Comparing the Heroes in The Dream of the Rood and Beowulf Essay

The  Heroes in The Dream of the Rood and Beowulf  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   In The Dream of the Rood, the poet has added elements of the idealized heroic death (as exemplified in Beowulf and The Battle of Maldon) to the crucifixion. He has also eliminated details of the story that tend to render Christ as a figure of pathos, in order to further Christ's identification with the other glorious warriors Anglo-Saxon poems.   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   When a hero meets his death, for example, he is usually surrounded by faithful retainers (as is Byrhtnoth) or at least one steadfast companion, such as Beowulf's Wiglaf. The gospel clearly states that Jesus died ignobly, in the most humiliating fashion possible, and that his disciples kept themselves from Golgotha in order not to be implicated alongside him. The crowd mocked Christ with fake veneration. The poet must realize, however, that his audience will not accept a Lord who did not die a radiant death, and was not universally lamented. He says instead that "all creation wept, bewailed the king's death -- Christ was on the cross." After Jesus is taken down, the poet asserts that a grave was carved for him "of bright stone", and that the soldiers sung a dirge for him in the eventide. Men came "from afar, hastening to the prince." [165] The rood extols upon Christ's shining beauty as he died. Very noble, but there's little biblical suppo rt for this account. Also rooted in the heroic tradition is the subsequent gold-plating and raising of the cross. Just as Beowulf asked that a "bright mound" be erected in his honor, and the gold in the dragon's cave becomes as a monument to him, so do the disciples unearth and gild the rood. The idea of God himself lacking a proper gold-drenched headstone was unthin... ...e most such works, it tries to convince heathens to convert by co-opting the extant value system. Christ emerges as a powerful king who will stoically suffer for us, and reward us, for the price of our piety. Sources Cited and Consulted Heaney, Seamus, trans. Beowulf: A New Verse Translation. New York: Farrar, Straus, and Giroux, 2000. Mitchell, Bruce and Fred C. Robinson (eds.). "The Dream of the Rood: or A Vision of the Cross." A Guide to Old English, 6E. Oxford: Blackwell Publishing, 2002. 256-263. O'Keeffe, Katherine O'Brien. "Heroic values and Christian ethics." The Cambridge Companion to Old English Literature. Ed. Malcolm Godden and Michael Lapidge. Cambridge: Cambridge University Press, 1992. 107-125. Wheelock, Jeremy I. "The Word Made Flesh: 'Engel Dryhtnes' in The Dream of the Rood." English Language Notes. March 2000, Vol. 37 Issue 3: 1.

An Analysis of My Personality Type

Your main points and each step are clear but you did not label them correctly. Good observations, points and outcomes documented throughout the paper. Conclusions/Summary References/Citations (4) Good job/ Citations throughout each section Spelling/Grammar Good job/ Be sure to use active voice page Count/l_MIT (4) 20 PAP Format/Errors See PAP comments throughout the paper Overall Comments: Very Good paper! This paper has demonstrated that you understand the core objectives and learning outcomes for this assignment and the meaning of your personal assessment.Remember that graduate level writing is a continuous improvement process. A solid best practice is writing a paper and then putting it down and reading it when you are fresh. You will often pick up small mistakes by doing this. Fix some of the little mistakes found in this paper and you will strengthen your work on future assignments. It is evident you paid attention to getting your paper right†¦ You are doing graduate level writing. Enjoyed reading your work †¦ Great job! This paper discusses my personal results of the Myers-Briggs Type Indicator personality test and the Jung Typology Test.It also details how analyzing and understanding personality types is relevant to organizational behavior. The first section of this paper details and discusses the specific aspects of my personality based on the tests mentioned above. Each specific personality preference is analyzed and validated based on my type and temperament. Examples from my personal and professional life are utilized during the validation. The second section off this paper addresses what have learned about the Myers-Briggs and Jung Typology personality tests and how this knowledge can be used by an employee, co-worker, and manager of an organization .Seem,'rods: personality, type, organizational behavior Richard Nixon once said, â€Å"Don't try to take on a new personality; it doesn't work† (â€Å"Quotes on Personality', 2014). Bel ieve that this is excellent advice. Instead of trying to develop a new personality, perhaps people should learn to better understand the personality that they have. After taking the Myers- Briggs Type Indicator personality test and the Jung Typology Test, I have a better understanding of my own personality and also the personality traits of other people around me.In the first section of this paper I will detail and discuss the specific aspects of my personality based on the tests mentioned above. In the second section of this paper I will explain how what I learned about personality types relates to organizational behavior and how it will help me be a better employee, co-worker, and manager. Aspects of My Personality Type After taking both the Myers-Briggs Type Indicator personality test and the Jung Typology Test, I was classified with the Introverted Sensing Thinking Judging (1ST J) personality type.SITS personality types are considered quiet reserved people who are loyal, faithfu l, and dependable (â€Å"Psychological Type†, 2014). They tend to express a strong sense of duty and commitment and are recently very serious individuals (â€Å"Jung Typology Test†, 2014). Gist's believe in laws and traditions and they