Quantum Gravity Definition and Explanation

Quantum Gravity Definition and Explanation Quantum gravity is an overall term for theories that attempt to unify gravity with the other fundamental forces of physics (which are already unified together). It generally posits a theoretical entity, a graviton, which is a virtual particle that mediates the gravitational force. This is what distinguishes quantum gravity from certain other unified field theories   although, in fairness, some theories that are typically classified as quantum gravity dont necessarily require a graviton. Whats a Graviton? The standard model of quantum mechanics (developed between 1970 and  1973) postulates that the other three fundamental forces of physics are mediated by virtual bosons. Photons mediate the electromagnetic force, W and Z bosons mediate the weak nuclear force, and gluons (such as quarks) mediate the strong nuclear force. The graviton, therefore, would mediate the gravitational force. If found, the graviton is expected to be massless (because it acts instantaneously at long distances) and have spin 2 (because gravity is a second-rank tensor field). Is Quantum Gravity Proven? The major problem in experimentally testing any theory of quantum gravity is that the energy levels required to observe the conjectures are unattainable in current laboratory experiments. Even theoretically, quantum gravity runs into serious problems. Gravitation is currently explained through the theory of general relativity, which makes very different assumptions about the universe at the macroscopic scale than those made by quantum mechanics at the microscopic scale. Attempts to combine them generally run into the renormalization problem, in which the sum of all of the forces do not cancel out and result in an infinite value. In quantum electrodynamics, this happened occasionally, but one could renormalize the mathematics to remove these issues. Such renormalization does not work in a quantum interpretation of gravity. The assumptions of quantum gravity are generally that such a theory will prove to be both simple and elegant, so many physicists attempt to work backward, predicting a theory that they feel might account for the symmetries observed in current physics and then seeing if those theories work. Some unified field theories that are classified as quantum gravity theories include: String theory / Superstring theory / M-theorySupergravityLoop quantum gravityTwistor theoryNoncommutative geometryEuclidean quantum gravityWheeler-deWitt equation Of course, its fully possible that if quantum gravity does exist, it will be neither simple nor elegant, in which case these attempts are being approached with faulty assumptions and, likely, would be inaccurate. Only time and experimentation will tell for sure. It is also possible, as some of the above theories predict, that an understanding of quantum gravity will not merely consolidate the theories, but will rather introduce a fundamentally new understanding of space and time. Edited by Anne Marie Helmenstine, Ph.D.

How to Conduct a Hypothesis Test in Statistics

How to Conduct a Hypothesis Test in Statistics The idea of hypothesis testing is relatively straightforward. In various studies, we observe certain events. We must ask, is the event due to chance alone, or is there some cause that we should be looking for? We need to have a way to differentiate between events that easily occur by chance and those that are highly unlikely to occur randomly. Such a method should be streamlined and well defined so that others can replicate our statistical experiments. There are a few different methods used to conduct hypothesis tests. One of these methods is known as the traditional method, and another involves what is known as a p-value. The steps of these two most common methods are identical up to a point, then diverge slightly. Both the traditional method for hypothesis testing and the p-value method are outlined below. The Traditional Method The traditional method is as follows: Begin by stating the claim or hypothesis that is being tested. Also, form a statement for the case that the hypothesis is false.Express both of the statements from the first step in mathematical symbols. These statements will use symbols such as inequalities and equals signs.Identify which of the two symbolic statements does not have equality in it. This could simply be a not equals sign, but could also be an is less than sign ( ). The statement containing inequality is called the alternative hypothesis and is denoted H1 or Ha.The statement from the first step that makes the statement that a parameter equals a particular value is called the null hypothesis, denoted H0.Choose which significance level that we want. A significance level is typically denoted by the Greek letter alpha. Here we should consider Type I errors. A Type I error occurs when we reject a null hypothesis that is actually true. If we are very concerned about this possibility occurring, then our value for alpha shoul d be small. There is a bit of a trade-off here. The smaller the alpha, the most costly the experiment. The values 0.05 and 0.01 are common values used for alpha, but any positive number between 0 and 0.50 could be used for a significance level. Determine which statistic and distribution we should use. The type of distribution is dictated by features of the data. Common distributions include z score, t score, and chi-squared.Find the test statistic and critical value for this statistic. Here we will have to consider if we are conducting a two-tailed test (typically when the alternative hypothesis contains a â€Å"is not equal to† symbol, or a one-tailed test (typically used when an inequality is involved in the statement of the alternative hypothesis).From the type of distribution, confidence level, critical value, and test statistic we sketch a graph.If the test statistic is in our critical region, then we must reject the null hypothesis. The alternative hypothesis stands. If the test statistic is not in our critical region, then we fail to reject the null hypothesis. This does not prove that the null hypothesis is true, but gives a way to quantify how likely it is to be true.We now state the results of the hypothesi s test in such a way that the original claim is addressed. The p-Value Method The p-value method is nearly identical to the traditional method. The first six steps are the same. For step seven we find the test statistic and p-value. We then reject the null hypothesis if the p-value is less than or equal to alpha. We fail to reject the null hypothesis if the p-value is greater than alpha. We then wrap up the test as before, by clearly stating the results.

