A Lab Practical And Making Conclusions On The Findings - 550 Words

A Lab Practical And Making Conclusions On The Findings (Lab Report Sample) Content: DISSECTION OF FETUS PIGName of student:Professor:Course:Date:Abdominal cavity dissectionPlace the fetal pig in dissecting tray ventral side facing up. Tie the pig; legs spread eagle. Cut through the skin without removing the umbilical cord. After getting done with cuts, locate umbilical vein which leads the umbilical cord to the liver. Cut the umbilical veinin order to open the abdominal cavity.ObservationsDiaphragm- this is a muscle that divides the thoracic and abdominal cavity, and is located near the ribcage.Liver- measured 6.5cm anchor x5.0cm high. It is a lobed structure which measured 6.5cm anchor x 5.0 highGall bladder- measured 1.5 anchor. It is greenish in color and is located underneath the liver. It is also attached to the duodenum by the bile duct.Stomach- measured 5.5cm anchor x 2.0cm. It rests underneath the pig's left side. It is pouch-shaped; at the top of the stomach is the esophagus. At each end lies valves namely cardiac sphincter valve and pyloric sphincter valve respectively. They are responsible for controlling food entering and leavingThe stomach is followed by the small intestines composed of duodenum and ileum (straight portion and curly part respectively)The ileum is held into position by a structure known as mesentery. The ileum has some blood vessels which are known as mesenteric arteries.Pancreas- Measured 4.5cm x1.5cm. It is located underside the stomach and is connected to the duodenum by pancreatic duct.Spleen- measured 6.5cm anchor X 1.5cm. It is a flattened organ, lies across the stomach towards the far left side of the pig.The ileum measured 313cm long and widens at the end to become the large intestines.The rectum lies outside the pig or the anusKidneys are bean-shaped, and they lie on either side of the pig. They both measured 2.0cmanchor x 4cm high.In the umbilical cord, umbilical cords are visible and in between them the urinary bladder lies.DNA difference in human and pigWe, the human beings have an enorm ous amount of genetic material in common with pigs. We are omnivorous mammals hence, can gain weight easily. It is a fact that we share some genes.All living organisms are made up of genetic materials with information encoded in the DNA, subdivided int...

Essay about Preventing Global Warming - 3042 Words

Preventing Global Warming The Earth is a dynamic, constantly changing environment in which the hydrosphere, atmosphere, and biosphere all interact. When one changes slightly the change is then felt through out the spheres. Humans need to understand that the change they cause can have a potential for a disastrous affect on the environment. From injecting the atmosphere with greenhouse gas, or deforestation, all the unnatural things done to the environment will have an unnatural affect that will have to be dealt with. We as humans have a moral responsibility to reduce global warming gasses by changing our modes of transportation, to stop deforestation, and increase government funding into research to inhibit global warming for†¦show more content†¦The rest of the world is still living the ways of the past by only producing enough energy for life. While the industrialized world is producing gases that not only hurt their nation’s inhabitants, but the rest of the world inhabitants as well. I nhabitants are not just humans, but animals and plants that make up the world. With increasing gas emissions the powerful nations of the world are making a weaker world environment. Automobiles are a major producer of greenhouse gas. One gallon of fuel burned puts five pounds of carbon dioxide into the atmosphere. Let’s say that an average car gets 25 miles to the gallon, and that car has a ten gallon tank. Every time a car gets filled up with gas, another fifty pounds of carbon dioxide have been put back into the atmosphere, and that is just one car. The automobile industry is very important to the world economy, so I am not saying that we should stop making cars, but there are other solutions. The recent trend of hybrid electric cars that get up to fifty miles to the gallon are becoming more popular. Also public transportation is very important. City dwellers that live downtown, do not need to drive their cars to work. Every major city has a form of public transportation that can get anyone around the city, and for that gallon of gas a bus burns the same five pounds reaches the atmosphere, but instead of oneShow MoreRelatedPreventing Globa l Warming Essay1219 Words   |  5 PagesGlobal Warming Global warming is a grave issue that is affecting not only the United States, but the whole world as well. Various international strategies need to be implemented so that these issues can be tackled. If taken seriously, the issue of global warming can not only be overcome, it can be prevented as well. Global warming is an event that will affect many people and animals all over the world. Humans will be affected the most due to global warming because of things like temperatureRead More Solutions to preventing the spread of global warming and its affects1632 Words   |  7 Pagesâ€Å"The American flag has gone through changes over time; those changes have made an impact on our country and made it what it is today.† Our earth is like the American flag, it is constantly changing, and one issue that affects our earth is global warming. We now live in an industrialized world which is filled with many new technologies that provide goods and services to us, provide us with energy and electricity and transportation. These new technological advances have made our lives much easier toRead MoreGlobal Warming Is Caused By Emission Of Greenhouse Gases Essay1358 Words   |  6 PagesGlobal warming is caused by emission of greenhouse gases. 