are generally conservative in nature (Kroger, Teethes, & Rutledge, 2002). In the following paragraphs will discuss the validity of the different letters of my personality type and how they specifically relate to me.Introvert Preference On the Jung Typology Test, I scored a distinct preference of 67% introversion over extroversion. As an introvert, I tend to focus within myself for satisfaction. Frequently I have to force myself to interact with people in a social setting. I rarely enjoy hanging out in large groups of people. I prefer to spend time alone and would consider myself a â€Å"home body'. When I do go out, it is usually to a place where I don't have to interact with people on a personal level.Sitting in a dark movie theatre wi th my family or eating dinner at a restaurant are perfect examples of a low threat social setting. Throughout my life I have always had 1 or 2 deep friendships as opposed to a large group of friends. An occasional weakness with introverts is they are sometimes reel octant to work with others (Kroger, Teethes, & Rutledge, 2002). In my professional life, I am not quite as introverted. As a military member and manager of people, I have to interact with my subordinates and peers on a daily basis in order to facilitate mission accomplishment.Sensing Preference With a sensing presence of 62%, according to the Jung Typology Test, I seem to conform to approximately 70% of the U. S. Population regarding this preference (Kroger, Teethes, & Rutledge, 2002). Sensors are defined as individuals that prefer to get their information in a literal way from their 5 senses as opposed to getting information in a figurative way like an intuitive arson would (â€Å"Psychological Type†, 2014). In bo th my personal and professional life prefer to deal in facts and live by a set of rules. As a 25 year military veteran, have been conditioned to respond and react exactly this way.I tend to rely on my experiences to help me analyze the specifics as they are presented to me. A major weakness with my preference for sensing is that sometimes refuse to look at things from another perspective. Thinking In this measured area of the Jung Typology Test, I demonstrated a clear propensity for the thinking preference with a rating of 88%. As a manager in he military profession, pride myself on my ability to be objective, fair and firm. As a supervisor I frequently make difficult decisions and firmly believe that it is more important to be respected than liked. Always try to look at things from a logical perspective and try not to let my personal feelings get in the way of my decisions. One down side with the thinking preference is that it is possible to forget about the people perspective when you are making decisions (â€Å"Psychological Type†, 2014). Judging Preference The judging preference was my most definitive personality preference with rating of 100% on the Jung Typology Test. In my military profession I live by a schedule, make decisive judgments, and always try to follow the established rules and regulations. Onto like to wait until the last minute to do things. I am also very conservative and regulated in my approach to my personal and professional life. One weakness of my overwhelmingly strong judging preference is that frequently have little patience with people that are procrastinators, poor planners, or unable to make decisions. SITS Personality with a SO Temperament People with SITS personalities are considered internally focused individuals ho exhibit; strong senses of duty, good organizational skills, are driven to succeed, are honest, and value their integrity (â€Å"Psychological Type†, 2014).My temperament is a Sensing Judging (SO). SO temperaments desire to be associated with significant institutions or organizations (Kroger, Teethes, & Rutledge, 2002). As a Non-commissioned Officer in the united States Air Force this makes perfect sense. I enjoy the daily challenges associated with being an administrator and manager. I have a deep respect for the chain of command within my organization, and pride myself on being reliable. A active byproduct is that in my personal life my SO temperament can sometimes be overwhelming for my children because I tend to be a task master.Relating Personality Types to Organizations After reading Type Talk at Work, I have a greater knowledge of the 16 different personality types and how they relate to organizational behavior. As a manager in an organization, it is essential that I am able to calculate the internal strengths and weaknesses of my employees (Fisher, 2012). Understanding how to analyze an individual based on their personality type can be of enormous benefit to me as a super visor. Throughout my years as an enlisted manager in the IIS Air Force, I have learned that each individual is different and you have to manage them accordingly.For example; if I have to assign someone as training instructor, probably would look for an extrovert over an introvert. Since having someone who is comfortable speaking in front of people would be vital for this position, an extrovert personality would be a better choice. Motivation is also different based on personality. Extroverts enjoy being rewarded in public, while introverts might prefer a more low key setting. As a manager it is also important for me to understand how my own personality type effects my management style.As a SITS personality type, occasionally have a tendency to dismiss the perspectives of others. I also am a very â€Å"by the book† manager. Understanding the weaker characteristics of my personality type will help me to control them so they don't corrupt my ability to manage my organization (â €Å"Psychological Type†, 2014). Reading and learning about the 16 different personality types has been very enlightening from a personal and professional perspective. Understanding he four different personality preferences and how they work together to make up my personality will benefit me throughout my life.

