What is an Anti-Hero Definition †Plus 10 Examples!

What is an Antis! What is an Antis! There’s something comforting about a protagonist who always does the right thing for the right reasons, like Superman. But there’s something compelling about a morally ambivalent protagonist who sometimes does the right thing, and only sometimes for the right reasons - like Tyrion Lannister.While Superman is a traditional take on a heroic protagonist, Tyrion is a decidedly skewed version. In other words, he’s an anti-hero.Let’s dig a little deeper into exactly what an anti-hero is, and why they’ve become so prevalent in stories. Learn all about the morally grey protagonists that readers love: the anti-hero Anti-Hero DefinitionAn anti-hero is a protagonist who lacks some of the conventional attributes of a traditional hero - like courage or morality. While their actions are ultimately noble, they don’t always act for the right reasons.For instance, they might save someone from a dangerous situation because it furthers their interests, not because they actually care about helping others.How is an anti-hero different from an anti-villain?While the two types of characters can be easily confused, the difference boils down to this:The anti-hero (or AH) does the right thing, but maybe not for the right reasons - and they lack a lot of the characteristics we’ve come to expect of tradition heroes.The anti-villain (or AV) does the wrong thing, but their motives are often noble - or, at least, sympathetic. Anti-villains typically have some characteristics we don’t commonly associate withâ€Å"bad guys.†At the end of the day, if you’re not quite sure whether a character is an anti-hero or an anti-villain, ask yourself this: who does the story ask readers to root for? If that character is morally grey, they’re likely the anti-hero. The morally grey character who opposes them is probably the anti-villain.Check out our post full of anti-villain examples to learn more.How is an anti-hero different from a villain-protagonist?Few books have been successfully written from the perspective of a completely irredeemable, morally reprehensible character. Readers want to be able to root for the protagonist at least a little bit. Exceptions include Humbert Humbert from Lolita, Patrick Bateman from American Psycho, and Tom Ripley from The Talented Mr. Ripley. By the end of these books, you’re likely waiting on tenterhooks for the protagonist to be brought to justice.These characters are classified as â€Å"Villain Protagonists.† They’re different from anti-heroes because the author purposefully avoids giving readers a reason to cheer for them. An anti-hero is a morally grey character we’re still encouraged to root for. But a villain protagonist is a â€Å"bad guy†- who happens to be the main character in the story.5 Types of Anti-HeroesNot all anti-heroes are created equally. In fact, TV Tropes classifies a â€Å"sliding scale† of these morally ambiguous protagonists. Unsurprisingly, the first type is†¦1. The Classic Anti-HeroTypical qualities of a fictional hero include confidence, bravery, stoicism, intelligence, handsome looks, and superb fighting capabilities. The Classic Anti-Hero is the inverse of these things: self-doubting, fearful, anxious, and lacking in combat skills. In general, the character arc of this AH follows them overcoming their â€Å"weaknesses† in order to vanquish the enemy.This type of AH is not necessarily on the grey scale of morality, they simply defy readers’ preconceived notions of heroism. id=attachment_18919 style="width: 1290px" class="wp-caption aligncenter">Olivia Pope from Scandal, V from V for Vendetta, Deadpool, Dexter, Nancy Botwin from Weeds, Arthur Dent from The Hitchhiker's Guide to the Galaxy, Selina Meyer from Veep - once you know what an anti-hero is, there is no shortage of opportunities to spot them.If you’re looking to write your own controvertible protagonist, check out the following in-depth blog posts aimed at helping authors develop compelling characters.Character Development: How to Write Characters Your Readers Won't Forget 9 Common Types of Fantasy Characters (With Examples) How to Write a Compelling Character Arc 12 Character Archetypes Every Writer Should Know How to Create a Character Profile: the Ultimate Guide (with Template)Did we miss any anti-heroes who deserve a mention? Drop their name - or any other thoughts or questions - in the comments below!

