...Simplifying Radicals Notes Often when we have a radical expression, we need to simplify it. A radical is in simplified form if it meets 3 criteria: * There are no perfect nth-factors inside the radical * There are no fractions inside a radical * There are no radical signs in the denominator of a fraction In this section, we will deal only with the first criterion – that there be no perfect nth factors inside the radical sign. To simplify we will be using the definition of fractional powers: Definition of Fractional Exponents We have worked with the first part of this definition before, but we will use the last part in simplifying. Study the following examples: Example. Use the definition of fractional exponents to rewrite the radical expression in exponential form. 1. By our definition, we can rewrite this as: 2. When we have a square root, the index is understood to be 2. We can write in the index and then proceed as above: Sometimes we can simplify our result after writing in exponential form: 3. Applying the definition we get . If we simplify the exponent, , and so the problem simplifies to 4. Applying the definition and simplifying we get 5. Again, the index of the square root is 2 and so In addition to the definition of fractional exponents, we will also use the following: Rule of Radicals 1: This rule can either be used from left to right or from right to left. Simplifying Square...
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...EOQ Practices Q1: Suppose you are responsible for ordering inventory. You have the following information. It costs $5 to hold one widget in inventory for a year It costs $100 to place an order for widgets, regardless of size Customers demand 2,500 widgets every year (Sales are distributed evenly throughout the year) Solution: = square root of [(2 x 2,500 x 100) / 5] = square root of (100,000) = 316.228 E0Q = 316 ------------------------------------------------- Q2: The I-75 Carpet Discount Store in North Georgia stocks carpet in its warehouse and sells it through an adjoining showroom. The store keeps several brands and styles of carpet in stock; however, its biggest seller is Super Shag carpet. The store wants to determine the optimal order size and total inventory cost for this brand of carpet given an estimated annual demand of 10,000 yards of carpet, an annual carrying cost of $0.75 per yard, and an ordering cost of $150. The store would also like to know the number of orders that will be made annually and the time between orders (i.e., the order cycle) given that the store is open every day except Sunday, Thanks giving Day, and Christmas Day (which is not on a Sunday). SOLUTION: Cc = $0.75 per yard Co = $150 D = 10,000 yards The optimal order size is The total annual inventory cost is determined by substituting Qopt into the total cost formula: The number of orders per year is computed as follows: ------------------------------------------------- ...
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...Solving Radical Equations Solving Radical Equations Topic Index | Algebra2/Trig Index | Regents Exam Prep Center (This lesson will work primarily with radicals that are square roots.) A "radical" equation is an equation in which the variable is hiding inside a radical symbol (in the radicand). is a radical equation is NOT a radical equation To solve radical equations: 1. Isolate the radical (or one of the radicals) to one side of the equal sign. 2. If the radical is a square root, square each side of the equation. (If the radical is not a square root, raise each side to a power equal to the index of the root.) 3. Solve the resulting...
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...MATH133 Unit 3 – Individual Project – C 1) Solve the following equations algebraically. You must show all your work. Learn how to type math roots and fractions by clicking on the link in the assignment list. Alternately, you may type [pic] as cuberoot(x) and show raising to the nth power as ^n, like x 3 is typed x^3. a) [pic] Answer: t = 8 Show your work here: T to the power of (2/3)* (3/2) = 4 to the power of (3/2) = 2 to the power of 2 * (3/2) = 2 to the power of 3 = 8 b) [pic] Answer: x = 32 Show your work here: The power of 5 square of x = 3 – 1 = 2 so x = 2 to the power of 5 = 32 c) [pic] Answer: x= 5/ 11 Show your work here: 3(x - 1) *2/3 =2*3*(x - 1) - 3(x - 1) (5x - 3)/(x - 1) 2(x-1) = 6(x - 1) - 3(5x - 3) 2x -2 =6x - 6 - 15x + 9 11x =2 - 6 + 9 =5 x=5/ 11 2) Solve algebraically and check your potential solutions: a) [pic] Answer: x = 2 Show your work here: [pic] [pic] X = 2: square root of 2 +2 then subtract 2 = 0 this answer works X = -1: square root of -1 + 2 then subtract (-1) = 0 this answer doesn’t work So x = 2 b) [pic] Show your work here: 4(x - 2) – x =-2 then 4x – 8 – x = -2 so 3x = 6 then x=2 What potential solution did you obtain? Explain...