Developing academic skills for Business and Management Essay

Developing academic skills for Business and Management - Essay Example Between 1996 and 2010 a lot of research has taken place in the field of family owned business and a lot of theory has been developed (James, Jennings & Breitkruz, 2012). Now a new breed of researchers wants to validate those findings and theories by their research on Asia based family owned business. This new field of research is essential to validate or negate the findings of researchers in the field who have researched on similar enterprises in other countries. This new lot of researches aims to find out whether the previous finds are universal and robust in their conclusion or are particular and country specific, or in other words specific to the western world. According to Johns’ (2006) research into the field of family owned business it has been increasingly found that that there has been lot of research on the business enterprises but the researches on family owned business have slowly disappeared. This goes hand in hand with the real life situation where family owned businesses are slowly losing their relevance and are being converted to professionally managed business. James, Jennings and Breitkruz suggested and invited other scholars to indulge in more research in the field to research into the subject to understand the association between family and their business (James, Jennings & Breitkruz, 2012). Another thing that is important to study in the field of family business particularly with respect to Asian countries is the role of context in shaping this family business. By context it is meant over here the circumstances or conditions that influences or the influencing factors in the family business. It is important to note t hat although the overall characteristics and conditions of business environment is similar to the countries present in the Asia pacific region , there still exists subtle differences. For example, in underdeveloped

Conflict analysis of Israel Palestine Research Paper

Conflict analysis of Israel Palestine - Research Paper Example On the other hand, the Hebrews referred to Palestinian territory as the land of Israel. Thus, it made the decision of the Zionist be problematic in nature. In late 1930, the UN Partition plan and Peel Partition Plan redefined the territorial location of the Jews and proposed the establishment of a Jewish state in Palestine. The Zionist took over the best Coastal and Valley areas alienating the indigenous Arab people. In this case, Jesrusalem, Judea and Samaria were bound together to become the West Bank. The Arab people rejected the UN Partition plan in 1947 and considered Zionist as a threat to their people. This is because the plan gave authority to Palestine to take over 75 percent of the Arab state making the Arabs to become refugees in the neighboring state Israel. This created a refugee problem in Israel over three decades, but a new political equation was formed in the 1967 and the late 1980’s war (Hunnicutt 2011). Palestinians had refused to respond to any official or diplomatic relation with Israel. This led to more Jewish settlements in Israel leading to the conflict between Palestinians and Israelites. This paper analyzes the main conflict between the two nations; Palestine and Israel. During late 1940’s and 1960’s, conflicts made Palestinians to run away voluntarily while others were forced to evacuate. They were moved to bordering countries and thus turned out to be refugees. An estimated 4 million Palestinians are refugees, and most of these refuges live in camps in the Gaza Strip, Syria, West Bank and Lebanon. The refugees get assistance from the United Nations and other bodies and individual willing for help (Faruqi 2011). Even though the Palestinians did not have an army in Palestine at this time, rockets were fired on a frequently from Gaza heading to Israel. In return, the Israelis who lived in the

