Blog #11: Concussions and math

One of the most common injuries within sports such as Football, Soccer, and boxing, are concussions. For those who don't know the exact definition of a concussion, it is a type of neurological impairment to the brain caused by some type of truama. Concussions generally happen to 5-10% of athletes in any sport. 75% of concussions for males occur in football. This is due to the fact that an average professional football player will receive 900 to 1500 direct blows to the head which raises the probability that they will get a concussion. Additionally, the average professional athlete will tackle at a rate of 25 miles per hour. As for females, 50% of concussions occur from Soccer from flying soccer balls.
 However, Age is also a factor to consider. For a high school athlete, his or her frontal lobe is still developing until the age of 25. Therefore, there chances of receiving a concussion is much higher, and damage is more peramanent for that of an adult. 53% of high school athletes have had a concussion before participating in a high school sport while 36% of collegiate athletes have received multiple concussions.

Works Cited
 http://www.concussiontreatment.com/concussionfacts.html#sfaq9

Blog #10: Gaussian with back substitution vs gaus Jordan

We can also solve systems of linear equations with matrices. The key to solving any system with matrices is forming an augmented matrix, which we can find by using the coefficients of the variables. Remember that the columns are the variables and the rows are the values of the coefficients for each equation. From there we can solve using the Gaussian elimination method or the Gaus Jordan method.

Elementary Row Operations

1. We can interchange 2 rows

2. Multiply a row by a constant

3. Add two rows together.

Steps to Gaussian elimination

1. Create an augmented matrix

2. Use ERO's to rewrite in row echelon form

3. Write a system of equations and use back substitution.

Make sure that everything below your leading ones are zero. The top values don't have to be zero.

Be sure to work column by column.

Steps to Gaus Jordan Method: essentially we are using the same steps as the other elimination method. however, it is important to note that we should only have leading ones and zeroes. Therefore we don't need any new systems of equations. 

Sample problem #1 is  using the Gaus Jordan method. Sample problem #2 is solved using Gaussian elimination. 

Remember that whenever we multiply an equation by a constant, we have to multiply everything in that row. This is shown through the error of another student.

blog #9: prezi on vocabulary regarding matrices.

http://prezi.com/pxvzhbfuuv8i/?utm_campaign=share&utm_medium=copy

post #8: How to strength relates to speed

As a fellow athlete, I have always wanted to improve my athletic performance in strength and speed. However, I have never been so sure what the relationship between the two were. As it turns out, the magnitude of speed is directly proportional with the magnitude of strength if we were to eliminate the factors of weight, endurance, and efficiency. Basically, if an athlete were able to dead lift 500 pounds with perfect form, he or she should potentially be able to apply that maximum amount of force on each step. This is simple physics, if we were to apply more force on the ground, we would increase the distance of our stride and therefore go faster.
However, we must always consider technique. Running with poor technique such as: landing on the back of your heel, leaning too much backwards, or opening up the knee angle too much can lower our running efficiency to 74%. This means that, each of these poor techniques decrease the amount of force we apply on the ground.

Works Cited
http://www.athletesacceleration.com/the-simple-math-behind-running-faster/

Post #7: Chapter 7 review

This is a study guide basically for what my class has learned on Systems of Equations and inequalities.
Systems of Equations (2 variables, 2 equations)
In a system  of linear equations, we have to be able to find the values of both variables. This can be found in the following ways:
1) substitution: solving for one variable in one equation, and plugging it in the variable in the other equation.
2)elimination: basically adding two equations together to get rid of a variable.

We can apply our knowledge of Systems of linear equations in something known as Break Even. This is the point where the total Revenue equals the total cost.
Total Cost = (cost per unit)(number of units) + initial cost
Total Revenue = (Price per unit)(number of units)
since total cost = total Revenue, we can basically set the equations equal to each other using substitution and easily find our number of units, and later on our cost and revenue price.

Systems of Equations (3 variables, 2 or 3 equations)
For a system with 3 equations and 3 variables, we practically do the same thing as we would for a system with 2 variables and 2 equations. The plan is to use our knowledge of Substitution and Elimination to gradually eliminate more and more variables.
As for a system with only 2 equations, follow the simple steps:
1. Eliminate x and solve for y
2. Eliminate y and solve for x.
In this way, we will be solving in terms of Z. Don't forget that Z is a constant in this case, and we will have to replace it with a constant a instead.

