Keystone Homeschool: Omkar

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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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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.

Non Conventional Energy Resources (Omkar Nayak)

Introduction to non conventional energy resources:

non conventional energy resources : Types of non conventional energy resources

The different types of non-conventional sources of energy:

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

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.

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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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

...........

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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Star Formation (Omkar Nayak)

Introduction on star formation:

Precursors to Star Formation

Empty Space, Interstellar Clouds and Cloud Collapse

History of Protostar:

Star Formation

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Function of Cell Membrane (Omkar Nayak)

Introduction to function of cell membrane:

Functions of membrane:

The following are the major functions of cell membrane

Other functions of cell membrane

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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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Wind Electric Power (Omkar Nayak)

Introduction to wind electric power:

Wind electric power is generated by harnessing the wind energy to generate the power It is the world's fastest growing energy source. Wind electric power is becoming an important resource to meet the increasing power demand as wind energy is a renewable and free resource.

Generation of wind:

Wind is a form of solar energy. Winds caused by the uneven heating of the earth's surface by the sun due to irregularities of the earth's surface and by the rotation of the earth. Wind flow are change by the earth's geographical conditions. This wind energy can be "harvested" by modern wind mills which converts the kinetic energy of wind to generate electricity.

Wind turbines or wind electric generators convert the kinetic energy of the wind into mechanical power.This mechanical power rotates the turbine blades which rotate rotor of the generator that convert mechanical power into electrical power.

Generation of wind electric power

The energy of the wind will be harnessed with wind electric generators or turbines. When the wind flows that passes the turbine's rotor blades, the blades rotate and convert the wind energy into kinetic energy. This Kinetic energy of blades makes the rotor to spin inside a generator according to Faraday's law of electromagnetic induction the kinetic energy is converted into electrical energy. Once the wind energy is converted into electrical energy, the electrical energy flows through power cables in the turbine down's to the turbine tower to connect with the output of the other wind turbines in the wind farm before entering into power transmission. The wind generated power is directly proportional to the wind speed. The greater is the wind speed, the more electrical energy it will be generated. In Wind farms we will see more than one wind turbine working to generate electricity - this is called a wind farm. All the wind turbines will work independently and generate individual power that will be collected from all the wind turbines before feeding for transmission networks.

Construction of wind electric generator to generate wind electric power

Each wind turbine or electric generator has four key parts:

Foundation: Wind turbine is a massive structure that must have a strong foundation to withstand the force from strong winds and it has to support the overall height and the length of the rotor blades.

Tower: Power generation equipments is kept in the tower. The tower consists of the blades and power generation equipments high above the ground level into the smoother where stronger wind currents are blowing. Access to the nacelle and rotor can be done through the tower.

Nacelle: The nacelle can be simply said as heart of the turbine, where the generator, gearbox and turbine drive train parts are held. The generator set inside the nacelle is used to convert the wind energy into kinetic energy and then it will transform into electrical energy.

Rotor: Almost wind turbines have three blades that are attached to the rotor. Blades in wind turbines tested thoroughly to ensure that they can withstand most severe weather conditions.

Generator: When the rotor rotates inside the magnetic poles or stator of the generator according to Faradays law of electromagnetic induction that is "the EMF induced in a coil is directly proportional to the rate of change of flux linkage.This generated power is step up with a transformer and feed to transmission networks.

Pros and Cons of wind electric power

Pros of wind electric power:

Wind energy is a Renewable source and Non-Polluting Resource.

Wind energy is a source of clean, non-polluting form of generation of electricity.

Unlike conventional power generation plants the wind plants does not cause air pollution or emitting of greenhouse gases.

Cons of wind electric power:

The initial installation cost of the wind generator is very high due to utilizing of sophisticated equipments.

Rotor rotation produces much noise resulting in noise pollution.

Power generation is directly depends upon the availability of wind energy which is unpredictable.

Wind mills need to be generated in remote areas where the wind resource is abundant so power transmission and installation cost is high.

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Practice Dividing Decimals (Omkar Nayak)

Introduction to Practice Dividing Decimals:

The method for dividing the decimals by decimals is same as dividing the whole numbers. The decimal on the top of the division line is said to be numerator and the decimal on the below the division line is said to be denominator. The condition for the decimals in the division method should not be zero. Dividing the decimals is in the form of a ? b = c. The decimals representing "a" is said to be dividend. The decimals representing "b" is said to be divisor. The resultant answer is called quotient. Let us see about practice dividing decimals in this article.

