Friday, January 31, 2020

Los angeles city Essay Example | Topics and Well Written Essays - 1000 words

Los angeles city - Essay Example The question thus arises if this is really something to be bothered about and if it does pose a threat to users of technological devices. There may be disadvantages to the use of gadgets however it is not as bad or destructive to people’s interpersonal relationships or social life as some experts claim it to be, as documented in this paper. For many parents, cell phones are viewed as instruments for them to keep in touch with their children and also for emergency purposes. Nevertheless, the increasing number of virtual communications is now causing alarm because it is viewed as a threat to the development of interpersonal skills of children. Such problem is presented by Sherry Turkle in her article entitled â€Å"No Need to Call†. She cites some examples of people who seem to be unable to communicate well with others but are now able to hide behind their computers to communicate with friends. For instance, the author tells that Elaine, a teenager, views texting and emailing as a preferred means of communication for shy people and even for outgoing people because they are able to edit and think about what they say before they send the message to the recipient (374). Unlike telephone calls and face to face interactions wherein the response should be quick and could not be edited or even taken back, texting serves as a convenient way of communicating. However, the confidence one has when he is communicating virtually, is often not displayed during close encounters and this worries experts. The same concern is shared by some parents but some disagree with the idea. Hilary Stout also gives examples of parents who are optimistic about social networking that strengthens some of the examples given by Turkle. For instance, she mentions Robert Wilson, a father of a 14-year-old shy and introverted Evan, who is worried about his son’s social life. When Evan signed up for facebook, Robert was glad to find

Thursday, January 23, 2020

The Cask of Amontillado by Edgar Allan Poe Essay -- Papers Essays Poe

The Cask of Amontillado by Edgar Allan Poe In ?The Cask of Amontillado?, Edgar Allan Poe takes us on a trip into the mind of a mad man. Poe uses certain elements to convey an emotional impact. He utilizes irony, descriptive detail of setting, and dark character traits to create the search of sinful deceit. Poe also uses first person, where the narrator is the protagonist who is deeply involved. The purpose is to get the reader to no longer be the observer. He wants them to see with Montressor?s eyes, hear with his ears, and to react as he would. There is no real violence in the modern sense of the word. However, it is more horrifying because rather than seeing it through our eyes, we feel it through words. This short story is a great example of how descriptive imagery and irony can give an overall mood of horror and impending evil. The story provides the reader with the feeling of deception and a curiosity of the darkness of the murderous plot. Poe?s style is what makes this a masterpiece of horror. ?The Cask of Amontillado? is a powerful tale of revenge. Poe does not disappoint us as his audience, as we are invited to visit the inner workings of a sinister mind. Telling the story from Montressor?s point of view, intensifies the effect of the moral shock and horror. Through Poe?s use of irony, this short story is a carefully crafted story of revenge with ironic wordplay. Montressor seeks revenge in an effort to support his time-honored family motto: ?nemo me impune lacessit? or (no one attack me without being punished). Montressor, the sinister narrator of this tale, pledges revenge on Fortunato for an insult. The character of Montressor provides the pinnacle of deceit and belligerence needed to portray the story?s sin. ... ...ntressor?s catacombs, ?I drink to the buried that repose around us,? not knowing he soon would join them. The sinful deceit in ?The Cask of Amontillado? is linked to Poe?s use of irony, descriptive detail, and character traits. The short story successfully creates an emotion of sin and deceit. Through his writing techniques we get a vivid idea of his deception and darkness. The damp catacombs of ?The Cask of Amontillado? complement the dark doings, but the setting gives closure to the total effect in a subtle fashion. Although, a short story, Poe creates a nightmare that is almost guaranteed to give his readers a sleepless night. As the ?cask? of Amontillado draws Fortunato into the ?casket?, we get a feeling of our own fear. Bibliography: Poe, Edgar A. The Cask of Amontillado. Edgar Allan Poe: Sixty-Seven Tales. Avenel, New Jersey: Gramercy Books, 1985.

