Reviewing Homers Iliad and Odyssey Sophocles Oedipus Rex

Question: Describe about the Reviewing Homers Iliad and Odyssey Sophocles Oedipus Rex? Answer: Homers Iliad and Odyssey are supposed to be the most convenient epic ever written in any literature. Himself being blind, approach of Homer in developing such epic is nothing less than adventurous. This study is going to set the frame of review of Homers Iliad and Odyssey, Sophocles Oedipus Rex having been compared with Prometheus Bound by Aeschylus. Iliad is nothing but a notary of love and treachery. Myrsiades is of this view if Paris would not have been licentious in its character in eloping with gorgeous Helen, in no way the novel would have been framed. At the same time, it may not have let the literature to have such warriors like Achilles, Odysseus or Hector. Act of revenge by red haired Menelaus instigated Agamemnon to siege the walls of Troy. On the other hand, division of Gods within the two clashing groups, Apollo, Poseidon on the side of Troy and Athena on Greece (Bagby). Wealth and overbearing attitude of Agamemnon can crushing and crumbling down against the great Trojan worriers until the Great Trojan Horse episode that destroyed the organized approach of Trojans. Irony of fate came crushing down severely on Troy (Vergados). Blasphemy of fate also let Agamemnon and great warrior Achilles to be killed severely. Homer paints up every inches of the epic having been tinged with essential intricacies. Journey of Odysseus back to its native country, Ithaca from the battlefield of Troy after its fall is jotted down in Odyssey. Surprising, the journey took around ten years. Telemachus approach of protecting the state and her mother Penelope from the hand of her suitors of the court, first let the plot of the epic to be developed. Different mythical creatures like Siren, Calypso came alive in this epic and presented their role in the development of the epic as well. Using of the metaphors, according to Bagby, by Homer has enlivened the epical approach. Both the linear and the non-linear poetic style of the poem helps it becoming succinctly noteworthy. Curtin has essentially stated that the complete journey of life of a human being has been presented by the writer. Homer put Odysseus into succinct adventurer and explorer. A prompt geographic sequence is succinctly maintained by the writer that has gone coherent in developing the context of the epic. But again the hand of divinity could not have been avoided. It seems to have created problems, however, as the epic tells all is for good is restored ultimately. Oedipus Rex a marvel presented by Sophocles is a tragedy that historically presents how a common man Oedipus becomes a king and had killed his father married his mother only to fulfill the prophesy. The play has been written in the classical format as described by Aristotle. Presentation of catharsis in the play is literally significant. Being in the top of the power, Oedipus started misusing his power that landed him down to such a position (Davies). The play essentially projects how own fault leads a human being slide down from the essence of top being reverse to the portrayal of destiny as the sole cause of all the downfall. Although the appearance and application of divinity is gallant in this play, however, it is needed to be stated that presentation of Freudian reality in the play has made Sophocles to become essentially developed (Mahony). Divine curse preached on the mistakes of Oedipus seem to have let his character to be suffering from several problems. Presenting life as a matter of essential vortex fueled the play to have developed essentially. In order to compare the ancient tragic theories with Oedipus Rex, Iliad and Odyssey application of them in Prometheus Bound by Aeschylus seem to have also a successful presentation (Marshall and Ojiako). As the action of the play is limited, approach of the speeches and other necessary thoughts seems to have gained weight. Again the victory of Zeus, rather say divinity with the fight of human being is essentially presented through the pages of the play (Kitagawa). Similar to Iliad and Oedipus Rex human essence is cryptically attained in this play. But the ray of hope in the fall is essentially attained and manifested that leads in persuading lustrous approach. Critical approaches are put behind in order to present more coherence. Throughout this study the researcher has tried to present the knowledge gathered from the different tragic drama and epics. Conflict between the divinity and human existence presented in every epoch is also presented in the context of study. Reference List: Bagby, L. M. J. 'Thomas Hobbes: Translations Of Homer: The Iliad And The Odyssey'.The English Historical ReviewCXXV.514 (2010): 721-723. Web. Curtin, Kevin Thomas. 'The Natural: Our Iliad And Odyssey'.The Antioch Review43.2 (1985): 225. Web. Davies, MJ. 'Diabetes Myths And Legends: The Iliad And The Odyssey'.Practical Diabetes International28.1 (2011): 37-40a. Web. Kitagawa, Teizo. 'The Irony Of Fate'.Seibutsu Butsuri50.1 (2010): 006-007. Web. Mahony, Patrick. 'The Oedipus Rex Of Sophocles And Psychoanalysis'.Int. J. Appl. Psychoanal. Studies7.4 (2010): 290-306. Web. Marshall, Alasdair, and Udechukwu Ojiako. 'From The Myth Of Prometheus To Strategic Resilience: Two Cognitive Paradigms Linking Risk And Innovation'.Prometheus28.4 (2010): 343-360. Web. Myrsiades, Kostas.Approaches To Homer's Iliad And Odyssey. New York: Peter Lang, 2010. Print. Vergados, Athanassios. 'Form And Function Of Some Theban Resonances In HomerS Iliad And Odyssey'.Trends in Classics6.2 (2014): n. pag. Web.