Personal Finance Concepts Investing Essay Example for Free

Personal Finance Concepts Investing Essay According to the finance researchers a portfolio refers to an appropriate collection of investments for an institution or a single individual. An investment portfolio is constructed by financial advisors or a retainer their main task involves investment analysis that are useful; during purchasing of stocks and bonds, and other business assets. . Cliff uses his present finances to determine his future holding and finance position. Cliff financial statement seems to spread in many fields, he invests in fixed assets and even before he could fully exploit his new investment strategy he is already investing in shares and bonds. Basically this is diversification and investing assets such as bonds and shares in such a scenario is exposing a high percentage of ones investment at risk (Grant 2005). Cliff is a risk taker hence he is more likely to invest in income securities and unwarranted investment such as the equities. Hence Cliff will tend to have very low cash holding and shares, in addition he is not expected to hold high levels of securities as savings since his age is allows him to have a long time to invest in most cases age is a great determinate in an individuals saving amount and investment, though Cliff will tend to save for his future plans such as his wedding plans, his marginal propensity to save will still be quite low. Since Cliff is earning an approximate of $340000 he I expected to distribute his earning to his present and future expenses, A great source of cliff’s finances is in terms of bonds and shares which are a good way to invest but the shortcoming with Cliff’s investment is the fact that he did not take a good research before imposing a big sum of his money into the investment, the investment in bonds and shares involve a high percentage of risk and for that reason if they are not carefully researched on they bring high degrees of losses or very little profits. In that light they are not included in the construction of a portfolio, instead the items that can be included in the construction of a portfolio are savings, cash at hand and revenue that is already attained or the degree of risk is not too high. Using Cliff’s example he can spread his earning such 30% of his total earnings is equities, 40% income securities, 20% sundry expenses and 10 % as savings. The assumption is that cliff is a young risk taker hence his securities will tend to be and also his savings and cash. Â  Below is an example of Cliff’s portfolio: References Frasca , R, (2006) – Personal Finances: An Integrated Planning Approach, 7th Ed – Pearson Prentiss Hall Grant, R (2005) Contemporary Strategy Analysis Blackwell Publishing Karnani, A (1981) – Business Portfolio: an analytical Approach – Harvard Publishing .

A Helping Hand for College :: Expository Classification Essays

A Helping Hand for College    Approximately 60% of all students enrolled in higher education receive some type of financial assistance. Financial aid is provided to students for many reasons. The primary reason is to increase the accessibility for families that are unable to afford the full cost of higher education. Scholarships, loans, and federal work studies are categories of financial aid given to help students further their education.    A scholarship is a financial award given to students in recognition of achievement, such as academics or athletics. Other scholarships are awarded to minorities and women to increase their access to higher education. In many cases, the qualifications for a scholarship include financial need as well. A scholarship does not require repayment. Most scholarships are given to students who attend business schools, technical and vocational schools, nursing schools and 2-year colleges.    A loan is an award offered by various government and private agencies. The interest rates are lower than those of regular bank loans, and in most cases interest is not charged while a student is enrolled in college; repayment is also extended over a long period of time. There are loans for students and parents. Student loans are the most common form of financial assistance to students. They are available for both undergraduate and graduate studies. They are issued by commercial banks and state student loan authorities at an interest rate considerably lower than the current market level and guaranteed by the federal government. The loan must be repaid within a ten-year period beginning six months after the student's graduation.    Federal work study is another type of student financial aid. It is a part-time job co- financed by the government and a college to allow students to earn money to help pay educational expenses. The program encourages community service work and work related to a student's course of study. The salary will be at least minimum wage, but it may be higher, depending on the type of work and skills required. The total federal work study awarded depends on when a student applies, the level of need, and the funding level of a college. An undergraduate student is paid by the hour. A graduate student may be paid by the hour or receive a salary.

Was Magellan Worth Defending

Magellan is intelligent. UT another way you cool describe him is cruel. Another reason he was worth is because he was just try Eng to deliver spices. At that point he was completely innocent But on the other Han d he did lead his crew to their death. So at that point he was not worth defending. Beck cause he left with 270 men and came back with 18 but, Magellan was not one of the 18. So he was not worth defending right now. Another way someone could argue that he was not worth defending is that he made his crew do all the work. Some captions are like that but they probably did a lot more work than he did.Then again he was one of the people who want to sell spices. With that at least some of the spices got to where they were supposed to. So t hat is one big reason why he is worth defending. But still someone could argue both WA Another thing he did was help discover the world. And that is one huge reason why he is worth defending. He also did make a bunch of towns change religion ins, and if they refused he threatened them. People should have the choice of religion, s oh lot Of people would not defend him because of that. He also made his crew eat old biscuits, at rats, and drink yellow water.When he did that he probably got his crew re ally sick. But after all that he is kind worth defending. Was Magellan worth defending? After all the stuff that he did to his crew. But he did have some good in him. My opinion he was worth defending. But I have my reasons. Some of them are he helped discover the world, he was intelligent, h e was just trying to sell spices, and much much more. So for all the bad stuff he did he al so had some good. In my own opinion the good toward the bad. Including Magellan was a kind bad person but he was worth defending.

