## Monday, December 30, 2013

Happy MMXIV !!  For those not good with Roman Numerals,

M = 1,000
X = 10
I = 1
V = 5

Not used in 2014 are some commonly used Roman Numerals

C = 100
L = 50

Remember IV = 4,  IX = 10,  CM = 900

## Monday, December 23, 2013

With Christmas just a day away, there will only be 365 days until the next Christmas eve.  That's 8,760 hours, 525,600 minutes and 31,536,000 seconds.

8,760    525,600 and 31,536,000 are actually the first three terms of a geometric sequence with common ratio of 60.

FYI... Merry Christmas everyone!

## Thursday, December 19, 2013

There are a few ways to remember how to factor the sum and difference of cubes.  First, remember all the perfect cubes from 1 to 10. Those cubes are as follows

1, 8, 27, 64, 125, 216, 343, 512, 729, 1000

The formulas for factoring sum and difference of cubes are as follows:

a^3+ b^3 = (a+b)(a^2 - ab + b^2)

a^3 - b^3 = (a-b)(a^2 + ab + b^2)

You can remember the terms by thinking of a and b in the first set of parentheses then squaring a, multiplying a and b and squaring b. The signs between terms for sum of cubes is same, negative, positive and for difference of cubes it's negative, positive, positive.

You can remember the signs another way.. Same, Opposite, Always Positive.  If you remember the word SOAP it will help you get the correct signs when factoring.

## Thursday, December 12, 2013

When verifying trigonometric identities, it's generally a good idea to get everything in terms of sine and cosine. That's not always the case, but many times it's helpful.

Remember that sin^2(x) + cos^2(x) = 1
1 + tan^2(x) = sec^2(x)
1 + cot^2(x) = csc^2(x)

csc(x) = 1/sin(x)
sec(x)= 1/cos(x)
tan(x) = sin(x)/cos(x)
cot(x) = 1/tan(x) = cos(x)/sin(x)

Because all the trig functions are based off of sine and cosine, you can clearly see why this would be a benefit when verifying.

It's also a benefit when solving trigonometric equations.

## Saturday, December 7, 2013

Suppose you flip a coin 6 times and want to know the probability of obtaining 4 or more heads in the 6 tosses.  This is a binomial distribution problem with n = 6, x = 4 and p = .5.

Suppose you flip a coin and want to know what the probability that the first head you obtain is on the 3 third roll. This is a geometric probability distribution problem.

Whenever you want to know the probability of some event occurring for the first time on the xth trial, you have a geometric probability distribution problem.

## Monday, December 2, 2013

Remember with conditional probability, such as probability of event A given event B is defined as follows: P(B/A) = P(A and B)/P(A) P(A and B) = P(A)P(B) if events A and B are independent, therefore if A and B are independent, P(B/A) = P(B) and P(A/B) = P(A) If A and B are not independent then P(A and B) = P(A/B)P(B)