tutoring for the students.

Solved problem 1: Write standard form of the given scientific notation 3.432 ? 102

Solution:

Given 3.432 ? 102

To find the standard form just multiply the scientific notation by 10.

10 are raised with the powers of 2. So shift the decimal point two places to the right side. 3.432 --> 343.2

3.432 ? 102 = 343.2

Solved problem 2: Find the least common multiple of 3 and 8

Solution:

Given 3 and 8

To find the least common multiple (LCM), we have to list out the multiples of 3 and 8.

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30

Multiples of 8: 8, 16, 24, 32, 40, 48

The least common multiple of 3 and 8 is 24. Since 24 is the least common number that comes first in the multiples of both 3 and 8

Solved problem 3: Find the prime numbers in the given series of numbers 14, 16, 19, 21, 25, 29

Solution

Prime numbers are divisible only by 1 and the number itself. It does not have any other multiples. Here we check the given numbers

Multiples of 14 = 1, 2, 7, 14

Multiples of 16 = 1, 2, 4, 8, 16

Multiples of 19 = 1, 19

Multiples of 21 = 1, 3, 7, 21

Multiples of 25 = 1, 5, 25

Multiples of 29 = 1, 29

So here 19 and 29 are the prime numbers of the given series of numbers.

Number theory homework tutoring

Below are some of the practice problems about number theory homework tutoring.

1. Find the prime numbers of the series given below

35, 37, 39, 41, 45

2. Find the LCM of 7 and 9

3. Write the standard form of the scientific notation given 5.243x 102

4. Find the LCM of 11 and 6

5. Find out the prime numbers of the given 42, 63, 70,71

Answer

1. 37, 41

2. 63

3. 524.3

4. 66

5. 71

A number is a mathematical object used in counting and measuring. A notational symbol which represents a number is called a numeral, but in common usage the word number is used for both the abstract object and the symbol, as well as for the word for the number. In addition to their use in counting and measuring, numerals are often used for labels (telephone numbers), for ordering (serial numbers), and for codes (ISBNs).Let us see about the articles is solving math number problems.

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Neutron Star Black Hole (Nandan Nayak)

The birth, life and death of a star is determined by interplay of nuclear reactions and the gravitational forces. The nuclear reactions that take place in the interior of the star will create a radiation pressure which in turn tries to push the star outward. However the gravitational forces between the particles of the star will try to pull it inward towards the center.When there is a balance between the outward radiation pressure and the inward gravitational pressure the star attains stability. However, when the nuclear fuel inside the core of a massive star gets exhausted, the star collapses under its own enormous gravitational force., As a result the star shrinks to a smallest size. This collapsed star will be so dense that even light cannot escape from it. Such an entity in the cosmos is called 'Black hole'

Introduction to Neutron Star Black Hole

A star is formed when a large amount of interstellar gas, mostly H2 and He starts to collapse on itself due to the gravitational attraction between the gas atoms or molecules . As the gas contracts it heats up due to atomic collisions. As the gas continues to contract, the collision rate increases to such an extent, that the gas becomes very hot, and the gas atoms are stripped off their electrons, and the matter is in a completely ionized state, containing bare nuclei and electrons. Such a state of matter is called plasma state. Under these conditions, the bare nuclei have enough energy to fuse with each other. Thus hydrogen nuclei fuse in such a manner to form helium with the release of large amount of energy in the form of radiation. The radiation emitted in this process is mostly emitted in the form of visible light, UV light, IR light etc., from its outer surface. This radiation is what causes the star to shine, which makes them visible (Ex : Sun and other visible stars).

Neutron star black hole : Process

The star at the stage is halted from gravitational collapse( contraction) since the gravitational attraction of matter towards the centre of the star is balanced by the out ward radiation pressure. A star will remain stable like this for millions of years, until it runs out of nuclear fuel such as H_ and He. The more massive a star is , faster will be the rate at which it will use its fuel because greater energy is required to balance the greater gravitational attraction owing to greater mass i.e., massive stars burn out quickly. When the nuclear fuel is over, i.e., when the star cools off, the radiation pressure is not sufficient to halt the gravitational collapse. The star then begins to shrink with tremendous increase in the density. The star eventually settles into a white dwarf, Neutron star or Black hole depending upon its initial mass

Neutron Star and Black Hole : Conditions

For a star to become a neutron star, its initial mass must be greater than ten solar masses. (M> 10Ms ). As a star with initial mass M > 10 Ms cools off the large mass of the star causes it to contract abruptly, and when it runs out of fuel it springs back and explodes violently. This explosion flings most of the star matter into space and such a state of star is called a Supernova. A supernova explosion is very bright and outshines the light of an entire galaxy. The mass of the matter left behind is greater than 1.4 Ms . If the mass of the left over matter is between 1.4 Ms and 3 Ms Neutron stars evolve. At this stage the repulsion between electrons will not be able to halt further gravitational collapse. Under such conditions, the protons and electrons present in the star combine to form neutrons. After the formation of neutrons, the outward degeneracy pressure between neutrons prevents further gravitational collapse, and the matter left over is called the Neutron Star.