Procedure for Practice Dividing Decimals

Step 1:

The divisor can be making into a whole number by multiplying both the divisor and dividend by the same number such as 10, 100, 1000, 10000, etc.

Or else move the decimal point to the right side of the divisor and the dividend by the same number of places.

Step 2:

Put the divisor on the left side of the division bracket and put the dividend inside the division bracket.

Step 3:

Multiply the decimals with a number 10, 100, 1000 according to the places given in the problem to make it as a whole number.

Or else if the divisor having two digits after the decimal point, then move the decimal point two digits after the given number in both the divisor and the dividend.

Step 4:

Continue with the dividing method as for whole numbers and put the decimal point in the quotient exactly as it is in the dividend.

Example Problems for Practice Dividing Decimals

Example 1:

Practice dividing decimals 0.99 by 0.3

Solution:

Let us write the given problem 0.99 as dividend and 0.3 as divisor.

0.3)0.99(

Step 1:

Multiply the dividend 0.99 ? 10 = 9.9 or else move the decimal point after one digit to make it as a whole number.

Multiply the divisor 0.3 ? 10 = 3 or else move the decimal point after one digit to make it as a whole number.

Step 2:

Put the divisor on the left of the division bracket and dividend inside the division bracket.

3)9.9(

Step 3:

Continue dividing the decimal as on whole number dividing.

Check whether 3 go into 9 for how many parts and multiply the terms of 3 with 1, 2, 3, etc. The number 3 can go into 9 for 3 times and the remainder is 0. Subtract the product from the dividend and put down the next digit to divide.

3)9.9(3

---------------

Step 4:

Check whether the number 3 can go into 9 for how many parts and multiply the terms of 3 with 1, 2, 3, etc. The number 3 can go into 9 for 3 times. Subtract the product from the dividend above.

3)9.9(3

---------------

The decimal appoint can be put as same as in the dividend. In dividend it is before one digit likewise put the decimal point in the divisor as 3.3.

The solution for dividing 0.99 by 0.3 is 3.3.

Example 2:

Practice dividing decimals 0.9846 by 0.18

Solution:

Let us write the given problem 0.9846 as dividend and 0.18 as divisor.

0.18)0.9846(

Step 1:

Multiply the dividend 0.9846 ? 100 = 98.46 or else move the decimal point after two digits to make it as a whole number.

Multiply the divisor 0.18 ? 100 = 18 or else move the decimal point after two digits to make it as a whole number.

Step 2:

Put the divisor on the left of the division bracket and dividend inside the division bracket.

18)98.46(

Step 3:

Continue dividing the decimal as on whole number dividing.

Check whether 18 go into 98 for how many parts and multiply the terms of 18 with 1, 2, 3, etc. The number 18 can go into 98 for 5 times and the remainder is 8. Subtract the product from the dividend and put down the next digit to divide.

18)98.46(5

---------------

----------------

Step 4:

Check whether the number 18 can go into 84 for how many parts and multiply the terms of 18 with 1, 2, 3, etc. The number 18 can go into 84 for 4 times. Subtract the product from the dividend and put down the next digit to divide.

18)98.46(54

------------------

-------------------

126

-------------------

Step 5:

Continue with the division at last we got,

18)98.46(547

------------------

-------------------

126

-------------------

--------------------

The decimal appoint can be put as same as in the dividend. In dividend it is before two digits likewise put the decimal point in the divisor as 5.47.

The solution for dividing 0.9846 by 0.18 is 5.47.

Student Teacher Relationships (Omkar Nayak)

Introduction to student teacher relationships:

Man is a social animal and he makes several relationships. However there is one relationship that teaches him the true value of all the other relationships and that relationship is the student- teacher relationship. A teacher makes a student a sophisticated person and also teaches him to be good all throughout his/her life. In this relationship its not only the student who gains enormous knowledge but it is also the teacher who learns many things from the student. A student's success depends entirely on how a teacher takes this relationship. A lot of understanding is needed while dealing with a student and if the teacher is impatient in handling the student this relationship might loose its charm and it will finally break the mutual understanding of both. Moreover it is important for us to know that not only the emotional and social but also the academic success of a student depends on a teacher. Let us further see the unique aspect of this relationship.