Wednesday, January 15, 2020

Solving Quadratic Equations

While the ultimate goal is the same, to determine the value(s) that hold true for the equation, solving quadratic equations requires much more than simply isolating the variable, as is required in solving linear equations. This piece will outline the different types of quadratic equations, strategies for solving each type, as well as other methods of solutions such as Completing the Square and using the Quadratic Formula. Knowledge of factoring perfect square trinomials and simplifying radical expression are needed for this piece. Let’s take a look! Standard Form of a Quadratic Equation ax2+ bx+c=0Where a, b, and c are integers and a? 1 I. To solve an equation in the form ax2+c=k, for some value k. This is the simplest quadratic equation to solve, because the middle term is missing. Strategy: To isolate the square term and then take the square root of both sides. Ex. 1) Isolate the square term, divide both sides by 2 Take the square root of both sides 2Ãâ€"2=40 2Ãâ€"22= 40 2 x2 =20 Remember there are two possible solutions x2= 20 Simplify radical; Solutions x=  ± 20 x= ± 25 (Please refer to previous instructional materials Simplifying Radical Expressions ) II. To solve a quadratic equation arranged in the form ax2+ bx=0.Strategy: To factor the binomial using the greatest common factor (GCF), set the monomial factor and the binomial factor equal to zero, and solve. Ex. 2) 12Ãâ€"2- 18x=0 6x2x-3= 0Factor using the GCF 6x=0 2x-3=0Set the monomial and binomial equal to zero x=0 x= 32Solutions * In some cases, the GCF is simply the variable with coefficient of 1. III. To solve an equation in the form ax2+ bx+c=0, where the trinomial is a perfect square. This too is a simple quadratic equation to solve, because it factors into the form m2=0, for some binomial m. For factoring instructional methods, select The Easy Way to Factor Trinomials ) Strategy: To factor the trinomial, set each binomial equal to zero, and solve. Ex. 3) x2+ 6x+9=0 x+32=0Factor as a perfect square x+3x+3= 0Not necessary, but valuable step to show two solutions x+3=0 x+3=0Set each binomial equal to zero x= -3 x= -3Solve x= -3Double root solution IV. To solve an equation in the form ax2+ bx+c=0, where the trinomial is not a perfect square, but factorable. Similar to the last example, this is a simple quadratic equation to solve, because it factors into the form mn=0, for some binomials m and n.Strategy: To factor the trinomial, set each binomial equal to zero, and solve. Ex. 4) 2Ãâ€"2-x-6=0 * Using the factoring method from The Easy Way to Factor Trinomials, we need to find two number that multiply to give ac, or -12, and add to give b, or -1. These values are -4 and 3. Rewrite the trinomial with these two values as coefficients to x that add to the current middle term of -1x. 2Ãâ€"2- 4x+3x-6=0Rewrite middle term 2Ãâ€"2- 4x+3x-6=0 2xx-2+ 3x-2= 0Factor by grouping x-22x+3= 0Factor out the common binomial (x-2) x-2=0 2x+3=0Set each binomial equal to zero x=2 x= -32Solutions V.To solve a quadratic equation not arranged in the form ax2+ bx+c=0, but factorable. Strategy: To combine like terms to one side, set equal to zero, factor the trinomial, set each binomial equal to zero, and solve. Ex. 5) 6Ãâ€"2+ 2x-3=9x+2 -9x -9x 6Ãâ€"2- 7x-3= 2 -2 -2 6Ãâ€"2- 7x-5=0 * To factor this trinomial, we are looking for two numbers that multiply to give ac, or -30, and add to give b, or -7. These values would be 3 and -10. Rewrite the trinomial with these two values as coefficients to x that add to the current middle term of -7x. 6Ãâ€"2+ 3x-10x-5=0Rewrite middle term 6Ãâ€"2+ 3x-10x-5=0 3x2x+1-52x+1=0Factor by grouping Careful factoring a -5 from the second group 2x+13x-5=0 Factor out the common binomial (2x+1) 2x+1=0 3x-5=0 Set each binomial equal to zero x= -12 x= 53Solutions Now that we have explored some examples, I’d like to take this time to summarize the strategies used