Designing an Office Space Essay

Designing a new office space for a law firm requires careful consideration and planning. Not only must the space be esthetically pleasing, but must function well for those who work within it. In addition, there are many other considerations that must be addressed. Among them are what type of space to choose, budgetary constraints, room for expansion, and technology. CHOOSING A SPACE The old adage in real estate goes â€Å"location, location, location.† This also holds true when considering a space for your firm. In our fact pattern the supervising attorney has two choices. The first is a shared space with five other solo practitioners. The second is a suite of offices that are located adjacent to a mid-sized firm. I would recommend to the supervising attorney that we choose the suite of offices. We would be given the opportunity and space to expand as our firm grows. Also, by locating ourselves adjacent to a mid-sized firm, we position ourselves to appear as a larger firm than what we are. This can help to create a positive first impression the first time clients visit the office. If we were to position ourselves within an office with five other practitioners, it would be less apparent to clients that we were running our own firm. BUDGETARY CONCERNS Although leasing as individual office space is often more expensive than sharing space with other attorney’s, I believe the firm would benefit from having its own space for several reasons. Image, along with reputation, is a key factor when a client chooses a firm. We want to convey to clients that we are a successful firm and having our own space will help to convey that. Also, sharing an office space with attorneys who practice other areas of law could lead to an uncomfortable environment or situation for our clients. A woman coming to see her divorce attorney may feel uncomfortable sharing a waiting room with a man, possibly charged with a violent crime, waiting to see his criminal defense attorney. EXPANSION PLANS By selecting to lease a suite of offices to use rather than a shared space, we afford ourselves the opportunity and space to expand. As the firm grows and takes on additional partners, we will need to increase our office space to accommodate both the attorney as well as support staff. Below is a sample layout for a sole practitioner law firm that I have designed with expansion in mind. When the time comes to expand, we can take over the adjacent office to create a space that closely mirrors the original space. By utilizing a single hallway between offices we increase efficiency and when we expand we can create a horseshoe shaped walk way within the office. AMENITIES The space will have many features and amenities that will enhance the client experience while increasing productivity. The reception area will have multiple seating areas. Large, oversized sofas will provide a comfortable place for clients to wait until they are seen. Small coffee tables will be available for clients to use to work from. A small buffet with coffee, tea, and pastries will be available for clients to enjoy. Each of these things will provide a positive first impression for the client as well as a comfortable experience. Both the attorney as well as the legal assistant will have private offices which will be adjacent to each other. This provides a way for them to communicate effectively as well as collaborate on cases as needed. The attorney’s office shall be sufficiently large enough to house reference materials and books in large custom bookshelves. The legal assistant’s office will also have bookshelves as well as file cabinets for storage. Attorneys will have a small room designated strictly for meeting with clients. This allows the attorney to meet with a client outside of their personal workspace. The client meeting room will feature a table that seats six people comfortably. Since one of our areas of practice is family law, the room will have a small armoire in which children’s toys can be stored for times when the client brings small children with them. A large conference room will be created for depositions and general meetings. It will have a large table capable of seating at least ten people. There will also be additional room available for a court reporter to record depositions. The conference room will be located across the hall for convenience to both the attorney and legal assistant. Additionally, the office will have several rooms dedicated to specific functions. There will be a copy room with an adjacent supply room. The copy room will house a copier as well as a fax and scanner. Locating the supply room adjacent to the copy room will create easy access for copy room supplies. A large break room with kitchen will allow the firm to have an area for caterers to set up in if we are having a large function. It will also serve as a lunch area or break room for staff. An I.T. room will house all of our computer servers as well as central phone equipment. The office will also have a large room dedicated to file storage. Inside the file storage room we will utilize fire resistant file cabinets to protect records. TECHNOLOGY Part of conveying a positive and successful image to clients will be the use of the latest available technologies within the office. The firm will adopt software that allows for cloud computing. This will allow both the attorney and the legal assistant to access information from both inside the office as well as outside. Wi-Fi will be provided in the office to facilitate the use of iPads and laptops. This will allow staff to take their laptop or iPad room to room during the course of their workday as they move from case to case. CONCLUSION Every decision that is made in the planning stages of designing a firm’s office layout can have both good and bad consequences. It is extremely important to give careful thought to how the space is laid out and how those who work in the space will utilize it. It is my belief that the plans laid out above would provide a way to achieve the firms goals of putting forth a positive and successful image, provide a path to expansion, as well as provide a space that will maximize efficiency and productivity. REFERENCES Roper, B.D. (2006). Practical Law Office Management. New York, NY: Thompson Delmar Learning.

