Effects of Metallurgy On Human History Essays

Effects of Metallurgy On Human History Essays Effects of Metallurgy On Human History Paper Effects of Metallurgy On Human History Paper This moon mental discovery led to all the technology h unmans have ever add and ultimately shaped all aspects of our lives, including science, economy my, architecture, and war. The use Of Bronze made many civilizations rich by supplying trade w says, and even when Bronze became obsolete, it was because of the knowledge of how to w Ark Bronze that led our species to learning how to manipulate the arguably most important mate Arial known as Iron. Iron led to all the navigational tools we used to discover the New World, and a Iso led to major industrial and agricultural tools such as plows and the infamous steel mills in the Industrial Revolution, shaping our modern world. The shift from stone carved tools of the primitive humans to copper and born zee tools was monumental. When this shift occurred, the era that dawned around 3500 BC would later be known as the Bronze Age and it was the first marker for the rise of large, com peel civilizations. The Ancients originally did not discriminate between copper and bronze, but as they continued to make these early metal tools, they came to realize that the bronze ones, we re for some reason far stronger and more efficient than copper tools Pure copper and bronze, an alloy of copper and tin, were used indiscriminately at first; this early period is sometimes called the Copper Age (Bronze Age) . This knowledge was spread throughout Eurasia and Africa thanks to rising civilizations in Asia and the Mediterranean. Groups of people such as the Greg eke, Chinese, and Egyptians became very wealthy thanks to the production of these tools, and t he creation of trade routes they could make a profit from it. In the Columbia Electronic Encyclopedic IA, the reference Bronze Age mentions how this era allowed civilizations to take better advent age of the surrounding and clear out large wooded areas for civilizations to flourish humans were able to exploit efficiently the temperate forests (Iron Age) The Bronze Age led to the very earliest of navigation tools. In Ancient Greece, the production of bronze tools with more than 50 dials were very early astrolabes created by the ancient astronomers. These navigational tools were remarkably advanced, and could do the four basic math functions to help Nava iGATE and locate stars (Scholastic News Edition 5/6). Another major effect of bronze and metal I n general was the creation of the technique of casting metal. Casting metal differed from forging g because casting involved making a clay cast around a wax object and then pouring the molten metal into the cast Molten bronze was poured into the mold, melting and replacing the wax (Cur ray, 35) . This process was so important because a very similar technique was later copied b y the Europeans during the Industrial revolution and is still used today to create large precise metal Structures such as steel bars and supports. While bronze was inferior in many ways to the e metals that would soon be its successor, bronze did manage to completely jump start human civic location and led us to the discovery of altering the much more useful metal known as iron. As the Bronze Age neared its end at around 800 BC, humans were looking to I prove tools even further. This resulted in the discovery of Iron metallurgy. This time marked the beginning of the Iron Age which extends until the present day. The Iron Age w as the beginning of modern technology and uses of metal. With the introduction of iron in the ancient world, Effects Of Metallurgy On Human technology made a huge jump. Iron could be used to make a more durable an d flexible weapon, and also was more abundant in Europe. This led to the major leap forward in agricultural technology. Plows could be made out iron and attached to cows and other lard GE animals to sow fields Goddard plows and wheeled vehicles acquired a new importance and change d the agricultural patterns. (Iron Age). This led to an increase in population support, which in turn led to more citizens with time to discover and invent new sciences and technology y. Iron also allowed things like the compass to be built. In China, the very first compasses were m add using lodestones, or iron ore, and they had dials made of bronze (Anderson, 25). If t here was no knowledge about iron or bronze, then we would be lacking both compasses a ND astrolabes, and we would have never been able to navigate on the seas. Forging iron proved t o be the most useful technology we had developed in the Ancient world. Iron could be used for everything from eating utensils, to cheap wheels, which would revolutionize both travel a ND war, by allowing people to make chariots and carriages. Another feat iron allowed WA s massive deforestation for a growing empire. Iron axes were far cheaper and more dour able, so a group of men could cut down dozens of trees a day,allowing a lot faster collecting of m trials. While bronze certainly served its purpose as a jump starter for human civilizations, t was not nearly as useful as iron was when it came to advancing the tech oenology of humans. While iron and bronze certainly were the driving forces behind technology, the eye also were being utilized by many other aspects of society. One of these aspects is an economy and trade. After the Bronze Age had been around for a couple hundred years, ma NY large and centralized civilizations were forming, such as Rome and China. Like modern day countries, these empires needed a currency for trading and for their citizens to support themselves. In Rome, for example, the Romans used a currency entirely based off of metal c ions. These metal coins are key fragments of history, because of a handful of reasons. The coins from Rome have either dates or important relevant events from that time period imprinted on them, also depending on the material the coin was made out of, and how it was made he Piped show the available technology and available metals at the time when they are found on a given archaeological site, they can help to date buildings and other ruins (Kaplan, 5 4) . The time these coins came from are crucial because they can continue to alter history by tithe ere depicting crucial events we never knew of, and they can help us date ruins they were found in or near so we can get a better grasp of our own histories. All of this information helps us further understand the story of the economic system that evolved into the one we have today. With a common metal currency in the ancient world, commerce was booming . Silk and spices were getting shipped from Asia and India to Rome, while Africa was tar ding ivory and gold for salt (Bentley Ziegler, 488). With all of the trading going on in this time period, competition arose. This is relevant because competition normally led to battle s and war, which was monumentally impacted by both bronze and iron weaponry used through hoot them. With the introduction of bronze, the first swords were made by Middle Easterners and Cells. These long knives were made for personal battles and were adopted by nearly every Inca .NET civilization. His caused the need for armor. Armor was built to counteract swords and for CE the creators of the swords to come up with new innovative weapons to pierce or get around the armor. This conflict is clearly shown with the creation of the Lubberly, which was a Viking s word designed to pierce through the southern Europeans chainman armor. With the introduction n of swords and armor, large battles between enemy nations could ta ke place. While these lard GE battles went on, new things were invented when the Iron Age came along, such as chariots. The sees chariots gave the warrior all the speed and mobility of a cavalry unit and the stability of a gar mounded archer. These large battles eventually were seen throughout Europe and Saiss history sees, such as the Crusades in the Middle East and the conquests of Genesis Khan. However, m teals didnt only affect land wars, but they also greatly affected naval battles as well. In 2011 , a group of archaeologists excavated the wreckage Of a Roman warship from the battle WI the Cartage over trading. Within the wreckage, they salvaged a huge bronze ram positioned on the bow of the boat.