thus far in solving quadratic equations. Keeping in mind the goal is to isolate the variable, the format of the equation will dictate the strategy used to solve. When the quadratic does not have a middle term, a term with a power of 1, it is best to first isolate the squared term, and then take the square root of both sides.This essentially will result in two solutions of opposite values. For quadratics that do not have a c-value, arrange the equation so that ax2+ bx=0, and then factor using the GCF. Set the monomial, or the GCF, and the binomial equal to zero and solve. When the quadratic has one or more ax2’s, bx’s, and c’s, the like terms need to be combined to one side of the equation and set equal to zero before determining if the trinomial can be factored. Once factored, set each binomial equal to zero and solve. Keep in mind while combining like terms that a must be an integer greater than or equal to 1.The solutions to cases such as these may result in a double root solution, found when the trinomial is factored as a perfect square, or two unique solutions, found when the trinomial is factored into two unique binomials. There may be other cases where a GCF can be factored out of the trinomial before factoring occurs. Since this unit is focused on solving quadratic equations, the GCF would simply be a constant. The next example to illustrates while it’s helpful to factor out the GCF before factoring the trinomial, it is not imperative to do so and has no impact on the solution of the quadratic equation. VI.To solve a quadratic equation in which there is a GCF among the terms of a trinomial. Strategy (A : To determine the GCF between the terms of the trinomial once it is in standard form, factor out the GCF, factor the trinomial, set each binomial equal to zero, and then solve. Ex. 6A) 12Ãâ€"2- 22x+6=0 26Ãâ€"2- 11x+3=0 * To factor this trinomial, we are looking for two numbers that multiply to give ac, or 18, and add to give b, or -11. These values would be -9 and -2. Rewrite the trinomial with these two values as coefficients to x that add to the current middle term of -11x. 26Ãâ€"2- 9x-2x+3=0Factor out the GCF of 2 from each term 3x2x-3- 12x-3=0Factor by grouping 22x-33x-1=0Factor out the common binomial (2x-3) 2x-3=0 3x-1=0Set each binomial equal to zero x= 32 x= 13 Solutions Strategy (B): To factor the trinomial, set each binomial equal to zero, and solve. Ex. 6B) 12Ãâ€"2- 22x+6=0 * To factor this trinomial, we are looking for two numbers that multiply to give ac, or 72, and add to give b, or -22. These values would be -18 and -4. Rewrite the trinomial with these two values as coefficients to x that add to the current middle term of -22x. 12Ãâ€"2- 18x-4x+6=0 x2x-3- 22x-3=0Factor by grouping 2x-36x-2= 0Factor out the common binomial (2x-3) 2x-3=0 6x-2=0 Set each binomial equal to zero x= 32 x= 26= 13Solutions * Notice in Ex 6A, since the GCF did not have a variable. The purpose of factoring and setting each binomial equal to zero is to solve for the possible value(s) for the variable that result in a zero product. If the GCF does not have a variable, it is not possible for it to make a product of zero. With that said, in later topics there will be cases where a GCF will include a variable, leaving a factorable trinomial.This type of case results in a possibility of three solutions for the variable, as seen in the example below. 3xx2+ 5x+6=0 3xx+2x+3=0 3x=0 x+2=0 x+3=0 x=0 x= -2 x= -3 At this point we need to transition to solving quadratics equations that do not have trinomials that are factorable. To solve these types of equations, we have two options, (1) to Complete the Square, and (2) to use the Quadratic Formula. Essentially, these two methods yield the same solution when left in simplified radical form. For the remainder of this unit I will o the following: * Explain how to Complete the Square * Provide examples utilizing the Completing the Square method * Prove the Quadratic Formula starting with Completing the Square * Provide examples solving equations using the Quadratic Formula * Provide an example that parallels all three methods in this unit * Provide instructional strategies for solving quadratic equations VII. How to Complete the Square Goal: To get x ±m2=k , where m and k are real numbers and k? 0 For equations that are not factorable and in the form ax2+ bx+c=0 where a=1, 1.Move constant term to the side opposite the variable x. 2. Take 12 of b and square the result. 