For the Unit 3 summary assignment, we were assigned the task of demonstrating a mathematical concept presented to us throughout the past week. For this assignment, I chose to demonstrate how to solve quadratics with radicals (3.3)
Solving Quadtratics with Radicals
Let’s say you have a quadratic equation that is unsimplified. The first thing you would usually want to do is to turn it into Ax2 =-+ bx + = 0 ( general form). But what if you have a Radical expression mixed into the equation? leaving the radical sign intact would not work with quadratics, so the first step is to square everything under the radical sign to get rid of the radical sign. In return, we would have to square everything on the other side of the equation as well. After that, your values should be ready to simplify and to be turned into Ax2 + Bx + C = 0 form. With the Ax2 + Bx + c Form, you can then go ahead and factor and solve your equation to find your x values.
Important Note: When dealing with radicals, ALWAYS check both your solutions as one of them could not work!
Ex 1 :
When dealing with coefficients, leave them as they are and make sure to use them while factoring.
For the Unit 2 summary assignment, were assigned the task of demonstrating a mathematical concept learned throughout the past week. For this post, I chose to demonstrate my understanding of dividing Radical expressions.
Dividing Radical Expressions
Let’s say you have a number divided by radical. The first thing you want to do is take the radicand at the denominator section of the fraction and use that to rationalize your denominator. The way you would Rationalize it is by multiplying both the denominator and numerator by what’s at the bottom of the fraction (denominator/ radicand). make sure to not multiply with the coefficient next to radicand, as we are only using the radicand to rationalize in this case. Afterwards, you want to evaluate the fraction by multiplying your values correctly, reducing numbers that can be reduced, and then simplifying the radicand if it’s a perfect square.
Ex :
Note: Multiplying a fraction by 1 will not change its value
Dividing Radical Expression with BINOMIALS
When the radical denominator is a binomial, we use the conjugate to rationalize the denominator.
What’s the Conjugate? : The conjugate can mean the opposite of the given expression. for example, The conjugate of 2x+3 would be 2x-3. Make sure you know that the conjugates will always cancel each other out.
Unlike the example in the first explanation, instead of only using the radicand to rationalize fraction, we take the entire expression at the denominator spot and use the conjugate of the expression to rationalize the entire fraction. If you see conjugates at the denominator, you can simply cancel them out. Multiply the Denominator and numerator and simplify as much as possible.
Let’s face it. No matter what we have or how much we possess, there’s always going to be that feeling of wantingmore. That, my friends, is The Disease Of More. As explained in the article, written by mark manson, the disease of more is more or less not being satisfied with where you are at that moment. While always trying to improve can be a good thing, always feeling the need to improve yourself can be a problem. A good example of this can be shown through Pat Riley, hall of Fame NBA coach who led six teams to the NBA championship. He explains why the teams who win the championship are often dethroned, not through other teams, but y forces from the organization itself. They are stuck with a tunnel vision of winning the championship, only to feel as if it isn’t enough. At first, that “more” was to win the championship. After winning, it becomes more money, more media attention, more fame, etc… as Pat puts it “what was once a cohesive group of hardworking men begins to fray. Egos get involved. And the psychological compositions of the team changes.” I think it’s safe to say that I have been guilty of the disease of more. I have also had that voice in the back of my head telling me that I need to do more, and I can’t remember a time where that did any good. It goes to show that we need to be motivated in life by something more than our own happiness. It means that we have to be driven by something greater than ourselves, whatever that may be. The article was definitely eye-opening to me. It’s always good to be improving yourself. The truth is that if you want to improve yourself, you need to appreciate where you are in the moment. What you do now will determine where you will end up. live in the moment.
We have become accustomed to forming opinions and judgments before understanding and educating ourselves. Whether it be about a subject, a place, or a group of people, some would like to refer to our incomplete perceptions as ‘’The single story.’’ After learning about the general idea of single stories and stereotypes through videos and articles we went over in class, Ms. Shong assigned us the New Media 11 Challenge. Similar to Michael Wesch’s experiment with his Anthropology 101 students, we were each paired up with someone different from you and getting to know them through a series of questions. I was paired up with Oscar and we both went through a series of questions to get to know each other. During our conversation, we covered a lot of topics in order to recognize our differences and similarities. Surprisingly, we had more in common than I ever would have expected. I realized that first impressions can only go so far.
On the topic of first impressions and stereotypes, In Chimamanda Adichies Ted Talk, she explained her single story view of Mexicans. The things she saw on the media made her think that Mexicans were abject immigrants. One day, Adiche went to visit Mexico. On her first day, she felt a slight surprise. She came to realize that Mexicans were ordinary people having a good time. They were going to work in the market place, smoking, laughing, and working. She put herself in a foreign situation and pursued the idea of opening up and understanding. At the end of the day, Adiche only came to realize the danger of single stories. Like she says in her speech “show a people as one thing, as only one thing, over and over again, and that is what they become.”
