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Speed, Time, Distance

Last modified on 2014-03-01


Speed = Distance / Time

Distance = Speed * Time

Time = Distance / Speed

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Acceleration

Last modified on 2014-02-16


Acceleration is a vector quantity that is defined as the rate at which an object changes its velocity. An object is accelerating if it is changing its velocity.

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Newton's Second Law of Motion

Last modified on 2014-02-08


Newton's second law of motion can be formally stated as follows:

The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.

This verbal statement can be expressed in equation form as follows:

a = Fnet / m

The above equation is often rearranged to a more familiar form as shown below. The net force is equated to the product of the mass times the acceleration.

Fnet = m  a
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Venn Diagram & Principle of Inclusion and Exclusion

Last modified on 2013-11-19


Suppose there are N objects out of which there are exactly N_a objects of type a and N_b objects of type b. Also, suppose there are exactly N_{ab} objects that are of both type a AND b. Then, how many objects are NOT of type a OR bdouble-circles.jpg  More...


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Images in Plane Mirrors

Last modified on 2013-09-04


plane_mirror_image

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Arithmetic Sequence

Last modified on 2013-08-17


A Sequence is a set of things (usually numbers) that are in order.

In an Arithmetic Sequence the difference between one term and the next is a constant.

Example: 1, 4, 7, 10, 13, 16, 19, 22, 25, ...

This sequence has a difference of 3 between each number.

Suppose in an arithmetic sequence:  More...


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Division, Quotient and Remainder

Last modified on 2013-03-05


A "quotient" is the result of a division problem. For example: For 6/3, "2" is the quotient, 6 is the dividend, and 3 is the divisor.

Sometime when dividing, there is something left over, it is called the remainder. For example: For 7/3, "2" is the quotient, 7 is the dividend, 3 is the divisor, and "1" is the remainder. 7/3 = 2 R 1.

dividend = divisor * quotient + remainder

For example:

7 = 3 * 2 + 1

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Tree Planting Problem

Last modified on 2012-09-26


Along a yard, T trees are planted at equal distances and the yard is divided into S segments:
 
If a tree is planted at each end of the yard, then T = S + 1
If a tree is planted at only 1 end of the yard, then T = S
If no tree is planted at the end of the yard, then T = S -1
 
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Average, Mean, and Median

Last modified on 2012-10-02


Arithmetic mean (average) = (X1+X2+X3+...+Xn) / n

Geometric mean = (X1 * X2 * X3 * ... * XN)1/N

Median refers to the middle number (in a sorted list of numbers).

To find the median, place the numbers you are given in value order and find the middle number.  More...

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Ivy League Universities Financial Aid Calculators

Last modified on 2014-12-15


Here are the links to calucating how much you will need to attend Ivy League universities and how much financial aid you can expect. Run these financial aid calculators and see how it all shakes out for your family.

Harvard: https://college.harvard.edu/financial-aid/net-price-calculator
Yale: http://admissions.yale.edu/yale-net-price-calculator
Princeton: http://admission.princeton.edu/financialaid/estimator

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