The Gap Company Strategies

The Gap (Gap) is a well known name in the retailing world for clothing and related accessories for men, women and kids, sold under the reputed brand names like Gap, banana republic, old navy, Forth Towne etc.. Primarily operating in North America, the company operates more than 3,000 stores worldwide, having stores in United States, Canada, the United Kingdom, France, Ireland and Japan.Advertising We will write a custom report sample on The Gap Company Strategies specifically for you for only $16.05 $11/page Learn More Key resources for Gap include the human resource headed by the competent strategists in the form of its top management and a renowned brand identity. While the strategists provide plans and policies the motivated work force seems to ensure proper implementation of these plans. Services of people like Karyn Hillman, and Liz Claiborne too proved crucial in implementing the plans set up by Pressler. Brand equity on the other hand is an impor tant intangible asset for the company. It not only creates a product identity, but it also helps in establishing lasting relationship with customers. The brand identity adds significant value to the range of products offered by the company. A company will not be in a position to take advantage of its resources, if there is no matching determination and capability to implement the plans. Gap has the capability to take on its competitors head-on by unleashing a range of competitive measures like penetrative pricing, entering into strategic tie-ups with the likes of designer Roland Mouret in order to offset the losses. Thanks to such strategies, the company was able to sustain the losses during periods of sagging sales, while the crack was duly filled up in due course. Gap also has the ability to invite the attention of its customer, even when the company goes for an overhaul of its strategies and positioning of its products in the market. In 2003 the business of Gap Inc bounced back w hen the management decided to reposition the three main brands. The sales saw an upswing after 29 months of straight decline. Gap’s understanding of the changing fashion ideas is one of the key core competencies of the company. The brand ‘Old Navy’ was an instant hit amongst the younger crowed, when the company shifted its focus to teenagers in the year 2000. The expertise in fashion wear and the company’s ability to translate this expertise into developing and manufacturing trendy cloths is another core competency for Gap. Three findings of the case include; Gap’s majority hold on the North American market, Gap’s dwindling sales figures in recent years, Overdependence on the North American Market.Advertising Looking for report on business economics? Let's see if we can help you! Get your first paper with 15% OFF Learn More It is worthwhile here to mention that while on the one hand the overwhelming presence of Gap in the North American market is a strong point for the company, the overdependence on this market becomes a weaker link for Gap. If for some reason, another competitor emerges in the North American market, the company would find it difficult to leverage its potential. The news of tapering sales graph in recent years is certainly not a healthy sign for the company. What is particularly worrying is the fact that many of the key executives have also started deserting the company in search for better opportunities. Increasing competition, availability of a number of other brands, and counterfeit products are also going to give tough times to Gap in times to come. In view of the above analysis, it is quite clear that Gap has the strength to become a leading brand in the market, but it needs to set its house in order, by setting priorities for the immediate as well as for the long term future. Huge market potential in the South Asian region in general and in India and China in particular needs to be tapped by adopting appropriate market penetration strategies. Reference Wheelen, Thomas L and J. David Hunger (2010). ‘Strategic Management and Business Policy: Achieving Sustainability’, Twelfth Edition. Prentice Hall, New Jersey. This report on The Gap Company Strategies was written and submitted by user Aileen Pate to help you with your own studies. You are free to use it for research and reference purposes in order to write your own paper; however, you must cite it accordingly. You can donate your paper here.

Introduction Essay Sample

Introduction Essay SampleAn introductory theology essay sample is a writing sample intended to help students understand their target areas of study and to give them a plan for further study. The usual format of this sample consists of three sections: Objectives, Glossary, and Tables. Following is a sample of an introductory essay and its outline.Objectives: What do you want to learn about in theological study? Briefly summarize your objective. This question should be asked when students first attend to an essay assignment. If you have not written this essay before, ask yourself, 'What would I want to know about?' I.e., what would be of most interest to me as a Christian.Glossary: A glossary for the purpose of understanding the work is included at the end of the essay. While the final essay should not be written in accordance with a bibliography, it should provide a list of related works. The Glossary should be coherent with the essay, yet it should also be appropriate to the context of the essay. The Glossary must be explained in brief terms to students and should be learned. The Glossary should not be used as a glossary of Christian words but should be used in more than one place in the essay.Tables: tables with explanations is included at the end of the essay and completes the outline. Students can learn the most that can be known from this writing sample. The Tables are a way to provide the reader with a general summary of the essay in the process of understanding it. They are a summary of the values of the entire essay and therefore should not be used to simply list facts and statements.Conclusion: A conclusion is required in a theology essay sample for the purpose of completing the essay. The Table provides an overview of the whole essay and an analysis of the major areas.Notes: The author has included a line for the purpose of reading them if desired. He has emphasized a couple of points in the essay. Students may take the opportunity to implement these p oints.In conclusion, the structure of this writing sample should be easy to understand. The example used as an outline can assist the student to comprehend it more completely. It provides the writing student with a written outline of an essay and encourages the student to write an essay on the topic of interest. The writer should use all of the vocabulary and grammatical form of the essay and avoid plagiarism.