During Michael Wesch’sHow To Stop Hating Video, he says ‘’ Open up to others and try to understand why they love what they love.” At first, being assigned with a random partner seemed like it would be a little bit awkward and uncomfortable. After getting to know Oscar, I was surprised about how much we had in common. I realized that being with people different from you isn’t a bad thing. What Wesch is saying is that maybe the things we think we hate might become enjoyable if you find a deeper meaning to it and that there is more to people than we think. Who knows, maybe it will be the thing that has been missing in your life. I wasn’t dreading the idea of being paired up with someone random, but I also wasn’t the most excited. In the end, I came to realize how enjoyable the experience was. Honestly, I’m looking forward to doing another project similar to this one in the future.
After searching through many essays, articles, and stories, the title of this essay had caught my attention. Being content with yourself, in my opinion, is the gateway to realizing happiness. The essay, written by Kamaal Majeed, had a form of connection with me because, like Kamaal, I am also in high-school, and the content in his writing should be recognized by people our age. Kamaal, being a black student in his high school, was made fun of by other students for not being a stereotypical black kid. After enrolling in honors for his math class, students made fun of the fact that he was a black student in an honors class. Kids went as far as to ask him to act more black. Despite all the comments, Kamaal continued to be himself and to do what he loves. Kamaal shows us that to be content, you need to do what you love and not seek the approval of others. Like he says, “In high school, popularity depends on whether or not you are willing to follow trends.” Although his self-respect has made him disliked and cause him a lack of popularity, he embraced it. He came to realize that others being content with him wasn’t as important as being content with himself. Being happy with yourself is crucial if you want to be happy in general. I think there’s a lot of kids my age who need to understand this matter as we are going into adulthood and it doesn’t get easier after high school. The essay made me think that worrying about what others think about you won’t bring you happiness. Do what you love doing and be yourself. Be different from the rest.
Why is it important that we become aware of the water?
We have become very accustomed to our surroundings and we seem to adapt to our environment very easily. We have been living blindly to the fact the media that we consume every day is slowly pulling us out of reality. It’s almost as if the media we consume, the technology we use and depend on, is making us less human. It brings us to a point where we need to take a step back and think about why we need to see the water. You may be thinking “What’s the water?”. The water, explained by David Foster Wallace in a commencement speech explains that the water is our perception of our surroundings. To put it simply, we currently cannot see the water. The media we are consuming and the information we bring in makes us think we know what’s going on in the world when the sad reality is that we don’t know what’s going on. The water has nothing to do with our knowledge, but more about our simple awareness of what is real.
As we’ve seen it through history and even nowadays, polarization in our society is an ongoing problem and is a prescription for disaster. Polarization in our society results in sharply contrasting beliefs and opinions, which creates disagreements and conflicts within a society/country. the article that stood out to me was one that talked about problems with political polarization in the united states. People In the united states tend to be very passionate about their political beliefs. The problem with this is that these people tend to only follow and watch out for what they are following. With this being a problem, liberals and conservatives are segregating themselves into their bubbles of ideologies and not considering other things. The political segregation of everyone is taking effect on the federal government. We need the federal government to be able to function as a society and to stop problems within it. If we continue like this, the federal government won’t be able to function. The political polarization and the segregating ideologies it creates is a direct example of our internet. Although we have all the world’s information at our fingertips, the internet’s algorithms create a lack of diversity, which limits us to what we see. And as we are all living blindly to the fact that we aren’t aware of the environment and others, the water becomes more and more invisible by the minute. The true perception of reality becomes limited to something false.
Liberals and conservatives need to take the time to think about one another. We all need to come to an understanding of each other and we have to put each other into perspective. With no middle ground to our understanding and beliefs, how are we going to see improvement? If we continue to be apathetic towards others that need empathy and help, we will start to see that there will be no one there for us when we need it the most. And weir’s “The Egg” Put things into perspective. The Egg shows that you are every person who has ever lived. The theory is about reincarnation and shows that time doesn’t exist, because you can get reincarnated into the past. The Egg’s main message of this theory is to treat people the way you want to be treated. The actions you take upon others may be actions towards yourself. It may not be on as deep of a level as it sounds, so let me explain. we need to understand that there isn’t much separating us, humans. We all live on the same planet. The more destruction we cause to one another and the more we stop taking care of our planet, we are only causing damage to ourselves. We must start to look at the bigger picture and to realize that we are in this together. We need to be aware of the water.