3. Add this term to both sides. 4. Create your perfect square set equal to some constant value k? 0. VIII. To solve quadratic equations using the Completing the Square method. Ex. 7)x2+ 6x-5=0 * Since there are no two integers that multiply to give ac, or -5, and add to give b, or 6, this trinomial is not factorable, and therefore, Completing the Square must be used to solve for x. x2+ 6x+ _____ =5+ _____ Move constant to the right x2+ 6x+ 62 2=5+ 62 2Take 12b, square it and add it to both sides 2+ 6x+9=14Simplify x+32=14Factor trinomial as a perfect square x+32= 14Take the square root of both sides x+3=  ± 14Simplify x= -3  ± 14Solve for x; Solutions Ex. 8) 2Ãâ€"2+ 16x=4 * Before proceeding with Completing the Square, notice a? 1 and the constant term is already on the opposite side of the variable terms. First step must be to divide both sides of the equation by 2. x2+ 8x=2Result after division by 2 x2+ 8x+ _____ =2+ _____ Preparation for Completing the Square x2+ 8x+ 82 2=2 + 82 2 Take 12b, square it and add it to both sides x2+ 8x+16=18 Simplify x+42=18Factor trinomial as a perfect square +42= 18Take the square root of both sides x+4=  ± 32Simplify x= -4  ±32Solve for x; Solutions At any point during the solving process, if a negative value exists under the radical, there will be NO REAL SOLUTION to the equation. These types of equations will be explored later once the imaginary number system has been learned. IX. Quadratic Formula The Quadratic Formula is another method to solving a quadratic equation. L et’s take a look at how the standard form of a quadratic equation can be transformed into the Quadratic Formula using the Completing the Square method.Ensure a coefficient of 1 for x2 by dividing by a, and move the constant term to the right ax2+ bx+c=0Standard Form of a quadratic equation ax2a+ bxa+ c a= 0 a x2+ b ax+ c a= 0 x2+ b ax= – c a * The square of half of what is now the b term, or the middle term, is 12 †¢ b a2= b2a2= b24a2 Complete the Square Get common denominator on the right Factor trinomial as a perfect square Take the square root of both sides Simplify Solve for x Quadratic Formula x2+ b ax+ b24a2 = – c a + b24a2 x2+ b ax+ b24a2 = – 4ac 4a2 + b24a2 x2+ b ax+ b24a2 = -4ac+b24a2 + b 2a2= -4ac+b24a2 x+ b 2a2= -4ac+b24a2 x+ b2a=  ± -4ac+ b22a x= -b 2a  ± -4ac+ b22a x= -b  ± b2- 4ac2a X. To solve quadratic equations using the Quadratic Formula. Ex 9. ) 2Ãâ€"2- 8x+ 5=0 a=2 b= -8 c=5 Substitute Evaluate Subtract Simplify radical Simp lify fraction; Solutions x= -b  ± b2- 4ac2a x= –8  ± -82- 42522 x= 8  ± 64 – 404 x= 8  ± 244 x= 8  ± 264 x= 4  ± 62 Ex. 10) 2x=5-4Ãâ€"2 * Notice this equation is not in the standard form for quadratic equations. Before identifying the values for a, b and c, the equation must be arranged in ax2+ bx+c=0 form.After adding 4Ãâ€"2 and subtracting 5, we get 4Ãâ€"2+ 2x-5=0 a=4 b= 2 c=-5 Substitute Evaluate Add Simplify x= -b  ± b2- 4ac2a x= -2  ± 22- 44-524 x= -2  ± 4+808 x= -2  ± 848 x= -2  ± 2218 Simplify fraction; Solution x= -1  ± 214 As in Completing the Square, if a negative value results under the radical, there’s NO REAL SOLUTION. XI. Compare all three methods learned Factoring| Completing the Square| Quadratic Formula| Ex. 11) 4Ãâ€"2- 8x-5=0 * Two integers that multiply to give -20 that add to give -8 are -10 and 2. x2- 10x +2x-5=02x2x-5+ 12x-5= 02x-52x+1= 0 2x-5=0 2x+1=0x= 52 x= -12| Ex. 11) 4Ãâ€"2- 8x-5=0 * First step is to obtai n a coefficient of 1 for the x2 by dividing both sides of the equation by 4. x2- 2x- 54= 04Ãâ€"2- 2x- 54=0x2- 2x=54Ãâ€"2- 2x+ _____=54+ _____x2-2x+ 22 2 =54+ 22 2 x2- 2x+1=54+1Ãâ€"2- 2x+1=94x-12= 94x-12= 94x-1=  ± 32x=1  ± 32x= 52 x= -12| Ex. 11. ) 4Ãâ€"2- 8x-5=0a=4 b= -8 c= -5x= -b  ± b2- 4ac2ax= –8  ± (-8)2-44-52(4)x= 8  ± 64+80 8x=8  ± 1448x= 8  ± 128x= 208 x= -48x= 52 x= -12| XII. Instructional StrategiesThis is such a wonderful unit that builds on the familiar skills like solving equations, while setting up the transition to exploring the graphical nature of quadratic solutions. Check out Being Strategic in Solving Equations Part I & II to learn more about the flexibility in equation solving. Students have quite a bit of flexibility in solving quadratic equations as well. This unit follows the factoring lessons in most curriculums very closely. Essentially, the only new material in this unit is the Completing the Square and the Quadratic Formula.It is i mperative that you teach this unit in a progressive nature as I have laid out here, starting with what students are familiar with, adding one layer at a time to arrive at the more complex equations as illustrated in Examples 7 – 10. Throughout the beginning of this unit, pose questions to students such as * Does the equation have a middle term, or does the equation have a b term? * Is the equation in standard quadratic form? * Is there a greatest common factor? * Is the trinomial factorable? * Can the trinomial be factored as a perfect square? How many unique solutions does the equation have? Encourage students to ask these questions back to you or other students as equations are solved in class. This will cause students to slow down and think carefully about the type of equation they are solving. With that said, there is usually more than one approach to solving most equations. Take for instance Example 11. Even if the equation is factorable, the Completing the Square method and the Quadratic formula can be used to solve the equation; however, it may not be the most efficient method.Often students will gravitate towards the formula because they are comfortable with mindless substitution and computation that’s involved with a formula. Needless to say, they quickly realize they must be meticulous weaving in and out of the steps so not to lose a sign or simplify incorrectly. In many cases, taking the scenic route, or the more elaborate method of solution, will cause careless errors throughout the solving process. The goal is for student to learn the process of examining what they have been given and proceed with the method of solution that makes sense for the given equation.To encourage this type of analysis and discourse, provide opportunities for students to showcase these skills. One activity is to group students in 3’s, provide them with a quadratic equation to solve, have each student demonstrate one of the methods of solution, and then decide as a group which method was the most efficient or strategic. When presenting to the class, have each student explain why their method was, or was not the most efficient. In a class, this could be 10 or more equations solved. Don’t shy away from including equations that are missing terms or equations that are not in standard form.These might prove to be more difficult, since they are required to think more carefully about what they have been given, but they are very valuable learning tools. Following this activity, provide students with an equation, and without requiring them to solve using paper and pencil, have them explain, either verbally or in written form, which method they think would be the most strategic or most efficient. Keep in mind, there is room for opinion in these responses. Simply listen and evaluate students thought process as they explain. Skills such as these are invaluable and will help create well rounded mathematical thinkers.

