When graphing exponential functions, the information increases so quickly it is impossible to get everything to fit on a normal sized graph. For example, if you say that in one hour three people get information and they pass it onto three more people the next hour, who in turn each pass it on to three other people, the number of people with information goes form 3 to 243 in about 5 hours. If you make it so information is passed at a more realistic amount of time, say every 15 seconds, then 243 people have seen the information in only 105 minutes (1.75 hours). Now lets make it so 100 people saw the information at first and passed it on to 100 more. That would make it so that 10,000 people would have seen it in an hour, 1,000,000 in two hours and 100,000,000 in three. That is a lot of people in a short amount of time. As time passes, the number of people who have seen the information keeps increasing by larger and larger amounts. If the graph is adjusted, the values increase by the equation x equals y to the x power. So 3 hours (x) would equal 3(y) to the 3rd power which is 27. Information travels extremely fast, and looking at the work we've done, it is easy to see how quickly it can ruin someones life.
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Recently, the picture above has been circling around Facebook, Instagram and Twitter. It claims that if the money from the Powerball was divided by the population of the United States, every person would get 4.33 million dollars. People were shocked at the news, and many were convinced that this money would end poverty in the United States. This picture was shared from person to person and posted on social media so the idea spread. The only problem with it is that the math isn't right at all. The real calculation would mean that each person gets $4.33, not 4.33 million dollars. With the help of the media, one persons error was spread across the United States. This false information gave people the wrong idea about the money in the United States and it took people a long time to realize the truth about the information. If only that person had divided correctly.
Many of us have had a lot of experience with math and yet we still don't apply it correctly in everyday life. Does the phrase "give 110%" ring a bell? That saying has come to mean "give your best effort". Sayings like that don't make any sense from a mathematical standpoint and yet they are used often in everyday life. How does something like this come to be? I personally have theory that the saying was repeated from person to person incorrectly or was simply heard wrong, making it so everyone thought it was the true saying. (Similar to how I spent most of my life thinking it was a "doggie dog world" instead of dog eat dog world). Another explanation for this saying would be due to the lack of appreciation or application of mathematics in everyday life. The U.S. is behind other countries in math and science and was ranked number 27 out of 34 for math performance by the Programme for International Student Assessment (PISA) in 2012. A lot of other countries put more emphasis on mathematics in school and life, but the U.S. doesn't seem to do so. This lack of emphasis leads to saying and ideas in everyday life that aren't actually mathematically correct.
The formula for Picks theorem is
A= i + (b/2) -1 where: i=lattice points where grid lines intersect b= number of boundary points To solve for polygon A , Q and R, you would substitute the values into the formula. A(A)= 25 + (12/2) -1 A(A)= 30 A(Q)= 10 + (12/2) -1 A(Q)= 15 A(R)= 11 + (10/2) -1 A(R)= 15 Looking at the areas, you can see that A= Q + R because 30=15 + 15 It is possible to prove that the calculated areas are correct by using other methods. Fro one, you could draw a shape around the polygon, and calculate the area of the shapes around the polygon and subtract that number from the area of the shape. The number you get should equal the area. ex: The area of the rectangle around polygon A = 48 The added areas of the shapes around the polygon=18 And 48-18=30, which was the previously calculated area for polygon A You could also calculate the area by drawing a shape inside the shape and then adding that area to the areas of the other shapes not in the rectangle. ex: drawing a trapezoid in polygon A splits in into 1 rectangle and 2 triangles The area of the trapezoid= 22 The areas of the other shapes=8 And 22+8=30 which is the previously calculated area of polygon A The difference between these methods and Pick's Theorem is that Pick's calculates just the area of the polygon, while the other methods calculate different areas and add or subtract them to make the polygon's shape. While watching a video where a high school student talked about the fourth dimension, I was struck by the idea of traveling so fast that you actually traveled in time. I then watched Stephen Hawking's Train Ride into the Future and found out more on the subject.
The universal " speed limit is 186,000 miles per second (the speed of light). In the video I watched, they explained the idea of moving fast to time travel by imagining a very fast train on a track around the world. The train would have to move so it went around the earth 7 times every second to be fast enough. Because of the laws of physics, the train could never reach the speed of light, but it could get close. The train would be protected form moving that fast. If a child were to run forward, the laws of nature would slow down time on the train to prevent their added speeds from moving at the speed of light. Time would pass slower on the train than it would on Earth. If the train left on January 5th, 2050 and came back on January 1st, 2150, the passengers on board would have only been there for a week. One week and they would have traveled 100 years into the future.This is amazing. If we could find the technology to build some train or ship that could move close to the speed of light, we could travel into the future. With technology, we could go wherever we want, even the future. The grade of a road is an important concept that all drivers should learn about and understand. The grade of the road is the slope of the road and it refers to the tangent of the angle the surface to the horizontal. That means that the grade is rise over run ( the formula for slope). The grade of a road is established in order for cars to know how well they would be able to go up a road. If a road had a grade of say, 33% (which happens to be the grade of the world steepest road, located in New Zealand), it would be very hard for cars to go up it, and they would accelerate a lot on the way down. By saying a road has a % grade, you are saying that the road has a slope or incline of that percent. You can never really understand how a person feels, or why they behave a certain way until you put yourself in the same position. Take my sister as an example. At times she would get upset and angry about what I, at the time, considered to be small things: my parents talking to me first, me being praised for good grades, etc. I was always immensely annoyed at her reactions. Why did she have to overreact and be so emotional? Why couldn't she just be happy for me? I didn't really understand how she felt until I put my self in her shoes. I was the older sister who was always did everything before her. I was my parents first child and they treated me differently than they treated her. When I thought about this I understood why she was upset. She sometimes felt that her and her accomplishments weren't as important. It was after seeing this that I could really be kind and supportive towards her, and make sure that my parents did the same. Kindness is really about putting yourself in someone else's shoes. you can be the most supportive and helpful when you understand someones emotions and motives. Just recently I saw an interview with Dustin Hoffman where he talked about playing a woman in Tootsie. This experience gave him an insight on being a woman and made him realize the things he could do in order to be kinder. So get out there and be kind. Be supportive of other peoples beliefs and opinions and remember to try and talk a walk in someone else's shoes.
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AuthorIsabel Benak Archives
September 2018
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