Discussing Friendship Lesson for English Learners

Discussing Friendship Lesson for English Learners Friendship is central to everyones life. Ive found over the years that students are always happy to speak about their friends. An added bonus is that speaking about friends requires students to speak in the third person - always useful practice for the dreaded s in the present simple. Discussing work or conversations about love can be fruitful, but if there are problems at work or at home, students might not want to discuss these popular topics. Friendship, on the other hand, always provides good stories. Use these quotes about friendship to help students explore their notions, preconceived ideas, expectations, etc. about their own friendships, as well as discuss what true friendship really means. As quotations generally provide insight into the topic, ask students to use the questions to help guide them through a discussion of each quotation. Aim: Improving conversational skills related to friendshipActivity: Exploration of the meaning of quotes related to friendshipLevel: Intermediate to advanced Outline Take a quick classroom survey rating their workplace asking students for a definition of friendship.Compare and contrast traditional views of friendship with the current trend of liking and friending on social networks.Read one of the quotes on work. Discuss as a class using the questions provided in the handout.Have students get into small groups of three to four students.Ask students to use the questions to discuss the quotes and how they relate to their own friendships.As a class, ask students if there were any comments/views that surprised them and why.As a class, clarify the characteristics of a good friend. Write a list on the board separating acquaintance and friend. What are the differences between the two?As a follow-up exercise, ask each student to write a short cause and effect essay based on their favorite quote about friendship. Students should include the reasons why they believe the quote is true and what effects following the advice should have. Questions Evaluate each quote below using these questions. Does the quote define friendship? How?Does the quote seem to suggest the differences between a true friend and someone who is not?Does the quote provide a key to success in friendships? If yes, what seems to be the key?Does the quote caution you about something concerning friendship?Is the quote humorous? If yes, whats the point of the joke?Which quote seems the closest to your own definition of friendship?Which quote do you disagree with? Why? Quotes â€Å"Dont walk behind me; I may not lead. Dont walk in front of me; I may not follow. Just walk beside me and be my friend.† ― Albert Camusâ€Å"Its the friends you can call up at 4 a.m. that matter.†Ã‚  Ã¢â‚¬â€¢ Marlene Dietrichâ€Å"The capacity for friendship is Gods way of apologizing for our families.†Ã‚  Ã¢â‚¬â€¢ Jay McInerney, The Last of the Savagesâ€Å"The worst part of success is trying to find someone who is happy for you.†Ã‚  Ã¢â‚¬â€¢ Bette Midlerâ€Å"Anybody can sympathize with the sufferings of a friend, but it requires a very fine nature to sympathize with a friends success.†Ã‚  Ã¢â‚¬â€¢ Oscar Wildeâ€Å"Wishing to be friends is quick work, but friendship is a slow ripening fruit.†Ã‚  Ã¢â‚¬â€¢ Aristotleâ€Å"A friend may be waiting behind a strangers face.†Ã‚  Ã¢â‚¬â€¢ Maya Angelou, Letter to My Daughterâ€Å"Friendship is delicate as a glass, once broken it can be fixed but there will always be cracks†Ã ‚  Ã¢â‚¬â€¢ Waqar Ahmedâ€Å"Friendship is always a sweet responsibility, never an opportunity.†Ã‚  Ã¢â‚¬â€¢ Kahlil Gibran, The Collected Worksâ€Å"The antidote for fifty enemies is one friend.†Ã‚  Ã¢â‚¬â€¢ Aristotle

Solid Geometry on SAT Math The Complete Guide

Solid Geometry on SAT Math The Complete Guide SAT / ACT Prep Online Guides and Tips Geometry is the branch of mathematics that deals with points, lines, shapes, and angles. SAT geometry questions will test your knowledge of the shapes, sizes, and volumes of different figures, as well as their positions in space. 25-30% of SAT Math problemswill involve geometry, depending on the particular test. Because geometry as a wholecovers so many different mathematical concepts, there are several different subsections of geometry (including planar, solid, and coordinate). We will cover each branch of geometryin separate guides, complete with a step-by-step approach to questions and sample problems. This articlewill be your comprehensive guide to solid geometry on the SAT. We’ll take you through the meaning of solid geometry, the formulas and understandings you’ll need to know, and how to tackle some of the most difficult solid geometry problems involving cubes, spheres, and cylinders on the SAT. Before you continue, keep in mind that there will usually only be 1-2 solid geometry questions on any given SAT, so you should prioritize studying planar (flat) geometry and coordinate geometry first. Save learning this guide for last in terms of your SAT math prep. Before you descend into the realm of solid geometry, make sure you are well versed in plane geometry and coordinate geometry! What is Solid Geometry? Solid geometry is the name for geometry performed in three dimensions. It means that another dimension- volume- is added to planar (flat) geometry, which only uses height and length. Instead of flat shapes like circles, squares, and triangles, solid geometry deals with spheres, cubes, and pyramids (along with any other three dimensional shapes).And instead of using perimeter and area to measure flat shapes, solid geometry uses surface area and