72% of the totally emitted greenhouse gases Is carbon dioxide. CO2 is inevitably created by burning of fuels like e.g. Oil, diesel, petrol etc. The use of such fuels can be minimized by using alternative fuels which do not contain carbon or contain less carbon. The alternative fuels such as ethanol produced from renewable lignocellulosic resources or fuels produced from seawater. Research on improving ethanol production is accelerating forRead MoreEssay on Global Warming is Causing Climate Change535 Words   |  3 PagesGlobal warming is the increase in the earth’s atmospheric temperature. Naturally occurring gases such as carbon dioxide, methane, nitrous oxide, ozone and water vapor trap heat from the sun, preventing it from leaving the atmosphere. These naturally occurring gases along with human made hydro fluorocarbons (HFCs), per fluorocarbons (PFCs), and sulfur hexafluoride (SF6) are collectively known as greenhouse gases. 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The global warming hourglass ad attempts to emphasize the importance of immediately solving earth’s impending environmental problems by appealing to the emotions of fearRead MoreGlobal Warming Is A Product Of Green House Effect1437 Words   |  6 PagesGlobal warming is the most talked topic in our time. It is the increasing temperature of Earth’s surface, oceans and atmosphere. There is an evidence that shows earth temperature increased by 1.4% since late 18 00s, which sounds small number but scientist predicted the temperature will rise another 2 to 11.5 degrees F over next 100 years. Global warming is a product of green house effect. Question is, what is greenhouse effect? In common word, the interaction between Earth’s atmosphereRead MoreEssay The Beginning of Global Warming 1288 Words   |  6 PagesOne may believe Global Warming is tedious and a myth and show no concern for the environment surrounding them. The reason for choosing this topic of Global Warning is because Global Warming is a reality that the world must recognize. People must understand the many changes occurring on earth as well as the people all over the world have prevented global warming. The earth has many changes that have occurred in the past and further events waiting to occurring in the future. There are many facts toRead MoreChanging Perspective From Global Warming1554 Words   |  7 PagesChanging Perspective from Global Warming to Climate Change Global warming is one of the biggest problems facing the world today. Global warming is the rise in the earth’s mean surface temperature. This is due to increase of greenhouse gases such as carbon dioxide, which affects life forms on the earth’s surface. The scientific consensus as summarized by the Intergovernmental Panel on Climate Change (IPCC) is that the global average surface temperature has risen over the last century. Many

Role Of The Vestal Virgin As A Priestess Of Isis - 1451 Words

The purpose for my essay is to explore the role of the Vestal Virgin as and a priestess of Isis within the fabric of the Roman Empire society. (3) The time period I will examine to better cover this topic shall be from the establishment of these cults in early Rome, to the time of 394 B.C.E (1) in which Christianity became to the chosen religion of Rome. Within this paper I plan on covering their role, their culture, and their impact upon ancient Rome. To the ancient Romans, Vesta was the goddess of the hearth which was regarded as the heart of every home and the Vestal Virgin was her chosen priestess. (1) It was in the house that Vesta was the most revered because she was the goddess of the hearth and of fire. (2) Because the hearth was†¦show more content†¦First of all, she had to be between 6-10 years old and mentally and physically sound. (3) Secondly, both parents had to be living and she had to be a daughter of a free-born Roman resident. Finally, once she was selected to become a Vestal Virgin, the girl was sworn to celibacy for a period of 30 years. (3) After three decades of serving Vesta she could retire. Once retired the former Vestal would be regarded as an honored citizen of Rome, given a pension, and could wed. (2) The main tasks of a Vestal Virgin included the maintenance of the fire sacred to Vesta, the collection of water from a sacred spring, the preparation of ceremonial food, and protecting sacred objects. As a result, being a Vestal Virgin came with unique privileges. To begin with, a Vestal always travelled by carriage and perpetually had the right-of-way. Secondly, a Vestal had a place of honor at all public events. A Vestal could also own property, make a will, and vote. (1) She could free condemned prisoners and slaves. Finally, a Vestal Virgin was considered to be sacred, thus death was the penalty for anyone harming her. (3) But with the privileges there came serious consequences for being a Vestal Virgin. Allowing the sacred fire of Vesta to die out was a serious offense and was punishable by being beaten with a cat-o -nine-tails. A Vestal’s chastity was considered to have a direct bearing on the health of Rome. (3) The punishment for

Social Media Speech free essay sample