U.S. Football Terms in Spanish

U.S. Football Terms in Spanish Everywhere in the Spanish-speaking world, fà ºtbol is that sport known in the United States as soccer. If you want to talk about what people in the U.S. mean when they say football, the term is usually fà ºtbol americano. U.S.-style football is perhaps the most popular U.S. spectator sport that hasnt exported well. So it shouldnt come as  a surprise that many of the key English terms for the sport, especially ones such as touchdown that dont have an equivalent in other games, have entered the Spanish lexicon unchanged. Others have been borrowed from other sports: Offside is fuera de juego, just as in soccer. And then there are a few calques as well, such as gol de campo for field goal. Glossary of Football Terms in Spanish Following are the Spanish translations of many common football terms as used by the National Football League, U.S. sports TV networks, Fundà ©u BBVA, and other sources. blitz - la cargablock - el bloqueo, la bloqueada, bloquearbye - el descanso, la fecha librecenter - el centrocheerleader - la cheerleader, la animadorachin strap - el barbuquejocleat - el taco de la botaEl pase pantalla clsico comienza con formacià ³n de carrera.clipping - el clipping, el bloqueo ilegal por atrscoach - el entrenadorcornerback - el esquinerodead ball - el balà ³n muertodefense - la defensadefensive end - el exterior defensivodown - el down, el intento, la oportunidaddrive - el drive, la serie ofensivaend zone - la zona de anotacià ³n, la zona final,  detrs de las diagonalesface mask - la mscara, la barrafield goal - el gol de campofirst/second/third/fourth and ten - primero/segundo/tercero/cuarto y diezfootball (the ball) - el balà ³n, el ovoidefootball (the game) - el fà ºtbol americanoformation - la formacià ³nfoul - la faltafullbac - corredor de poderfumble - el balà ³n libre, el balà ³n suelto, el balà ³n perdidogoal - el golgo alpost - el posteguard - el guardiahalfback - el corredor rpidohalftime - el intermedio, el descanso, entre tiemposhelmet - el cascohuddle - pelotà ³n, la pià ±ainterception - la intercepcià ³n, la interceptacià ³ninterference - la interferenciajersey - la camiseta, el jerseykickoff - la patada, el saqueline of scrimmage - la là ­nea de golpeo, là ­nea de ataqueleague - la ligalocker room - el vestuarioneutral zone - la zona neutraloffense - el ataqueoffside - fuera de juego, la posicià ³n adelantadaout of bounds - fuera de là ­mites, fuera del campoovertime - el suplementario, el tiempo extrapass (completed, incompleted) - el pase, el lanzamiento (completo, incompleto)penalty - la infraccià ³nplaying field - el campo, el terrenoplayoff - el partido de desempartepoint - el puntopoint after touchdown - el punto extra, el punto adicionalpossession - la posesià ³npreseason - la pretemporadapunt - el depeja, la patada de despeja, despejar, patear un despejepunter - el despejadorquarter - el quartoquarterback - el pasador, el lanzador, el mariscal de camporecord - el rà ©cordreferee - el rbitroregular season - la temporada regular, la campaà ±areturn - la devolucià ³n;, el retornoroughing - la rudezarun - la carrerasack - el sack, el placaje al lanzador, la capturasafety - el safety, la autoanotacià ³nshoulder pad - la hombrerasideline - la bandaslotback - el receptor libresnap - el snap, el saque, el centro, el intercambiostandings - la clasificacià ³n, la tabla de posicionessudden death - el muerte sà ºbitaSuper Bowl - el Super Bowl, el Sà ºper Tazà ³n, la Sà ºper Copatackle (action) - la parada, la atajada, la derribada, el placaje, la tacleada, el derribotackle (player) - el tackleteam - el equipotee - el base, el apoyo, el teethigh pad - la musleratight end - el receptor cerradotouchback - el touchbacktouchdown - el touchdown, la anotacià ³nturnover - la perdidas de balà ³nunsportsmanl ike conduct - conducta antideportivawide receiver - el receptor abiertowildcard - el equipo comodà ­n (a comodà ­n in playing cards is the joker)yard (unit of measurement) - la yardayellow flag - el paà ±uelo amarillo Sample Spanish Sentences About Football Una patada corta es un tipo especial de kickoff que se usa cuando el equipo ofensivo necesita recuperar el balà ³n para seguir atacando. (And onside kick is a special type of kickoff used when the offense needs to recover the ball in order to continue its drive.) La muerte sà ºbita consiste en que el primero que marque un gol, à ©se gana. (Sudden death means that the first to make a goal gains the victory.) Un pase de 19 yardas de Matt Ryan a Austin Hooper puso el marcador 14-0 en favor de los Falcons en el Super Bowl. (A 19-yard pass from Matt Ryan to Austin Hooper put the score 14-0 in favor of the Falcons in the Super Bowl.) El pase pantalla clsico comienza con formacià ³n de carrera. (The classing screen pass begins with a running formation.)

The Power of Positive Thinking Essay Example | Topics and Well Written Essays - 750 words

The Power of Positive Thinking - Essay Example When a thought feels comfortable in people’s minds, it stimulates the development of neural pathways that turn out to be extremely resilient to transition (Quilliam 21). Over time, people’s routines of thought can turn out to be so profoundly entrenched that they are conscious of how they are nourishing their minds. Notably, how an individual perceives a glass as half full or half empty reflects on his or her general viewpoint on life and themselves. A positive thinking sees the bright side of things and yields delight, health, happiness, auspicious results in life, broadens the mind, and builds skills and healthy relationships. If an individual adopts a positive mind, they train their minds to anticipate noble outcomes, growth and success. Health Benefits Researchers have continued to explore the benefits of positive thinking on people’s health. Existing research indicates that positive thinking have a myriad benefits to an individual’s health. It reduces the risks of cardiovascular diseases in spite of factors such as smoking habits, age and obesity. It also contributes to a longer lifespan, increased immunity to common cold, better adapting skills during hardships, and decreased levels of stress and depression (Mayo Clinic 1). A study carried out on college students at the begging and the end of the semester established that positive thinking is associated with low stress levels. Additionally, positive thinking lowers blood pressure and allows an individual to age gracefully. This is primarily because of reduced stress levels (Mayo Clinic 1). ii. Bringing Happiness and Healthy relationships When an individual thinks positively, he or she is surrounded by auspicious thoughts. This yields happiness, which is contagious. It makes the people that hang around an individual happy too. This also assists people shun negative thoughts and become more optimistic (Peale 32-4). On a different angle, this increases a person’s luck in love. People will accept an individual who is positive and will yield healthy and happy relationships, since they focus on the noble and favorable aspects of the other person (Quilliam 34). iii. Building skills set The benefits of positive do not just stop after feeling happy and healthy. Indeed, the most paramount benefit of positive thinking is the improved aptitude to build skills and develop resources that can be used later in life. For instance, a child who frolics, plays with colleagues and swings in branches outside develops his or her physical skills, social skills of communicating and int eracting with other people freely and creative skills of examining and exploring the world around them. In this manner, the positive feelings of play and happiness trigger the child to develop skills that are essential in daily life (Clear 1). These skills stay for a long time than the emotions that caused them. Later in life, the athletic skills obtained by the child may earn a scholarship into a college or the communications skills attained may assist him or her be a desirable and effective business manager (Byrne 27-30). The joy that prompted the exploration and generation of new capabilities is long gone in this stage, but the skills still remain. Researchers have named this phenomenon as â€Å"widen and build† because positive thoughts widens an individual’s sense of possibilities and opens his or her mind resulting to development of new skills and resources that offer value to other fields and aspects of life (Clear 1). iv. A broad sense of mind and Increased Pos sibilities When an individual thinks positively and experiences positive emotions such as joy, satisfaction and affection,