Sequences on SAT Math Complete Strategy and Review

Sequences on SAT Math Complete Strategy and Review SAT / ACT Prep Online Guides and Tips A series of numbers that follows a particular pattern is called a sequence. Sometimes, each new term is found by adding or subtracting a certain constant, sometimes by multiplying or dividing. So long as the pattern is the same for every new term, the numbers are said to lie in a sequence. Sequence questions will have multiple moving parts and pieces, and you will always have several different options to choose from in order to solve the problem. We’ll walk through all the methods for solving sequence questions, as well as the pros and cons for each. You will likely see two sequence questions on any given SAT, so keep this in mind as you find your perfect balance between time strategies and memorization. This will be your complete guide to SAT sequence problemsthe types of sequences you’ll see, the typical sequence questions that appear on the SAT, and the best ways to solve these types of problems for your particular SAT test taking strategies. What Are Sequences? You will see two different types of sequences on the SATarithmetic and geometric. An arithmetic sequence is a sequence wherein each successive term is found by adding or subtracting a constant value. The difference between each termfound by subtracting any two pairs of neighboring termsis called $d$, the common difference. 14, 11, 8, 5†¦ is an arithmetic sequence with a common difference of -3. We can find the $d$ by subtracting any two pairs of numbers in the sequence, so long as the numbers are next to one another. $11 - 14 = -3$ $8 - 11 = -3$ $5 - 8 = -3$ 14, 17, 20, 23... is an arithmetic sequence in which the common difference is +3. We can find this $d$ by again subtracting pairs of numbers in the sequence. $17 - 14 = 3$ $20 - 17 = 3$ $23 - 20 = 3$ A geometric sequence is a sequence of numbers in which each new term is found by multiplying or dividing the previous term by a constant value. The difference between each termfound by dividing any neighboring pair of termsis called $r$, the common ratio. 64, 16, 4, 1, †¦ is a geometric sequence in which the common ratio is $1/4$. We can find the $r$ by dividing any pair of numbers in the sequence, so long as they are next to one another. $16/64 = 1/4$ $4/16 = 1/4$ $1/4 = 1/4$ Ready...set...let's talk sequence formulas! Sequence Formulas Luckily for us, sequences are entirely regular. This means that we can use formulas to find any piece of them we choose, such as the first term, the nth term, or the sum of all our terms. Do keep in mind, though, that there are pros and cons for memorizing formulas. Prosformulas provide you with a quick way to find your answers. You do not have to write out the full sequence by hand or spend your limited test-taking time tallying your numbers (and potentially entering them wrong into your calculator). Consit can be easy to remember a formula incorrectly, which would be worse than not having a formula at all. It also is an expense of brainpower to memorize formulas. If you are someone who prefers to work with formulas, definitely go ahead and learn them! But if you despise using formulas or worry that you will not remember them accurately, then you are still in luck. Most SAT sequence problems can be solved longhand if you have the time to spare, so you will not have to concern yourself with memorizing your formulas. That all being said, it’s important to understand why the formulas work, even if you do not plan to memorize them. So let’s take a look. Arithmetic Sequence Formulas $$a_n = a_1 + (n - 1)d$$ $$\Sum \terms = (n/2)(a_1 + a_n)$$ These are our two important arithmetic sequence formulas. We’ll look at them one at a time to see why they work and when to use them on the test. Terms Formula $a_n = a_1 + (n - 1)d$ This formula allows you to find any individual piece of your arithmetic sequencethe 1st term, the nth term, or the common difference. First, we’ll look at why it works and then look at some problems in action. $a_1$ is the first term in our sequence. Though the sequence can go on infinitely, we will always have a starting point at our first term. (Note: you can also assign any term to be your first term if you need to. We’ll look at how and why we can do this in one of our examples.) $a_n$ represents any missing term we want to isolate. For instance, this could be the 4th term, the 58th, or the 202nd. So why does this formula work? Imagine that we wanted to find the 2nd term in a sequence. Well each new term is found by adding the common difference, or $d$. This means that the second term would be: $a_2 = a_1 + d$ And we would then find the 3rd term in the sequence by adding another $d$ to our existing $a_2$. So our 3rd term would be: $a_3 = (a_1 + d) + d$ Or, in other words: $a_3 = a_1 + 2d$ If we keep going, the 4th term of the sequencefound by adding another $d$ to our existing third termwould continue this pattern: $a_4 = (a_1 + 2d) + d$ $a_4 = a_1 + 3d$ We can see that each term in the sequence is found by adding the first term, $a_1$, to a $d$ that is multiplied by $n - 1$. (The 3rd term is $2d$, the 4th term is $3d$, etc.) So now that we know why the formula works, let’s look at it in action. Now, there are two ways to solve this problemusing the formula, or simply counting. Let’s look at both methods. Method 