Partial Fractions
Remember to do the following steps

1. Multiply by the LCD.

2. Distribute

3. Bring the terms together

4. Factor out the variable.

5. Equate

6. Solve

7. Write as a partial fraction.

Linear programming 

Basically for this we always have to find our constraints in order to find the feasible region. This is the only hard part, after finding the region we must find the vertices of it. Using the coordinates of the vertices, we plug them into our z equation in order to find our maximum and minimum.

Blog #6 Sports Science, NFL Defensive Tackle vs Average Joe

Basically, I was watching this very funny, interesting sports science video yesterday, and realized that football includes physics in it. In this particular video, scientists are determining how strong the NFL really is by matching up Defensive lineman, Kris Jenkins, with the sports science host. I honestly think that this was really funny seeing the lab rat getting destroyed every single time. Basically don't mess with an NFL athlete.
http://www.youtube.com/watch?v=2QOEIQ3_Kuo

Blog #5 systems of inequalities

Sketching the graph of an inequality:

1. Replace the inequality sign with an equal sign, and sketch the graph of the resulting equation.

A. Remember that dashed (less than, greater than) or solid lines ( less than or equal to or greater than or equal to) 

2. Test one point in each of the regions formed by the graph In step 1. If the point satisfies the inequality, shade the entire region to denote that every point in the region satisfies the inequality.

3. A solution of a system of inequalities in x and y is a point (x,y) that satisfies each inequality in the system.

4. For a system of inequalities, it is helpful to find the vertices of the solution region.

Tips

-be sure to set everything equal to y since y=mx+b.

- use different colors to graph everything

-be sure or shade every region covered by a certain equation in order to find the solution region more easily

1. Less than goes left or down from the equation line.

2. Greater than goes right of the equation line or up.

Here's an example.

Blog #4 partial fractions

Welcome to another day of Mathland!! Today In the Mathland I was practicing problems on a difficult process known as partial fractions. It's basically finding two smaller fractions that make up a bigger rational fraction. But through this blog post, I hope I can make your life easier with these tough thingies. 

To solve any partial fractions we must:

1. Multiply by the LCD

2. Distribute

3. Bring terms again

4. Factor the variables out

5. Equate with other side

6. Solve a system of equations.

7. Write as a partial fraction.

As seen in number nine I factored the denominator into two terms and used terms A and B in order to represent the coefficients. Then I found a common denominator which was x^2 + x and distributed the terms. I rearranged the terms together and factored the variables in order to help me equate. This equation was 0x+1 = x(A+B) + A. In this way (a+b) would have to equal 0 and A =1 . If we were to solve the system of equations we would find that b=-1 . Using substitution I would right this as a partial fraction. 

Of course this is just a basic lesson on how to do these things but these are the mains steps for more difficult problems.

educreations on tri linear system of equations. post #3

 Here's an example of how to solve for a system of linear equation with three variables. In this particular system of equations, it was very square, meaning three equations for three variables. I used the previously mentioned methods of elimination and substitution.
http://itunes.apple.com/us/app/educreations-interactive-whiteboard/id478617061?ls=1&mt=8

Mathland day 2. Blog #2

Yesterday I learned how to solve systems of linear equations by using substitution. In Mathland today we learned how to do the same by using elimination. 

Method of elimination

1. Obtain coefficients that differ only in sign

2. Add equations to eliminate a variable.

3. Back substitute to solve for second equation.

4. Check your solution! 

Example 1

5x + 3y =9 

2x-4y=14 

If we chose to eliminate y, we will make sure they have opposite signs but the same variable. Therefore we have to multiply he first equation by 4 and the second equation by 3. Giving us:

20x + 12y = 36

6x - 12y = 42

We will then add the equations to only have x

26x = 78

X=3 

If we plug the value of x back into an equation we can algebraicly find y

5(3) + 3y =9 

3y = 6

Y=2 

Example 2

Elimination is a very effective way of solving the variables for solving equations. I actually prefer using elimination rather than substitution whenever I can, but both are equally as effective and easy! 

"Stay chill. Stay swag Mathland!"

Blog #1 (1/6/14)

Today in Mathland (1/6/14), we basically relearned how to do systems of linear equations. A system is when we are given two or more variables in an equation and are given two or more different types of equations in order to solve for those variables. An example of this could be x+y=2 and x-y=4. The way we learned to solv this is with the use of substitution. Since in equation2 x =y+4 we can replace the x in equation one with the value we found for x. Through algebra y=-1 and we can now substitute back in any equation to find x which is 3.