Personal Development Plan Essay Example | Topics and Well Written Essays - 1750 words

Personal Development Plan - Essay Example This requires funds, which are not always available. In this case, I will have to prove to an organization that my research is in accordance to the vision of their company and aiming at improving science and technology in the country. Attaining this chance will give me a good chance to d my research work. I will also be able to get first hand skills and opportunities. I will also be able to improve m communication and social skills within the company of my research. This will widen the scope of my knowledge and I will be able to learn various challenges individually. Apply for lots of jobs in my field of study. Engage in internship and volunteer jobs within my field of career and my dream working stations. Engage in 8 hours lecturing within a week in the University to improve my teaching skills and solicit for a job while still seeking for a job Securing these two jobs will be a dream come true. I will be able to put my practice at work. I will also be able to improve my communication status. My living standards will also improve, as I will be under payroll. I will also be able to meet various opportunities in my field of operations After securing good grades at master’s level, it will be easy to pursue my doctorate degree. This includes applying well within the stipulated time. I will also ensure that all the necessary requirements are available on time and above all that, I am qualified for the position to further my studies. Owing to good experience at field work I will ensure I work hard and pass my exams and learn more from the course You should identify the level where on the scale you think you are and also comment on what evidence your assessment is based in the space beside each component part of the skill. Evidence needs to be hard evidence eg results or feedback from tutors or employers. I have good communication skills especially since I am a trained teacher through my field of agriculture

Software for Human Services Organization Essay Example for Free

Software for Human Services Organization Essay Southern Nevada Adult Mental Health Services is an organization that services the mental health population. This population has continued to grow, and because of the increased turnaround in clients served the company had to invest in multiple software products. Electronic Health Record or (EHR) is one of the software programs that are used by Southern Nevada Adult Mental Health Services. This software is designed to be shared with several different health care providers or settings. The Electronic Health Record software is an electronic collection of systematic health information about a certain population or client. Using Electronic Health Record software will be the digital backup version for a client’s paper chart. Electronic Health Record systems are client centered records that are recorded in real-time. Authorized users of this system are able to obtain this secure information instantly. Using the Electronic Health Record software client’s medical, mental, and treatment records are tracked faster. This program was designed to go further than the normal intake data that is gathered in a provider’s office and is inclusive of a larger view of a client’s care. Electronic Health Record software has tools that will allow providers to make accurate decisions pertaining to client’s mental health care. Southern Nevada Adult Mental Health Services use Electronic Health Record software to streamline and automate the workflow for different providers. One of the benefits of Electronic Health Record software is that Southern Nevada Adult Mental Health Services authorized employees has easier access to client’s medical history. This history consist of radiology images, diagnoses, treatment plans, allergies, results from a test that was taken, immunization records, medications, and laboratory results. Using this software to centralize client’s records electronically has helped the communication between other agencies flow smoothly. Southern Nevada Adult Mental Health Services use Electronic Health Records software to track information from  other organization, non-profit agencies, and other human services provider who may have provided services to a client. Some of these services are Medicaid approval or reimbursement, clinic management, subsidized housing, drug rehabilitation, and section eight housing. An advantage of this software is the improvement of client’s care, efficiency, safety, client-centeredness, and equity. This software allows each clinician involved in the client’s care the ability to share and obtain the client’s medical history and other pertinent information with other medical providers. Pharmacies, medical imaging facilities, schools, emergency facilities, and other clinics are a few providers that are authorized to receive client’s information from Southern Nevada Adult Mental Health Services in a digital format. As more and more health care providers continue to migrate to digital electronic management because of the advantages, there are some disadvantages to using Electronic Health Records software. One of the disadvantages can be the initial start-up cost may become pricey in the beginning. This consists of hardware installations, training of staff, and software upgrades. It does not matter if the facility that is converting to digital Electronic Health Records is large or small the start-up cost will be expensive. If administrative staff, nurses, and doctors are not too familiar with the way the new system is operated, these individuals will waste more time trying to figure it out. This can sometime force the administrative staff, nurses, and doctors that are uncomfortable with this software take longer to master a task, this is wasted time that could be used for other important missions or serving clients. Another downfall or disadvantage of using this software is the concerns of client ’s security. Most individuals think a disadvantage would be the security vulnerability for the client’s medical records. The ultimate concern is that hackers are still out there and may steal client’s personal information and possible compromise their identity. It does not matter how many password encryptions, security features added, and firewalls are put up, hackers can get in there. However, there are also companies that specialize in security measures for the maintenance of Electronic Health Records software. Client Track software is another software that is used at Southern Nevada Adult Mental Health Service. Several of Southern Nevada Adult Mental Health Service case managers, social workers, and other field professionals have  their mobile device set up so that they can have full access to enter the client’s chart and work on it without having to be at work. Client Track is optimized to be compatible with mobile Firefox, Apple iPad, iPhone, Chrome, Safari Web Brower, and iPod touch. Client Track has allowed Southern Nevada Adult Mental Health Services to take providing services t o a whole new level. Client Track has made it possible for employees to input important case notes in the client charts while they are continuing to work in the field. Different facilities can expedite the check in the process of a client by incorporating other mobile devices and iPads. This software will only allow designated staff to access areas pertaining to their job title. Client Track software has been an asset and benefit to Southern Nevada Adult Mental Health. The collaboration, compliance, efficiency, and outcomes have shown to be another benefit of using Client Track. Other communities, agencies and multiple programs can collaborate and transfer client’s information amongst each other securely and smoothly. Most agencies and programs have stakeholders, which they are required to report outcomes, activities, and services rendered, Client Track provide an automatic update with this information, which can be obtained by the stakeholders on an as needed basis. The efficiency of Client Track will eliminate having to use spreadsheets and give more time for staff to help the clients that are in need. Since Southern Nevada Adult Mental Health Services have been using Client Track software, the service to client’s outcome has increased. One of the advantages of using Client Track software is that this software is configured to meet various types of software. Homeless Management Information System or (HMIS) is a software application that is used daily by human service workers nationwide. Individual’s would think that an organization the size of Southern Nevada Adult Mental Health Service will be the determining factor of the software chosen, this company has chosen the software that is a better fit, which allows them to communicate with several agencies. A possible challenge that may be encountered from the implementation process is the difficulty comparing the associated health IT products and EHRs products. Because of the newness of this software there were not a lot of competitors to compare to. References Gungor, F. (2014). OneSource DocumentManagement. Retrieved from http://www.onesourcedoc.com/blog/bid/71535/Disadvantages-of-Electronic-Medical-Records Health IT.GOV. (2013). Retrieved from http://www.healthit.gov/providers-professionals/faqs/what-are-advantages-electronic-health-records