1arithmetic sequence formula If we use our formula for arithmetic sequences, we can find our $a_n$ (in this case $a_12$). So let us simply plug in our numbers for $a_1$ and $d$. $a_n = a_1 + (n - 1)d$ $a_12 = 4 + (12 - 1)7$ $a_12 = 4 + (11)7$ $a_12 = 4 + 77$ $a_12 = 81$ Our final answer is B, 81. Method 2counting Because the difference between each term is regular, we can find that difference by simply adding our $d$ to each successive term until we reach our 12th term. Of course, this method will take a little more time than simply using the formula, and it is easy to lose track of your place. The test makers know this and will provide answers that are one or two places off, so make sure to keep your work organized so that you do not fall for bait answers. First, line up your twelve terms and then fill in the blanks by adding 7 to each new term. 4, 11, 18, ___, ___, ___, ___, ___, ___, ___, ___, ___ 4, 11, 18, 25, ___, ___, ___, ___, ___, ___, ___, ___ 4, 11, 18, 25, 32, ___, ___, ___, ___, ___, ___, ___ And so on, until you get: 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81 Again, the 12th term is B, 81. Sum Formula $\Sum \terms = (n/2)(a_1 + a_n)$ Our second arithmetic sequence formula tells us the sum of a set of our terms in a sequence, from the first term ($a_1$) to the nth term ($a_n$). Basically, we do this by multiplying the number of terms, $n$, by the average of the first term and the nth term. Why does this formula work? Well let’s look at an arithmetic sequence in action: 10, 16, 22, 28, 34, 40 This is an arithmetic sequence with a common difference, $d$, of 6. A neat trick you can do with any arithmetic sequence is to take the sum of the pairs of terms, starting from the outsides in. Each pair will have the same exact sum. So you can see that the sum of the sequence is $50 * 3 = 150$. In other words, we are taking the sum of our first term and our nth term (in this case, 40 is our 6th term) and multiplying it by half of $n$ (in this case $6/2 = 3$). Another way to think of it is to take the average of our first and nth terms${10 + 40}/2 = 25$ and then multiply that value by the number of terms in the sequence$25 * 6 = 150$. Either way, you are using the same basic formula. How you like to think of the equation and whether or not you prefer $(n/2)(a_1 + a_n)$ or $n({a_1 + a_n}/2)$, is completely up to you. Now let’s look at the formula in action. Kyle started a new job as a telemarketer and, every day, he is supposed to make 3 more phone calls than the day previous. If he made 10 phone calls his first day, and he meets his goal, how many total phone calls does he make in his first two weeks, if he works every single day? 413 416 426 429 489 As with almost all sequence questions on the SAT, we have the choice to use our formulas or do the problem longhand. Let’s try both ways. Method 1formulas We know that our formula for arithmetic sequence sums is: $\Sum = (n/2)(a_1 + a_n)$ But, we must first find the value of our $a_n$ in order to use this formula. Once again, we can do this via our first arithmetic sequence formula, or we can find it by hand. As we are already using formulas, let us use our first formula. $a_n = a_1 + (n - 1)d$ We are told that Kyle makes 10 phone calls on his first day, so our $a_1$ is 10. We also know that he makes 3 more calls every day, for a total of 2 full weeks (14 days), which means our $d$ is 3 and our $n$ is 14. We have all our pieces to complete this first formula. $a_n = a_1 + (n - 1)d$ $a_14 = 10 + (14 - 1)3$ $a_14 = 10 + (13)3$ $a_14 = 10 + 39$ $a_14 = 49$ And now that we have our value for $a_n$ (in this case $a_14$), we can complete our sum formula. $(n/2)(a_1 + a_n)$ $(14/2)(10 + 49)$ $7(59)$ $413$ Our final answer is A, 413. Method 2longhand Alternatively, we can solve this problem by doing it longhand. It will take a little longer, but this way also carries less risk of incorrectly remember our formulas. As always, how you choose to solve these problems is completely up to you. First, let us write out our sequence, beginning with 10 and adding 3 to each subsequence number, until we find our nth (14th) term. 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49 Now, we can either add them up all by hand$10 + 13 + 16 + 19 + 22 + 25 + 28 + 31 + 34 + 37 + 40 + 43 + 46 + 49 = 413$ Or we can use our arithmetic sequence sum trick and divide the sequence into pairs. We can see that there are 7 pairs of 59, so $7 * 59 = 413$. Again, our final answer is A, 413. Only one more formula to go. Almost there! Geometric Sequence Formulas $$a_n = a_1( r^{n - 1})$$ (Note: while there is a formula to find the sum of a geometric sequence, but you will never be asked to find this on the SAT, and so it is not included in this guide.) As with the first arithmetic sequence formula, this formula will allow you to find any number of missing pieces, including your 1st term, your nth term, or your $r$. And, as always with sequences, you have the choice of whether to solve your problem longhand or with a formula. Method 1formula If you’re one for memorizing formulas, we can simply plug in our values into our equation in place of $a_n$, $n$, and $r$ in order to solve for $a_1$. We are told that Mr. Smith has 1 dollar 5 days later, which would be the 6th day (meaning our $n$ is 6), and that the ratio between each term is $1/4$. $a_n = a_1( r^{n - 1})$ $1 = a_1({1/4}^{6 - 1})$ $1 = a_1({1/4}^5)$ $1 = a_1(0.00097656)$ $1/0.00097656 = a_1$ $1024 = a_1$ So the 1st term in the sequence is 1024, which means that Mr. Smith starts with $1024 on Monday morning. Our final answer is 1024. Method 2longhand Alternatively, we can, as always, solve them problem by hand. First, set out our number of terms in order to keep track of them, with our 7th term, $1, last. ___, ___, ___, ___, ___, 1 Now, because our ratio is $1/4$ and we are working backwards, we must multiply each term by 4. (Why? Because ${1/{(1/4)} = 1 * 4$, according to the rules of fractions). ___, ___, ___, ___, 4, 1 ___, ___, ___, 16, 4, 1 And, if we keep going, we will eventually get: 1024, 256, 64, 16, 4, 1 Which means that we can see that our 1st term is 1024. Again, our final answer is 1024. As with all sequence solving methods, there are benefits and drawbacks to solving the question in each way. If you choose to use formulas, make very sure you can remember them exactly. And if you solve the questions by hand, be very careful to find the exact number of terms in the sequence. It can be all too easy to accidentally find one term more or fewer if you’re not carefully labeling or otherwise keeping track of your terms. I'm preeeeetty sure it's not a proper math formula unless mystery variables and exploding test tubes are involved somehow. Typical SAT Sequences Questions Because all sequence questions on the SAT can be solved without the use or knowledge of sequence formulas, the test-makers will only ever ask you for a limited number of terms or the sum of a small number of terms (usually 12 or fewer). As we saw above, you may be asked to find the 1st term in a sequence, the nth term, the difference between your terms (whether a common difference, $d$, or a common ratio, $r$), or the sum of your terms (in arithmetic sequences only). You also may be asked to find an unusual twist on a sequence question that combines your knowledge of sequences or your knowledge of sequences and other SAT math topics. For example: Again, let us look at both formulaic and longhand methods for how to solve a problem like this. Method 1formulas We are told that the ratio between the terms in our sequence is 2:1, successive term to previous term. This means that our common ratio is 2, as each term is being multiplied by 2 in order to find the next term. (Note: if you are not familiar with ratios, check out our guide to SAT ratios.) Now, we can find the ratio between our 8th and 5th terms in a few different ways, but the simplest waywhile still using formulasis simply to reassign our 5th term as our 1st term instead. This would then make our 8th term become our 4th term. (Why the 4th term? The 5th and 8th terms are 3 spaces from each other5th to 6th, 6th to 7th, and 7th to 8thwhich means our 1st term must be 3 spaces from our new nth term1st to 2nd, 2nd to 3rd, 3rd to 4th). Once we’ve designated our 5th term as our 1st term, we can use the strategy of plugging in numbers and assign a random value for our $a_1$. Then we will plug in our known values of $r$ (2) and $n$ (3) so that we can find our $a_n$. Let us call $a_1$ 4. (Why 4? Why not!) $a_n = a_1( r^{n - 1})$ $a_4 = 4(2^{4 - 1})$ $a_4 = 4(2^3)$ $a_4 = 4(8)$ $a_4 = 32$ So the ratio between our 4th term and our 1st term (the equivalent of the ratio to our 8th term and our 5th term) is: $32:4$ Or, when we reduce: $8:1$ The ratio between our 8th term and our 5th term is $8:1$ Our final answer is C, $8:1$. As you can see, this problem was tricky because we had to reassign our terms and use our own numbers before we even considered having to use our formulas. Let us look at this problem were we to solve it longhand instead. Method 2longhand If we choose to solve this problem longhand, we will not have to concern ourselves with reassigning our terms, but we will still have to understand that there are 3 spaces between our 8th and our 5th terms (8th to 7th, 7th to 6th, and 6th to 5th). Since we used the technique of plugging in our own numbers last time, let us use algebra for our longhand method. We know that each term is found by doubling the previous term. So let us say that our 5th term is $x$. ___, ___, ___, ___, x, ___, ___, ___ This would make our 6th term $2x$. ___, ___, ___, ___, x, 2x, ___, ___ And we can continue down the line until we get: ___, ___, ___, ___, x, 2x, 4x, 8x This means that our ratio between our 8th term and our 5th term is: $8x:x$ Or, in other words: $8:1$ Our final answer is, again, C, $8:1$. Again, you always have the choice to use formulas or longhand to solve these questions and how you prioritize your time (and/or how careful you are with your calculations) will ultimately decide which method you use. Now let's take a look at our SAT sequence question strategies. Tips For Solving Sequence Questions Sequence questions can be somewhat tricky and arduous to work through, so keep in mind these SAT math tips on sequences as you go through your studies: 1) Decide before test day whether or not you will use the sequence formulas Before you go through the effort of committing your formulas to memory, think about the kind of test-taker you are. If you are someone who loves to use formulas, then go ahead and memorize them now. Most sequence questions will go much faster once you have gotten used to using your formula. However, if you would rather dedicate your time and brainpower to other math topics or if you would simply rather solve sequence questions longhand, then don’t worry about your formulas! Don’t even bother to try to remember themjust decide here and now not to use them and save your mental energy for other pursuits. Unless you can be sure to remember themcorrectly, formulas will hinder more than help you on test day. So make the decision now to either memorize your formulas or forget about them entirely. 