Facebook, Twitter and Tumblr are just a few of the websites that consume the vast majority of anyone who can afford a computer or phone’s life. While it is such a huge part of our lives, it leads to the question, do we even enjoy it? Or is it just another way for people to fit in with today’s society? It is undeniable that social media makes our lives easier. Within the clicks of a few buttons you can plan something with your friends, have a whole conversation with somebody or share your opinions with the whole world. Many people have referred to it as a way of socialising, but it just isn’t the same as meeting up with somebody and going somewhere together. While it seems as though we are just making friends in a whole new way, social media is quickly becoming something that we will not be able to live without. We will write a custom essay sample on Social Media Speech or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page For example, when you are out at a party, despite there being an endless amount of new people to converse with, you still see many people take a break in the middle and sit down to check their Facebook feeds or what people they’ve never met before are talking about on Twitter. Although it is normal for people to want to know what is happening in the world around them, is it really that difficult to put the phone away or turn the computer off for a while and just talk to somebody face-to-face? While social media is one of the easiest ways to communicate between friends, it has also become a way to start fights or bring down a specific person. If you have ever been on any social media websites, chances are you have most likely seen a virtual fight happening right before your eyes. Usually these fights are something that become forgotten after a day, but sometimes somebody defending their friends can turn into a violent battle between people who are clueless about what they are even fighting for. It is arguable that the social media of today is making people dumber. The fragmentation of already simple words, the misuse of grammar and the many new slang words being developed because we are having too many conversations to handle are just some of the things that have made communicating easier than social media had in the first place. While this is an acceptable way to talk virtually, it is a way of language being adapted by the younger generations that can affect their education. Not just in the way that people have learned to ignore grammar and spelling, but also making people lazier. While social media has its good aspects such as communicating with people from other cities or countries who you never would have met otherwise, easy communication or staying up to date with what is happening globally, its many flaws have made it more of a villain than a hero of today’s society. It all leads to the question, will we ever be able to leave the grasp that social media has on all of us? Or are we doomed to live in a society that has been overtaken by the endless power that social media exerts?

The Impact of Short-Staple Cotton Essay Example

The Impact of Short-Staple Cotton Essay The discovery of short-staple cotton was a major turning point not only in America’s economic history, but as well as utilization of slaves. Initially, the short-staple cotton variety had no commercial value as it had shorter cotton fibers, which reduces yarn and cloth quality, and fibers that were tightly attached to the seed, causing a longer time to separate the actual fiber from the seed without damaging it. On the other hand, the long-staple cotton fibers were exactly the opposite of their short cotton counterparts which was why the majority of fiber production was done using the longer variety (Philipps, 2004).However, in 1793, Eli Whitney invented a machine called, â€Å"cotton gin,† that enabled mass production of short-stapled cotton. The cotton gin, which was the short term for â€Å"cotton engine,† used wire teeth attached into a rotating wooden cylinder to snare the cotton fibers and pull them through a grate. The slots in this grate were too narrow f or the cotton seed to pass, so that the fibers were pulled away from the seed (Philipps, 2004). This invention eliminated the long and tedious task of removing the short cotton fiber from the seed and reduced the risk of damaging it. However, although the cotton was produced in large quantities, the cotton gin significantly reduced the quality of the fiber, causing resistance from English buyers. But due to the need to further expand the production of cotton and due to the assurance that cotton production would cost lower using the cotton gin, the American South decided to proceed using the short-staple variety.The adaptation of the short staple cotton and the cotton gin caused significant changes in the US South, most of important of which is that it led to the first United States patent system, which described who has exclusive rights over the machine. It also led to the use of more slaves as the operation of cotton gins required little skill. The production of the short stapled c otton boosted the economy of the South and resulted in the country being one of the chief exporters of cotton today (Murrin, 2006).Murrin, J. M. (2006). Liberty, Equality, Power: A History of the American People. Belmont, CA: Wadsworth Publishing.Phillips, W. H. (2004). Economic History Services: Cotton Gin. Retrieved October 18, 2007 from http://eh.net/encyclopedia/article/phillips.cottongin

Inequalities on ACT Math Strategies and Practice

Inequalities on ACT Math Strategies and Practice SAT / ACT Prep Online Guides and Tips Inequality questions come in a variety of shapes and forms on the ACT, but, no matter their form, you will see approximately three inequality questions on any given test. This means that inequality questions make up 5% of your overall ACT math test. Now, 5% of your test might not sound like a lot, but with only a quick brush-up on inequalities, that's an additional 5% of your questions that you're bound to rock! This will be your complete guide to inequalities on the ACT: what they are, the different types of ACT math problems on inequalities, and how to solve them. What Are Inequalities? An inequality is a representation that two values are not equal or that two values are possibly not equal. There are different types of inequalities and different symbols to denote these different relationships. ≠  