The Stranger and The Guest Essays -- Character Analysis, Daru, Meursau

French playwright Albert Camus once said, â€Å"Nobody realizes that some people expend tremendous energy merely to be normal.† In The Stranger and The Guest the overarching theme that those who do not conform to typical societal values and do not adequately relate to others are appraised as a threat to society as a whole. In both works the protagonists isolate themselves, and society isolates them because of their non-conforming beliefs. Both Daru and Meursault are not able to accept the abstract ideals of society, and prefer isolation. For them relating to the physical world is much easier to relate to because it is concrete and definite, rather than the ambiguity of the moral ideals held by society. As a result of this objection to society they become indifferent and detached from societal expectations, intern this allows both protagonists to defy the rules of society, and expunge their innate flaws. In the Guest, Daru constantly observes the landscape, especially the sun and the snow on the rocky, empty plateau. Daru discusses the burning of the sun â€Å"the earth shriveled up little by little, literally scorched every stone bursting into dust under one’s foot† (Guest 304). Despite the debilitating drought, followed by unhelpful snow around home, Daru does not complain, but instead observes and respects the landscape for being his only home. Daru does not associate his home with family or friends, rather with the physical qualities of it. The schoolmaster is like â€Å"a monk in his remote schoolhouse, nonetheless satisfied with the little he had and with the rough life† (Guest 304). Even though he is isolated and lives in a secluded area, he enjoys the quiet and solitude in which he is liberated from being at a close proximity to s... ...ecause he believes that society’s laws are flawed. Meursault and Daru are both considered outsiders of society because they are not able to understand the other characters in the story. This is because each character represents an aspect of society, like Balducci in the Guest, and everyone in the courtroom in The Stranger represents the law and justice system. Camus uses the actions and words of seemingly unimportant characters to allude to the flaws and problems of society. In both works of Camus, the protagonists view the other characters in the story from an outsider view, allowing for a new perspective in which society and its problems can be assessed by the reader. By making the protagonists detached from society, one can truly see the underlying issues within society. That is why the isolation and alienation of Meursault and Daru are crucial in Camus’ works.

Good Vs. Evil Divine Justice in King Lear Essay

The play King Lear displays betrayal, deceit and . These three components are all familiar in classic Shakespearean tragedies. King Lear features betrayal by various characters in the play. These characters devastate and, in some instances, end the lives of other characters in the play. However, the characters that betray and deceive are eventually destroyed by their many lies and evil actions. With their self-devastation, a sort of divine justice is served. Divine justice is served when the wrong doings of a man or woman catches up to them and they are dealt a penalty for their sins. This sort of justice cannot be given by a court or social order. Only fate can deal such a hand. In King Lear divine justice must be faced for the betrayals one man has played. The man is Edmund. Edmund is the illegitimate son of the Earl of Gloucester and his betrayal runs deep in the play. Divine justice is served when Edmund is slain by his half brother Edgar in this classic good vs. evil fight. Divine justice is a result of people doing things in conflict with the natural order of the universe. When a violation occurs, a divine power must reconcile the evil or unnatural act. In King Lear, Edmund violates natural law and he is faced with . Edmund is the illegitimate son of the Earl of Gloucester and brother to Edgar. Unlike Edmund, Edgar is the legitimate son of Gloucester and Edmund s him for it. The motive for the evil acts Edmund commits is because of his for Edgar and his greed for power. Edmund’s first betrayal is to his brother. Edmund makes their father believe that Edgar is plotting to kill him. Edmund thinks this is the best way to get rid of Edgar. Readers in the time of Shakespeare believed heavily in good and evil and the idea of divine Justice. The people believed that if one were to go against nature or, the natural order, it created an imbalance then justice had to be paid by a divine power. Edmund believes that the stars and the moon, which represent the higher power has nothing to do with what happens here on earth. Edmund displays his hatred of the gods and people who believe in them when he says. â€Å"This is the excellent foppery of the world, that, when we are sick in fortune, often the surfeit of our own behavior, we make guilty of our disasters the sun, the moon, and the stars: as if we were villains by necessity; fools by heavenly compulsion; knaves, thieves, and treachers, by spherical predominance; drunkards, liars, and erers, by an enforced obedience of planetary influence; and all that we are evil in, by a divine thrusting on:† ( Act. 1 Scene 2. Line 113 – 121) This Quote tells us that Edmund is a cynic and even an atheist. He admits that he is a villain and he is not scared of a higher power. Because of the time period in which King Lear was written, and the ideas of fate and divine powers, it would be likely that a reader of that time would recognize Edmund as a real evil person and that the evil he commits will be punished by the divine. It seems that Edmund is doomed from the very beginning because his violations of natural order by plotting to kill his brother and by his contempt for the gods. Edmund continues to plot against his brother and Edgar runs away and becomes a Poor Tom, which is an insane beggar. Edmund’s second violation of natural order, which will result in punishment, is the betrayal of his father. The betrayal of Glouchester, his father, begins with a note from the French that tells of the invasion of England. Edmund tells the Duke of Cornwall about the letter and the Duke pulls out the eyes of Glouchester because he is a so-called traitor. These two acts of evil result in divine justice. In the play divine justice is seen in the battle between Edgar and Edmund. A classic good vs. evil fight will give Edmund his divine justice. Edmund is confronted by the brother he betrayed and is killed. However, before he is killed Edmund says something to Edgar that tells us that he realizes his fate and that his wrong actions have come back to face him when he says † Thou has spoken right. ‘Tis true. The wheel is come full circle. I am here. â€Å"(Act. 5, Scene 3, Line 199-200). The â€Å"wheel† Edmund refers to is the wheel of fortune. All his betrayals have come full circle and it is now time to be judged. As Edmund dies the reader sees divine justice being served. Although Edmund was slain by the brother he betrayed and, not by a bolt of lightning from above, we still see divine justice being served. Divine justice does not come in a single act; it comes in the course of fate or destiny. It is perfect how the good son kills the evil son and England is saved. The perception is that had Edmund won, England would have fallen into chaos and, when Edgar won, it was like a new England was formed out of the chaos of the unnatural evil Edmund had created. Divine justice is so important Lear and all stories because it ensures the triumph of good over evil. The battle is long and always a struggle, but thanks.

