Well I did not really know a whole lot about pi until I did some research about it just now. Pi really confuses me and makes my mind spin to think about because of the fact that it goes on forever, and literally has no end. Because of the fact that Pi is irrational, it is impossible to express Pi as a ratio of two integers such as 22/7 or any other common fractions. Pi is used to find the area and circumference of circles, but because Pi is irrational, it is impossible to square a circle. This is really all I know about the number Pi.
Y=mx+b is an equation that you use to make a line on a graph. M equals the slope of the line. B is the Y-intercept or point on the Y-axis where the line starts. X and Y are the domain and range of the line. All of these components are what make any line that is straight.
So, for example, when you are given an equation for a line such as y=2x+3 you could make a line from it. You first look at "b," the y-intercept, which is 3 so you put your first point on the number three on the Y axis. Once you know the starting point of the line you can use the slope to find more points that will be on the line. In this case the slope is 2. That means that, from the y-intercept, you go over two points and up one. So the coordinates of the next point on this line would be (1,5). Once you have done this you can make the line. That is how you make a line using y=mx+b, and how the equation works. So today I have to compare two different prices of different quantities of Mountain Dew soda. So first of all there is the 12 pack which is a total of 144 ounces of soda, and costs $4.99. The other quantity is the 1 liter (33.8oz), and that costs $1.99. Now you would probably want to know which one of these is a better deal, so you aren't wasting your money. The way you know which deal is better is by finding out which one costs less per ounce. So here is how you do that
All that you really have to do to solve this is divide the price by the number of ounces, or set it up as a unit rate. But its easier just to divide. So first you have to divide 4.99 by 144. When you do that you get a number that rounds off to .03 which means that each ounce of soda in a 12 pack has a value of $.03. Then you divide 1.99 by 33.8 and you get a number that rounds off to .06 which means that each ounce of Mountain Dew in a 1 liter bottle is worth $.06. So with this information you known that it is cheaper to buy a 12-pack of Mountain Dew over a 1 liter bottle. And that is how you compare prices. This semester I have learned a lot about math since I have been taking algebra, which is a new type of math to me. It has been pretty easy to understand, but some things were harder. For example, at the end of last quarter we learned about solving more complex equations and systems by using methods such as substitution and elimination. These topics could get a little tricky and confusing to me, and they still are, but not as much as they were at first. My teacher explains everything very well in class and on the videos we watch for homework, so even if you don't get it at first you will eventually understand. So this is basically all that has recently been hard for me this semester in algebra.
For the most part math has been relatively easy for me throughout my career as a student, but it definitely hasn't been my best subject. In sixth grade I remember math being pretty easy, but I think more complex proportion problems were hard for me. I guess this was difficult for me just because there were a lot of steps involved in solving those problems and if you can't do one step, then you can't solve the rest of the problem. So that was what was most difficult for me. I guess I finally figured out how to do it by just figuring out how to do it one day, or asking a teacher, friend or my parents.
So far I haven't really struggled with anything in my algebra class other than maybe inequalities which can sometimes get confusing, but I understand them now. More recently, I was kind of confused with solving systems using substitution and elimination. What we are doing in algebra is very interesting. This past week we have worked on how to find out when and where two cars will hit each other when they are going toward each other at different speeds. Or also when one car will catch up to the other when they start at different points, and the one in the back is faster. So I am going to explain how to solve these kinds of problems. First of all you need to find out the speed of each car, and also their starting point. Then you can get the equations for each line.
So here is an example of two equations: y= 40x+10, y= -25x+400. So the way you start is by putting the two equations together, and you do that by changing it to 40x+10= -25x+400, since those two equal each other. You know that because they both equal "y" so they must equal each other. So once you have this you just have to solve for "x". You end up getting x=6. Then you plug 6 in for "x" in either of the two equations. It doesn't matter which one because they are equal to each other. Once you do that you solve the problem to get what "y" equals. In this case "y" equals 250. So now you have the coordinates of the point where these two cars will hit each other: at (6,250). This is how you get the coordinates to where two objects will hit each other or one catch up to the other. My example was of two cars hitting, but this works for the catching up as well. This method will work every time. So, I am supposed to explain why square roots might be called that. Well I think the reason they are called that is because of the way you find the area of a square. Think of it, squares have four sides each with the same length, and you multiply two of those sides by each other to get the area. For example if you have a four inch square, you multiply four by four to get the area which is sixteen. So now you have sixteen. What is the square root of that number? Well its four because four times four is sixteen. Another example is if you have a five inch square. Multiply five times five and get an area of twenty-five. Then take twenty-five and find the square root of that which is five. So basically square root is just like area, but backwards, and a number can always be traced back to its root, or base, as a square.
So the question is "why is a number raised to a negative power always less than one, but not ever less than zero. Well negative exponents are a confusing topic, but I will try my best to explain them. There are different ways to solve a problem with negative exponents, but this is how I was taught. All that you have to do is first find the reciprocal of the number. So if you have 4^-2 you would change 4 to 1/4 and negative 2nd power to positive 2nd power, and now have 1/4^2. So then you just multiply 1/4 by itself and you get .0625 which is less than one, but not less than zero. This is actually a very simple method and the good thing is that it will work with any and every problem that has a negative exponent.
An exponent is a number placed after and above another number that shows the power of that number, or how many times you use that number in a multiplication. So if it says 2^3 it means that you have to do 2x2x2 which is 8. And if it says 8^4 you multiply eight by itself four times, which equals 4096. So that is basically how exponents work. Also, if you see exponents in a long problem where you have to use the order of operations, exponents would be the second operation you do after parentheses only. It is the "E" in PEMDAS, if you have always wondered about that like I did until I found out that it meant exponents. So for example if you had the expression 3+2-2^3+(4-2)=, you would first do what is inside the parentheses, which equals two. So now you have 3+2-2^3+2. Next you solve the exponents, 2^3, which is 8, so you now have 3+2-8+2=. Then you just finish the problem by working left to right. So now you know how exponents work, and what to do when you see them in a problem with order of operations.
 This is a picture of the math game that we played this morning. In this game we had to fill the blank circle with the difference of the two numbers that it is between. For example, on the right side of the picture there is the verticle line with the number 19 on top, 3 at the bottom, then a blank space in the middle. What you are supposed to do is find the difference of those two numbers, so the number in the blank space would be 16. You are supposed to do this all around each square until you get to the middle. When you do this game with just whole numbers it is very easy, but there are also modes where you use decimals, fractions or money. These are much harder. So that is what this math game was all about.
| AuthorMy favorite sports are water polo and soccer. ArchivesJune 2013 Categories |
RSS Feed