is the "unequal" sign. Whenever you see this sign, you know that two values are not equal, but nothing more. We don't know which value is greater or less than, just that they are not the same. If we have $y ≠  x$, we do not know if $y$ is greater or less than $x$, just that they do not equal one another. is the "greater than" sign. Whichever number or variable is facing the opening of the sign is always the larger of the two values. (Some of you may have learned that the sign is a "crocodile" and that the crocodile always wants to eat the larger value). For instance, $x 14$ means that $x$ can be anything larger than 14 (it can even be 14.00000000001), but it cannot be 14 and it cannot be less than 14. is the "less than" sign. Whichever number is facing away from the opening of the sign is the lesser of the two values. This is just the greater than sign in reverse. So $14 x$ is the exact same equation we had earlier. $x$ must be larger than 14, 14 must be smaller than $x$. ≠¥ is the "greater than or equal to" sign. This acts exactly the same as the greater sign except for the fact that our values can also be equal. Whereas $x 14$ meant that $x$ could only be any number larger than 14, $x ≠¥ 14$ means that $x$ could be equal to 14 or could be any number larger than 14. ≠¤ is the "less than or equal to" sign. Just as the less than sign acted as a counter to the greater than sign, the less than or equal to sign acts counter to the greater than or equal to sign. So $x ≠¥ 14$ is the exact same thing as saying $14 ≠¤ x$. Either way, we are saying that 14 is less than or equal to $x$, $x$ is greater than or equal to 14. Each symbol describes the relationship between two values, but we can also link multiple values in a string. For instance, we can say: $5 x 15$ This gives us both an upper and a lower limit on our $x$ value, because we know it must be both larger than five and less than 15. If we only had $5 x$, the upper limit of $x$ would stretch into infinity, and the same with the lower limit if we only had $x 15$. For tips on how to keep track of which signs mean which, check out this article. The inequality crocodile is always hungry for the most it can get, om nom nom. How to Represent Inequalities We can represent inequalities in one of three different ways: A written expression A number line A graph Let's look at all three. Inequalities as written expressions use only mathematical symbols and no diagrams. They are exactly what we have been working with above (e.g., $y 37$). An inequality number line allows us to visualize the set of numbers that represents our inequality. We use a dark line to show all the numbers that match our inequality, and we mark where the inequality begins and/or ends in two different ways. To mark the beginning of an inequality that is "greater than" or "less than," we use an open circle. This shows that the starting number is NOT included. To mark the beginning of an inequality that is "greater than or equal to" or "less than or equal to," we use a closed circle. This shows that the starting number IS included. We can also combine these symbols if our inequality equation requires us to use two different symbols. For instance, if we have $-3 x ≠¤ 3$, our number line would look like: And finally, we can have inequalities in graphs for any and all types of graphs on the coordinate plane (more on the coordinate plane coming soon!). "Greater than" will be above the line of the graph, while "less than" will be below the line of the graph. Greater: This is true no matter which direction the line of the graph extends. Less: In terms of markings, inequality graphs follow the same rules as inequalities on number lines. Just as we use an open circle for "greater than" or "less than" inequalities, we use a dashed line for inequality graphs that are "greater than" or "less than." And just how we use a closed circle for "greater than or equal to" or "less than or equal to" inequalities, we use a solid line for our graphs that are greater or less than or equal to. And now to dive right in to ACT inequality problems! (Awkward flailing optional). Typical ACT Inequality Problems There are three different types of inequality questions you'll see on the ACT, in the order from most to least common: #1: Solve an inequality equation (find the solution set) #2: Identify or answer questions about an inequality graph or number line #3: Find alternate inequalities that fulfill given information Let's look at each type- what they mean and how you'll see them on the ACT. #1: Solving an Inequality Equation This is by far the most common type of inequality question you'll see on the ACT. You will be given one or two inequality equations and must solve for the solution set of your variable. Inequality problems work exactly the same way as a single variable equation and can be solved in the same way. Just think of the inequality sign as being the same as the equals sign. So you will perform the same actions (adding, subtracting, multiplying, and dividing) on each side. For instance: $9 + 12x 45$ $12x 36$ $x 3$ The only difference between equations and inequalities is that the inequality sign flips if you multiply or divide each side by a negative. For instance, $10 - 4x 50$ $-4x 40$ $x -10$ Because we had to divide each side by -4, we had to reverse the sign of the inequality. Alternatively, we can also use the strategy of plugging in answers (PIA) or plugging in numbers (PIN) to solve our inequality problems. Because all ACT math problems are multiple choice, we can simply test out which answers match our equation (and which do not) or we can choose our own values for x based on the information we know, depending on the problem. Let's look at an example of how this looks on the ACT, whether we solve the problem algebraically or by