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...want. More than anything in this world. I’ve never been this scared in my whole life. Please all I want is a heartbeat. HEARTBEAT By the fray You're gonna move that truck on the highway The rain is coming down and you're on the run. You gotta feel the breath in your body. We gotta keep on running til' we see the sun. Ohwww you gotta fire and it's burnin' in your way. Ohww it didn't burn out, but It burns much the same. And when you told everybody "i'd fall in the flame" If you love someone, love them all the same. If you LOVE someone, love them all the same. Ohwww feel your heartbeat. And ohwww, comin' around, comin' around, comin' around You love somebody, love them all the same. You gotta love somebody, love them all the same. I'm Singing, Ohwww, Feel Your Heartbeat, OH. I'm trying to put it all back together. I've got a story and I'm tryin' to tell everybody. I got kerosene in a desire. I'm trying to start a flame in the heart of the night Ohwww you gotta fire and it's burnin' in your way. Ohww it didn't burn out, but It burns much the same. And when you told everybody "i'd fall in the flame" If you love someone, love them all the same. If you LOVE someone, love them all the same. Ohwww feel your heartbeat. And ohwww, comin' around, comin' around, comin' around You love somebody, love them all the same. You gotta love somebody, love them all the same. I'm Singing, Ohwww, Feel Your Heartbeat, Yeah. Ohwww, owhhhhhh, owwwwhhhhh, owwhhhhhhhh ...
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...Research Essay Proposal Topic: Spice Girls and the normalizing spread of girl power Using Spice Girls as a point of study, I intend to research the spread in American popular culture of the ‘girl power’ phenomenon. It would discuss the nature of the idea (that female appearance and sensuality, and equality need not be mutually exclusive), how the concept relates to perceptions of gender roles and power through the lens of girl culture (for mainly the tween and teen groups) and the ways in which Spice Girls – as a major cultural phenomenon of the 1990s – promoted and normalized the idea. Depending on available information and depending on what the word count will allow, the essay will also look into the origins of the idea within pop (eg. Riot Grrrl, statements by Madonna, etc) and touch upon critiques of the supposed feminist aspects of the girl power movement, linking it to materialistic and consumerist norms of American and western culture. Sources: Primary Spiers, B., Fruchtmann, U., Thompson, B., Fuller, K., and Curtis, J. Spice World: The Spice Girls Movie. Culver City, Calif: Columbia TriStar Home Video, 1998. Lyrics from selected songs from the albums Spice (1996), Spiceworld (1997) and Forever (2000). Assorted interviews will also be identified, quoted and analysed. Secondary Whiteley, S. Women and Popular Music: Sexuality, Identity, and Subjectivity. London: Routledge, 2000. Print. Inness, S. A., Millennium Girls: Today's Girls Around the World. Lanham, Md:...
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...herself and a friend for a cup of cocoa. Following they talk about Jackie and love. In the story, a third person narrator appears, and it is seen from Ellen’s point of view. Ellen is a lesbian, and she had had a relationship with Jackie, who passed away about a year earlier. She is born on Valentine’s Day and she had become editor of the food section and had written a cookbook. At the time, when Jackie passed away, and Tobie were to live with her father, she was very sad. She did not get a chance to say goodbye to Jackie during the last rituals, because of the father, and that has made a deep wound inside of her. She does not feel like Tobie belongs to her – them - anymore, and she miss both of them very much. Now she has moved on a bit, and can look back and recall without too much pain, but there is many things about Tobie, that reminds her of Jackie and the past. Tobie is a girl with blond hair, which is cut short, and physically she looks like her father with the sharp, angular face. She looks like her mother in the warmth and quickness of her smile. She is a girl, who likes to have her own money, and she likes to have a cup of cocoa, which Ellen used to make for her, when she lived there. Besides that, she is the type of person, who never has had an abundance of friends, only special ones who were very close. Just like Ellen, she misses her mother. When she grows up, she wants to have a relationship as beautiful as what her...