2) Write your values down and keep your work organized Though many calculators can perform long strings of calculations, sequence questions by definition involve many different values and terms. Small errors in your work can cause a cascade effect and one mistyped digit in your calculator can throw off your work completely. Even worse, you won’t know where the error happened if you do not keep track of your values. Always write down your values and label your terms in order to prevent a misstep somewhere down the line. 3) Keep careful track of your timing No matter how you solve a sequence question, these types of problems will generally take you more time than other math questions on the SAT. For this reason, most sequence questions are located in the last third of any particular SAT math section, which means the test-makers think of sequences as a â€Å"high difficulty† level problem. Time is your most valuable asset on the SAT, so always make sure you are using yours wisely. If you feel you can (accurately) answer two other math questions in the time it takes you to answer one sequence question, then maximize your point gain by focusing on the other two questions. Always remember that each question on the SAT math section is worth the same amount of points and you will get dinged if you get a question wrong. Prioritize both your quantity of answered questions as well as your accuracy, and don’t let your time run out trying to solve one problem. If you feel that you can answer a sequence problem quickly, go ahead! But if you feel it will take up too much time, move on and come back to it later (or skip it entirely, if you need to). No matter which method you choose to use, trust that you'll find the one that best suits your needs and abilities. Test Your Knowledge Now let’s test your sequence knowledge with real SAT math problems. 1) 2) What is the sum of the first 10 terms in the arithmetic sequence that begins:13, 21, 29,... 450 458 474 482 490 3) Answers: 200, E, 2035 Answer Explanations: 1) The number of squirrels triples every three years, so this is a geometric sequence. As always, we can either count longhand or use our formulas. Let’s look at each way. We first need to count how many times three years has passed between 1990 and 1999. Including the year 1990 and the year 1999, there are 4 terms for every 3 years between 1990 and 1999. 1990, 1993, 1996, 1999 This means that 1999 is our 4th term and 1990 is our 1st term. Now let’s plug in our values into our formula. $a_n = a_1( r^{n - 1})$ $5400 = a_1(3^{4-1})$ $5400 = a_1(3^3)$ $5400 = a_1(27)$ $200 = a_1$ Our first term is 200. There were 200 squirrels in 1990. Alternatively, we can simply find the number of squirrels in 1990 by counting by hand. Again, we need to find the number of groups of 3 years between 1990 and 1999, inclusive. 1990, 1993, 1996, 1999 Now, let us plug in our known value for 1999 and find the rest of our terms by dividing each term by 3. ___, ___, ___, 5400 ___, ___, 1800, 5400 And so on, until you get: 200, 600, 1800, 5400 Again, our first term is 200. There were 200 squirrels in 1990. 2) We are asked to find the sum of this arithmetic sequence, which means we can either use our formula or count our sequence by hand. Method 1formulas First, we need to determine our common difference, $d$, in the sequence. To do so, let us subtract one of our neighboring pairs of numbers. $21 - 13 = 8$ Before we can find our sum, however, we must find our $a_10$. This means we need to use our first arithmetic sequence formula: $a_n = a_1 + (n - 1)d$ $a_10 = 13 + (10 - 1)8$ $a_10 = 13 + 72$ $a_10 = 85$ Now that we know our $d$ and our $a_10$, we can plug in our values to find our sum. $(n/2)(a_1 + a_n)$ $(10/5)(13 + 85)$ $(5)(98)$ $490$ Our final answer is E, 490. Method 2counting If you do not want to remember or use your formulas, you can always find your answer by counting. First, we must still determine our $d$ by subtracting our neighboring terms: $29 - 21 = 8$ Now, we can find the value of all our terms by continuing to add 8 to each new term until we reach our 10th term. 13, 21, 29, ___, ___, ___, ___, ___, ___, ___ 13, 21, 29, 37, ___, ___, ___, ___, ___, ___ 13, 21, 29, 37, 45, ___, ___, ___, ___, ___ And so on, until we finally get: 13, 21, 29, 37, 45, 53, 61, 69, 77, 85 Now, we can either add them up individually ($13 + 21 + 29 + 37 + 45 + 53 + 61 + 69 + 77 + 85 = 490$), or you can, find your pairs of numbers, beginning from the outside in. We can see that there are 5 pairs of 98, so $5 * 98 = 450$ Our final answer is E, 490. 