Theory of Parabolas Essay Example for Free

Theory of Parabolas Essay A parabola is designed on a basic formula, Y=ax^2+bx+c, which allows it to achieve a curve not seen in a normal line graphed using a Y=mx+b format. To the left is a graph who’s formula is y=x^2, where a=1, b=0, and c=0. I have isolated the (a) factor to see its effects on the parabola. Below is a graph where I have changed the (a) multiple times. The result is that as the (a) decreases, the mouth of the parabola widens due to the fact that (a) is essentially the slope of the parabola. Now, watch what happens when the (a) becomes negative. Now the mouth of the parabola is opening down and as we increase (a), the parabola widens. When (a)1, the parabola closes up horizontally. So from this, we can infer that if (a) is 0, then the result will be a straight line going along the X axis which is no longer a parabola. Now we will look at how the (b) factor changes the parabola, below is the origional graph from the top of the paper except the red line represents the same parabola with a (b) added onto it. The original equation was Y=x^2(blue line) and the new equation is Y=x^2+x(red line). The change is moving the vertex of the parabola left ? and down ? but the shape of the parabola it’s self is unchanged. Here are some other examples of changing (b) in a parabola with a steady (a) As seen in the graph, (b) only moves the parabola to the sides and down (as the numbers increase, the vertex moves left and down and decreasing is vice versa), but somehow fails to move the parabola up past the point X=0 on its own (making the (a) negative will flip the parabola). So now we have a slope (a) and a vertex (b), but we still need our Y-intercept which will be our (c) As shown from the graph, our parabolas Y-intercepts match up with our (c) factor, completing the equation -Fun fact, the word parabola came from the Greek words para, meaning beside, and bole, meaning to throw

Taking Our Freedom for Granted Essay -- United States History Historic

Taking Our Freedom for Granted Our country was founded on the idea of freedom: freedom from a king, freedom to believe in whatever one wants to believe in and freedom to openly express these beliefs with others. Through careful examination of what the authors during this period of history were expressing, I have found a greater respect for our freedoms. Thomas Jefferson, Benjamin Franklin and Thomas Paine are all familiar names to high school students in the United States. However, their principles are not familiar and I was shocked to learn that I had not previously read a majority of the works these men created to provide a foundation for our country’s belief system. Due to these works, I realize how much I have taken our freedom for granted. These men had radical ideas: the government can’t impose a religion on us, religion has nothing to do with the church and questioning one’s beliefs is vital to their faith. While learning where our country’s religious roots were first planted, I’ve also learned just how important it is to question and probe everything we’re told. Why do I go to church? Because I’m supposed to, because my parents do, because that’s the â€Å"rule† set by my religion. If I were to stop attending church, I would be a bad Christian. However, isn’t it true that if I attend church yet do not truly believe in what I’m doing, this is just as bad? Paine wrote, â€Å"When a man has so far corrupted and prostituted the chastity of his mind, as to subscribe his professional belief to things he does not believe, he has prepared himself for the commission of every oth er crime† (644). I believe Paine is saying that to tell yourself that you do believe in attending church when you know deep inside you are having doubts and... ... would be found deeply embedded in freedom and equality. The British government’s hostile ways in forcing a religion upon the people can be seen as horrible and yet, it was the very thing that allowed our country to strive so purposefully towards the freedom to believe anything one wants. Certain situations that seem bad can also â€Å"†¦bring things and men to light, which might otherwise have lain forever undiscovered† (966), as Paine wrote. And without these discoveries, we would be a people bound to a leader and dependent on everything that is told to us. Instead, we have become a people of great diversity, in both culture and belief, appearance and demeanor, and we refuse to give up this freedom that our founding fathers established. For, as Paine wrote, â€Å"†¦he whose heart is firm, and whose conscience approves his conduct, will pursue his principles unto death† (969).

