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3D Geometric Objects in SAT Math

Quick: how do you find the volume of a cylinder? Do you know the formula? The SAT will give it to you at the beginning of each math section, along with some other geometric facts, but you should know them anyway. At least, you should be familiar with how you get those formulas. Start from 2D shapes The area of a square is . If you just add in the next dimension, you have the volume of a cube, . The same is true for any object that has two congruent 2D shapes at its ends, e.g. a cylinder or a prism. Since a circle’s area is , a cylinder’s volume is that, multiplied by the other dimension. . If you’re trying to find the distance between two points in a figure, start with the two dimensional shapes—the faces of the object—and find whatever measurements you can from there. And of course you should draw in any extra lines that the figure doesn’t show. They, too, will be possible to work with as pieces of 2D shapes, like triangles. They’re easier to deal with. Remember the meaning of words describing 3D shapes Some questions prey on students who mix up vertexes, edges, and sides (or faces). Don’t fall for the SAT’s tricks! A side is a two dimensional shape. If you rolled the object on the ground, it could possibly stand on a side. Compare that to an edge, which is where two sides meet. It’s one-dimensional. Think of the edge of a knife to help remember the word. A cube (like a die) rolled on the ground is pretty much never going to land on an edge. And a vertex is a single point with no dimensions. It’s just another word for â€Å"corner.† The tip of a cone is a vertex, for example. Just another geometry problem Most 3D shapes aren’t much more difficult to deal with than their two dimensional counterparts, at least not mathematically. Visualizing can be a little bit tricky, it’s true, but don’t freak out if you see a 3D shape. Take it one dimension at a time.

How to Prepare Yourself For College Essay on How to Prepare Yourself For College

How to Prepare Yourself For College Essay on How to Prepare Yourself For CollegeA good process analysis essay on how to prepare yourself for college should help you think more creatively, focus on the big picture, and prepare yourself for college in a way that is more meaningful. Writing this type of essay may seem easy and entertaining, but the challenge is knowing how to present your ideas in an essay format that is fresh and interesting. Here are a few tips to help you write a great essay on how to prepare yourself for college.First, make sure you have enough time to complete your assignment. College is a big commitment. If you are pressed for time, write everything you have to do the day before your next class. If you have an advanced level course to take or an advanced level class, you may want to wait until the last possible moment so that you can manage to squeeze in the required writing.Second, write according to your writing style. You don't have to write using the format of a thesis statement or topic statement. Use a variety of different styles to come up with a unique and original essay.Third, try to choose a topic that interests you and that you have written about before. It can be anything from a personal anecdote to a research paper about a local geography or environment.Fourth, practice your writing. Use a resource such as flashcards, jot down your ideas, or use a paper or pen and paper to make sure you get it right the first time.Fifth, use humor and metaphors to connect your ideas. Talk about topics that interest you and those that make you uncomfortable, but don't let them dominate your essay. A good idea is to write about a topic that you are not comfortable talking about. Then, write about what you know, how you learn, or why you need to learn about it.Sixth, avoid using the grade point average as a way to communicate your message. Instead, use it as a way to show how you have done well in your academic work.Lastly, make sure that you are f amiliar with the essay format of the level course you are taking. That way, you will be able to choose the right format for your essay, your essay will not come out confused, and you will be able to learn the format.

The Unraveling of Courtly Love Responses to Petrarchan form in Wyatt, Sidney, and Shakespeare - Literature Essay Samples