The Secret of Ella and Micha Chapter 10

Ella I can remember the first time I wanted to kiss Micha as clearly as the day I found my mother dead. Both times were equally as terrifying, but in two different ways. Micha and I had been sitting on the hood of his car at our secret spot tucked away in the trees, staring out at the lake. It was harder than hell to get back to the spot, but the view and serenity made it worth it. It had been quiet between the two of us for a while, which was normal except for the jealousy stirring inside me over Micha's latest hook up, Cassandra. I'd never felt this way before and it puzzled me. It wasn't like the girl was anything special to Micha, but he'd told Ethan that she had the potential to be girlfriend material and it was bugging me. Micha's arms were tucked under his head and his eyes were shut as the sunlight beamed down on him. His shirt had ridden up and I could see his tattoo peeking out. As I stared at it the urge to run my fingers along it drove me crazy. â€Å"I don't like Cassandra,† I abruptly sputtered out, sitting up quickly. Micha's eyebrows knitted as his eyes gradually opened against the sunlight. â€Å"Huh?† â€Å"That Cassandra girl you were talking about the other day,† I said, staring out at the water rippling in the gentle breeze. â€Å"I don't think you should date her.† He rose up on his elbows. â€Å"Because you don't like her?† â€Å"No†¦Ã¢â‚¬  I tucked strands of my auburn hair out of my eyes. â€Å"I just don't want you to date her.† The wind filled the silence. Micha sat up and wrapped an arm around my shoulder. â€Å"Okay, I won't,† he said as if it was as simple as breathing. I pressed back a smile, not fully understanding why the hell I was so happy. Micha lay back down and drew me with him. I rested my head on his chest and listened to his heart beating, steady as a rock, unlike mine which was dancing inside my chest. The longer I stayed in his arms, the more content I became. I felt safe, like nothing could hurt me, but I was in complete denial that I was starting to fall in love with my best friend. *** It's been a week since the car racing incident and I've been hiding out in my bedroom living on mac n' cheese and Diet Dr. Pepper. Dean still hasn't headed home, but Lila did the morning after the race. She wanted to stay, but I didn't want her to and I think her dad wasn't too keen on the idea either. It's been kind of lonely, though. I still haven't listened to Micha's voicemail, and the constant flashing on the screen torments me. I decide to take a break from the house today and do something I've been meaning to do for a while. I want to sketch my mother's grave because I won't always be close enough to visit it. It's been bothering me the entire eight months that I've been gone. I feel guilty because it was me who put her there and then I just left her. I collect my sketch book and pencils from the drawer of my night stand, slip on my shoes and sunglasses, and head out the front door where I'm less likely to run into Micha. It's a warm day and the blue sky glitters with sunshine. I walk up the sidewalk toward Cherry Hill and decide to make a last minute stop at Grady's. I knock on the trailer door and Amy, the nurse, answers it wearing blue scrubs. â€Å"Oh, hi Ella, I don't think Grady's up for any visitors today, sweetie.† â€Å"But he told me to stop by,† I say stupidly. â€Å"I know it's a little later than I told him and I'm sorry.† â€Å"He's not mad at you, Ella,† she says kindly. â€Å"I've just got him hooked up on oxygen and he's got a cough.† I shield my eyes from the sun and stare up at her. â€Å"Is he okay?† She sighs, leaning against the doorframe. â€Å"He's just having a rough day today, but try back in a few days, okay hun.† I nod and back down the steps as she shuts the door. I stare helplessly at the back window which leads to Grady's room. He's sick and there's nothing I can do. I have no control over this. Micha was right. I can't control everything. As horrid images of my mom's death flash through my mind, I run into the field and throw up. *** The town's cemetery is located up on Cherry Hill, which on foot is quite a hike, but I enjoy the break from the reality of life. There is no one up there – there hardly ever is. I push through the gate and situate by a tree right in front of my mom's headstone. It's a small cemetery bordered by trees and the grass is covered with dry leaves. As I sketch the lines of the fence and the vines that coil it, I angle downward and draw the curve of her tombstone. I become lost in the movements, adding wings to the side of it, because she was always so fascinated with flying. A few weeks before her death, my mother begged me to go on a walk with her. I gave in even though I had plans that day. It was sunny and the air smelled like cut grass. It felt like nothing could go wrong. She wanted to go to the bridge so we walked all the way across town to the lake. When we arrived there, she climbed on the railing and spread her hands out to balance as her long auburn hair flapped in the wind. â€Å"Mom, what are you doing?