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Here's our prezi on the vocabulary for chapter 8.
http://prezi.com/poqksnaiqwz_/?utm_campaign=share&utm_medium=copy
Friday, January 31, 2014
Thursday, January 30, 2014
Lesson 8.1
Today we learned two different methods of elimination using matrices, the Gaussian Elimination and the Gauss Jordan Elimination. These two methods are somewhat similar, but personally, I think the Gauss Jordan Elimination is way easier and faster.
The Gaussian Elimination deals with inputting a given system of equations in matrices, and then creating your diagonal of 1's, which will give you a new set of equations. Eventually you will have a given solution to one of your terms, and then you just plug and chug and you'll be able to solve for your other variables.
The Gauss Jordan Elimination is a little different, because it deals with finding your constants within your matrices, just by making all the numbers outside of your diagonal 1's zeroes. It gets a little tricky to do this, but once you do, everything is really simple and your answers come right on the page.
Here are some examples:
#3
In addition, referring to the error analysis, the problem was incorrect due to the fact that the student did not correctly zero out the first zero, because he or she did not ally the (-1) to the whole row. In conclusion, the answer should actually be (7,-3).
The Unsolvable Math Problem
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As I was looking for things to post today, I came across an article about a college student who had ACCIDENTALLY solved a math problem that mathematicians since Einstein have been trying to solve.
The student had been studying very late the night before a test and ended up sleeping in and attending the class late. When he arrived, he quickly began the three problems that had been posted on the board. He was having a hard time on the last one, and it almost seemed impossible, but he suddenly found a method that worked and was able to finish just before time was called. Later that night, the student received a call from his professor whom seemed frantic. The student thought that he had failed the whole test, but in reality, the professor told the student that the third problem was an example of an "impossible equation" and the student was able to solve it! The student was quite amazed with himself, especially since he wasn't even supposed to do the problem in the first place!
So I guess you could say that you never what's going to happen when you just do all the problems on the board, maybe you'll find a solution to something that hasn't been solved in centuries!
The name of this man was George Dantzig. During the time of his revelation, he was a student completing his Doctorate at UC Berkeley in 1946.
As I was looking for things to post today, I came across an article about a college student who had ACCIDENTALLY solved a math problem that mathematicians since Einstein have been trying to solve.
The student had been studying very late the night before a test and ended up sleeping in and attending the class late. When he arrived, he quickly began the three problems that had been posted on the board. He was having a hard time on the last one, and it almost seemed impossible, but he suddenly found a method that worked and was able to finish just before time was called. Later that night, the student received a call from his professor whom seemed frantic. The student thought that he had failed the whole test, but in reality, the professor told the student that the third problem was an example of an "impossible equation" and the student was able to solve it! The student was quite amazed with himself, especially since he wasn't even supposed to do the problem in the first place!
So I guess you could say that you never what's going to happen when you just do all the problems on the board, maybe you'll find a solution to something that hasn't been solved in centuries!
Tuesday, January 28, 2014
Math Soup for the Body and Soul
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How do you make seven an even number?
You take the s out!
Why should the number 288 never be mentioned?
It's two gross.
Why did I divide sin by tan?
Just cos.
What do you call friends who love math?
Algebros.
Even though these were a little corny, I still found them pretty funny, but also kind of sad that people could even think of Math jokes. This just shows how everybody has their own preference, and that some people actually enjoy math and wouldn't mind using it as a subject of a joke, or of a talk, or of anything really.
Chapter 7 Review
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Chapter 7 was filled with lots of different concepts including old and new. From elimination am substitution, to linear programming. Another thing we learned that was somewhat new but also old was breakeven. There's a possibility this was done in Algebra 2, but all it involves is substitution, which was definitely from algebra. Break even is used to find the point at which a business' cost and revenue are the same. In order to find this, you must use two equations.
Total revenue= (price per unit)(# of units sold)
Total cost = (cost per unit)(# of units sold) + initial cost
Here's an example:
Sorry this i late, but I'm battling illnesses.
Thursday, January 16, 2014
Dyscalculia
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Dyscalculia means difficulty in learning arithmetic, such as difficulty in understanding numbers, and learning math facts! This is a disability similar to dyslexia. But, it is less common and only exists between 3 and 6% of the population, in addition a quarter of children with dyscalculia have ADHD.
Dyscalculia comes from Greek and Latin which literally means "counting badly". This disorder might seem quite silly and an excuse to have a bad Math grade, but it is a real disorder with many problems that come with it. For instance, one with dyscalculia can have difficult reading analog clocks, difficulty stating which of two numbers is larger, problems with differentiating between left and right, as well as an inability to concentrate on mentally intensive tasks.
Though people with Dyscalculia have a more difficult time with math, there are treatments to help remediate it. For instance, forms of educational therapy as well as direct stimulation have been proved to demonstrate selective improvement in results.
Personally, I think that Dyscalculia is a disorder that many people are unaware of, and that there's a possibility that I could have it too! Especially when it comes to Math Analysis...
Dyscalculia means difficulty in learning arithmetic, such as difficulty in understanding numbers, and learning math facts! This is a disability similar to dyslexia. But, it is less common and only exists between 3 and 6% of the population, in addition a quarter of children with dyscalculia have ADHD.
Dyscalculia comes from Greek and Latin which literally means "counting badly". This disorder might seem quite silly and an excuse to have a bad Math grade, but it is a real disorder with many problems that come with it. For instance, one with dyscalculia can have difficult reading analog clocks, difficulty stating which of two numbers is larger, problems with differentiating between left and right, as well as an inability to concentrate on mentally intensive tasks.
Though people with Dyscalculia have a more difficult time with math, there are treatments to help remediate it. For instance, forms of educational therapy as well as direct stimulation have been proved to demonstrate selective improvement in results.
Personally, I think that Dyscalculia is a disorder that many people are unaware of, and that there's a possibility that I could have it too! Especially when it comes to Math Analysis...
Lesson 7.5
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Systems of inequalities are the next step after solving a system of equations, but we'll still be using everything eventually. In order to solve a system of inequality, a graph will be needed in order to find the solution that will satisfy all the inequalities.
Here are the steps:
Replace the inequality sign with a equal sign, and sketch the graph of the resulting equation.
>dashed lines (greater than or less than)
>solid lines (greater than or equal to or less than or equal to)
Test one point in each 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.
Solution of a system of inequalities in x and y is a point (x,y) that satisfies each inequality in the system
For a system of inequalities it is helpful to find the vertices of the solution region.
Here's an example:
Just always remember to check which vertices satisfy the inequality that includes x and y!
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