volume to measure its three dimensional shapes. A circleis a flat object. This is plane geometry. A sphere is a three-dimensional object. This is solid geometry. On the SAT, most of the solid geometry problems are located at the end of each section. This means solid geometry problemsare considered some of the more challenging questions (or ones that will take the longest amount of time, as they often need to be completed in multiple pieces).Use this knowledgeto direct your study-focus to the most productive avenues. If you are getting several questions wrong in the beginning and middle sections of each math section, it might be more productive for you to take the time to first refresh your overall understanding of the math concepts covered by the SAT. You can alsocheck out how to improve your math scoreor refresh your understanding of all the formulas you’ll need. Note: most of the solid geometry SAT Math formulas are given to you on the test, either in the formulas box or on the question itself. If you are unsure which formulas are given or not given in the math section, refresh your formulas knowledge. This is the formula box you'll be given on all SAT math sections. You are given the formulas for both the volume of a rectangular solid and the volume of a cylinder. Other formulas will often be given to you in the question itself. But whilemany of the formulas are given, it is still important for you to understand how they work and why. So don’t worry too much about memorizing them, but do pay attention to them in order to deepen your understanding of the principles behind solid geometry on the SAT. In this guide, I’ve divided the approach to SAT solid geometry into three categories: #1: Typical SAT solid geometry questions #2: Types of geometric solids and their formulas #3: How to solve an SAT solid geometry problem with our SAT math strategies Solid geometry adventure here we come! Typical Solid Geometry Questions on the SAT Before we go through the formulas you'll need to tacklesolid geometry, it's important to familiarize yourself with the kinds of questions the SAT will ask you about solids. SAT solid geometry questions will appear in two formats: questions in which you are given adiagram, and word problem questions. No matter the format, each type of SAT solid geometry questionexiststotestyour understanding of the volume and/or surface area of a figure. You will be asked how to find the volume or surface area of a figure or you'll be asked to identify how a shape's dimensions shift and change. Diagram Problems A solid geometry diagram problem will provide you with a drawingof a geometrical solid and ask you to find a missing element of the picture. Sometimes they will ask you to find the volume of the figure, the surface area of the figure, or the distance between two points on the figure. They may alsoask you to compare the volumes, surface areas, or distances of several different figures. This is a typical "comparing solids" SAT question. We'll go through how to solve it later in the guide. Word Problems Solid geometry word problemswill usually ask you tocomparethe surface areas or volumes of two shapes. They will often giveyou the dimensions of one solid and then tell youto compare its volume or surface area to a solid with different dimensions. By how many cubic feet is a box with a height of 2inches, a width of 6 inches, and a depth of 1 inch greater than a cylinder with a height of 4 inches and a diameter of 6 inches? This is a typical word problem question that might appear in the grid-in section of the SAT math Other word problems mightask you to contain one shape within another. This is just another way of getting you to think about a shape's volume and ways to measure it. What is the minimum possible volume of acube, in cubic inches,thatcouldinscribe a sphere with a radius of 3 inches? A) $12√3$ (approximately $20.78$) B) $24√3$ (approximately $41.57$) C) $36√3$ (approximately $62.35$) D) $216$ E)$1728$ This is a typical inscribing solids word problem. We'll go through how to solve it later in the guide. Solid geometry word problemscan be confusing to many people, because it can be difficult to visualize the question without apicture. As always with word problems that describe shapes or angles, make the drawing yourself! Simplybeing able to seewhat a question is describing can do wonders to help clarify the question. Overall Style of Solid Geometry Questions Every solid geometry question on the SAT is concerned with either the volume or surface area of a figure, or the distance between two points on a figure. Sometimes you'll have to combine surface area and volume, sometimes you'll have to compare two solids to one another, but ultimately all solid geometry questions boil down to these concepts. So now let's go through how to find volumes, surface areas, and distances of all the different geometric solids on the SAT. A perfect example of geometric solidsin the wild Prisms A prism is a three dimensional shape that has (at least) two congruent, parallel bases. Basically, you could pick up a prism and carry it with its opposite sides lying flat against your palms. A few of the many different kinds of prisms. Rectangular Solids A rectangular solid is essentially a box. It has three pairs of opposite sides that are congruent and parallel. Volume $\Volume = lwh$ The volume of a figure is the measure of its interior space. $l$ is the length of the figure $w$ is the width of the figure $h$ is the height of the figure Notice how this formula is the same as findingthe area of the square ($A = lw$) with the added dimension of height, as this is a three