† I said, reaching for the back of her shirt to pull her down. She sidestepped down the railing out of my reach and stared at the water below. â€Å"Ella May, I think I can fly.† â€Å"Mom, stop it and get down,† I said, not taking her very seriously at first. But when she turned her head and looked at me, I could see in her eyes that she wasn't joking. She really believed she could fly. I tried to stay as composed as possible. â€Å"Mom, please get down. You're scaring me.† She shook her head and her legs wobbled a little. â€Å"It's okay honey. I'll be fine. I can feel it in my body that I can fly.† I took a cautious step toward her and my foot bumped the curb of the bridge. The cement rubbed my toe raw and I could feel blood oozing out, but I didn't look down at it. I was too afraid to take my eyes off her. â€Å"Mom, you can't fly. People can't fly.† â€Å"Then maybe I'm a bird,† she said seriously. â€Å"Maybe I have wings and feathers and they can carry me away and I can become one with the wind.† â€Å"You're not a bird!† I shouted and reached for her again, but she hopped onto one of the beams and laughed like it was a game. I tugged my fingers through my hair and steadied onto the railing. It was a far fall, one that would crush our bodies on impact, even in the water. I braced my hands on the beams above my head. â€Å"Mom, if you love me at all, you'll get down.† She shook her head. â€Å"No, I'm going to fly today.† A truck rolled up and stopped on the middle of the bridge as I edged toward her. Ethan jumped out and didn't so much as flinch at the scenario. â€Å"Hey, Mrs. Daniels. How's it going?† I gaped at him and hissed, â€Å"What are you doing?† He ignored me. â€Å"You know it's not really safe out there.† My mom angled her head to the side. â€Å"I think I'll be okay. My wings will carry me away.† I was mortified, but Ethan didn't miss a beat. He rested his arms on the railing. â€Å"As much as that could be true, what if it's not? Then what? I mean is it really worth the risk?† I glanced back at my mom and she looked like she was weighing the options. She stared at the dark water below her feet and then at the bright sky above her head. â€Å"Maybe I should think about it for a little bit.† Ethan nodded. â€Å"I think that's probably a good idea.† She made a path across the beam and planted her feet on the railing. Ethan helped her down and we got her into the backseat of his truck. She fell asleep within minutes and I slumped my head back against the chair. â€Å"How did you do that?† I asked quietly. â€Å"One of my friends was tripping out of their mind one night and I had to talk him out of jumping off the roof,† he explained. â€Å"It was all about making her realize that there was more than one scenario.† I nodded and we stayed quiet for the rest of the drive to my house. Ethan never brought it up to me, nor did he treat me differently and I was grateful for it. After a doctor's visit, it was determined that my mother had started to suffer from ‘Delusions of Grandeur,' which happens sometimes in bipolar patients. I finally pull away from the drawing when it's nearly dark. I gather my sketchpad and pencils and head down the hill. In front of the arch iron entryway is Micha, sitting on the hood of his mom's car, wearing jeans, and a black and red plaid shirt. His head is tipped down and wisps of his blonde hair cover his forehead as he messes around with his phone. I stop a little ways off from him. â€Å"What are you doing here?† His eyes lift from his phone. â€Å"I'm waiting for you.† â€Å"How did you know I was here?† â€Å"I saw you leave with your sketchpad and head this way, so I came up to check on you.† I take a tentative step forward. â€Å"How long have you been sitting here?