When Sir Thomas Wyatt decided to introduce the sonnet to England, the result was unexpected to say the least. While Wyatt had been known for lighter riddles, songs and satires, he nevertheless made the surprising choice to focus on a brooding genre so far from his wheelhouse. Even though the English renaissance sonnet is often studied as an isolated genre, it is the composition of the Petrarchan model and its careful arrangement into sequence that establishes an expectation, consequently proving the indebtedness of the English sequences to Petrarch. Therefore the study of the English sonnet hinges on the understanding of its Italian foundation. The original sequences followed a formulaic progression, revealing the poet’s intent. Francesco Petrarca, the original sonneteer, illustrates the ideals of Courtly Love by apotheosizing Laura, a married woman constantly out of his reach. Similar to an Hymn of Love, albeit unrequited, his poetry seems inspired by a Troubadour style of Ode. This classical sonnet is traditionally a rhapsody of a pure lady, who’s beauty is beyond compare. The form of the poem is as follows: A fourteen line poem, with verses written in iambic pentameter, rhyming abba abba cde cde, and is divided into an octave and a sestet. The eighth line tends to be the end of a though, therefore naturally culminating with a syntactic stop. The aesthetic of the Petrarchan sonnet lies in its mechanic form. Norman C. Strageberg argues that this form favours an unified response to the poem in question. Unless the structure is organized in way to create a sense of cohesiveness, unity and movement, the object c annot be perceived as pleasing. The arrangement of the rhymes in their subgroups of quartets and tercets, also provides a visual of unity which helps the reader have a perceptual grasp of the sonnet. This explains the longevity of the form, as it ticks all the right boxes. The first octave sets up the lamenting lover pining over an impassive beloved, while the following sestet provides some transformation in the relationship between the beloved and poet, wether it be a rejection, acceptance or even death. The Petrarchan model is apparent but modified in the later English sonnets, which demonstrates the flexibility of its structure. The English form is usually composed of three quatrains and a couplet, has a rhyming scheme of abab cdcd efef gg. Even though the sonnet is organized in three stanzas, the basic structure is of two parts, the first being laid over the three quatrains, followed by a turn in line 13, and concludes with the final couplet. It also establishes an out-of-reach object of one’s affection who must be glorified, the quest to win them over, and the eventual denouement of the narrative. The shift is most apparent in the departure from the conventional plot, and in the demeanour of the speaker. This suggests a branching away from the idea of â€Å"Courtly Love,† and proves that the form provides a malleable canvas for exploring the subject of Love from all angles. One of the initial features to wander away from the Petrarchan form, is the apparent unraveling on the speaker himself. Wyatt’s â€Å"Whoso list to hunt,† is a translation of Petrarch â€Å"Una candida cerva,† a sonnet in which the speaker comes into an ethereal dream encounter with a golden doe. The laurel behind the doe imply she belongs to Caesar, meaning she is spoken for and beyond the speaker’s reach. That does not stop him from blindly following her until he falls into a stream, while she evaporates. Although the original speaker feels blessed to have had the vision, Wyatt’s version seems bitter. It is a loose translation to say the least, as it strips most of the otherworldly imagery and leaves place to a cynical disillusion: Whoso list to hunt, I know where is an hind, But as for me, alas, I may no more. The vain travail hath worried me so sore, I am of them that farthest cometh behind. (Wyatt. â€Å"Whoso list a hunt.† 1-4) The speaker here, is caught in an exhausting hunt for the doe, who is believed to be Anne Boleyn, because her bejewelled collar hints that she has an owner who is identified as Caesar, a probable comparison to Henry VIII. The poem was most likely written while Boleyn was still alive, which adds an ominous element to her status as property. Given the awkward rhythm, the translation insinuates a complete deconstruction of the original to adapt it to english, and even appears to be a distant interpretation. The clumsiness of the meter may be a purposeful choice to show a frustration with Petrarch. The original poem is melodic and is written in a language expressing nothing but gratefulness after the encounter. Wyatt on the other hand, is being deliberately raw with his language, and the sonnet’s first line sets this up, as it is not the typical pentameter. The speaker is transparent with his injured feelings as he does not romanticize his pursuit. He is drained, yet cannot seem t o stop himself from continuing the chase, as evidenced by the enjambments which illustrate his breathless but unyielding state. He continues to chase, even though he knows it to be in vain. The final couplet presents a warning to the other suitors Noli me tangere, for Caesars I am, / And wild for to hold, though I seem tame.†(Wyatt. â€Å"Whoso list a hunt.