Marion camp memorial hospital Essays

Marion camp memorial hospital Essays Marion camp memorial hospital Paper Marion camp memorial hospital Paper The Marion Camp Memorial Hospital provides convalescent care for patients with long-term illnesses as well as for patients who require extended periods at physical therapy. The average length of stay at the hospital is for months. The hospital is supported through a combination of state and federal funding, medicare payments, and private donations. Less than 10 percent of the hospital’s revenue is derived from the patients. The hospital director, H.  John (Big Jack) Pace, has become increasingly concerned with the number of complaints the hospital is receiving on various aspects of its health care, and he recently made this the main topic at the monthly staff meeting. In the attendance of the meeting were Alan Carter, chief physician: Nancy Ames, supervisor of nursing; Phil Rogers, manager of support services; and Charlotte James, assistant director. Mr. Pace began the meeting with a brief statement outlining some of the many complaints he’d received, which ranged from cold meals to beds not being changed often enough. https://healtheappointments.com/private-hospital-vs-public-hospitals-essays/ Some of the complaints were from hospital employees themselves. Mr. Pace indicated that he hoped that this wasn’t the start of a decline in the quality of health care. However, his main concern was an upcoming inspection for reaccreditation by the state. In his words, â€Å"You know how they can pick up on something like this and blow it all out of proportion. † Charlotte James, who has been investigating the problem, reported that she was having difficulties because â€Å"doctors, nurses, dieticians, and support people have different definitions of quality.† She also noted that most of the complaints seemed to relate to support services rather than medical care, and Phil Rogers tended to agree with her, but he indicated that he had not been able to â€Å"turn things around. † He pointed out that support people (nurses’ aids, kitchen workers, janitors, painters, etc. ) were unskilled or semiskilled personnel who generally received the minimum wage. He noted that the turnover was high, morale was low, there were no professional standards, and few workers viewed themselves as a part of the â€Å"health care team. †

Assignment 301TaskA Essay

Assignment 301TaskA Essay Assignment 301TaskA Essay Assignment 301 Steven Morgan Task A Candidate No: Understanding Roles, Responsibilities and Relationships in Education and Training Information leaflet To pass on knowledge is one of your roles as a teacher; however, this in part only scratches the surface. You will be responsible to know your students and their needs, so be understanding on how the learner learns. This will make not only their experience a good one, but make you a better teacher. If you have knowledge, let others light their candles at it. ~Margaret Fuller. You will ensure a safe environment where learners feel comfortable and are able to participate fully in the course content. Teachers will comply with any guidance on Health and safety and other legislation relating to safeguarding the rights of individuals whether they are children or adults with or without specific needs and requirements. You will also be familiar with relevant policies and procedures and any local standing orders, this will encourage inclusiveness and appreciation of those with differences and seeing these as wealth and not a hindrance. You will develop to promote inclusion of all those who want to learn and those who are reluctant at first to learn. You will also encourage personal achievement. As part of ensuring that you have a safe environment you must make sure that the learning environment is as needed and that optimal class participation is achievable, heat, light and access and egress are suitable for all. You will conduct getting to know you ice breakers to allow class bonding as this will help you in not only getting to know the learners but the learners being put at ease with each other. The setting of ground rules will set the boundaries of the course; group participation is the key here and will allow the learners to set some of their own ground rules. Not only will these set the limits for the class but can be used to reinforce behaviour if need be. As the teacher you will be responsible to plan and assemble the required course content which will be tailored to meet the demands of the task that you have been set. The use of different resources and learning methods such a PowerPoint, videos or handouts must enhance the learner’s experience. This has to be customized to the needs of the learner, to include any specific needs where reasonably can be met. If a child can’t learn the way we teach, maybe we should teach the way that they learn. ~ Ignacio Estrada. The delivery of sound structured lessons will be of a high standard and

Reflections, Rotations, and Translations ACT Geometry Strategies and Practice