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...SOLUTION TO ORGANIZATION’S INFORMATION OVERLOAD Abstract Information overload has been an increasing problem not only at work but just life in general. Information overload is when we receive too much information more than what we can handle and be able to make the right decisions (http://www.ptg-global.com). As an example, I’d go to work and my email inbox would have at least 30 emails every day. Before finish reading the first one, more would come in. There’d be so much information coming in that I don’t know which one to do process first. I’d spend most of my time in the office receiving information and responding to them then I do anything outside the office, like go to lunch. Introduction An organization’s solution to its information overload rather it be social system or technical system all depends on its mission or customers (http://www.ptg-global.com). There is no right or wrong answer because not all organizations are the same. Analysis In the military, depending on your Military Occupation Specialty (MOS) the solution goes both ways too. In some MOS you would only need social system. For instance our cooks, they are more in to the social system. They cannot rely on the technical system to help them fulfill their responsibilities. They have to be the ones operating the equipment or tools in order for them to be able to prepare the food and have them ready and served for the Soldiers. In my MOS, an Automated Logistic Supply Specialist, we rely on...
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...ORGANIZATIONAL ANALYSIS The Strengths and the Weaknesses of the situation are internal factors since they are within the band’s direct influence. STRENGTH Robin Hood’s supreme leadership and his group’s increasing size were to be considered as the major strength. Robin also has a strong team of lieutenants and each task was properly delegated to them. These three lieutenants are Will Scarlet who is in charge intelligence and scouting, Little John in charge of discipline and archery training, Scarlock who oversees the finances, and Much responsible for provisions. The brand recognition the Merry men posses has also been a strength. The group’s popularity among farmers and townspeople helped them to access resources of the surrounding towns and communities. WEAKNESS One of the problems faced by Robin Hood was the increasing size of the band he has made. At first, he believed that strength lay in numbers and that the more Merry men he had, the greater force it would be for him to fight the Sheriff. However, the increasing size of the organization resulted to a huge dilemma. As more men were recruited, Robin Hood’s organization experienced disarray as he was only supported by three people for the functions and was certainly under employed. Robin also lacked familiarity with his men which gave him a hard time on enforcing rules and regulations, and the decline of vigilance among his band. Due to the increasing size of the organization, other issues arise-- the food...
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...Case Synopsis 1: Robin Hood Robin Hood and his merry men are now in trouble because wealthy travelers (their source of revenue) are avoiding the forest. As is often common in an entrepreneurial organization, the Merry Men were highly motivated by Robin Hood’s leadership. Therefore, Robin had previously relied on informal communication to organize and implement operations. Robin is pleased with the growing size and influence of his organization. However, growth has meant that specialized duties have begun taking up most of the men’s time, leaving a command vacuum between Robin and the first line recruits. In addition, they are now all located in a large encampment that can be seen for miles. This creates the probability of a surprise attack on their position. Growth has also put great pressures on resources, so now they must harvest the forest more thoroughly. Rich travelers are avoiding the forest, so in desperation Robin is considering robbing the poorer travelers, which means his lieutenants must now tell their men to rob their brothers and fathers. What started as a rebellion has been routinized into banditry. Robin must therefore begin to question the Merry Men’s mission. Should it still be an extension of his private grudges and aspirations? Has the organization acquired a new mission, if so what is it? On whose behalf should the organization formulate its mission! Summary of Discussion Questions 1. What is strategy? 2. What strategic problems does Robin...
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...content, busy background, and lacking basic organization information leaves a bad first impression. Another issue is a site not being regularly maintained and frustrating its users with out of date and missing information. Working links are helpful, but choosing a “click here option” that doesn’t open or leads to “page not found” can try a user’s patience. By the same token, having unwanted content in the form of outside ads or suggestion pop-ups during use can add to user annoyance. An additional website stumbling block is poorly formatted menu options and the absence of an internal search feature. Website users should be able to easily follow menu options to drill down to the level of information they need versus being hit with too much information upfront or complicated menu features that seem like a convoluted maze. Having a search option that throws a user outside of the website into a Google search versus searching internally can cause undue irritation. Information seekers come to a website looking for particular information, and if they wanted a generic web search they could easily accomplish that on their own. Finally an additional draw back that causes website user angst is the lack of easily found contact information. Some websites fail to make their contact information easy to find or purposefully leave it off and force their customers to use a “contact us” form or online...