PIA. The inequality $3(x+2)4(x-3)$ is equivalent to which of the following inequalities? F. $x-6$G. $x5$H. $x9$J. $x14$K. $x18$ Solving Method 1: Algebra First, distribute out the variable on each side. $3(x + 2) 4(x - 3)$ $3x + 6 4x - 12$ Now, we must isolate our variable just as we would with a single variable equation. $6 x - 12$ $18 x$ Just as we saw back in our definitions, we know that we can also flip the inequality sign if we also switch the sides of our values. So $18 x$ is the same as saying $x 18$. Our final answer is K, $x 18$ Solving Method 2: Plugging in Answers Though it will often take a little longer, we can also solve our inequality problems by testing out the values in our answer choices. Let's, as usual when using PIA, start with answer choice C. Answer choice C says $x$ is less than 9, so let us see if this is true by saying that $x = 8$. If we plug in 8 for $x$ in the equation, we'll get: $3(x + 2) 4(x - 3)$ $3(8 + 2) 4(8 - 3)$ $3(10) 4(5)$ $30 20$ This is true, but that doesn't necessarily mean that it is the correct answer. Just because we know that $x$ can be equal to 8 or less doesn't mean it can't also be greater than 8. All we know for sure is that we can eliminate answer choices F and G, since we've problem that $x$ can be larger than each of them. So let us now go the opposite route and look at the highest value $x$ can be, given our answer choices. Answer choice J gives us $x 14$ and answer choice K says that $x 18$, so what would happen is we gave $x$ a value between the two? Let us say that $x = 16$ $3(x + 2) 4(x - 3)$ $3(16 + 2) 4(16 - 3)$ $3(18) 4(13)$ $54 52$ Because our inequality works for $x = 16$, we know that $x$ can be greater than $x 14$ and can, therefore, be greater than all the answer choices except for answer choice K (the answer choice that gives us our largest possible value for $x$). This is enough to tell us that our final answer is K. Our final answer is, again, K, $x 18$ #2: Inequality Graph and Number Line Questions For these types of questions, you will be asked to identify a graph or a number line from a given equation. Alternatively, you may be asked to infer information from a given inequality graph. Either way, you will always be given the graph on the coordinate plane. We know that the sum of $x$ and $y$ must be greater than 1, so let us imagine that one of those two variables is equal to 0. If we say that $x = 0$, then y alone has to be greater than 1 to make the sum of $x$ and $y$ still be greater than 1. We also know that we indicate that a value is "greater than" on a graph with a dashed line at the value in question and a filled in area above the value. The only graph with a dashed line at $y = 1$ and that has a shaded area above this value is graph J. This means graph J is more than likely our answer, but let's confirm it just to be safe. Because the sum of $x$ and $y$ must be greater than 1, the alternative possibility to $x = 0$ and $y 1$ is that $y$ equals zero, so $x$ must be greater than 1. To show this, we would need a dashed line at $(1, 0)$ and a shaded area above it, all of which graph J has. Now, to finish confirming that graph J is indeed our answer, we would simply do what we did to locate the lower limit of our graph in reverse so that we can find the upper limit. If $x + y 2$, then, when $x = 0$, $y$ must be less than 2, and when $y = 0$, $x$ must be less than 2. This would give us dashed lines at $(0, 2)$ and $(2, 0)$, both of which are on graph J. Our final answer is J. #3: Finding Alternate Inequality Expressions The rarest form of inequality questions on the ACT will ask you to use given inequalities and find alternate inequalities that must be true based off this given information. Let's look at one of these in action, to better see how this type of question works. If $x$ and $y$ are real numbers, such that $x1$ and $y-1$, then which of the following inequalities must be true? A. $x/y1$ B. $|x|^2|y|$ C. $x/3-5y/3-5$ D. $x^2+1y^2+1$ E. $x^{-2}y^{-2}$ There are two different ways we can solve this problem, by plugging in our own numbers or by working through it based on our logic and knowledge of algebra. We'll go through both methods here. Solving Method 1: Plugging in Numbers (PIN) Because we have a problem with multiple variables in both the problem and in the answer choices, we can make life a little easier and give our variables numerical values. Now, we do have to be careful when using this method, however, because there are infinite variables to choose from for both $x$ and $y$ and so more than one answer choice might work for any given variables we give to $x$ and $y$. If two or more answer choices work, we must simply pick new variables- eventually only the correct answer will be left, as it must work for ALL values of $x$ and $y$. When it comes to picking our values for $x$ and $y$, we can also make life easy by picking values that are easy to work with. We know that we must divide both $x$ and $y$ by 3 in answer choice C, so let us pick values that are divisible by 3, and we know we must square our values in several answer choices, so let us pick numbers that are fairly small. Now let's just say that $x = 6$ and $y = -9$ (Why those numbers? So long as they fulfill the given information- and they do- then why not!) And let us plug these values into our answer choices. Answer choice A gives us: $x/y 1$ If we plug in our values, we get: $6/{-9}$ $-{2/3}$ This is NOT greater than 1, so we can eliminate answer choice A. Answer choice B gives us: $|x|^2 |y|$ If we plug in our values, we get: $|6|^2 |-9|$ $36 9$ This is correct, so we will keep answer option B in the running for right now. Answer choice C gives us: $x/3 - 5 y/3 - 5$ If we plug in our values, we get: $6/3 - 6 {-9}/3 - 5$ $2 - 6 -3 - 5$ $-4 -8$ This is correct, so we will keep answer