Problem-Solution Essay Essay

It only comes once every four years. It is a day of unity, expression, equality and freedom. Every citizen over the age of eighteen in the United States has the opportunity –the right– to be a part of something huge. Presidential Election Day. The long awaited day that is consumed by the media, Facebook, and Twitter months in advance. An individual can choose to voice an opinion with discretion and secrecy in the voting booth, or one could also choose a more vocal approach with heated debates, obnoxious campaign signs, and even the occasional protest. After all, this is the land of the free, and if there’s one thing Burger King has taught me, it‘s that in the United States you really can â€Å"have it your way.† So why is it, then, that in the midst of the exciting and tumultuous day of our general election, I see the youth of the country sitting in their dorm rooms with absolutely no intent of casting their ballots? Seeing firsthand the lack of political activity among my peers and all those belonging to Generation Y makes me question whether or not I should care enough to vote myself. There is no argument that young voters (ages 18-34) have increasingly shown a lack of voter turnout in general elections. According to an article by The New Republic, 53 percent of 18-29 year-olds visited the polls in 1972. By the year 2000, that figure had dropped to 35 percent, which became a new historical low. So why is this a problem for me and my fellow Generation Y brothers and sisters? The answer is clear and simple. By choosing not to vote, we are also choosing not to have anyone represent our ideals and political agendas in government. At a time with increasing student-loan debt, a shocking unemployment rate and overall declination of the quality of life, Generation Y has more reason now than ever to start affecting political change. â€Å"People who try to have influence on government are going to have more influence than people who do not try† (Wilson 161). All of this begins with the polls. Many causes of political apathy among the younger generation have been noted, and in some cases, several attempts have been made to attract these voters. Registration is one of these causes and this resonates in particular with college students. First-time voters have to get a registration form, learn how and when to register, and then deliver it. Most college students will have to request absentee ballots if they are unable to go to their designated polling stations on Election Day. Unlike the older generation, younger voters are typically not yet settled and therefore the voting process takes more effort. According to the Center for Information and Research on Civic Learning and Engagement, over a quarter of college students reported that they did not register to vote because they didn’t know how or had missed the deadline. However, there have been steps to make this process simpler including the motor-voter bill of 1993. This allows citizens to register to vote as they are applying for a driver’s license (Wilson 166). Perhaps one of the biggest causes for lower voter turnout among young people was identified through the honesty of my own roommate. Paige Toepper, my roommate and also fellow first-time voter, did not go to the polls for the 2012 election simply because she had not previously been engaged in the political issues and felt ill-equipped to suddenly be making such decisions. â€Å"I haven’t been following up on politics until this point and I don’t believe I should vote for something when I’m not even sure what it is that I am voting for.† Once I heard this from my roommate, I found it to be a common theme on my entire floor. The problem isn’t that Generation Y doesn’t care to vote but, rather, that no one has really had the chance yet to be exposed to politics in an informative light where we feel confident in our own beliefs. My proposal for the solution to this problem begins in the education system. We should integrate politics and current events into our curriculum for high school students. This would also include the entire process for registering first-time voters, so that those who have not been exposed have a base to fall back on. The lack of voter turnout among the younger generation is a serious problem for the future of America if young people aren’t allowing their voices to be heard and to influence government. If people do not start voting while they are young, there is no way to know if they will ever begin to exercise this fundamental right. Being able to integrate politics as part of high school curriculum is an easy way to start getting the young generation engaged and involved. By doing this we can begin to push forward new innovative ideas and ultimately begin to successfully form our future as a society.

William Golding essays

William Golding essays William Golding is a very influential author who wrote many different works. Some of his works are: The Lord of the Flies, The Inheritors, Freefall, Paper Men, and The Double Tongue. One of his first and probably most popular works to this day is The Lord of the Flies. William Golding was born in 1911 in Cornwall, England. He was educated at the Marlborough Grammar School, where his father taught, and later at Brasenose College, Oxford. Williams father wanted him to become a scientist so he had him take science classes; however William soon had a deep interest in literature and began to study the Anglo-Saxon period. He was very interested in this and became very dedicated to studying and writing about the Anglo-Saxon period. Eventually he decided to also start writing poetry. While attending Oxford he studied English literature and philosophy. After a short period of time in which he worked at a settlement house and in small theater companies as both an actor and a writer, Golding became a schoolmaster at Bishop Wordsworth's School in Salisbury. During the Second World War he joined the Royal Navy and was a part of the sinking of a ship called the Bismarck. After the war he retuned to Bishop Wordsworth School where he kept teaching until the early sixties. In 1954 William published his first novel, The Lord of the Flies. The Lord of the Flies is a novel about a group of British school children whom get stranded on an island. This book shows how refined and civilized the children are when they arrive on the island and how savagery they became towards the end of the book. At first the kids are very organized and refined but as the book progresses it shows how they become unorganized and totally different. Im sure that this book was a factor in William Golding winning the Nobel Prize in 1983 for literature. In 1988 William Golding became Sir William Golding, this means he was knigh ...