Reflections, Rotations, and Translations ACT Geometry Strategies and Practice SAT / ACT Prep Online Guides and Tips Reflections, rotations, translations, oh my! Whether you’re dealing with points or complete shapes on the coordinate plane, you can spin 'em, flip 'em, or move 'em around to your heart’s content. And, often enough, you’ll be asked to do so on the ACT. This will be your complete guide to rotations, reflections, and translations of points, shapes, and graphs on the ACT- what these terms mean, the types of questions you’ll see on the test, and the tips and formulas you’ll need to solve these questions in no time. Before You Continue Reflection, rotation, and translation problems are fairly rare on the ACT, only appearing once per test, if at all. If you’re shooting for a perfect or nearly perfect score and want to make sure you have all your bases covered, then this is the guide for you. But if you still need to brush up on your fundamentals, then your focus will be better spent on studying the more common types of math problems you’ll see on the test. Remember, each question is worth the same amount of points, so it is better that you can answer three or four questions on integers, triangles, or slopes than to answer one question on rotations. So if you’ve got a solid grasp of all your foundational math topics (or you just really, really like coordinate geometry), then lets talk reflections, rotations, and translations! What is a Reflection? A reflection in the coordinate plane is just like a reflection in a mirror. Any point or shape can be reflected across the x-axis, the y-axis, or any other line, invisible or visible. This line, about which the object is reflected, is called the "line of symmetry." Let's look at a typical ACT line of symmetry problem. To find our lines of symmetry, we must divide our figure into symmetrical halves. This means that each side must be a reflection of the other, about a line. If we connect opposite angles in our figure, we will have several lines of symmetry. Let us do so. Now, from here, we can see that there are also lines of symmetry between our interior angles, like so: If we put them together, we get this. But wait! We can count our total number of lines (diameters, since they're spanning the entire length of the circle), but we CANNOT count each individual point that connects to the circumference of the circle as a line of symmetry. The number of actual lines of symmetry will be half the number of connecting points, because we need to only count each line one time. Because this is a busy figure, let us look at it a little more simplistically. Here, we have gotten rid of the other half of each line of symmetry and transformed them into all the radii of the circle. Now we can count the lines of symmetry without fear that we are double-counting one line. If we count them as they are, we can see that there are eight lines of symmetry total. Our final answer is H, 8. Nature's take on lines of symmetry in action. What is a Rotation? Objects in the coordinate plane can also be rotated (turned) clockwise or counterclockwise. Imagine that we can adjust the object with our hands- it will spin, while still lying flat, like a piece of paper on a tabletop. We must always select a point to act as the center point for our rotation. This center point of our rotation can be anywhere on the coordinate plane or on the shape in question (notice that it does NOT have to be the center of the shape). Let us look at a visual demonstration of this. We can have an object that rotates about its own center. A trapezoid is rotating about its center. Or the same shape can also be rotated about a different point. Here, the trapezoid is rotating about a point on the base of the trapezoid. But on the ACT, you'll almost always be asked to rotate an object "about the origin." This means that the origin (coordinates $(0,0)$) acts as your center of rotation. The angle about which the object moves is called the angle of rotation. As we rotate an object, the angle of rotation will be: Positive when we move the object counterclockwise Negative when the object is rotating clockwise. A positive angle of rotation. A negative angle of rotation. You can see that our shape ended up in the same place, but it got there by being rotated either $+180Â °$ or $-180Â °$. On the other hand, sometimes the ACT will have you rotate objects in a way that runs counter to these standard rules. Always follow the given instructions, even if they seem to contradict mathematical laws. For instance, (We will walk through this question later in the guide) We will walk through how to solve this question later in the guide, but for now notice that the question asks you to rotate the circle 90 degrees clockwise. Really, the degree measure would be $-90$ degrees, even though it is technically correct to say that you’re moving $+90$ degrees in a certain direction. Because this can be confusing and seemingly contradicts the rules of rotation degrees (though technically does not), just follow the information you are given in the question, rather than trying to overcomplicate the problem. As you might also guess from the above question, if you are asked to rotate an object on the ACT, it will be at an angle of 90 degrees or 180 degrees (or, more rarely, 270 degrees). These are nice numbers that evenly divide the coordinate plane into four parts, and each of these degree measures has a standard rule of rotation, when rotating a point about the origin. Let us look at these rotation rules. Some rules are more helpful than others. Rotation rules and formulas happen to be quite useful. Rotation Rules/Formulas Whether you are asked to rotate a single point or a full object, it is easiest to rotate