Tuesday, January 7, 2020

Essay on Gloria Naylors Mama Day - 1241 Words

Gloria Naylors Mama Day It is impossible to interpret Gloria Naylor’s 1988 novel, Mama Day, in one way. There are multiple standpoints that a reader can take in explaining various events that occur throughout the book, as well as different ways that the characters in the book interpret these events. The author never fully clarifies many questions that the story generates so as to leave the readers with the opportunity to answer them based on their own personal experiences and beliefs. The multiplicity of perspectives in Gloria Naylor’s Mama Day is embodied in the legend of Sapphira Wade and the dynamics between logic and the supernatural and between George and Cocoa. Sapphira Wade is a character that Naylor uses as a tool†¦show more content†¦The descendents of Sapphira all received deeds to pieces of land in Willow Springs in 1823. How the descendants of a slave woman came to inherit the land of slave owner is unclear because different interpretations of the event that occurred in 1823 seem to have been developed from generation to generation. For instance, some say Sapphira â€Å"smothered Bascombe Wade in his very bed,† while others say she â€Å"persuaded Bascombe Wade in a thousand days to deed all his slaves every inch of land in Willow Springs† and â€Å"poisoned him for his trouble† (Naylor 3). These different interpretations apparently lead to the development to the use of the phrase â€Å"18 23† as a slang term. For some, the phrase seems to represent death and destruction whereas others use it synonymously with deception. But no matter what actually happened in 1823, the fact that so many vie ws are accepted by the community conveys to the reader the importance of open-mindedness in reading the book. Naylor continues to suggest the significance of open-mindedness by providing the reader with the opportunity to choose more than one way to explain Mama Day’s encounter with Bernice. Bernice decides to seek the advice of Mama Day, who is known to have miraculous healing abilities, when she has trouble conceiving. Mama Day gives Bernice pumpkin seeds and puts her under the impression that they are â€Å"magic seeds† (Naylor 96). This gives Bernice time to buildShow MoreRelatedAnalysis Of Gloria Naylors Mama Day1144 Words   |  5 PagesGloria Naylor’s Mama Day, through prefatory documents at the beginning of the novel, is able to further her rewrite of the African experience post-slavery. Naylor published Mama Day in 1988. During that year the term African American had been coined by Jesse Jackson. By using this term today we are able to honor our cur rent place as American while also giving recognition and preserving our African Heritage Through the use of three prefatory documents Naylor is able to rewrite the historical AfricanRead More Gloria Naylors Mama Day Essay940 Words   |  4 PagesGloria Naylors Mama Day Gloria Naylors Mama Day takes place in two distinct environments, each characterized by the beliefs and ideologies of the people who inhabit the seemingly different worlds. The island of Willow Springs, comprised solely by the descendants of slaves, is set apart from the rest of the United States and is neither part of South Carolina nor Georgia. As such, its inhabitants are exempt from the laws of either state and are free to govern themselves as they see fit. 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E-mail: anslinjegu@gmail.com ---------------------------------------------------------------------------------------------------------------- Abstract This paper strews a panoramic view of Gynocentrism as a literary critical theory and its ramification in the form of the human relationshipRead MoreThe Tempest By William Shakespeare And Mama Day By Gloria Naylor1919 Words   |  8 PagesThe Tempest by William Shakespeare and Mama Day by Gloria Naylor are two fantastic stories that both belong to the genre magical realism, which is where magical elements are incorporated into realistic fiction. Prospero the main character is robbed of Dukedom and marooned on an island with his infant daughter where he meets natives and fire demons who do his bidding. Mama Day the main character in Gloria Naylor’s novel is a no nonsense woman who uses her magic to help the other residents of theirRead MoreGoophered Grapes Pre Ready 1 Essay example2710 Words   |  11 PagesMonthly† is a Bostonian publication that centered on politics, literature, science and the arts. While these topics are not reserved for our society’s elite s o much these days, it was much more so back then and the creators of the magazine definitely thought of themselves as part of our nation’s cultural elite. Even to this day, at least some of the staff at â€Å"The Atlantic† feel this way. Managing editor, Cullen Murphy gave a presentation and presented its founders like this; At a moment in our history