3) Because the price of our mystery item raises by $2 every year, this is an arithmetic sequence. Again, we have multiple ways to solve this kind of problemusing formulas, or counting longhand. Method 1formulas $a_n = a_1 + (n - 1)d$ $100 = 10 + (n - 1)2$ $100 = 10 + 2n - 2$ $100 = 8 + 2n$ $92 = 2n$ $n = 46$ Now, we know that 100 is the price at our 46th term, but this is not the same thing as 46 years from 1990. Remember: the number of terms from the 1st is always 1 fewer space than the actual count of the term. For instance, the 1st term in a sequence is 4 spaces from the 5th term and 5 spaces from the 6th term. Why? 1st to 2nd, 2nd to 3rd, 3rd to 4th, 4th to 5th. We can see it takes 4 total spaces to go from the 1st term to the 5th. For our price problem, our $n$ is 46, which means that the year will be $46 - 1 = 45$ actual spaces away from our starting term. So: $1990 + (46 - 1)$ $1990 + 45$ $2035$ The price will be $100 in 2035. Method 2counting Because each new term is determined by adding 2, it will take us a long time to get from 10 to 100. We can speed up this process by first finding the difference between the 1st and last term: $100 - 10 = 90$ And then we can divide this difference by the common difference, $d$: $90/2 = 45$ It will take 45 years to get to the price to raise to $100. 45 years after 1990 is: $1990 + 45$ $2035$ Again, the price will be $100 in 2035. Yeah! You toppled those sequence questions! The Take Aways Though sequence questions can take some little time to work through, they are usually made complicated by their number of terms and values rather than being actually difficult to solve. So long as you remember to keep all your work organized and decide before test-day whether or not you want to spend your study efforts memorizing, and you’ll be able to tackle any number of sequence questions the SAT can throw your way. As long as you keep your values straight (and don’t get tricked by bait answers!), you will be able to grind through these problems without fail. What’s Next? Now that you've taken on sequences and dominated, it's time to make sure you have a solid handle on the rest of your SAT math topics. The SAT presents familiar concepts in unfamiliar ways, so check out our guides on all your individual SAT topic needs. We'll provide you with all the strategies and practice problems on any SAT math topic you could ask for. Running out of time on SAT math? Not to worry! Our guide will show you how to maximize both your time and your score so that you can make the most of your time on test day. Don't know what score to aim for? Follow our simple steps to figure out what score is best for you and your needs. Looking to get a perfect score? Check out our guide to getting a perfect 800 on SAT math, written by a perfect-scorer! 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 ofpractice 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:

Impulse - Force Over Time

Impulse - Force Over Time Force applied over time creates an impulse, a change in momentum. Impulse is defined in classical mechanics as a force multiplied by the amount of time it acts over. In calculus terms, the impulse can be calculated as the integral of force with respect to time.  The symbol for impulse is J or Imp.   Force is a vector quantity (the direction matters) and impulse is also a vector in the same direction. When an impulse is applied to an object, it has a vector change in its linear momentum. Impulse is the product of the average net force acting on an object and its duration.  J  Ã‚  F̅Δt Alternately, impulse can be calculated as the difference in momentum between two given instances.  Impulse change in momentum force x time. Units of Impulse The SI unit of impulse is the same as for momentum, the Newton second N*s or kg*m/s. The two terms are equal. English engineering units for impulse are pound-second (lbf*s) and slug-foot per second (slug*ft/s). The Impulse-Momentum Theorem This theorem is logically equivalent to Newtons second law of motion: force equals mass times acceleration, also known as the force law. The change in momentum of an object equals the impulse applied to it.  J  Ã‚  ÃŽâ€ p. This theorem can be applied to a constant mass or to a changing mass. It is relevant especially to rockets, where the mass of the rocket changes as fuel is expended to produce the thrust. Impulse of Force The product of average force and the time in which it is exerted is the impulse of force. It is equal to the change of momentum of an object that isnt changing mass. This is a useful concept when you are studying impact forces. If you increase the time over which the change of force happens, the impact force also decreases. This is used in mechanical design for safety, and it is useful in sports applications as well. You want to reduce the impact force for a car hitting guardrail, for example, by designing the guardrail to collapse as well as designing parts of the car to crumple on impact. This lengthens the time of the impact and therefore the force. If you want a ball to be propelled further, you want to shorten the time of impact with a racket or bat, raising the impact force. Meanwhile, a boxer knows to lean away from a punch so it takes longer in landing, reducing the impact. Specific Impulse Specific impulse is a measure of the efficiency of rockets and jet engines. It is the total impulse that is produced by a unit of propellant as it is consumed. If a rocket has a higher specific impulse, it needs less propellant to gain altitude, distance, and speed. It is the equivalent of the thrust divided by the propellant flow rate. If the propellant weight is used (in Newton or pound), specific impulse is measured in seconds. This is often how rocket engine performance is reported by manufacturers.

