Autism prevalence in the USA.

The symptoms of autism are drastic and devastating. These can be remediated to some degree, but treatment is imperfect. In addition to this, autism and other mental disorders are becoming more common in American as well as global society. Unfortunately, the causes of this terrible epidemic are unknown. Perhaps there is a genetic gene that spreads around. Or maybe the air is so polluted with chemicals, it may affect the development of a child by damaging the brain. Nevertheless, the percentage of children diagnosed with autism has substantially increased. According to the Centers for Disease Control and Prevention (CDC), in 2000, Autism Spectrum Disorder of all levels was prevalent in about 1 in 150 children of all ethnicities and gender in the United States. In a recent statistic, CDC, on March 27, 2014, discovered that autism was prevalent in 1 in 68 children in the United States. However, ASD was 5 times as common in male children (1 in 42) than it was in female children (1 in 189).  ASD is extremely prevalent in other countries as well. In Asia and Europe, ASD is prevalent in 1% of the population. In South Korea, it is reported that ASD is prevalent in 2.6% of individuals (CDC.gov). As seen through the studies throughout the decade, autism prevalence has increased by 45% in 10 years. Today in the United States, about 1.5% of children are diagnosed with autism, which means that a large minority of the population requires heavy special education. The prevalence of autistic kids is larger than the number of doctors in the United States. According a census in 2004, .29% of the population (1 in 300 people) are doctors. Therefore, not only does their need to be more quantity and better quality of special education, but there is also a need for prevention methods.

10.4: Rotating Conics

Hello Mathland!!Let's review the difficult... wait cross that out.... simple concept of Rotating Conics!
Basically all we are doing is rotating a conic by a certain angle.

Here are some Main equations for rotating conics
Ax^2 + Bxy + Cy^2 + Dx +Ey + F = 0
A'(x')^2 + C'(y')^2 + D'x' + E'y' + F' = 0
cos 2 theta = A-C/B
x = x'cos theta - y'sin theta
y = x'sin theta + y' cos theta.

Here are the steps to rotate a conic
1. Find the angle using cos 2theta = A-C/B
2. substitute the angle measure value from the unit circle to the equations in terms of x and y in order to get x' and y'
3. substitute these values into the original equation, and pray that the xy term is eliminated.

10.6 polar coordinates

Wussup mathletes in the wonderful mathland, here is another review of polar coordinates
Remember that they are denoted by (r, theta), where r is the distance from the center and theta is the angle of the line from a polar axis.
Now, how do we convert between rectangular equations to polar equations.
Here are some conversion formulas
x=r cos theta
y = r sin theta

tan theta = y/x
r^2 = x^2 + y^2

here's an example:
3x - 2y = 6
3(r cos theta) - 2(r sin theta) = 6
(r( 3 cos theta - 2 sin theta) = 6)/ (3cos theta - 2 sin theta)
r = 6/(3 cos theta - 2 sin theta)

Effect of age on athletic performance

Obviously at first glance, athletes tend to deterioate as they reach the age of 30. However, why do they do so? Can a trained 50 year old past athlete beat a nonathletic 25 year old to a race? Well first of all, at age 25, the muscles and mind of an individual have completely developed, and they have reached their peak. Additionally, their maximum oxygen consumption, VO2max is also at its greatest potential. For athletes at 25 especially, their VO2 max is extremely high, since they train their body to do so. However, after the age of 30, VO2max decreases approximately by 10%, thus causing muscles to deterriorate. It continues to drop for the remainder of an individual's life. THis comes to the next question, can a trained 50 year old beat a nonathletic 25 year old? Although it sounds unlikely, the answer is yes. For athletes that continue to train, their VO2max does not drop as fast for that of nonathletes. This is why it is extremely important to exercise, since it usually results in a healthier body. Therefore, if an athlete continues to train until he's 50, he can potentially beat a nonathletic 25 year old in a race.

works cited
http://www.svl.ch/SportsAge.html

12.4: limits at infinity and limits of sequences

Limits of infinity: as the limit of f(x) as x approaches -infinity is L1. The limit of f(x) as x approaches infinity is L2.

Here are some rules regarding limits of infinity 

The limit of 1/x^r as x approaches infinity is 0. The limit leans towards the right 

The limit of 1/x^r as x approaches -infinity is 0. Limits leans towards left.

For rational functions... Say a^n/b^m 

If n<m, the limit is 0

If n=m the limit is a/b

If n> m, there is no limit

For example

An = 2n + 1/n+4.... 

N=m 

Limit = 2/1=2

Notes for 8.1 presentation

8.1: matrices and systems of equations
Vocabulary
Matrix: a rectangular array that displays series of terms through m rows and n columns.
Augmented matrix: matrix derived from a system of linear equations. Elementary row options: the means in which we can rearrange matrices. 1. Interchange two equations
2 multiply an equation by a nonzero equation
3. Add a multiple of an equation to another equation.
Row-echelon form: the necessary form we need for augmented matrices and system of equations.
1. Rows consisting mainly of zeroes belong at the bottom
2. First nonzero has a 1
3. For each row the leading 1 in the higher row is to the left of the lower one.

How to solve system of equations through gAussian elimination with back substitution.
1. Get the matrix in row-echelon form using elementary row operations
2. Use back substitution to solve for each variable.

Gauss-Jordan elimination
1. Obtain the reduced row-echelon form using elementary row operations. 2. Variables are equal to the coefficients on the right. 

Techniques for evaluating limits

Limits of polynomial and rational functions

1. If p is a polynomial function and c is a real number,

Lim p(x) = p(c)

2. If r is a rational function given by r(x) = p(x)/q(x), and c is a real number such that q(c) doesn't = 0 

Lim r(x) = r(c) = p(c)/q(c)

Since we cannot have a limit that doesn't have a solution, we must rearrange the function to find the limit. We can do this in two ways

1. Cancellation (factoring) 

2. Rationalizing (multiplying. By conjugate)

Example of cancellation 

15 is cancellation. 17 is rationalizing