option C in the running for now as well. Because B and C are both correct, we will need to come back and test them both again with different values later. Answer choice D gives us: $x^2 + 1 y^2 + 1$ $6^2 + 1 -9^2 + 1$ $36 + 1 81 + 1$ $37 82$ This is NOT true, so we can eliminate answer choice D. Answer choice E gives us: $x^{-2} y^{-2}$ $6^{-2} -9^{-2}$ $1/{6^2} 1/{-9^2}$ $1/36 1/81$ Now this is indeed true, but what if we had chosen different values for x and y? Let's say that we said $x = 9$ and $y = -6$ instead (remember- so long as the numbers fit with the given information, we can use any values we like). $x^{-2} y^{-2}$ $9^{-2} -6^{-2}$ $1/{9^2} 1/{-6^2}$ $1/81 1/36$ Whoops! Answer choice E is no longer correct, which means we can eliminate it. We are looking for the answer choice that is always true, so it cannot possibly be answer E. Now we are left with answer choices B and C. Let's look at them each again. While we saw that our values for $x$ and $y$ meant that answer choice B was indeed true, let's see what would happen if we choose a much smaller value for $y$. Nothing is stopping us from choosing -6,000 for $y$- remember, all that we are told is that $y -1$. So let us use $y = -6,000$ instead. $|x|^2 |y|$ $|6|^2 |-6,000|$ $36 6,000$ This inequality is NOT true anymore, which means we can eliminate answer choice B. This means that answer choice C must be the right answer by default, but let's test it to make absolutely sure. Let us try what we did with answer option E and reverse the absolute values of our $x$ and $y$. So instead of $x = 6$ and $y = -9$, we will say that $x = 9$ and $y = -6$. $x/3 - 5 y/3 - 5$ $9/3 - 5 {-6}/3 - 5$ $3 - 5 -2 - 5$ $-2 -7$ No matter how many numbers we choose for $x$ and $y$, answer choice C will always be correct. Our final answer is C, $x/3 - 5 y/3 - 5$ Solving Method 2: Algebraic Logic As we can see, using PIN was successful, but required a good deal of time and trial and error. The alternative way to solve the problem is by thinking of how negatives and positives work and how exponents and absolute values alter these rules. We know that $x$ must be positive and $y$ must be negative to fulfill the requirements $x 1$ and $y -1$. Now let us look through our answer choices to see how these expressions are affected by the idea that $x$ must always be positive and $y$ must always be negative. Answer choice A gives us: $x/y 1$ We know that any fraction with a positive numerator and a negative denominator will be negative. And any negative number is less than 1. Answer choice A can never be correct. Answer choice B gives us: $|x|^2 |y|$ An absolute value means that the negative sign on $y$ has been negated, so this might be correct. But y can be any number less than -1, which means its absolute value could potentially be astronomically large, and $x$ can be any number greater than 1, which means its absolute value might be comparatively tiny. This means that answer choice B is not always correct, which is enough to eliminate it from the running. Answer choice C gives us: $x/3 - 5 y/3 - 5$ Now let's look at each side of the inequality. We know that any fraction with a positive number in both the numerator and in the denominator will give us a positive value. This means we will have some positive value minus 5 on the left side. We also know that any time we have a negative value in the numerator and a positive value in the denominator, we will have a negative fraction. This means we will have some negative value minus 5 on the right side. We also know that a negative plus a negative will give us an even greater negative (a smaller value). If we put this information together, we know that the left side may or may not be a negative value, depending on the value of $x$, but the right side will only get more and more negative. In other words, no matter what values we give to $x$ and $y$, the left side will always be greater than the right side, which means the expression is always true. Now this should be enough for us to select our right answer as C, but we should give a look to the other answer choices just in case. Answer choice D gives us: $x^2 + 1 y^2 + 1$ We know that if we square both a positive number and a negative number, we will get a positive result, so the negative value for $y$ is no longer in play. This inequality will therefore be true if the absolute value of $x$ is greater than the absolute value of $y$ (e.g., $x = 10$ and $y = -9$), but it won't be true if the absolute value of $y$ is greater than the absolute value of $x$ (e.g., $x = 9$, $y = -10$). This means that the inequality will sometimes be true, but not always, which is enough to eliminate it. Finally, answer choice E gives us: $x^{-2} y^{-2}$ We know that a number to a negative exponent is equal to 1 over that number to the positive exponent (e.g., $5^{-3} = 1/{5^3}$). This means that each value will be a fraction of 1 over the square of our $x$ and $y$ values. This will give us two positive fractions and $1/{x^2}$ will only be larger if the absolute value of $x$ is smaller than the absolute value of $y$. But, because our $x$ and $y$ values can be anything so long as $y$ is negative and $x$ is positive, this will only sometimes be true. We can therefore eliminate answer choice E. This leaves us with only answer choice C that is always true. Our final answer is C, $x/3 - 5 y/3 - 5$ "Win a war," "Rock the ACT"- we'd say the two are basically one and the same. ACT Math Strategies for Inequality Problems Though there are a few different types of inequality problems, there are a few strategies you can follow to help you solve them most effectively. #1: Write Your Information Down and Draw It Out Many problems on the ACT, inequalities included, appear easier or less complex than they actually are and can lead you to fall for