Student- teacher relationship's uniqueness:

Student- teacher relationship is unique in its own way. The unique aspect of this relationship is that the teacher is a colleague/ friend and the teacher as well for a student simultaneously. They share knowledge amongst each other without any selfish motive. If a student studies hard and succeeds in a given field it gives a lot of content and happiness to the teacher. This also makes a tough bond between them. If we leave the relationship at the school level, one of the most satisfying relationships can be seen at the college level where teachers grow with their students. A good student-teacher relationship is basically sharing relationship of something unique that no one else has experienced. But to keep freshness and liveliness in this relationship it is important that both of them respect each other and share things with each other.

Student- teacher relationship and the academic success:

As we spoke about in the previous paragraphs that a student's academic success is dependent on this relationship and hence it also calls for a lot of hard work that each one of them puts to acheive a single goal. To enhance this relationship a teacher must approach the student in a positive way so that the student walks on the right path. With the guidance and motivation of a teacher the student develops and grows in every field. This belief of a teacher in a student helps to boost the morale and confidence of a student which helps the student in a long run. Mutual understanding is the basic thing that both have to develop to make this relationship shine like a bright star in the sky.

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Wind Generated Power (Omkar Nayak)

Introduction to wind generated power:

Wind power is generated by harnessing the wind energy to generate the power and is the world's fastest growing energy source. Wind power is becoming more important to meet the increasing power demand as wind energy is a renewable and free resource.

How is power is generated from wind?

The energy of the wind will be harnessed with wind turbines. When the wind flows that passes the turbine's rotor blades, the blades rotate and convert the wind energy into kinetic energy. This Kinetic energy of blades makes the rotor to spin inside a generator according to Faraday's law of electromagnetic induction the kinetic energy is converted into electrical energy. Once the wind energy is converted into electrical energy, the electrical energy flows through power cables in the turbine down's to the turbine tower to connect with the output of the other wind turbines in the wind farm before entering into power transmission. The wind generated power is directly proportional to the wind speed. The greater is the wind speed, the more electrical energy it wil generated. In Wind farms we will see more than one wind turbine working to generate electricity - this is called a wind farm. All the wind turbines will work independently and generate individual power that will be collected from all the wind turbines before feeding for transmission networks.

Description about Wind Turbine or mill

Inside a wind turbine:

Each wind turbine or wind mill has four key parts:

Rotor: Almost wind turbines have three blades that are attached to the rotor. Blades in wind turbines tested thoroughly to ensure that they can withstand most severe weather conditions.

Whether wind turbines are safe to use?

Each wind mill or turbine has an internal computer system that will monitors the direction and the speed of the wind, and that internal system allows it to automatically set itself to operate at a safe level. If there is any errors or damages to the turbine due to working at over capacity(due to high wind speed and strength), the automated system in the turbines will shut down automatically.

Advantages and disadvantages of Wind generated power

Advantages of wind energy:

The greatest advantage of using wind energy is that it generates electricity without emitting any dangerous greenhouse gases .Generates power without the Combustion of fossil fuels .

Wind energy has little effect on the environment, this is because:

Wind energy is a renewable resource, so it can never run out

Wind farms lessen the need for us to use fossil fuels to generate electricity.

Disadvantages of wind energy:

Though the wind energy is a greatly environmental friendly option to generate power,The installation cost is high due to installing a lot of turbines in one place in order to generate more power to meet the power demand.

This giant rotor structure produces more noise while rotating and hence it is noisy .

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What is Dark Matter (Omkar Nayak)

Introduction on what is dark matter:

Dark Matter and Dark Energy are hypothetical concepts hypothesized in the late 1990's to explain accelerating expansion of universe. Prior to the discoveries made possible by Hubble Space Telescope (HST) it was believed that expansion of universe has to stop at some point of time due to force of gravity. It followed that there should be at least some signs of slowing down.

HST made it possible to observe very distant supernovae with a startling discovery that the universe is actually accelerating its pace of expansion. There was no explanation for the observed phenomenon even though there had to be a cause.

Explanation of what is dark matter

Attempts to explain this discovery of accelerating expansion of universe led theorists to come up with conjectures. One possibility was that long-discarded version of Einstein's theory of gravity and its hypothesis of a "cosmological constant" may be correct. Second possibility was that there could be some strange kind of energy-fluid that filled space with the last possibility being that Einstein's theory of gravity may need to be revised to include some kind of field overcoming gravity and causing this observed cosmic acceleration.

The correct explanation is still unknown but the possible solution has been named as dark energy. Existence of dark energy in large quantity can be safely assumed due to its effect on expansion of the universe. But beyond that it is an absolute mystery. It is estimated to constitute about 70% of the Universe with its twin dark matter constituting about 25%. Everything else observable by instruments known to us is estimated to constitute less than 5% of the universe. May be dark energy and dark matter are the normal phenomena of space as what we consider normal and observable is a very small component of the whole.