the point/shape by focusing on each individual point in question. You can determine the new coordinates of each point by learning your rules of rotation for certain angle measures. Each of the three degree measures- 90, 180, or 270- will shift the coordinates of your original point to a different, calculable, position on the graph. If rotating counterclockwise (a positive angle of rotation), you can use these rules to find your new coordinate points. If you're a little rusty on which quadrants of the $xy$-coordinate plane have positive and negative $x$- and $y$-coordinates, you should take a quick detour to our article on graph quadrants before moving on. [Note: these formulas only apply when rotating an object about the origin. If you are asked to rotate objects about another center of rotation (as with the circle question above), these rules will NOT apply.] Let us say we begin with a point at coordinates $(8, 3)$. For 90 degree rotations: $(a, b)$ = $(-b, a)$ A 90Â ° rotation bring our original coordinates of $(8, 3)$ to $(-3, 8)$. For 180 degree rotations: $(a, b)$ = $(-a, -b)$ A $180Â °$ rotation brings our original coordinates of $(8, 3)$ to $(-8, -3)$. For 270 degree rotations: $(a, b)$ = $(b, -a)$ A $270Â °$ rotation brings our original coordinates of $(8, 3)$ to $(3, -8)$. (And, of course, a 360 degree rotation will bring you right back to the beginning at $(a, b)$ again!) A $360Â °$ rotation bring our original coordinates of $(8, 3)$ back to $(8, 3)$ once again. Keep your head on you- those rotations can be a doozy! What is a Translation? In addition to reflecting or rotating an object, we can also translate the object to another place on the coordinate plane. Translation is the act of "sliding" our point or shape along the coordinate plane in a particular direction. The shape can be translated up or down (or both!) any amount of distance along the plane. It maintains its shape and bearing, but is simply located elsewhere in the plane. The way to notate that a translation is to occur is to say: $T_{a,b}(x,y)$ This means that your final coordinates for this point will be: $(x+a,y+b)$ For example, What is the new point for $T_{5,−2}(−3,6)$? A. $(3, 3)$B. $(2, 4)$C. $(-3, 6)$D. $(11, -5)$E. $(-1, -2)$ We know that we must add together our translated points to the corresponding $x$ and $y$ values of our original coordinates. So: $T_{5,−2}(−3,6)$ $(−3+5,6+−2)$ $(2,4)$ Our new coordinates for this point are at $(2, 4)$ You can see why this is true if we look at it on a graph. Here, we have our starting point of $(-3, 6)$. Now, we are moving positively (to the right) 5 spaces and negatively (downwards) 3 spaces. If we started at $(-3, 6)$, this wll put our new point at $(2, 4)$. Our final answer is B, $(2, 4)$. Typical Reflection, Rotation, and Translation Problems Again, these types of questions are fairly rare on the ACT, and you will only ever see one question on reflections, rotations, or translations, if indeed you see any at all. That said, there are four different types of reflection/rotation/translation problems that will show up, when they appear. These questions will be either a reflection, rotation, or translation questions about: #1: Points #2: Shapes in the coordinate plane #3: Function graphs #4: Shapes and their lines of symmetry Let’s look at all three. Points Because a point is individual, points are the simplest objects to be rotated, reflected, or translated. Each point will always be made up of an $x$ and $y$ coordinate- written $(x,y)$- but you only have to keep track of the solitary point and how it should shift and move, rather than having to keep track of it in relation to other points (as you will have to when working with shapes). Shapes Shapes are slightly more complicated to reflect or rotate than points are, due to the fact that all the points on a shape (and the lines connecting those points) will have a relationship with one another that must be maintained or altered in a controlled manner. This means that any shape rotation/reflection/translation will require more consideration and care, in order to make sure all your pieces are properly aligned. It is often much easier, when working with modified shapes, to map out the positions of the points alone. Don’t worry about the lines- mark the proper position of the new coordinates for the points and the lines will fall into place. Let's look at an example. The red line makes up one side of the trapezoid above. If this line has a slope of $3/2$, what is the slope of the line when the trapezoid is reflected across the $x$-axis? A. $−2/3$B. $−3/2$C. $2/3$D. $3/2$E. $4/3$ Instead of focusing on the slopes themselves, let us map out the new trapezoid by its points and only then connect the lines. Now, if we connect the lines to actually make the trapezoid... We can find the new slope of the line by counting the rise of over the run. The rise is $-3$ and the run is $+2$. The new slope of the equivalent line in our trapezoid will be $−3/2$. Our final answer is B, $−3/2$ Function Graphs Function graphs can be reflected or translated just like shapes and points, though they CANNOT be rotated. (Why can functions not be rotated? If a function were rotated, it would fail the vertical line test (more on this is covered in our guide to ACT functions) and no longer be a function.) A reflected function. A translated function. A function CANNOT be rotated. A