bait answers. This illusion of ease may tempt you to try to solve inequality questions in your head, but this is NOT the way to go. Take the extra moment to work your equations out on the paper or even draw your own diagrams (or draw on top of the diagrams you're given). The extra few seconds it will take you to write out your problems are well worth the points you'll gain by taking the time to find the right answer. #2: Use PIN (or PIA) When Necessary If all you know about $x$ is that it must be more than 7, go ahead and pick a value for $\bi x$. This will help you more easily visualize and work through the rest of the problem, since it is generally always easier to work with numbers than it is to work with variables. As you use this strategy, the safest bet is to choose two values for your variable- one that is close to the definition value and one that is very far away. This will allow you to see whether the values you chose work in all instances. For instance, if all you know is $x 7$, it's a good idea to work through the problem once under the assumption that $x = 8$ and another time under the assumption that $x = 400$. If the problem must be true for all values $x 7$, then it should work for all numbers of $x$ greater than 7. #3: Keep Very Careful Track of Your Negatives One of the key differences between inequalities and single variable equations is in the fact that the inequality sign is reversed whenever you multiply or divide both sides by a negative. And you can bet the house that this is what the ACT will try to test you on again and again. Though the ACT is not engineered to trick you, the test-makers are still trying to challenge you and test whether or not you know how to apply key mathematical concepts. If you lose track of your negatives (an easy thing to do, especially if you're working in your head), you will fall for one of the bait answers. Keep a keen eye. #4: Double-Check Your Answer by Working Backwards (Optional) If you feel unsure about your answer for any reason (because so many of the answer choices look the same, because you're not sure if you handled the issue of negative numbers correctly, etc.), you can work backwards to see if your expression is indeed correct. For instance, let us look at the inequality we had earlier, when talking about the function of negatives on inequalities: $10 - 4x 50$ Again, we would go through this just as we would a single variable equation. $-4x 40$ $x -10$ But now maybe that answer doesn't feel right to you or you just want to double-check to be sure. Well, if we're told that $x$ must be greater than -10 to fulfill the inequality, let's make sure that this is true. Let us solve the expression with $x = -9$ and see if we are correct. $10 - 4x 50$ $10 - 4(-9) 50$ $10 + 36 50$ $46 50$ This is correct, so that's promising. But we found that $x$ needed to be greater than -10, so our expression should also be INCORRECT if $x$ were equal to -10 or if $x$ were less than -10. So let us see what happens if we have $x = -10$. $10 - 4x 50$ $10 - 4(-10) 50$ $10 + 40 50$ $50 50$ The inequality is no longer correct. This means that we know for certain that the solution set we found, $x -10$ is true. You will always be able to work backwards in this way to double-check your inequality questions. Though this can take a little extra time, it might be worth your peace of mind to do this whenever you feel unsure about your answers. Ready, set? It's test time! Test Your Knowledge Now let's put all that inequality knowledge to the test on some real ACT math problems. 1. The inequality $6(x+2)7(x-5)$ is equivalent to which of the following inequalities?A. $x-23$B. $x7$C. $x17$D. $x37$E. $x47$ 2. 3. If $r$ and $s$ can be any integers such that $s10$ and $2r+s=15$, which of the following is the solution set for $r$? A. $r≠¥3$B. $r≠¥0$C. $r≠¥2$D. $r≠¤0$E. $r≠¤2$ 4. Which of the following is the solution statement for the inequality shown below? $-51-3x10$ F. $-5x10$G. $-3x$H. $-3x2$J. $-2x3$K. $x-3$ or $x2$ 5. Answers: E, E, E, H, D Answer Explanations 1. This is a standard inequality equation, so let us go through our solve accordingly. First, let's begin by distributing out our equation. $6(x + 2) 7(x - 5)$ $6x + 12 7x - 35$ $12 x - 35$ $47 x$ Because we did not have to divide or multiply by a negative, we were able to keep the inequality sign intact. And because the expression $47 x$ and $x 47$ mean the same thing, we can see that this matches one of our answer choices. Our final answer is E, $x 47$ 2. We are given two graphs with equations attached and we must identify when one equation/graph is less than the other. We don't even have to know anything about what these equations means and we do not have to fuss with solving the equations- we can simply look at the diagram. The only place on the diagram where the graph of $y = (x - 1)^4$ is less than (aka lower than) the graph of $y = x - 1$ is between $x = 1$ and $x = 2$ on the coordinate plane. In other words, this inequality is true when $x 1$ and when $x 2$, or $1 x 2$. Our final answer is E, $1 x 2$. 