Algebra Functions on ACT Math Lesson and Practice Questions

Algebra Functions on ACT Math Lesson and Practice Questions SAT / ACT Prep Online Guides and Tips Functions. Just hearing the word is enough to send some students running for the hills. But never fear! Though function problems are considered some of the more challenging questions on the ACT, this is only due to the fact that most of you will be far more used to dealing with other math topics (like fractions, exponents, or circles) than you are functions. On the ACT, question difficulty is categorized by how familiar you are likely to be with any given question, and the only way to combat this challenge is to practice and get used to dealing with questions that are a little less familiar to you. You will generally see 3-4 function questions on any given ACT, so for those of you who are not yet comfortable with functions (or just want a tune up), this guide is for you. This will be your complete guide to ACT functions. We'll walk you through exactly what functions mean, how to use, manipulate, and identify them, and exactly what kind of function problems you'll see on the ACT. What Are Functions and How Do They Work? Functions act as a way to describe the relationship between inputs and outputs. They can be in the form of equations, graphs, or tables, but they will always describe this input-output relationship. It may help to think of functions like an assembly line or like a recipe- input eggs, veggies, and cheese, and the output is an omelette. Most often you'll see functions written as $f(x) = \an \equation$. The equation of the function can be as complex as a multivariable expression or as simple as an integer. Examples of functions: $f(x) = 14$ $f(x) = 2x + 10$ $f(x) = x^2 - 6x + 9$ Functions can always be graphed and different kinds of functions will produce different kinds of graphs. On a standard coordinate graph with axes of $x$ and $y$, the input of the graph will be the $x$ value and the output will be the $y$ value. Each input ($\bi x$ value) can produce only one output, but one output can have multiple inputs. In other words, multiple inputs may produce the same output. One way to remember this is that you can have "many to one" (many inputs to one output), but NOT "one to many" (one input to many outputs). This means that a function graph can have potentially many $\bi x$-intercepts, but only one $\bi y$-intercept. (Why? Because when the input is $x = 0$, there can only be one output, or $y$ value.) A function with multiple $x$-intercepts You can always test whether a graph is a function graph using this understanding of inputs to outputs by using the "vertical line test." A function will never hit more than one point on any vertical line. The vertical line test applies to every type of function, no matter how "strange" looking. Even "strange-looking" functions will adhere to the vertical line test. But any graph that fails the vertical line test (by intersecting with the vertical line more than once) is automatically NOT a function. This graph fails the vertical line test, which means it is NOT a function. If necessary, you can always spot a genuine function from a non-function by using the vertical line test. Function Terms and Definitions Now that we've seen what functions do, let's talk about the pieces of a function. Functions will be presented to you either by their equations, their tables, or by their graph (called the "graph of the function"). Let's look at a sample function equation and break it down into its components. An example of a function: $f(x) = x^2 + 12$ $f$ is the name of the function (Note: we can call our function other names than $f$. This particular function is called $f$, but you may see functions written as $h(x)$, $g(x)$, $r(x)$, or anything else.) $(x)$ is the input (Note: in this case our input is called $x$, but, just like with the name of our function, we can call our input anything. $f(q)$ or $f(\bananas)$ are both functions with the inputs of $q$ and $\bananas$, respectively.) $x^2 + 5$ is the equation that gives us the output once we plug in the input value of $x$ An ordered pair is the coupling of a particular input with its output for any given function. So for the function $f(x) = x - 6$, with an input of 2, we can have an ordered pair of: $f(x) = x - 6$ $f(2) = 2 - 6$ $f(2) = -4$ So our ordered pair is $(2, -4)$. (Again, our input value will represent our $x$ value and the result of the equation once that input value has been processed will be our $y$ value.) Ordered pairs also act as coordinates, so we can use them to graph our function graph. Now that we have all of our function pieces and definitions, let's look at how they work together. Different Types of Functions We saw before that functions can have all sorts of different equations for their output, which will change the shape of their corresponding graphs. Let's look at each type of equation and its graph. Linear Functions A linear function makes a graph of a straight line. The equation of a linear function can either be a simple number (e.g. ,$f(x) = 4$) or will have a variable that is NOT raised to a power higher than 1 (e.g., $f(x) = 3x + 3$). Why can the variable NOT be raised to a power higher than 1? Because $x^2$ can give you a single output ($y$-value) for two different inputs of $x$. For example, $-4^2$ and $4^2$ both equal 16, which means the graph cannot be a straight line. (We will look into this further in the next section on quadratic functions.) The standard equation of a line is: $y = mx + b$ $\bi m$ is the slope of the line. $\bi b$ is the $\bi y$-intercept. (For more on lines and slopes, check out our guide to ACT lines and slopes!) Examples of linear functions: $f(x) = x - 24$ $f(x) = 4$ $f(x) = 2x + 35$ Quadratic Functions A quadratic function makes a graph of a parabola, which is a "horseshoe" type graph that curves to open either up or down. It also means that our output variable will always be squared. The reason our variable must be squared (not cubed, not taken to the power of 1, etc.) is for the same reason that a linear function cannot be squared- because two input values can be squared to produce the same output (e.g. $5^2$ and $-5^2$ both equal 25). This gives us our curve. (Note: a parabola cannot open side to side because it would have to cross the $y$-axis more than once. This, we've already established, would mean it would fail the vertical line test and therefore NOT be a function.) This is NOT a quadratic equation, as it fails the vertical line test. A quadratic function is often written as: $f(x) = a^2 + bx + c$ The $\bi a$ value tells us how the parabola is shaped and the direction in which it opens. A positive $\bi a$ gives us a parabola that opens upwards. A negative $\bi a$ gives us a parabola that opens downwards. A large $\bi a$ value gives us a skinny parabola. A small $\bi a$ value gives us a wide parabola. The $\bi b$ value tells us where the vertex of the parabola is, left or right of the origin. A positive $\bi b$ puts the vertex of the parabola left of the origin. A negative $\bi b$ puts the vertex of the parabola right of the origin. The $\bi c$ value gives us the $y$-intercept of the parabola. (Note: when $b = 0$, the y-intercept will also be the location of the vertex of the parabola.) Don't stress if this feels like a lot of information for the moment- a little practice and organization will soon have you solving your function questions, no problem. Typical Function Problems ACT function problems will always test you on whether you properly understand the relationship between inputs and outputs. These questions will generally fall into four question types: #1: Functions with given equations #2: Nested functions #3: Functions with graphs #4: Functions with tables There may be some overlap between the three categories, but these are the main themes you'll be tested on when it comes to functions. Let's look at some real ACT math examples of each type. Function Equations A function equation problem will give you a function in equation form and then ask you to use one or more inputs to find the output (or elements of the output). In order to find a particular output, we must plug in our given input for $x$ into our equation. This will give us our final output, once we then solve the equation. So if we want to find $f(5)$ for the equation $f(x) = x + 7$, we would plug in 5 for $x$. $f(x) = x + 7$ $f(5) = 5 + 7$ $f(5) = 12$ So, when our input ($x$) is 5, our output ($y$) is 12. Now let's look at a real ACT example of this type: For the function $h(x)=4x^2-5x$, what is the value of $h(-3)$? A. -93B. -9C. 21D. 51E. 159 Though this function is named $h$ (instead of the usual $f$), the principles are exactly the same- we must plug in our input value of -3 in order to find our output. So let us plug in -3 for our $x$. $h(x) = 4x^2 - 5x$ $h(-3) = 4(-3)^2 - 5(-3)$ $h(-3) = 4(9) + 15$ $h(-3) = 36 + 15$ $h(-3) = 51$ Our final answer is D, 51. Nested Functions The second type of function problem you might encounter on the ACT is called a "nested" function. Basically, this is an equation within an equation. In order to solve these types of questions, think of them in terms of your order of operations. You must always work from the inside out, so first find the output for your innermost function. Once you've found the output of your innermost function, you can use that result as the input of the outer function. Let's look at this in action to make more sense of this process. Given $f(x)=4x+1$ and $g(x)=x^2-2$, which of the following is an expression for $f(g(x))$? F. $-x^2+4x+1$G. $x^2+4x-1$H. $4x^2-7$J. $4x^2-1$K. $16x^2+8x-1$ Because $g(x)$ is nested the deepest, we must use its output as the value of our input for $f(g(x))$. Essentially, instead of a number for $x$ in $f(x)$, we are given another equation, $g(x)$. And yet, the principle behind solving the function is exactly the same as we did above in our function equations section- replace whatever input we have with the variable in the output equation. So, to start with, we have two function equations. $g(x) = x^2 - 2$ $f(x) = 4x + 1$ Now let us replace $x$ in our $f(x)$ equation with the full equation of $g(x)$. $f(x) = 4x + 1$ $f(g(x)) = 4(x^2 - 2) + 1$ $f(g(x)) = 4x^2 - 8 + 1$ $f(g(x)) = 4x^2 - 7$ Our final answer is H, $f(g(x)) = 4x^2 - 7$ Function Graphs A function graph question will provide you with an already graphed function and ask you any number of questions about it. These questions will generally ask you to identify specific elements of the graph or have you find the equation of the function from the graph. So long as you understand that $x$ is your input and your equation is your output $y$, then these types of questions will not be as tricky as they appear. This question relies on us knowing how the formula for a quadratic equation works. If you remember from earlier, a quadratic equation requires a square power and will form a parabola. We are told that the $x$-coordinate value will be squared, so we know for a fact that this graph will indeed form a parabola and be a quadratic equation. This means we can eliminate answer choices F and G, as they are straight lines, not parabolas. Now, we are told that the $y$-coordinate value is 1 less than the $x$-coordinate square. We know that our standard quadratic formula equation is: $a^2 + bx + c$ $c$ gives us our $y$-intercept and, in this equation, we are told that it will be -1. This means we can eliminate answer choice H, as the $y$-intercept is not at -1. Finally, we are told that the points on our graph are the ONLY place where the $y$-coordinate is less than the $x$-coordinate. This means that our graph must open upwards, which means we can eliminate answer choice K. Our final answer is, therefore, J. Function Tables The last way you may see a function is in its table. Here, you will be given a table of values both for the input and the output and then asked to either find the equation of the function or the graph of the function. (Note: instead of using $x$ as our input, this problem has us use $t$. If you become very used to using $f(x)$, this may seem disorienting, so you can always rewrite the problem using $x$ in place of $t$. In this case, we will continue to use $t$, just so that we can keep the problem organized on the page.) First, let us find the $y$-intercept. The $y$-intercept is the point at which $x = 0$, so we can see that we are already given this with the first set of numbers in the table. When $t = 0$, $d$ (otherwise thought of as $f(t)$) equals 14.) Our $y$-intercept is therefore 14, which means that the equation of our line will look like: $y = mx + 14$ We can automatically eliminate answer choices B, D, and E, since their $y$-intercepts are not at 14. Now, let us use the strategy of plugging in answers to make our lives simpler. This way, we don't have to actually find the equation on our own- we can simply test which answer choices match the inputs and outputs we are given in our table. Our answer choices are between A and C, so let us first test A with the second ordered pair. Our