† 13-14) While the Petrarchan sequence celebrates the beloved and tries to win them over, the stakes do not depend on successfully wooing them. Indeed, the speaker in the Petrarchan tradition does not express their lust, and their love is meant to be pure, yet the English poets gradually let go of these restraints. Sir Philip Sidney writes his sequence Astrophil and Stella, describing his longing, in the guise of Astrophil, for the unattainable Stella. Here, the chaste Stella being Lady Penelope Devereux, is the quintessential Petrarchan Muse, who is compared to a star, and a â€Å"book of Virtue†. Considering Sidney was devastated when Devereux married Robert Rich, the future Earl of Warwick in 1851, and that she would later have an extra marital affair, going as far as successfully obtaining a divorce, it seems odd that he would not revise the angelic figure of Stella. However, unlike a quintessential Petrarchan suitor, Sidney’s Astrophil lacks self-control. In sonnet 71 †Å"Who will in fairest book Nature know,† the speaker’s true nature comes out in the final couplet. Stella is described as a book of Virtue where â€Å"shall he find all vices’ overthrow,† (Sidney.71.5) and is elevated to the status of a quasi-goddess. Despite being a symbol of Virtue, Astrophil gives in to his carnal thoughts, ‘â€Å"As fast thy virtue bends that love to good: /â€Å"But ah,† Desire still cries, â€Å"give me some food.†Ã¢â‚¬â„¢ The unraveling of form accompanies the unraveling of the speaker’s will. The presence of eye-rhymes is significant, as they illustrate the poet’s conflicting desires. The eye-rhyme of â€Å"good† and â€Å"food† is at a glance perfect, but sounds completely off. Much like the poet’s desire to maintain appearances, once it is put under the slightest of scrutinies, it falls apart. A recurring theme in the Renaissance English sonnet is a gradual corruption of the Muse. The starkest departure from the Petrarchan ideal depiction of the beloved figure, are undoubtedly the loved ones in Shakespeare’s sequence. Although similar in many ways, especially in the first half, the relationships are much more involved. The first Muse is a young man known as the ‘Fair Lord’, who’s beauty is described similarly as the figure of the beloved in Petrarchan sonnets. It isn’t until sonnet 33, that the speaker’s attitude towards the ‘Fair Lord’ shifts drastically. The speaker seems to feel betrayed by the young man, and the imagery of alchemy, which was believed to be part-magic and part-science, to turn common metal into gold, suggest some form of duplicity or trickery. In spite of this betrayal, the final couplet finds the speaker renewed in his adoration of love for the Fair Lord, as he declares â€Å"Yet him for this my lo ve no whit disdaineth;/ Suns of the world may stain when heavens sun staineth.† This visceral disappointment in the loved one, is far from the untouchable Laura or Stella. By criticizing the figure, and yet remaining faithful despite the â€Å"stain,† Shakespeare is developing a much more grounded vision of love and relationships. The beloved is magnificent, but not pure. They are inherently good, but not incapable of sin. The truest manifestation of love, is the speaker’s willingness to accept their flaws. The second Muse, also known as ‘The Dark Lady’, is perhaps the antithesis of a Petrarchan Muse, as is most famous in sonnet 130: My mistress eyes are nothing like the sun; Coral is far more red than her lips red; If snow be white, why then her breasts are dun; If hairs be wires, black wires grow on her head. (Shakespeare.130.1-4) At first glance, the sonnet is completely flipping the Petrarchan form and treating the subject as joke. Rather than taking on an overly serious tone and elevating his loved one to a cosmic level, the speaker is comparing her by negation. It begins by purposefully listing all the desired characteristics as qualities his dark lady does not possess. The final couplet subverts the previous lines with the speaker confessing â€Å"And yet, by heaven, I think my love as rare / As any she belied with false compare,† confirming the depth of his adoration for her. The Dark Lady is not an unblemished angelic being, but is a real woman who’s love is not skewered by blind idolatry. Understanding this particular sonnet requires a familiarity with the tradition Shakespeare is writing against. In other words, Shakespeare is rejecting the notion of ‘Courtly Love,’ by elevating a real love between physical human beings, and not belittling his beloved by falsely deifying her . That being said, even as Shakespeare admits to his beloved and him, mutually succumbing to their lust, the final result is just as unsatisfying as Petrarch’s unrequited spiritual love. Ultimately, the sonneteers of the English Renaissance were not only admirers of the Italian form, but innovators of the aesthetic. Their desire to express similar sentiment and eagerness to play with the material by reshaping within the constraint of fourteen lines in iambic pentameter, is most conspicuous in the evolution of the depiction of the relationship between speaker and Muse. The physical boundary gradually narrows, until the dichotomy veers from platonic love to the physical. In reality, this shift does not stop the hollow conclusion of these sequences from happening, as deification and consummation does not result in any form of transcendence for the poet. Works Cited: Glaser, Joe. â€Å"Wyatt, Petrarch, and the Uses of Mistranslation.† College Literature, vol. 11, no. 3, 1984, pp. 214–222. JSTOR, www.jstor.org/stable/25111613. Neely, Carol Thomas. â€Å"The Structure of English Renaissance Sonnet Sequences.† ELH, vol. 45, no. 3, 1978, pp. 359–389. JSTOR, www.jstor.org/stable/2872643. Shapiro, Michael. â€Å"Sound and Meaning in Shakespeares Sonnets.† Language, vol. 74, no. 1, 1998, pp. 81–103. JSTOR, www.jstor.org/stable/417566. Simon, Margaret. â€Å"Refraining Songs: The Dynamics of Form in Sidneys ‘Astrophil and Stella.’† Studies in Philology, vol. 109, no. 1, 2012, pp. 86–102. JSTOR, www.jstor.org/stable/41511596. Stageberg, Norman C. â€Å"The Aesthetic of the Petrarchan Sonnet.† The Journal of Aesthetics and Art Criticism, vol. 7, no. 2, 1948, pp. 132–137. JST