David Hocking’s book The Nature of God in Plain Language Essay

It has to be said that the concept of trust has taken quite a hammering in society in the past twenty years.   During this time we have seen a host of previously considered â€Å"credible† people such as politicians, priests, childcare workers, teachers, babysitters and more exposed in the media as liars, cheats and criminals so is it any wonder that we might have trouble believing in an entity that has never actually been seen by anyone – someone like God for example.   David Hocking examines this issue of trust in relation to faith in his book The Nature of God in Plain Language.   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   One of the key factors illustrated in Hocking’s book is the fact that the Bible clearly states that God made man â€Å"in his own image†, so therefore God should be viewed as we might view other people around us, or perhaps more specifically in the way we view ourselves.  Ã‚   Hocking makes it clear that God is not some form of â€Å"force† but that instead he can be viewed to be a person like us, and therefore if we want to learn more about God then we can learn about him through looking at ourselves.   Hocking writes, â€Å"He possesses life, self-consciousness, freedom, purpose, intelligence and emotion† (65). One of the problems that stems from this viewpoint is that many people walk around with a very low opinion of themselves so it might be difficult to understand that while God is not ‘better’ than us, and therefore be considered as some paragon of perfection, he is an image of the very â€Å"best† that we could be to ourselves, for ourselves and to others. Hocking reinforces the fact about being a â€Å"friend of God† and points to the example of Abraham in the Old Testament who is cited as being a person who did look upon God, and did consider God to be his friend. We are not capable of being friends with a force, or source of higher power, which is why it is important for non-believers to understand that God does have elements of humanity, which we as humans share.   But the distance that is often perceived between God and man does help perpetuate the elements of mistrust about God as a creator of life, God as a loving father and God as the keeper of all men, especially if our own experience with trusting other human individuals has left us so cynical or jaded about the good in mankind Hocking believes that our growing cynicism is why trust is such an important concept when discussing a relationship with God. We should be able to trust our friends, our partners, and our family and this same trust needs to be found in God if he is to provide a positive influence in our own lives. Hocking illustrates the common problem we have as trusting individual’s when he explains about a woman that had been abused and let down continually by the significant people in her life including her parents that placed her in an institution, to friends and significant others she met throughout her life.   If she had been let down by so many people in her life it would be virtually impossible for her to consider that an unseen and unknown friend like God could care for a person he had never physically met, at least in her eyes, and is apparently unknown to her. Hocking believes this lack of trust can be overcome through three main factors that should be indicators of a whether or not a person might be trustworthy.   These three elements, telling the truth, doing what is right and fair, and being reliable, should provide the standards we measure the trustworthy nature of our friends and family, and Hocking explains how these same three factors can influence the level of trust we might have in God. The Bible illustrates countless examples of where God has proven himself in terms of these three measures of trustworthiness.   Hocking describes God as being â€Å"morally pure† and therefore it would be impossible for God to lie, to be unfair or be someone that could not be depended on.   Hocking refers to the Old Testament that showed how the people of Israel came to trust in God as they walked through the desert, and the New Testament that supported the fact that God could be counted on as a faithful being and one who is always with us.   If these ideas can be understood by an individual then with the passage of time it would be possible for all of us to trust in the one being that will never let us down. Hocking’s viewpoint on God being an accessible, trustworthy and righteous being, who can have influence on an individual in modern life is not a new concept, but understanding the importance of understanding ourselves so that we may understand God more clearly is not a common idea.   Many religious based Churches strive to create a distance between God and man and use concepts such as man’s inclination to sin on earth and generally be considered unworthy in God’s eyes as a way to maintain that distance. The fact that this distance between God and ourselves only serves the purpose of the Church as a governing body, rather than the individual is often overlooked by many theologians, but Hocking, despite his own religious affiliations, seeks to strip away the negative perceptions that the Church has upheld about man and God throughout the ages and instead paves the way for a life that can be had by any individual who could understand that God can be a friend in every sense of the word. The one stumbling block to this level of understanding is the level of mistrust that is perpetuated in modern society between individuals and groups.   The central premise of Hocking’s book is that to know God we have to know ourselves; to understand God we have to understand ourselves as individuals and to trust in God, we need to trust in others and ourselves.   Stripped of religious hype and forewarnings of doom and gloom that is often manifested by Church groups worldwide, Hocking’s book shows us that it is possible to have a relationship with our Lord, and that this relationship can be based on trust, regardless of the actions of others in our lives. Works Cited Hocking, David.   The Nature of God in Plain Language, Waco, Texas: Word Books, 1984