dimensional figure First, identify the type of question- is it asking for volume or surface area? The question asks about the interior space of a solid, so it's a volume question. Now we need to finda rectangular volume, but this question is somewhat tricky. Notice that we're finding out how much water is in a particular fish tank, but the water does not fill up the entire tank. If we just focus on the water, we would find that it has a volume of: $V = lwh$ = $(4)(3)(1) = 12\cubic\feet$ (Why did we multiply the feet and width by 1 instead of 2? Because the water only comes up to 1 foot; it does not fill up the entire 2 feet of height of the tank) Nowwe are going to put that 12 cubic feet of water into a second tank. This second tank has a total volume of: $V = lwh$ = $(3)(2)(4) = 24\cubic\feet$ Although the second tank can hold 24 cubic feet of water, we are only putting in 12. So $12/24 = 1/2$. The water will come up at exactly half the height of the second tank, which means the answer is D, 2 feet. Either way, those fish won't be very happy in half a tank of water Surface Area $\Surface\area = 2lw + 2lh + 2wh$ In order to find the surface area of a rectangular prism, you are finding the areas for all the flat rectangles on the surface of the figure (the faces) and then adding those areas together. In a rectangular solid, there are six faces on the outside of the figure. They are divided into three congruent pairs of opposite sides. If you find it difficult to picture surface area, remember that a die has six sides. So you are finding the areas of the three combinations of length, width, and height (lw, lh, and wh), which you then multiply by two because there are two sides for each of these combinations.The resulting areas are then all added together to getthe surface area. Diagonal Length $\Diagonal = √[l^2 + w^2 + h^2]$ The diagonal of a rectangular solid is the longest interior line ofthe solid. It touches from the corner of one side of the prismto the opposite corner on the other. You can find this diagonal by either using the above formula or by breaking up the figure into two flat triangles and using the Pythagorean Theorem for both. You can always do this is you do not want to memorize the formula or if you're afraid of mis-remembering the formula on test day. First, find the length of the diagonal (hypotenuse) of the base of the solid using the Pythagorean Theorem. $c^2 = l^2 + w^2$ Next, use that length as one of the smaller sides of a new triangle with the diagonal of the rectangular solid as the new hypotenuse. $d^2 = c^2 + h^2$ And solve for the diagonal using the Pythagorean Theorem again. Cubes Cubes are a special type of rectangular solid, just like squares are a special type of rectangle A cubehasa height, length, and width that are all equal. The six faces on a cube's surface are also all congruent. Volume $\Volume = s^3$ $s$ is the length of the side of a cube (any side of the cube, as they are all the same). This is the same thing as finding the volume of a rectangular solid ($v = lwh$), but, because their sides are all equal, you can simplify it by saying $s^3$. First, identify what the question is asking you to do. You're trying to fit smallerrectangles into a larger rectangle, so you're dealing with volume, not surface area. Find the volume of the larger rectangle (which in this case is a cube): So you can use the formula for the volume of a cube: $\Volume = s^3$ = $6^3 = 216$ Or you can use the formula to find the volume of any rectangular solid: $\Volume = lwh$ = $(6)(6)(6) = 216$ Now find the volume of one of the smaller rectangular solids: $\Volume = lwh$ = $(3)(2)(1) = 6$ And divide the larger rectangular solid by the smaller to find out how many of the smaller rectangular solids can fit inside the larger: $216/6 = 36$ So your final answer is D, 36 SurfaceArea $\Surface\area = 6s^2$ This is the same formulas as the surface area for a rectangular solid ($SA = 2lw + 2lh + 2hw$). Because all the sides are the same in a cube, you can see how $6s^2$ was derived: $2lw + 2lh + 2hw$ = $2ss + 2ss + 2ss$ = $2s^2 + 2s^2 + 2s^2$ = $6s^2$ Diagonal Length $\Diagonal= s√3$ Just as with the rectangular solid, you can break up the cube into two flat triangles and use the Pythagorean Theorem for both as an alternative to the formula. This is the exact same process as finding the diagonal of a rectangular solid. First, find the length of the diagonal (hypotenuse) of the base of the solid using the Pythagorean Theorem. Next, use that length as one of the smaller sides of a new triangle with the diagonal of the rectangular solid as the new hypotenuse. Solve for the diagonal using the Pythagorean Theorem again. Cylinders A cylinder is a prism with two circular bases on its opposite sides Notice how this problem only requires you to know that thebasic shape of a cylinder.Draw out the figure they are describing. If the diameter of its circular bases are 4, that means its radius is 2. Now we have two side lengths of a right triangle. Use the Pythagorean Theorem to find the length of the hypotenuse. $2^2 + 5^2 = c^2$ = $29 = c^2$ = $c = √29$, or answer C Volume $\Volume = πr^2h$ $π$ is the universal constant, also represented as 3.14(159) $r$ is the radius of the circular base. It is any straight line drawn from the center of the circle to the circumference of the circle. $h$ is the height of the circle. It is the straight line drawn connecting the two circular bases. This problem requires you to understand how to get both the volume of a rectangular solid and the volume of a cylinder in order to compare them. A right circular cylinder with a radius of 2 and