Conclusion on what is dark matter:

It is easier told what dark matter is not than defining what it is. Theoretical models for the composition of the Universe designed to match actual observations have led scientists to estimate the ratios of dark energy, dark matter and normal matter (70:25:5) given above.

We are certain that dark matter is not in the form of observable stars and planets. It is also not in the form of dark interstellar clouds of matter and it is not antimatter either. It is also not in the form of large black holes because these can be estimated by the number of observed gravitational lenses and there are simply not enough such lenses to make up 25% of dark matter.

There do remain a few viable hypothetical possibilities. One of these is baryonic matter made up of the dark matter all tied up in brown dwarfs or possibly in small, dense chunks of heavy elements. These have been hypothesized as massive compact halo objects. But the generally accepted view point is that dark matter actually made up of some other kind of particles like Axions or Weakly Interacting Massive Particles (WIMPS).

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Combinatorial Geometry (Omkar Nayak)

Introduction to combinatorial geometry:

Let us see combinatorial geometry. It is a unification of principles from the areas of combinatorics and geometry. It has agreement with combinations and planning of geometric objects with the discrete properties of these objects. It is disturbed with such topics like packing, covering, coloring, folding, symmetry, tilling, partitioning, decomposition, and illumination problems. It embraces the aspects of topology, graph theory, number theory, and other disciplines. This section is important in the late of prolific mathematician Paul.

Definition:

It is defined as, the set of subsets of the essential set and it expresses the automorphism group of each expression of this group is the subsets of automorphism group and the original geometry. The distinct combinatorial geometry initiates the new method for representing curves, surfaces and objects in computers. There are many theories representing the combinatorial geometry, the theories are followed below.

Theories:

Theory 1: Geometric number theory.

Theory 2: Geometric graph theory.

Theory 3: Geometric discrepancy theory.

Explanation:

Geometric number theory:

This is the division of pure mathematics concerning the properties of numbers, and integers. This is recounting the arithmetic elementary number theory. This theory also consists the some of the theories are elementary number theory, analytic number theory, algebraic number theory, computational number theory, and arithmetic algebraic geometry.

Geometric graph theory:

Geometric graph theory is one of the graph in which the vertex and edges are related with geometric objects. Geometric graph theory is an occupation of graph theory that studies about geometric graphs. The graph theory contains some graphs like straight line graph, intersection graph, Levi graph and visibility graph.

Geometric discrepancy theory:

The geometric discrepancy theory explains the deviation of a situation from the state one would like it to be. It is specified as theory of irregularities of distribution and it is referred the theme of classical discrepancy theory. It is the process of distributing points in some space that they are evenly distributed with respect to some subsets. This theory describes the study of predictable of distributions.

These are geometries used to represents the combinatorial geometry.

Digital geometry is the discrete set including to the digitized form or image of object of the Euclidean space. Discrete set of its point is replaced to the digitizing. Computer graphic and image analysis is the important area of the digital geometry. Important point of the digital geometry is the digitized the object, with precision and efficiency. Discrete geometry is the heavy overlaps part of the Digital geometry.

Digital geometry

Digital geometry include in learn of the definition and important properties of the digital object. Digital geometry is producing the full view of the points. Digital geometry is act as the integer representation. Digital geometry is not handing the double estimate. Digital geometry is used discrete framework for the image analysis. It is possible to the surface and volumes identified for the image.

Digital topology is the part of the digital geometry. It is used to the image arrays. It provides the bases of the image process operation. It does not use the homogeneous space of the approaches. Every way of the wave starting by increase in a achievement capabilities, computer control, storage space and bandwidth. Every new digitization wave gives the entire process tools. One of the modern disciplines is the digital geometry.

Digital geometry is also to be the digital picture. Pixel is the integer coordination represent by the digital geometry. It is the new advanced method of the mathematical. It is used to the visual computing, and processing. In the Digital geometry the shape description is the interesting area. It is used to digitizing the images. If they have the detailed information about the object the digitization is used.

More about the digital geometry:

Digital geometry is providing more or less the accurate of the viewing points. In the Digital geometry the object digitization is referred t the object. Digital geometry is used to the n- dimension digital spaces. Digital geometry is characterized by the regular rigid.