3. We know that $s 10$ and it must be an integer, so let us make life easy and just say that $s = 11$. Now we can use this number to plug into the equation. $2r + s = 15$ $2r + 11 = 15$ $2r = 4$ $r = 2$ We know that $r$ can be equal to 2 and that it is the nearest integer to our definition. This means that our answer will either be C or E. So let us now find which direction our inequality sign must face. Let's now try one integer larger than 11 to see whether our solution set must be less or equal to 2 or greater than or equal to 2. If we say that $s = 12$, then our equation becomes: $2r + s = 15$ $2r + 12 = 15$ $2r = 3$ $r = 1.5$ We can see now that, as $s$ increases, $r$ will decrease. This means our solution set will be that $r$ is equal to or less than 2. Our final answer is E, $r≠¤ 2$ 4. Though this problem is made slightly more complex due to the fact that it is a double inequality expression, we still solve the inequality the same way we normally would. $-5 1 - 3x 10$ If we think of this expression as two different inequality equations, we would say: $-5 1 - 3x$ and $1 - 3x 10$ So let us solve each of them. $-5 1 - 3x$ $-6 -3x$ Because we now must divide by a negative, we must reverse the inequality sign. $2 x$ And now let's solve our second expression: $1 - 3x 10$ $-3x 9$ Again, we must reverse our inequality sign, since we need to divide each side by a negative. $x -3$ Now, if we put the two results together, our expression will be: $-3 x 2$ Our final answer is H, $-3 x 2$ 5. Because we have a number line with two closed circles, we know that must use less than or equal to and greater than or equal to signs. We can see that the right side of the graph gives us a set of numbers equal to or greater than 3, which means: $x ≠¥ 3$ The left side of the graph gives us a set of numbers less than or equal to -1, which means: $x ≠¤ -1$ Our final answer is, therefore, D, $-1 ≠¥ x$ and $x ≠¤ 3$. And now, your reward for solving your inequality problems is oodles of Cuteness. The Take-Aways Inequalities are so similar to single variable equations that it can be easy to treat the two as the same. The test-makers know this, so it pays to be careful when it comes to your inequality questions. Remember the key differences (multiplying or dividing by a negative reverses the sign, and you can flip your inequality signs so long as you flip both sides of the expression) and keep careful track of the details to avoid all the common pitfalls and bait answers. After you've mastered the art of answering your inequality questions, that's another 5% of the test that you've dominated. You're well on your way to that score goal of yours now! What's Next? Want to brush up on any of your other math topics? Check out our individual math guides to get the walk-through on each and every topic on the ACT math test. Been procrastinating on your ACT studying? Learn how to get over your desire to procrastinate and make a well-balanced study plan. Running out of time on the ACT math section? We'll teach you how to beat the clock and maximize your ACT math score. Looking to get a perfect score? Check out our guide to getting a perfect 36 on ACT math, written by a perfect-scorer. Want to improve your ACT score by 4 points? Check out our best-in-class online ACT prep program. We guarantee your money back if you don't improve your ACT score by 4 points or more. Our program is entirely online, and it customizes what you study to your strengths and weaknesses. If you liked this Math lesson, you'll love our program. 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Living in Dorms Essay Example | Topics and Well Written Essays - 750 words

Living in Dorms - Essay Example Just like a metropolitan city, the dorm has its own network of corridors, individual (single) rooms, a 125 seat theater, a 24 hour coffee station, a fitness centre and a dining room with open-air seating. The rooms have been specially designed to be properly ventilated and create a peasant environment in the room so that the student can comfortably focus his complete attention towards his studies without any disturbance. Dormitory is not only a place for students to live in but also a place to learn how to live. There are many activities such as sports, singing competition, celebration for festivals, and gatherings customized for dormitory students to learn as well as to enjoy their dormitory life. Not only is the dormitory a place where students stay and study, it is also a positive environment where students integrate their intellectual, social and emotional development and inspire one another in their learning and research through social activities. Students coming from all corners of the world, their life at MIT, including residential life, social life, extracurricular activities, et cetera, is as important a part of the educational experience as class-work. ... The more people you interact with, and the more diverse that set of people is, the more you will learn. What the students wants is a lifestyle in which they can do their studies while carrying on their other activities simultaneously, else they loose focus on either of the fields. Recommendation regarding this aspect include that MIT should focus more of its resources towards supporting "community" housing, student life activities, social events, athletics, recreation; the types of things that allow people to interact and help make students and faculty feel that they are part of a larger community of scholars. It is within these informal settings that some of the best learning occurs at MIT. This required integrating the separate elements bringing together people from different living groups, and most importantly, bringing together faculty, students, and staff. That's why the 'Founders Group' of the dorm that was formed included both faculty as well as students. Residential life acti vities ideally should be controlled by the students who live in the dorm, using house taxes and elected governments to control their own programs. This teaches the students how to manage themselves, their expenses, events, activities and fellow-beings. The idea behind this was to encourage and measure students' ability to work together as a group, to make decisions for themselves, and to take leadership as a key element of the community education. Freshmen-on-campus decision was extremely opposed by many of the students, feeling that it was an attempt by the administration to take away students' very freedom and bring them under closer oversight and control by the administration. The student saw it