a height of 4 will have a volume of: $V = πr^2h$ = $π(2^2)(4) = 16π$ or $50.27$ The volumes for the rectuangular solids are found by: $V = lwh$ So solid A has a volume of $(3)(3)(3) = 27$ Solid B has a volume of $(4)(3)(3) = 36$ Solid C has a volume of $(5)(4)(3) = 60$ Solid D has a volume of $(4)(4)(4) = 64$ And solid E has a volume of $(4)(4)(3) = 48$ So the answer is E, 48 Surface Area $\Surface\area = 2πr^2 +2πrh$ To find the surface area of a cylinder, you are adding the volume of the two circular bases ($2πr^2$), plus the surface of the tube as if it were unrolled ($2πrh$). The surface of the tube can also be written as $SA = πdh$, because the diameter is twice the radius. In other words, the surface of the tube is the formula for the circumference of a circle with the additional dimension of height. Non-Prism Solids Non-prism solids are shapes in three dimensions that do not have any parallel, congruent sides. If you picked these shapes up with your hand, a maximum ofone side (if any) would lie flat against your palm. Cones A cone is similar to a cylinder, but has only one circular base instead of two. Its opposite end terminates in a point, rather than a circle. There are two kind of cones- right cones and oblique cones. For the purposes of the SAT, you only have to concern yourself with right cones. Oblique cones are restricted to the math I and II subject tests. A right cone has an apex (the terminating point on top) that sits directly above the center of the cone’s circular base. When a height ($h$) is dropped from the apex to the center of the circle, it makes a right angle with the circular base. Volume $\Volume = 1/3πr^2h$ $π$ is a constant, written as 3.14(159) $r$ is the radius of the circular base $h$ is the height, drawn at a right angle from the cone’s apex to the center of the circular base The volume of a cone is $1/3$ the volume of a cylinder. This makes sense logically, as a cone is basically a cylinder with one base collapsed into a point. So a cone’s volume will be less than that of a cylinder. Surface Area $\Surface\area = πr^2 + pirl$ $l$ is the length of the side of the cone extending from the apex to the circumference of the circular base The surface area is the combination of the area of the circular base ($πr^2$) and the lateral surface area ($πrl$) Because right cones make a right triangle with side lengths of: $h$, $l$, and $r$, you can often use the pythagorean theorem to solve problems. Pyramids Pyramids are geometric solids that are similar to cones, except that they have a polygon for a base and flat, triangular sides that meet at an apex. There are many types of pyramids, defined by the shape of their base and the angle of their apex, but for the sake of the SAT, you only need to concern yourself with right, square pyramids. A right, square pyramid has a square base (each side has an equal length) and an apex directly above the center of the base. The height ($h$), drawn from the apex to the center of the base, makes a right angle with the base. Volume $\Volume = 1/3\area\of\the\base * h$To find the volume of a square pyramid, you could also say $1/3lwh$ or $1/3s^2h$, as the base is a square, so each side length is the same. Spheres A sphere is essentially a 3D circle. In a circle, any straight line drawn from the center to any point on the circumference will all be equidistant. This distance is the radius (r). In a sphere, this radius can extend in three dimensions, so all lines from the surface of the sphere to the center of the sphere are equidistant. Volume $\Volume = 4/3πr^3$ Inscribed Solids The most common inscribed solids on the SAT will be: cube inside a sphere and sphere inside a cube. You may get another shape entirely, but the basic principles of dealing with inscribed shapes will still apply. The question is most often a test ofYou’ll often have to know the solid geometry principles and formulas for each shape individually to be able to put them together. When dealing with inscribed shapes, draw on the diagram they give you. If they don’t give you a diagram, make your own!By drawing in your own lines, you’ll be better able to translate the three dimensional objects into a series of two dimensional objects, which will more often than not lead you to your solution. Understand that when you are given a solid inside another solid, it is for a reason. It may look confusing to you, but the SAT will always give you enough information to solve a problem. For example, the same line will have a different meaning for each shape, and this is often the key to solving the problem. So we have an inscribed solid and no drawing. So first thing's first, make your drawing! Now because we have a sphere inside a cube, you can see that the radius of the sphereis always half the length of any side of the cube (because a cube by definition has all equal sides). So $2r$ is the length of all the sides of the cube. Now plug $2r$ into your formula for finding the volume of a cube. You can either use the cube volume formula: $V = s^3$ = $(2r)^3 = 8r^3$ Or you can use the formula to find the volume of any rectangular solid: $V = lwh$ = $(2r)(2r)(2r) = 8r^3$ Either way, you getthe answer E,$8r^3$ Notice how answer B is $2r^3$. This is a trick answer designed to trap you. If you didn't use parentheses properly in your volume of a cube formula, you would have gotten $2r^3$. But if you understand that each side length is $2r$ and so that entire length must be cubed, then you will get the correct answer of $8r^3$. For the vast majority of inscribed solids questions, the radius (or diameter) of thecircle will be the key to solving the question.The