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Solve Riemannian Geometry (Omkar Nayak)

Introduction to solve Riemannian geometry:

Solve Riemannian geometry refers solving the Riemannian manifolds and smooth manifolds using the Riemannian metrics. Riemannian metrics are nothing but the tangent space with the curves inner product which varies in smooth manner from point to point. To solve the Riemannian geometry we will use the Riemannian sums and Riemannian integrals method. Basically Riemannian geometry refers the elliptic geometry. Here we are going to solve the area of the curve underneath. We will see some example problems for solve Riemannian geometry.

Solve Riemannian geometry - formulas:

If we have to solve the Riemannian geometry we have to use the Riemann sums and integrals method. Using this we have to find the area of the given curve on the graph underneath. In Riemannian geometry the Riemann sums and integrals used in definite integration operation. The Riemann integral is defined by taking the limit for the given Riemann sums. It is based on Jordan measure.

If we want to use the Riemannian sums the formula is

'S = sum_(i = 1)^nf(y_i)(x_i - x_(i - 1))' Here xi - 1= y i= x. Here the choice of y i is the arbitrary.

If the y i = xi - 1 is for all i values then it is called Left Riemann sum.

If the y i = xi then it is called right Riemann sum.

The average of the above two Riemannian is called Trapezoidal sum.

If the y i = (xi - xi - 1) / 2 then we can call this as middle Riemann sum.

If we want to use the Riemannian integrals the formula is

' int_a^bf(x)dx=lim_(maxDeltax->0)sum_(k=1)^nf(x^n)Deltax'

Examples for solve Riemannian geometry:

Examples 1 for solve Riemannian geometry:

Find the area of the given curve under y = x2 among the limits 0 and 3 using Riemannian sum.

Solution:

The area below the curve of x2 among the limits 0 and 3 may be computed procedurally using the Riemann's Sum method. The interval 0 and 3 is divided into n number of sub intervals. Each sub interval gives the width of the 3/n. These are called width of the Riemann's rectangles. The sequence of all x coordinates can be defined as X1, X2 . . . , X n. Then the heights of the Riemann Rectangle boxes can be defined by the following (X1)2, (X2)2 . . . , (X n) 2. This is an important fact where Xi ='(3i) / n' .

The area of a single box will be (3 / n)(xi) 2

S =' (3 / n) xx (3 / n)^2 + . . . . + (3 / n) xx ((3i) / n) ^2+ . . . +(3 / n) xx (3)^2'

S = '27 / n^3 (1 + . . . + i^2 + . . . . + n^2)'

S = '27 / n^3((n(n + 1)(2n + 1)) / 6)'

S = '27 / n^3 ((2n^3 + 3n^2 + n) / 6)'

S =' 27 / 3 + 27 / (2n) + 27 / (6n^2 )'

S =' lim_(n-gtoo)( 27 / 3 + 27 / (2n) + 27 / (6n^2 ))'

S = '27 / 3' = 9

Examples 2 for solve Riemannian geometry:

Find the area of the curve under y = x3 among the limits 0 and 3 using Riemannian integral.

Solution:

In Riemann integrals help we can calculate the area above for the interval 0 and 3. Here

Riemann integral =' int_0^3(x^3)= (x^4 / 4)'

Now we have to take the limit is 0 and 3

If we applying the limit from 0 to 3 we get

= '3^4 / 5 - 0^4 / 4 = 81 / 4'

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Easy Division Problems (Omkar Nayak)

Introduction to easy division problems:

Let us see some content of easy division problems. Division is the operations in mathematics. This is one of the processes in arithmetic operation. The division is very easy for separate the group of events. The division is the opposite process of multiplication. The division problems are may be between integers or fractions. The integers are very easy to divide.

Definition:

Division is the process of dividing the objects together collection of larger objects. This process is used to easily separate from large number of objects. The division is very sufficient when compared to the subtraction. The solution is may be integer or floating. The division is signified as (/).

Steps for easy division:

Step 1: First change way of the given problem like should be written as division way.

Step 2: Next, we need to look at the first number of the given dividing number.

Step 3: Next, we want to see how many times that number divided by the given number.

Step 4: From that last step, we need to subtract the answer from the number. Repeat the step up to getting remainder as zero.

Examples:

Let us see some easy division problems.

Problem 1:

Find the easy value of the problems by division where the values are 34 and 6.

Solution:

The given values are 34 and 6.

Always dividend value should write outside and divisor value should write inside. The subtraction can be taken from left to right.