Sun Hydraulics Essay - 1623 Words

Sun Hydraulics: Leading in Tough Times Case Study Executive Summary Sun Hydraulics, an industry leader of hydraulic valves and manifolds, has seen steady growth over the past eight years. It has been a profitable company throughout the years with varying return on sales. Presently Sun is constrained by declining sales and high labor costs heading into the present recession. The horizontal corporate structure has proven ineffective in ridding itself of low performing employees that are weighing down the company and thus decreasing profitability. It is time for Allen Carlson, president and CEO of Sun Hydraulics Corporation, to address the employees and shareholders of his decision on how Sun plans to deal with labor and profits†¦show more content†¦The organization is multi-functional, created in Koski’s vision of â€Å"horizontal management†, with no job titles, no hierarchy, no departments, no budgets, no direct sales channels, etc. The employee’s feel strongly about this structure, as Chairman Cly de Nixon put it, â€Å"Sun’s unstructured environment is the key to our quality.† This unique approach created an active exchange of information among engineering, manufacturing, marketing, and commerce. This horizontal structure does have a downfall, unproductive workers can hide or simply do what they want and choose not to cooperate. Overall the structure seems to work for Sun, and employees genuinely are empowered to work for the greater good of the company. Financially speaking Sun Hydraulics has seen measure growth in sales from 1996 through 2000. Their revenues have grown from $47,374,000 to $66,268,000 from 1996 to 2000 respectively, but I was disappointed in Sun’s fluctuating profitability during this same time, seemingly caused by continually growing labor cost. As a percent of sales, profitability fluctuated from (1%) in 1996 to a high of 7% in 1998. There were steady increases in Labor and Manufacturing Overhead that have adversely affected the bottom line from the high water mark in 1998. As Allen looks to the future he faces aShow MoreRelatedNumerical Modeling And Validation Of Neo Hookean Materials2147 Words   |  9 Pagesutilized in the automotive manufacturing industry. Power steering units are generally hydraulic systems designed to assist in the steering of the wheels. Generally, the hydraulics pressure is generated from either the geroter (generated rotor), or a rotary vane pump, which are driven by the engine of the vehicle. The turning of the wheels is done by a hydraulic cylinder which has a force applied to it from a hydraulic cylinder, which is directly controlled by valves allowing for flow according to theRead MoreUse Of Hydraulic Systems Used From Ancient Egypt2203 Words   |  9 Pages______________ 1.1 Chronology of Hydraulics A machine could be described as a device which reduces human effort. Machines consist of various components which perform their intended operations to give the desired result. Engines, Vehicles, computers etc are all examples of machines we come across in our daily lives. Hydraulic machines are those devices which use the power of a liquid to perform simple work. 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This makes solar energy better option then the use of fossil fuel, however there are a couple of challengesRead MoreTaking a Look at Greek, Chinese and Indian Civilizations1995 Words   |  8 Pagesare the Earth spins on axis, theories of the motions of the planets according to the sun, formulas about the rotation and lunar orbits of Earth, described numerical and geometric rules for eclipse calculations, and he is the first known astronomer to have used a continuous system of counting solar days (â€Å"Aryabhata I†). Other Ancient Indian astronomers also came up with a cycle to synchronize the motions of the sun and the moon. Around 500 A.D., Aryabhata presented facts and ultimately a theory theRead MoreSolar Energy is Superior Essay991 Words   |  4 Pagesscientific process called desalination. Desalination is a chemical process in which natural compounds are separated from water, making the water clean and drinkable. Traditionally, sea water is propelled through hydraulic pumps which create a flow to separate the water from the sea salt. Hydraulic pumps require certain chemicals that are harmful to humans and these chemicals sometimes are cross-contaminated in the drinking water being produced. Personally, I don’t want to drink chemicals that are threateningRead MoreThe Hydraulic System Of Automatic Transmission System Essay1350 Words   |  6 Pages The hydraulic system in automatic transmission gives the system a smooth running which works under the basis of normal hydraulics. This consists of a complex maze and tubes that transmits the transmission fluid under pressure to the torque convertor and all other parts of the transmission. Present generation automatic transmission system is more complex and are assisted with computerized electrical components. Shift controlRead MoreAmerica Should Pursue Alternative Energy Sources Essay1235 Words   |  5 Pagesand 33% from soft-energy (alternative sources)† (((Smil, 47))) Most of the energy we use on a daily basis is not produced using clean methods. Some alternative energy sources that are already in place within the United Stats are wind, solar, and hydraulic. First, wind power is one alternative energy source that America should pursue. Wind power is one of most noticeable of the main alternatives. The power of wind is captured using tall wind turbines or windmills. These turbines are often found is