Mechanisms Used in Common Law and Civil Law in Transfer of Syndicated Coursework

Mechanisms Used in Common Law and Civil Law in Transfer of Syndicated Dept - Coursework Example It is also subject to being added upon by legislation from a law making legislature such as parliament. Here previous rulings give guidance on current cases and are referred to. It originated in England and is still used commonly there and in former Great Britain colonies such as Australia, New Zealand Canada and in most countries of the commonwealth. Debt syndication is a situation where many lenders come together to offer credit to an individual entity, a conglomerate, or a government to spread out the debt risk among the participating lenders (called the syndicate) and share in the profits of the debt proportionately under a single syndicated loan agreement. This paper gives an analytical introspection into common and civil law in reference to transfer of syndicated debt. Loan amounts involved in syndicated debts are normally much larger than normal debts, and a default could have serious ramifications on a single lender, hence the need to spread the risk among many lenders. There is a lead borrower known as the ‘agent’ that does most of the administrative work concerning the loan or contributes proportionally larger debts.1 A syndicated loan can be provided as a term loan provision where a specified amount of loan is provided over an agreed time period of time called the ‘term. In addition, the borrower is usually allowed, under the given circumstances, a brief time after the loan availability to withdraw money up to the maximum limit and then repays in installments (amortization) or once at the expiry of the term (bullet payment). The syndicated loan may also be provided as a revolving loan facility where the borrower draws portions of the loan amount for a given period, for instance, within three to six months after which the repayment is due and can draw from the loan facility to repay the outstanding loan. This is a concept which is referred to as rollover loan. A syndicated loan can also be in the form of a general loan where new bor rowers can come into the agreement under specific circumstances and may also combine rollover loans and multiple term loans. This is a concept which is legally defined within the law.2 The borrower usually starts by approaching the lead borrower (agent) who advises the said borrower and contacts other lenders. The agent is the contact person with the borrower and represents the views of the syndicate. The agent also monitors how the borrower meets terms and conditions of the loan agreement. In addition, the agent keeps all records, collects all payments and interest from the borrower, and then pays both members of the syndicate at a fee. After a loan is approved with the requisite legal requirements satisfied, the borrower can then access the loan under the agreed terms. In this case, the borrower may wish to transfer the loan to a third party for a variety of reasons listed in the following part of the discussion. Acquire Capital The borrower may sell its interest in the syndicated loan if it is a long term loan facility to get capital or benefit from new better loan facilities. Reduce or Avoid Loss The borrower may experience difficulties and decide to sell its loan commitment to distressed debt specialists Capital

Critique of Aristotle's Politics Essay Example | Topics and Well Written Essays - 1250 words

Critique of Aristotle's Politics - Essay Example Other types include tyranny, oligarchy and democracy, which are considered bad ones. It has been argued that there are a number of advantages and disadvantages that come with the type of government in practice. This affects the level of benefits of the people as well as the level of peace in a government. Benefits and disadvantages are associated with the types of government that Aristotle discusses in his classification of empires. This paper provides a discussion of those pros and cons. It also provides the argument whether these forms of rule would be suitable for the administration of the Roman Empire. Discussion One of the first political structures Aristotle refers to is a monarchy. He distinguishes a monarchy noting that, â€Å"The rule of a household is a monarchy, for every house is under one head: whereas constitutional rule is a government of freemen and equals† (Aristotle 279). Aristotle goes on to indicate that the major pros of a political monarchy are that the h ead of state is separated from the head of government. It has also been noted that there exists a great relationship between the leader and the people if the leader is a monarch. This is because people see the Royal Family as a family they can relate to. Indeed, at one point Aristotle even compares a monarchy to a family, with the head of the household constituting the King or Queen. The other pro is that this form of leadership ensures the interest of the nation is placed first in preference to other considerations. It is also a form of government that represents centuries of history and tradition. It is considered a tourist attraction due to its archaic nature, and tourists usually come to see the working palaces. This type of empire would have been successful in the Roman Empire during the reign of Diocletian which started in 284 CE. Since the monarch divided the empire into two, it would have ensured loyalty to the monarch from the eastern and the western empires. This would ens ure cases of disagreements and rebellion against the monarch are prevented. Aristocracy, on the other hand, is a form of rule which ensures the best rulers. There are certain pros associated with this form of rule. The main one is that it ensures the best