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Prime Factor, Greatest Common Factor, Least Common Multiple

Last modified on 2016-03-02


A Prime number can be divided evenly only by 1 or itself. And it must be a whole number greater than 1.

Prime Factorization is the process of finding all the prime factors of an integer. Here is a simple way. In the first diagram below, the prime factors of integer 891 is 3, 3, 3, 3, and 11.  More...


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Combination & Permutations

Last modified on 2014-12-06


in Mathematics we use the following definition:

Permutation Formula

Suppose 0!=1

p(n,m)=n(n-1)(n-2)……(n-m+1)= n!/(n-m)!

Combination Formula

c(n,m)=p(n,m)/m!=n!/((n-m)!*m!);c(n,m)=c(n,n-m);

 More...

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What college admissions officers look for in your essay

Last modified on 2014-12-05


Your college application essay or personal statement is your one opportunity to introduce yourself to the admission board, and put a voice to your test scores and GPA. Writing a self-reflective deeply personal essay can be trying. What do college admissions officers really look for?

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Can you write?

Fundamentally the essay should serve to show your writing skills. Writing is an essential part of college courses, and the application essay allows admissions officers to see if you will be able to meet the demands of the writing curriculum at their school. Your essay should be well organized and properly formatted, and free of grammar and spelling mistakes. Thoroughly proofread – don’t just spellcheck.  More...


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Who or Whom?

Last modified on 2014-11-08


When should you use who, and when should you use whom?
These days, it is becoming rare to see whom, because most of us use who in almost all cases. In fact, whom can sound rather pretentious and stuffy, For example:
To whom am I speaking?
Whom am I speaking to?
These sound very formal. Many of us would be more inclined to write or say:
Who am I speaking to?
Nonetheless, there are still a few stock phrases that use whom, even in contemporary English. For example:
To whom it may concern
In almost all other cases, it has become acceptable in contemporary English usage to use who.

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Thin Lens Equation & Magnification Equation

Last modified on 2014-11-01


Besides a diagram, you can also use the Thin Lens Equation and the Magnification Equation to determine characteristics of an image in curved lens (converging and diverging).

The Thin Lens Equation

1 / d0 + 1 / d= 1 / f  More...


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Geometrical Optics

Last modified on 2014-10-11


In this section, we study the reflection of light, focusing on how light is reflected in

Law of Reflection

The law of reflection states that the angle of incidence is equal to the angle of reflection. Remember that the angles are measured relative to the normal line.  More...


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Light as Electromegnetic Wave

Last modified on 2014-10-11


Electromagnetic Wave

From what we learned from the section on "Electromagnetism", we know that: 1) a changing electric field should create a magnetic field, and 2) a changing magnetic field can create an electric field.

An electromagnetic wave is a combination of electric and magnetic fields that vibrate together in space and time in a synchronous fashion and propagate through space (even vacuum) at the speed of light.

The electromagnetic wave is a  transverse wave.

The electric and magnetic fields oscillate in the direction perpendicular to the direction of propagation.

The EM wave propagates because the electric field recreates the magnetic field and the magnetic field recreates the electric field.

Doppler Effect for Electromagnetic Waves

Electromagnetic waves also experience the Doppler effect. As with sound, motion towards corresponds to a frequency shift upward and a wavelength shift downward, and motion away corresponds to a frequency shift downward and wavelength shift upward (the so-called red-shift).

For example, suppose we observed the light from a distant galaxy is received on Earth with a wavelength of 650nm. But it is known that the wavelength of this light upon emission was 625nm. Then we should know that this galaxy is receding from Earth.

Light as Electromagnetic Wave

Light is an electromagnetic wave –has both electric and magnetic parts and does not require a medium. A medium is any physical substance through which energy can be transferred. There are different types of electromagnetic waves, depending on their frequency levels and energy levels. Electromagnetic waves are formed when an electric field (shown as blue arrows) couples with a magnetic field (shown as red arrows). The magnetic and electric fields of an electromagnetic wave are perpendicular to each other and to the direction of the wave. Electromagnetic Waves have different wavelengths. When you listen to the radio, watch TV, or cook dinner in a microwave oven, you are using electromagnetic waves. Radio waves, television waves, and microwaves are all types of electromagnetic waves. They differ from each other in wavelength. Wavelength is the distance between one wave crest to the next.  More...


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3-D Objects

Last modified on 2014-10-10


Volume of cube = s3 where s is the length of any edge of the cube.

Surface area of cube = 6s2  Where s is the length of any edge of the cube. 
 
The volume enclosed by a pyramid is one third of the base area times the perpendicular height. As a formula: Formula for volume of a pyramid. Math Open Reference
Where b is the area of the base of the pyramid and h is its height. The height must be measured as the vertical distance from the apex down to the base. 
 
The total surface area of any pyramid, is sum of the surface areas of each face. In the case of a right pyramid, the side faces are all the same, so we can simply find the area of one and multiply by the number of faces. Once we add the area of the base, we have the total surface area.  More...

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Kenetic Molecular Theory of Gases

Last modified on 2014-10-08


The gas theory works on the following assumptions:

  • Particles are constantly moving in straight lines
  • There is elastic collision - no loss of energy - when particles collide
  • The particles' volume can be ignored
  • Particles don't attract one another (because they are so far away from each other)

The ideal gas law can be explained with the equation:  More...


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Virtual Image

Last modified on 2014-10-05


Virtual Image is an image formed by light coming from an apparent light source; light is not coming from the actual image location (actual light source).

 virtual_image

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