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...Major Themes in 'Much Ado About Nothing' Shakespeare’s treatment of love in Much Ado About Nothing differs from his other romantic comedies. Sure, it shares the same stagy plot, which finishes with the lovers finally getting back together, but Shakespeare also mocks the conventions of courtly love which was popular at the time. Although Claudio and Hero’s courtly marriage is central to the plot, their relationship is the least interesting thing in the play. Instead, our attention is drawn to Benedick and Beatrice’s unromantic backbiting – it is this relationship that seems more believable and enduring. By contrasting these two different types of love, Shakespeare manages to poke fun at the conventions of courtly, romantic love. Claudio uses highly contrived language when speaking of love, which is undermined by Benedick and Beatrice’s banter: “Can the world buy such a Jewel?” says Claudio of Hero. “My dear Lady disdain! Are you yet living?” says Benedick of Beatrice. As an audience, we are supposed to share Benedick’s frustration with Claudio’s transparent, pompous rhetoric of love: “He was wont to speak plain and to the purpose, like an honest man and a soldier … His words are a very fantastical banquet, just so many strange dishes.” Deception As the title suggests, there is a lot of fuss over very little in the play – after all, if Claudio wasn’t so impetuous, Don John’s rather weak plan wouldn’t have worked at all! What makes the plot so intricate is the use of deception...
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...characters in “Much Ado About Nothing” are the victims of deception, and because they’ve been deceived is the reason they act in the ways that they do. Even though the central deception is directed against Claudio in an attempt to destroy his relationship with Hero, it is the deception pertaining to Beatrice and Benedick which is the play's main focus. Almost every character in the play at some point has to make interpretations from what he or she sees, has been told or overheard. At the same time, nearly every character in the play at some point plays a part of consciously pretending to be what they are not. (Act I, Scene I) ”Thou wilt be like a lover presently and tire the hearer with a book of words. If thou dost love fair Hero, cherish it, and I will break with her and with her father, and thou shalt have her. Was't not to this end That thou began'st to twist so fine a story?” Here is when Don Pedro tries to put a spin on words making it sound like if Claudio really wants to be with Hero, they should first trick her into believing that Don Pedro is actually Claudio. They go on forward with the idea and as Don Pedro is swooning Hero with his words and charm at the masked ball and Claudio is actually eavesdropping near-by trying to make sure everything is going according to plan. Deception is one of the focal themes throughout the play which grows out of the love game. Deceit is not evil in nature; it can be used for the purpose good or bad outcomes. “In Much Ado About Nothing”...
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...The No Fear Shakespeare line by line translation offers a plaintive point of view of Shakespeare’s Othello. It has improved my understanding of the play as a whole and provided me with a new perspective. The most outstanding difference between the original play and the No Fear Shakespeare (NFS) text is the removal and simplification of the dialogue. Shakespeare uses a syntax that is sometimes difficult to understand, often putting the subject of a sentence after the verb. He also employs various types of figurative language such as metaphors, puns, and allusions. One benefit of reading the NFS is that it rearranges the original sentence structure to be more coherent. However, some of Shakespeare’s best work is lost in translation. While the...
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...“Much Ado About Nothing” is a comical play centered around scandals, love, and witty jokes. The antagonist of the play, Don John, schemes to make other characters suffer because of his on mishaps of being a bastard. As for the other characters, they play matchmaker to create happy relationships.Although “Much Ado About Nothing is depicted as a comical play, aspects of star-crossed lovers and deception reveal relevance to the moral of the story. In “Much Ado About Nothing,” deception, with the inherently evil connotation, reveals to have both negative and positive outcomes. Don Pedro disguises as Claudio in Act I and confesses his love to Hero at the mask ball because he feels that the two would make a perfect couple. Don John decides to...
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