people who can rule the country are given the authority to do so if the present leadership is hereditary. This ensures the country is ruled by the right people in the right direction. This form of rule would have been successful in the Roman Empire. In these regards, one considers that Aristotle extols the virtues of the aristocracy as being effective with many strongholds (Aristotle). The Roman Empire had various problems from attacks from the Vandals in 455 CE. This led to the removal of the Roman Emperor, Romulus Augustus from power by the Odovacar, a paid mercenary of the Romans as well as the leader of the Goths. This is what resulted in the end of the Roman Empire. The selection of the right leader would ensure he puts the ri ght defensive measures to ensure the people are protected and the multitude of strongholds would have constituted an effective defensive measure. This would have contributed to the continued existence of the Roman Empire. Tyranny can also be considered to have certain pros with respect to the Roman Empire. This is because only a tyrant is allowed to act in a manner that he wants without considering ethics. It allows the society to run free by assuming control irrespective to the nature of the control. Aristotle notes,

Simmons Case Study Essay Example | Topics and Well Written Essays - 1000 words

Simmons Case Study - Essay Example Other than one of it's plants, they were all run military style, turnover was high and it appeared to no one was very happy to be coming to work and even more important the managers had no sense of responsibility for their staff other then to drive them in their jobs. The economy had turned sour after 911 and their competitors were beginning to do somewhat better. To top it all, they had lost good contact with customers and with suppliers and had just instituted a bad set of foam that made their mattresses smell bad. In this atmosphere, their CEO wanted to institute a training program that was very expensive and very innovative. When money is tight, it is most difficult to think about pushing forward into something new, especially if you are at the helm, the CEO. On the average, during a recession the employees are at their lowest moral and the worth of an excellent leader becomes more important than ever. According to Leb (2009), there are many things that the leader must be able to do and certainly the ability to do and one of those is to inspire those who are employed by him. In support of innovation during hard times is a survey done by Bloomberg Business Week (2009), in which they surveyed CEO's that had put in place new and innovative programs during hard times in the economy and in their companies. ... It is easy for the leadership of an organization to throw up their hands, similar to the employees, and say "there is just nothing we can do right now" and ride it out. The biggest problem with that kind of attitude is the fact that someone will pull out of head while you are waiting. In evaluating whether this should happen, a couple of things came to mind. Simmons believes in CHOICES which is the caring, history, opportunity, innovation, customers, empowerment, and support. The culture of the company does not provide for this belief. Only one plant in the several has managed to accomplish this kind of atmosphere, therefore, they need to change their values and cultural beliefs or the way they do things. The other is ethical beliefs of fairness, respect, integrity, and fostering growth and development in others. Under the present organizations culture, none of these things are happening at the level of the employees as the present managerial group continues to run the company like a dictatorship and employees are generally very unhappy (Casciaro & Edmondson, 2007). The main objectives of GGOL were to help people understand what their full potential at work might be. Their philosophy was that "profitable organizational growth is a result of satisfied and loyal customers; a committed, cooperative, and creative organizational culture; and a leadership team that empowers and serves the workforce." After seeing the video, it became obvious that this is built from the individual up, not the other way. Employees must understand where they fit in and how to interact without fear and with trust, in order to improve the processes that would lead to

Bush Temporary Workers Program Essay Example | Topics and Well Written Essays - 250 words

Bush Temporary Workers Program - Essay Example The Program acknowledges that current immigration system in the United States is broken and suggest that a system of â€Å"matching willing employees with willing employers† will help reform the system. Position: While Bush Temporary Workers Program can be laudable, this is however counter-productive considering the current economic condition of the country. Where we have more than 10 % unemployment rate caused by the 2009 Financial Crisis. The economic health of United States have already changed dramatically and it is no longer as robust as before. Such, it can no longer accommodate additional workers to compete with domestic workers. While I have nothing against foreign workers who are as talented and productive as an American worker, I would prefer that scarce jobs will go to Americans first. Had this proposal of Bush been made during America’s economic peak, I would have nothing against it. But just not today where a job that will go to an immigrant worker will be a job that will be taken away from a prospective American job seeker. I understand that having more than 8 million undocumented workers can be a threat to national security. But taking away jobs from Americans who equally needs it, cannot justify the proposed immigration reform.