graph with more than one $y$ value (output) for the same $x$ value (input) is NOT a function. Function Translations We can translate our function up or down by adding or subtraction from our output. Adding to output translates the graph up. If this is the original placement of our graph, $f(x)$.... We can translate it up by adding to the output, aka $f(x)+5$. Subtracting from the output, on the other hand, moves the graph down. Again, if this is the original placement of our graph, $f(x)$.... We can translate it down by subtracting from the output, aka $f(x)−5$. This kind of translation will work on any function graph. We can also translate a function side to side (horizontally) by adding or subtracting from the input. Adding to the input will shift the graph left. If this is the placement of our original graph, $f(x)$... We can translate it left by adding to the input, aka $f(x+5)$ Subtracting from the input will shift the graph to the right. Again, if this is our original graph, $f(x)$... We can translate it right by subtracting from our input, aka $f(x−5)$ This kind of translation will work on any function graph as well. Function Reflections We can also reflect our function about a line of symmetry along the $x$ or $y$-axis. Making the output negative makes the function reflect across the $x$-axis (inverts it about the $x$-axis). $f(x)$ becomes $−f(x)$. Making input negative makes the function reflect across the $y$-axis. $f(x)$ becomes $f(−x)$ Lines of Symmetry As we saw with our earlier line of symmetry problem, the ACT will sometimes present you with a picture and ask you to identify the lines of symmetry. If you understand how a line of symmetry works (that everything on each half of the line must be symmetrical, i.e. a reflection), and you make sure to count each line only once, then you should be able to breeze through these questions without fail. If you feel you are in information overload right now, don't worry! You can always make notes and flashcards to review and memorize later; just understanding how and why rotations and translations work is enough for now. Strategies for Reflection and Translation Problems Though no two reflection/translation/rotation problems are exactly alike, there are a few tips and tricks to follow for any kind you may come across. #1: Draw your own graphs Sometimes you will be given a diagram, or half a diagram, and sometimes you won't. But always, when the test asks you to reflect, rotate, or translate a point or a shape, you must form your own new picture, either on the page or in your head. Because it is entirely too easy to make mistakes when working out math problems in your head alone, it is always a good idea to take a moment to sketch out a graph of the object’s new position in space (if not the old one as well). Seeing a diagram on the page is especially useful if you are asked to find more information, rather than simply identifying a new coordinate point (a feat in and of itself!). For instance, you might be asked to find the slope of a reflected or rotated line (as we saw above), or the product of two translated $x$-coordinates, or anything else the ACT might think of. Without making your own drawings and diagrams, it can be easy to become confused, fall for bait answers, and lose precious points. #2: Drill your rotation formulas When working with translations or reflections, it is simple enough to draw your own picture and line up your corresponding points, but when it comes to rotations, it can be much harder to visualize the movement of the point or the object. Even when you’ve mapped out the original point, rotations are often much trickier than they appear. Unless you have a paper cut-out of your point, shape, or function and want to spend your time spinning your scratch paper around in circles, it’s better to simply memorize your rotation rules for 90, 180, and 270 degrees. #3: Double-check, double-check, (triple-check) Rotations, reflections, and translations may seem simple (and, indeed, the underlying principles are not any more complex than anything else on the ACT), but the difficulty in solving these kinds of problems is in just how easy it is to mis-map a coordinate point or two. It is especially precarious, because the test-makers will throw as many bait answers at you as they possibly can. Nothing is more frustrating than when you know how to solve a problem, but go too quickly or too carelessly through your test and so end up getting the question wrong. Make sure you double-check that you’ve properly shifted your coordinates before you bubble in that final answer. Excited to do some practice questions? Test Your Knowledge Now let's test your knowledge on some real ACT math questions on reflections, translations, and rotations. 1. When $ABCD$ is reflected over the $y$-axis to $A'B'C'D'$, what are the coordinates $D'$? F. $(-12, 1)$G. $(-12,-1)$H. $(12,-1)$J. $(1,12)$K. $(1,-12)$ 2. The graph $y=f(x)$ is shown below. What could be the graph of $y=f(x−4)$? A. B. C. D. E. 3. 