First write the problem like given below. Like the division format.
Look the first number, it is 3. So, it cannot be divided by the number of 6. So, take another digit with that.
Now the total number is 34. Put calculation how many time will multiply by 6 for getting 34.
But, the number 34 cannot get from the 6th table. But we can get below number of 30 at 5 times.

So subtract from 34. getting remainder as 4 and 5 as quotation. 4 cannot be divided by 6. So 4 is remainder.
____
6 ) 34 ( 5
30
_________
4
________

4 is remainder and 5 is quotation.

Problem 2:

Find the easy value of the problems by division where the values are 25 and 5.

Solution:

The given values are 25 and 5.

Always dividend value should write outside and divisor value should write inside. The subtraction can be taken from left to right.

First write the given problem like division format.
Look the first number It is 2. It cannot divide by 5.
So, take another number 25. The 25 can be divided by 5.
Put calculation how many times want to multiple for getting 25. It is 5 times in mathmetics multiplication table.
Subtract both answers, we are getting 0 as remainder and 5 is quotation.
___
5) 25 ( 5
25
________
0
_________

0 is remainder and 5 is quotation.

Problem 3:

Find the easy value of problems by division where the values are 12 and 6.

Solution:

The given values are 12 and 6.

Always dividend value should write outside and divisor value should write inside. The subtraction can be taken from left to right.

First write the problem as division format.
Look the first. It is 1. It cannot be divided by 6.
So take next number too. Now it is 12. It can be divided by the number of 6.
Put multiplication for getting 12. It is in 2 times from 6th table.
Now, subtract 12 from given number. Remainder 0 and the quotation is 2.
___
6)12 ( 2
12
______
0
_________

0 is remainder and 2 is quotation.

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Number of Divisors (Omkar Nayak)

Introduction to Whole Number Divisors:

A division method can be done by using the division symbol ?. The division can be otherwise said to be inverse of multiplication. The one of the major operation in mathematics is division operation. In division, a ? b = c, in that representation "a" is said to be dividend and "b" is said to be divisor and "c" is said to be quotient. The letter "c" represents the division of a by b. Here the resultant answer "c' is said to be quotient. Let us see about whole number divisors in this article.

Whole Number Divisors for the Number 80

The numbers that can divide by 80 is said to be the divisors of 80.

Let us assume that 80 can be divided by 2, 4, 5, 8, and 10.

Example 1:

Divide the whole number 80 ? 2

Solution:

Let us write the given number 80 inside the division bracket. The divisor can be put it in the left side of the division bracket.

2)80(

The number 2 should go into 8 for 4 times. So, put 4 in the right side of the bracket.

2)80(40

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-------------------

The zero can be placed just near the 4 in the quotient place.

The solution for dividing 80 by 2 is 40.

Example 2:

Divide the whole number 80 ? 4

Solution:

Let us write the given number 80 inside the division bracket. The divisor can be put it in the left side of the division bracket.

4)80(

The number 4 should go into 8 for 2 times. So, put 2 in the right side of the bracket.

4)80(20

---------------

-------------------

The zero can be placed just near the 2 in the quotient place.

The solution for dividing 80 by 4 is 20.

More Problems to Practice for Finding the Divisors for 80

Example 3:

Divide the whole number 80 ? 5

Solution:

Let us write the given number 80 inside the division bracket. The divisor can be put it in the left side of the division bracket.

5)80(

The number 5 should go into 8 for 1 time. So, put 1 on the right side of the division bracket.

5)80(1

---------------

-------------------

Then the number 5 should go into 30 for 6 times. So put 6 just near the 1 on the quotient place.

5)80(16

---------------

----------------

The solution for dividing 80 by 5 is 16.

Example 4:

Divide the whole number 80 ? 8

Solution:

Let us write the given number 80 inside the division bracket. The divisor can be put it in the left side of the division bracket.

10)80(

The number 8 should go into 8 for 1 time. So put 1 on the right side of the division bracket.

8)80(10

---------------

----------------

The zero can be placed just near the 1 in the quotient place.

The solution for dividing 80 by 8 is 10.

Example 5:

Divide 80 ? 10

Solution:

Let us write the given number 80 inside the division bracket. The divisor can be put it in the left side of the division bracket.

10)80(

The number 10 should go into 8 for 0 times. So, take the digit as two digits in a given number of the division bracket.

Then the number 10 should go into 80 for 8 times. So put 8 on the right side of the division bracket.

10)80(8

---------------

-------------------

The solution for dividing 80 by 10 is 8.

Therefore, the divisors for the whole number 80 are 2, 4, 5, 8 and 10.

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