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Magnet Uses (Nandan Nayak)

Introduction to magnet uses:

Magnet is an object that produces a magnetic field. The so called magnetic field is invisible to human eye, but it solely responsible for creating the typical characteristic and property of a magnet, i.e. the invisible force that attracts other various ferromagnetic materials and objects like iron, and attracts and repels other magnets as well. There are permanent magnets that are naturally magnetized and create a consistent magnetic field around them. There are also materials that can be magnetized artificially and hence they get attracted to magnets. These are known as ferromagnetic materials and objects. Another aspect is the electro magnet. An electro magnet is made up of a coil which acts as a magnet when certain electric current passes through it. The magnetic moment determined the overall strength of a magnet while the magnetization determines the local strength of magnetism in a material.

Electro Magnets in details

In simple words, an electro magnet is made up by coiling an electric wire into number of lops called the solenoid. It is when electric current is passed through the wire; it creates a strong magnetic field around it, hence providing it the basic magnetic property of attracting ferromagnetic objects. There are a number of uses of an electro magnet. Electro magnets are used for manufacture of junkyard cranes, particle accelerators, magnetic resonance machines for detecting health problems, for manufacture of electric bells, for manufacture of magnetic locks, for magnetic separation of particles, for manufacture of MRI machines and mass spectrometers and other electro mechanical devices.

Common Uses of a Magnet

There are numerous uses of a magnet. Magnet is used in daily life and also for industrial purposes. It is dynamic and extremely resourceful. Following are some very vital uses of a magnet -

1) Credit Cards and Debit Cards: A wide use of magnets is in the manufacture of credit cards, debit cards and ATM cards. Behind each of these is a magnetic strip. The information is encoded in the magnetic strip and helps to contact the individual's financial institution and connect with their accounts.

2) For manufacture of electric motors and generators: There is a combination of an electro magnet and a permanent magnet found in motors that help to convert electric energy into mechanical energy. The reverse concept is used in generators which coverts mechanical energy into electric energy.

3) Medication: Now days the use of magnets by hospitals has increased substantially. Use of magnets has brought a revolution in the field of surgery and medication. The modern day doctors use the process of Magnetic Resonance Imaging. Through this concept, all the major problems of the patients are diagnosed by the doctors without performing any kind of invasive surgery.

4) For magnetic recording media: Video tapes, Computer Floppies, Hard Disks and etc. use the concept of magnetic reel which helps to encode the information on the magnetic coating which ultimately is transferred in the form of audio and video. This was arguably the revolution as far as the extensive use of magnets is concerned.

5) Miscellaneous: Other very vital uses of magnets are for manufacturing of toys, manufacturing of speakers and micro phones, industrial uses such as lifting heavy iron objects, manufacturing of transformers, for the process of manufacturing of jewellery, for manufacture of chucks that help in the field of metal working etc.

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Human Evolution Natural Selection (Omkar Nayak)

Introduction to human evolution natural selection:

Human evolution is scientifically known as anthropogenesis. The scientific name of Human is Homo sapiens. The study of human evolution involves many scientific disciplines such as physical anthropology, archaeology, linguistics and genetics. Human evolution is scientifically known as anthropogenesis. The scientific name of Human is Homo sapiens. The study of human evolution involves many scientific disciplines such as physical anthropology, archaeology, linguistics and genetics. Humans evolved from other hominids, great apes and placental mammals in million of years

Scientists have estimated that humans evolved from their common ancestor with chimpanzees about 5-7 million years ago though the direct lineage from the ancestor of both man and the modern apes to modern man is not known.

Apart from modern apes human shared a common ancestor with whales, chimpanzees and with kangaroos. Studies show that human and chimpanzees shared a common ancestor about 8 million years ago. With whales, common ancestry is tracked about 60 million years ago. Kangaroos and Human shared ancestry about 100 million years ago.

About natural selection:

Natural selection is predictable and efficient mechanism of evolution. Due to evolution species adapt to their environment. It shows the reproductive success of a species, their design in nature and evidence of evolution in action. Due to several environmental and climatic changes individuals needs certain characteristics to have a greater survival or reproductive rate than other individuals in a population. Natural selection leads to evolutionary changes in individuals and pass on these inheritable genetic characteristics to their offspring.

Natural selection as an agent of evolution:

Species come to possess genetic adaptations to the environment due to process of evolution and its working mechanism is natural selection. The process of natural selection acts through individuals and it determines which individuals have the best adaptations for reproductive success.

Natural selection is the central idea of Charles Darwin and Alfred Russel Wallace. The term was introduced by Charles Darwin in one of his books. The struggle for resources or struggle for existence will favor individuals with some variations over others and thereby change the frequency of traits within the population. This process is natural selection and the traits that have an advantage to those individuals who leave more offspring are called adaptations.

Although It is not the only mechanism of evolution but one of the most responsible process for the evolution. There are many difference of opinions among scientist regarding Theory of Evolution and natural selection but over time enough evidence accumulated to support evolution and natural selection.Now when Evolution is a fact, Natural selection is the best process which explains it.Evidence of natural selection are well-documented by observation and through the fossil record.

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