potential equation is: $d = t +14$ (or, in other words: $f(t) = t + 14$) And our ordered pair is: $(1, 20)$ So let us put them together. $f(t) = t + 14$ $f(1) = 1 + 14$ $f(1) = 15$ This is incorrect, as it would mean that our output is 15 when our input is 1, and yet the ordered pair says that our output will be 20 when our input is 1. Answer choice A is incorrect. By process of elimination, let us try answer choice C. Our potential equation is: $d = 6t + 14$ (or, in other words: $f(t) = 6t + 14$) And our ordered pair is again: $(1, 20)$ So let us put them together. $f(t) = 6t + 14$ $f(1) = 6(1) + 14$ $f(1) = 6 + 14$ $f(1) = 20$ This matches the input and output we are given in our ordered pair. Answer choice C is correct. (Note: it is generally a good idea to test more than one ordered pair, as two equations may occasionally get the same ordered pair. In this case, we stopped here as there were no other answer choices that could possibly match). Our final answer is C, $d = 6t + 14$. Now that we've seen our definitions, let's talk function strategy. How to Solve a Function Problem Now that you've seen all the different kinds of function problems in action, let's look at some tips and strategies for solving function problems. For clarity, we've split these strategies into multiple sections- tips for all function problems and tips for function problems by type. So let's look at each strategy. For All Function Problems #1: Keep careful track of all your pieces and write everything down Though it may seem obvious, in the heat of the moment it can be far too easy to confuse your negatives and positives or misplace which piece of your function (or graph or table) is your input and which is your output. Parenthesis are crucial. The creators of the ACT know how easy it is to get pieces of your function equations confused and mixed around (especially when your input is also an equation), so keep a sharp eye on all your moving pieces and don't try to do function problems in your head. #2: Use PIA and PIN as necessary As we saw in our function table problem above, it can save a good deal of effort and energy to use the strategy of plugging in answers. You can also use the technique of plugging in your own numbers to test out points on function graphs, work with any variable function equation, or work with nested functions with variables. For instance, let's look at our earlier nested function problem using PIN. (Remember- most any time a problem involves variables, you can use PIN). Given $f(x)=4x+1$ and $g(x)=x^2$, which of the following for $f(g(x))$? F. $-x^2 +4x+1$G. $x^2+4x-1$H. $4x^2-7$J. $4x^2-1$K. $16x^2+8x-1$ If we remember how nested functions work (that we always work inside out), then we can plug in our own number for $x$ in the function $g(x)$. That way, we won't have to work with variables and can use real numbers instead. So let us say that the $x$ is the $g(x)$ function is 3. (Why 3? Why not!) $g(x) = x^2 - 2$ $g(3) = (3)^2 - 2$ $g(3) = 9 - 2$ $g(3) = 7$ Now, let us plug this number as the value for our $g(x)$ function into our nested function $f(g(x))$. $f(x) = 4x + 1$ $f(g(3)) = 4(7) + 1$ $f(g(3)) = 28 + 1$ $f(g(3)) = 29$ Finally, let us test our answer choices to see which one matches our found answer of 29. Let us, as usual, start in the middle with answer choice H. $4x^2 - 7$ Now, we replace our $x$ value with the $x$ value we chose originally- 3. $4(x)^2 - 7$ $4(3)^2 - 7$ $4(9) - 7$ $36 - 7$ $29$ Success! We have found the answer choice that matches our found answer of 29. (Note: if you use this method on the test, make sure to test out your other answer choices to make sure you do not have any duplicate correct answers. We can skim over our answer options and see that none of them equal 29 after we replace our $x$ with 3.) Our final answer is H, $4x^2 - 7$ #3: Practice, practice, practice Finally, the only way to get truly comfortable with any math topic is to practice as many different kinds of questions on that topic as you can. If functions are a weak area for you, then be sure to seek out more practice questions. For Function Graphs and Tables #1: Start by finding the $\bi y$-intercept Generally, the easiest place to begin when working with functions is by finding the $y$-intercept. From there, you can often eliminate several different answer choices that do not match our graph or our equation (as we did in some of the examples above). The $y$-intercept is almost always the easiest piece to find, so it's always a good place to begin. #2: Test your equation against multiple ordered pairs It is always a good idea to find two or more points (ordered pairs) of your functions and test them against a potential function equation. Sometimes one ordered pair works for your graph and a second does not. You must match the equation to the graph (or the equation to the table) that works for every coordinate point/ordered pair, not just one or two. For Function Equations and Nested Equations #1: Always work inside out Nested functions can look beastly and difficult, but take them piece by piece. Work out the equation in the center and then build outwards slowly, so as not to get any of your variables or equations mixed up. #2: Remember to FOIL It is quite common for ACT to make you square an equation. This is because many students get these types of questions wrong and distribute their exponents instead of squaring the entire expression. If you don't properly FOIL, then you will get these questions wrong. Whenever possible, try not to let yourself lose points due to these kinds of careless errors. Ready to test your function knowledge? Test Your Knowledge Now let's put our function knowledge to the test, using real ACT math problems. 1. A function $f(x)$ is defined as $f(x)=-8x^2$. What is $f(-3)$? F. -72G. 72H. 192J. -576K. 576 2. 3. Consider the functions $f(x)=√x$ and $g(x)=7x+b$. In the standard $(x,y)$ coordinate plane, $y=f(g(x))$ passes through $(4,6)$. What is the value of $b$? A. $8$B. $-8$C. $-25$D. $-26$E. $4-7√6$ 4. 5. A function P is defined as follows: for $x0$, $(P(x)=x^5+x^4-36x-36$for $x0$, $P(x)=-x^5+x^4+36x-36$ What is the value of $P(-1)$? A. -70B. -36C. 0D. 36E. 70 Answers: F, C, A, F, A Answer Explanations: 1. Here, we have a simple function equation. So let us replace our given input (-3) for our $x$ value in order to find our output. Note that the reason this problem is tricky is due to the many negative signs and the placement of the square. But so long as we are careful and make sure to keep track of all our pieces, we can solve the problem just fine (without falling for bait answers!). $f(x) = -8x^2$ $f(-3) = -8(-3)^2$ $f(-3) = -8(9)$ $f(-3) = -72$ Our final answer is F, -72. 2. This question is a function table, so let us remember our function table tips and tricks. Before we begin, this problem may get slightly confusing, as the labels in the chart are different from that which we normally use. To visualize our data, we are given $x$ as a certain distance that the cart is at any given second, $t$. This means that our input is $t$ (seconds) and our output is $x$ (distance). Now that we can see this, let us work through the problem. First, let us find the $y$-intercept. Luckily for us, we are given a coordinate pair with $t = 0$, $x = 10$. Because $t$ is serving as our input value (our $x$-coordinate) and $x$ is serving as our output (our y-coordinate), we can see that our $y$-intercept is the point at which $t = 0$. This means that our $y$-intercept is 10. Knowing that this is a linear function and the graph of a line is $y = mx + b$, we can eliminate answer choices B, D, and E. None of those give the y-intercept as 10, so none of them can be the correct answer. Now let us use our PIA strategy to find the equation of the line using our existing coordinate points. So let us test the point $(2, 18)$ and see which of our remaining equations (answer choice A or answer choice C) gives us these coordinates. Let us first test answer choice A. $x = t + 10$ $x = 2 + 10$ $x = 12$ Answer choice A is incorrect. When $t = 2$, $x$ should equal 18. So let us test answer choice C instead to see if it lines up with our input and output of $(2, 18)$. $x = 4t + 10$ $x = 4(2) + 10$ $x = 8 +10$ $x = 18$ Success! We have found our proper equation. Our final answer is C, $x = 4t + 10$ 3. This is a nested function problem that requires us to understand that coordinate points can act as inputs and outputs. So if we solve the nested equation as we normally would (remembering to act inside out), we would see: $g(x) = 7x + b$ $f(x) = √x$ $f(g(x)) = √{7x + b}$ Remembering that $f(x)$ is essentially another way of saying $y$ (in terms of coordinates), we can say: $y = √{7x + b}$ Now, let us get rid of the root by squaring both sides (for more on roots and squares, check out our guide to advanced integers). This gives us: $y^2 = 7x + b$ We know that the function passes through the coordinate point $(4, 6)$, which means we can replace the x and y-values with our $x$ and $y$ in the function equation. So: $y^2 = 7x + b$ $(6)^2 = 7(4) + b$ $36 = 28 + b$ $8 = b$ Our final answer is A, $b = 8$. 4. In this type of graph question, we are being asked to identify how the two graphs interact. Even without knowing their equations, we can understand- just through the diagram- a good deal of information about our two functions. In this case, we can see that the two functions intersect at exactly two points. This means that they are equal at exactly two values of $x$. So answer choice F is correct. But before we select answer choice F, let us also take the time to eliminate our other answer options. We know that answer choice G is incorrect, because we have already established that the two graphs intersect at two points and so have two values of $x$ at which they are equal, not 1. Answer choices H and J are both wrong, because there are x-coordinate points at which the graph $f(x)$ is higher (larger) than that of $g(x)$ and $x$-coordinate points where $f(x)$ is smaller. Neither function is larger (or smaller) at all points of $x$ than the other function. And finally, answer choice K is also incorrect, as these are two different functions- quadratic and linear- not inverse functions. An inverse function would produce the same type of graph, just inverted. We know our original answer choice is correct and we have successfully eliminated the others. Our final answer is F. 5. This is a function that has two different equations depending on our input value. So we must first determine which equation we are using in order to find the output to our particular input. We are given that our input ($x$) is -1. We also know that we must use the second function equation for any $x$ that is less than 0. This means we must use the second function equation, $p(x) = -x^5 + x^4 + 36x - 36$ So now we just plug in our input value of -1 (being very careful about all of our negative signs). $p(x) = -x^5 + x^4 + 36x - 36$ $p(-1) = -(-1)^5 + (-1)^4 + 36(-1) - 36$ $p(-1) = -(-1) + (1) - 36 - 36$ $p(-1) = 1 + 1 - 36 - 36$ $p(-1) = 2 - 72$ $p(-1) = -70$ Our final answer is A, -70. Congrats! You've mastered ACT functions! The Take Aways Even though there are many different ways you can be presented with a function problem, the core principles are always the same. No matter the equation or the graph, functions are always looking at inputs and outputs and the relationship between the two. So long as you remember your function definitions (and the corresponding graph shapes) and keep a clear head, and you'll see that functions are not as difficult as they may have once appeared. What's Next? You've taken on (and conquered) one of the most difficult math topics on the ACT (go you!), but there are many more topics to cover. Next, take a gander at all the math topics on the test and then bulk up on any topic with which you feel rusty. Need to brush up how to complete the square? On your rules of roots and exponents? How about your triangle rules and problems? All of our ACT math guides come complete with strategies and practice problems for any topic you need. Feeling overwhelmed? Make sure you take a practice test and then see how your score stacks up so that you can set realistic milestones and goals. Running out of time on the ACT math section? Check out how to best beat the clock and maximize your score. Aiming for a perfect score? Our guide to getting a perfect 36 on the ACT math section (written by a perfect-scorer!) will help get you where you need to be. Want to improve your ACT score by 4 points? Check out our best-in-class online ACT prep program. We guarantee your money back if you don't improve your ACT score by 4 points or more. Our program is entirely online, and it customizes what you study to your strengths and weaknesses. If you liked this Math lesson, you'll love our program. Along with more detailed lessons, you'll get thousands of practice problems organized by individual skills so you learn most effectively. We'll also give you a step-by-step program to follow so you'll never be confused about what to study next. Check out our 5-day free trial:

Sleep Paralysis Essay Example | Topics and Well Written Essays - 2500 words

Sleep Paralysis - Essay Example Gregory Stores (2001, P. 21) argues that â€Å"the episode of paralysis may be accompanied by hallucinatory experiences or dreamlike experiences which can be very dramatic and alarming, sometimes including the appearance of people or creatures taking on a threatening aspect.† It was often believed until modern rationality took over the realm of thought in people that occurrences of such disorders were due to the influence of demonic and spiritual effect in vulnerable humans. David J. Hufford (1982), in his book2 exhaustively discusses this belief referring it to the â€Å"old hag† tradition that he learnt particularly form Newfoundland. Scientific theories, and approaches, on the other hand, have been devised with not one with solid hold on its understanding. In this paper, we shall make an attempt in understanding the phenomenon of sleep paralysis with various angles, particularly scientific and dogmatic. We shall try and find out its symptoms or the experience while it occurs and subsequently try to unveil its causes, scientific or otherwise. We shall then study its effects in human psychology or thought. A few direct experiences of people shall be quoted and a possibility of its cure or precaution shall also be analyzed before concluding. The occurrence of sleep paralysis is indeed intimidating and troublesome. It seems, to many, a trance-like situation where our body with its inability to perform movement or even to cry out for help remains still, as though spell-bound by some strange demonic or spiritual cause until we are relieved suddenly from a grip what was rigid and ominous indeed. It occurs just before we fall asleep or as we are awakening. Dr. Rose Windale (2008) in her website of health and wellness tips describes the experience as thus: â€Å"A person may struggle to breathe while experiencing sleep paralysis.