4. Answers: F, B, K, C Answer Explanations: 1. Because we need to reflect our trapezoid, let us draw ourselves a picture. Note: be very careful to reflect your shape around the correct axis. The way the diagram is laid out, you may be tempted to reflect your object across the $x$ axis, like so This will give you the wrong answer and lead you to fall into one of the bait answer traps. Because we are told to reflect the trapezoid across the $y$ axis, our graph will instead look like this: You can see, then, that the reflection of point D will be at coordinates $(-12, 1)$ Our final answer is F, $(-12, 1)$ 2. Because we are being asked to find $y=f(x−4)$ from our original $y=f(x)$, we are subtracting from our input value. (For more on function inputs and outputs, check out our guide to ACT functions). If you remember our definitions on how to translate functions from above, you know that subtracting from the input translates our graph to the right and has no affect on the height (meaning, the graph does not move up or down). The only graph example that moves the function to the right and does not move it up or down is answer choice B. Again, here is our original graph. And here is the graph for answer choice B. Our final answer is B. 3. We are supposed to reflect our given triangle, so let us use our most important strategy and draw our picture out, so that we won’t make any mistakes trying to do the problem in our heads. Once we have reflected our triangle about the line of symmetry x, we can see that the perimeter is made of: $y+z+z+y$ $2y+2z$ Or, in other words, $2(y+z)$ Our final answer is K, $2(y+z)$ 4. We are being told to rotate the point $(6, 6)$ on the circle 90 degrees clockwise about the center of rotation $(2, 3)$. Because we are not rotating our point about the origin, our rotation rules unfortunately will not apply to this problem. That means we must find another way to rotate our point 90 degrees clockwise. By far, the simplest way to solve this problem is to divide our circle into four by drawing two diameters perpendicular to one another. (Why divide the circle into four? A circle is 360 degrees, and $360/90=4$ By dividing our circle this way, we can see that a 90 degree rotation would put the point slightly below the x-axis at coordinates approximately $(5, -1)$. Our final answer is C, $(5, -1)$ Phew! That wasn't so hard, now was it? The Take Aways Though rare(ish), the occasional rotation, reflection, or translation question can certainly throw you for a loop if you’re unprepared for it. But nothing the ACT can put on the test is unsolvable (and, indeed, the test is designed to give you opportunities to succeed, even as it tests your diligence and eye for detail). Once you’ve got your basic building blocks and formulas down tight, you will be well on your way to mastering all your coordinate geometry questions and earning that perfect score. What’s Next? You’ve tackled reflections, translations, and rotations (go you!), so take a minute to look over all the math topics on the ACT. Making sure you’re prepared for whatever comes your way is most of the battle, so look to our individual ACT math guides- all of which have real practice questions!- to brush up on any weak areas in your mathematical portfolio. Want to master two of the most invaluable math strategies for mastering the ACT? Check out our guides on how to use plugging in numbers and plugging in answers to make sense of some of the trickiest ACT problems out there. Looking to get that perfect score? Look no further than our guide to getting a perfect 36 on the ACT math, written by a perfect scorer. 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:

Micro hydro power design Case Study Example | Topics and Well Written Essays - 3000 words

Micro hydro power design - Case Study Example n towards production of more environmental friendly energy as oppose to the use of oil, these includes all renewable energy sources such as wind, biomass, solar and more importantly hydro power since it is the most efficient way of producing power in large quantities without damaging the environment (U.S. Department of Energy, 2008). Water is the most abundant resource in the world and as result its energy, in the form potential energy can be dammed and utilized in production of electricity. The dam retains the water and the potential energy rises as the height above the base increases, this water is directed to a turbine by the use of penstock and after working on the turbine, it exists through the tailrace. The critical parts of the turbine includes the caps connected to a shaft, the flowing water exerts a rotary motion on the caps/blades, which causes the shaft to turn in a circular manner. This shaft connects to a generator with a core trapped in a magnet’s poles, which causes electromagnetic induction (USGS, 2008). This electricity generated is then transmitted via cabling to households or for other purposes. In summary, the flowing water and the generator forms the backbone of the hydropower. The water provides the force that turns a rotor with field windings. The windings are supplied with an excitation voltage to set up an electric field, with the rotation of the, magnetically induced current flows to the stator which is a cylindrical ring encased with another magnetic windings. The two windings are separated by about 2mm air gas (USGS, 2008). Today, hydropower systems are cable of producing power ranging from 1MG to 100MG with more possibilities of producing power in small scale with low flow parameters and micro generators. Small dams, commonly known as weirs are used to trap and retain the water, which is then directed to a turbine via piping systems, the generator that produce power for residential usage then utilizes the force. The project