radiusof the sphere will be equal to half the length of the side of a cube if the cube is inside the sphere (as in the question above). This means that the diameter of the sphere will be equal to one side of the cube, because the diameter is twice the radius.. But what happens when you have a sphere inside a cube? In this case, the diameter of the sphere actually becomes the diagonal of the cube. What is the maximum possible volume of acube, in cubic inches,thatcould be inscribed inside a sphere with a radius of 3 inches? A) $12√3$ (approximately $20.78$) B) $24√3$ (approximately $41.57$) C) $36√3$ (approximately $62.35$) D) $216$ E)$1728$ First, draw out your figure. You can see that, unlike when the sphere was inscribed in the cube, the side of thecube is not twice the radius of the circle because there are gaps between the cube's sides and the circumference of the sphere. The only straight line of the cube that touches two opposite sides of the sphere is the cube's diagonal. So we need the formula for the diagonal of a cube: $\side√3 = \diagonal$ $s√3 = 6$ (Why is the diagonal 6? Because the radius of the sphere is 3, so $(3)(2) = 6$) $3s^2 = 36$ $s^2 = 12$ $s = √12$ $(√12)^3 = 12√12 = 24√3$ Though solid geometry may seem confusing at first,practice and attention to detail will have you navigating the way to the correct answer The Take-Aways The solid geometry questions on the SAT will alwaysask you about volume, surface area, or the distance between points on the figure. The way they make it tricky is by making you compare the elements of different figures or by making you take multiple steps per problem. But you can always break down any SAT question into smaller pieces. The Steps to Solvinga Solid Geometry Problem #1: Identify what the problem is asking you to find. Is the problem asking about cubes or spheres? Both? Are you being asked to find the volume or the surface area of a figure? Both? Make sure you understandwhich formulas you'll need and what elements of the geometric solid(s) you are dealing with. #2: Draw it out Draw a picture any time they describe a solid without providing you with a picture. This will often make it easier to see exactly what information you have and how you can use that information to find what the question is asking you to provide. #3: Use your formulas Once you've identified the formulas you'll need, it's often a simple matter of plugging in your given information. If you cannot remember your formulas (like the formula for a diagonal, for example), use alternative methods to come to the answer, like the pythagorean theorem. #4: Keep your information clear and double check your work Did you make sure to label your work? The makers of the test know that it's easy for students to get sloppy in a high-stress environment and they put in bait answers accordingly. So make sure thevolume for your cylinder and thevolume for your cube are labeled accordingly. And don't forget to give your answer a double-check if you have time! Does it make sense to say that a box with a height of 20 feet can fit inside a box with a volume of 15 cubic feet? Definitely not! Make sure all the elements of your answer and your work are in the right place before you finish. Follow the steps to solving your solid geometry problems andyou'll get that gold Solid geometry is often not as complex as it looks; it is simply flat geometry that has been taken into the third dimension. If you can understand how each of these shapes changes and relate to one another, you’ll be able to tackle this section of the SAT with greater ease than ever before. What's Next? Now that you've done your paces onsolid geometry, it might bea good idea to review all the math topics tested on the SAT to make sure you've got them nailed down tight. Want to get a perfect score? Check out our article onHow to an 800 on the SAT Mathby a perfect SAT scorer. Currently scoring in the mid-range? Running out of time on the math section?Look no further than our articles on how to improve your score if you're currently scoring below the 600 rangeand how to stop running out of time on the SAT math. Want to improve your SAT score by 160 points? Check out our best-in-class online SAT prep program. We guarantee your money back if you don't improve your SAT score by 160 points or more. Our program is entirely online, and it customizes what you study to your strengths and weaknesses. If you liked this Math strategy guide, you'll love our program.Along with more detailed lessons, you'll get thousands of SAT Mathpractice 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:

Building Engineering Services Essay Example | Topics and Well Written Essays - 1500 words

Building Engineering Services - Essay Example The Manning's equation is given as Where V is the velocity of flow through the drains, R is the mean hydraulic radius, S is the slope of the channel and n the Manning's coefficient. As the flowing liquid would contain different types of materials like floating debris and other suspended particles, necessary care must be taken to prevent any potential problems that would adversely affect the flow. In order to maintain the fluid flow , a minimum velocity need to be maintained. This velocity, termed as self cleaning velocity, is necessary to prevent any particle deposition in the channel bed. Similarly, very high velocity could also harm the channel durability. The liquid flow at high velocity could damage the surface lining of the drains especially when the liquid being conveyed is highly abrasive. All drainage works must be prepared and laid as per the prevailing building regulation rules (ADS Inc, 2008). A minimum diameter of 150 mm must be adopted for all the drainage pipe connections involving more than 10 user locations. Grease separator must be included to all the drains connected to hotels or any cooking related centres. Addition of drains to the existing network must be through prefabricated units to avoid the use of saddles (ADS Inc, 2008). ... In such situations either Rocker pipes or filling compressible materials around the drains are the measures adopted. Finally, the rodent control measures like sealed inspection chambers, intercepting traps and solid gully covers are also very essential (ADS Inc, 2008). Rainwater systems The rainwater collected is not allowed to be discharged to the existing sewer lines. In the case of unavoidable situations , the order of priority of rainwater discharge is initially to a soakway then to a water course and finally to sewer (ADS Inc, 2008). The soakways proposed for such situations must be designed based on the data on the rainfall intensity, soil porosity tests and storage capacity. The details of swales, filters and the detention ponds may also be used. The modification to the roof area and gutter sizes besides providing symphonic and eaves drop system need to be followed as per the guidelines (ADS Inc, 2008). The locations that have more chance to produce the contaminated drainage must be separately handled. The areas affected by the petrol spill must try to direct all drainage to an oil interceptor before further segmentation. Inorder ensure sustainable use of resources the rainwater is put into different types of reuse operations. It is estimated that roof area of atleast 2000 sq ft would be able to gather atleast 1246 gallons during 1 inch rainfall (DoE, n.d.). It could be stored in small tanks placed below the ground surface and could store water when the rain water beings in considerable volume. In addition to the storage systems different types of recharge methods also could be adopted. This would result in significant improvement in the ground water level in the

Law of Property 1 Essay Example | Topics and Well Written Essays - 3000 words

Law of Property 1 - Essay Example Jane carried on paying the instalments on the loan. In 2009 Harry became ill and died. Jane has continued to pay the instalments to the friend direct. Under Harry’s will, all his property passes to his widow, Helena. There is ?1,000 still owing on the loan. Helena, as executrix of and sole beneficiary under the will, has applied for a possession order against Jane. Advise Jane. Students are advised not to consider the Land Registration Acts but to answer the question within the syllabus. 2. Augusta had a friend Julius, who was in financial difficulties. Augusta lent Julius ?5,000 " to get himself sorted out". At Augusta's insistence, Julius put the money into a separate bank account and told the bank, to whom he owed money, that the money was a special loan from Augusta. Julius used ?2,000 of the money to pay various debts before he was declared bankrupt. ?3,000 remains in the account. Augusta died leaving a will containing the following provisions: â€Å"To my son Cassius I leave ?20,000 to enjoy as he likes during his lifetime, provided that, at his death, he leaves any of the money that remains to his sister Demeter, The rest of my estate I leave to Gaius and Lucius on trust, so that they may make grants out of the income from this fund to any of the descendants of my illustrious ancestor Tarquin and their families.† Tarquin lived two hundred years ago and is reputed to have had many children both legitimate and illegitimate. Advise Cassius as to his rights and duties over the ?20,000. Advise Augusta’s executors as to whether they will be able to recover the balance of ?3,000 in Julius’ bank account. Advise Gaius and Lucius as to their powers and obligations with the regard to the residue of Augusta’s estate. Question 1 In the above, it is necessary to consider what rights Jane might have over the property. This will involve analysing how proprietary rights over property can be established. Under the Law of Property Act 192 5 the person registered on the deed for the property will be the legal owner of the estate1. This effectively means that Harry would have been the legal owner despite his promise to give the property to Jane if she paid off the loan. The effect of the Will would mean that the house would transfer in ownership to Helena, which would entitle her to dispose of it in any manner she sees fit2. However, this would create unfairness to Jane who has been paying the money owed to Harry and latterly to his friend on the understanding that she would have a right to the property. As there is no written agreement between Jane and Harry, and Harry has not expressly left the property to Jane in his Will, the only rights she might have in relation to the property would be an equitable interest3. As a result of this, Jane might have to rely on the doctrine of implied trusts to be able to claim a share of the property. Implied trusts can exist through statute or as a resulting or constructive trust. The latter 2 trusts exist in equity only and are applied by the courts to rectify any unfairness caused by the denial of legal property rights through the property only being registered in one parties’ name. A resulting trust occurs where there is evidence that the claimant has made payments towards the purchase price of the property but was not included on the register as an owner. Those relying on this principle have to prove that they expended the money in the belief that they would acquire an interest in the property,