† He slides off the hood and puts his phone away. â€Å"For a while, but I didn't want to disturb you. You looked too peaceful.† I press my lips together and stare at him, craving to sketch him like I used to. He would sit on my bed and it was like he owned my hand. â€Å"Look, about the other night, I think – â€Å" He strides across the grass toward me, moving so impulsively that there's no time to react as his finger covers my lips. â€Å"Just let it be for a while, okay?† Uncertain of his exact meaning, I nod anyway. He lets his finger fall from my lips, trailing a line down my chest, finally pulling away at the bottom of my stomach. â€Å"You want a ride home?† His voice comes out ragged. I glance at the grey sky and the birds flying across it. â€Å"That would be nice. Thank you.† Micha She's preoccupied during the drive and so am I. I was so pissed off about my father that I got into the car about to do something reckless, however, then I saw Ella wandering down the street, and I followed her. The way she walked was very entertaining, her auburn hair blowing in the wind, and the way she swayed her ass in the short denim shorts she was wearing. It calmed me down watching her sit up on the hill and draw, but I can't stop thinking about the phone conversation. â€Å"We should go somewhere,† I announce when we drive onto the main road. Ella jolts in her seat and turns away from the window. â€Å"I should probably go home.† â€Å"Come on.† I pout, hoping it'll win her over. â€Å"Just come with me somewhere and we can relax.† She's tempted. â€Å"Where exactly?† I turn the volume of the stereo down and let my arm rest on the top of the steering wheel. â€Å"To our spot by the lake.† â€Å"But it takes forever to get there.† Her eyes rise to the dark sky. â€Å"And it's getting late.† â€Å"Since when have you been afraid of the dark?† â€Å"It's not the dark I'm afraid of.† I sigh and downshift. â€Å"Come on, just you and me. We don't even have to talk. We can just sit in silence.† â€Å"Fine,† she surrenders, tossing her sketchpad into the backseat. â€Å"Just as long as you don't ask me questions.† I hold up my hand innocently. â€Å"Scouts honor. I'll keep my questions to myself.† Her eyes narrow. â€Å"I know you've never been in the scouts before.† I laugh, feeling the pressure lift from my chest. â€Å"It doesn't matter. I'll keep my questions to myself, but with everything else, all bets are off.† She pretends to have an itch on her nose, but really it's to obscure her smile and it makes me smile myself. *** Its pitch black by the time we reach our spot on the shore that's secluded by tall trees. The moon reflects against the water and the night air is a little chilly. I get my jacket out of the trunk and offer it to Ella, knowing she's cold because of the goosebumps on her arms and the way her nipples are poking through her shirt. She slips the jacket on and zips it up, covering up her perky nipples. I sigh, hop onto the hood, and open my arms for her to join me. Hesitantly, she climbs onto the hood, but stays at the front, with her feet propped up on the bumper, gazing out at the water. I scoot down by her and keep my knees up, resting my elbows on them. â€Å"What are you thinking about?† Her eyes are huge in the moonlight. â€Å"Death.† â€Å"What about death?† I wonder if we're finally going to go back to that night. â€Å"That Grady's going to die,† she whispers softly. â€Å"And there's nothing I can do about it.† I brush her hair back from her forehead. â€Å"You need to stop worrying about everything that can't be controlled.† She sighs and leans away from my hand. â€Å"That's just it, though. It's all I can think about anymore. It's like this fixation I have no control over which makes no sense because I'm fixated on controlling the uncontrollable.† She's breathing wildly. Shit. I need to calm her down. â€Å"Hey, come here.† I loop my arms around her waist and lie her down on the windshield with me. She rests her head on my chest and I play with her hair, breathing in her vanilla scent. â€Å"Do you remember when you decided that it would be a good idea if you climbed up the scaffolding in the gym?† â€Å"I wanted to prove to Gary Bennitt that I was as tough as the boys.† She buries her face into my shirt, ashamed. â€Å"Why do you remember everything?† â€Å"How could I forget that? You scared the hell out of me when you fell. Yet, somehow you managed to land on the board just below it.† â€Å"I thought I was going to die,† she murmurs. â€Å"I was so stupid.† â€Å"You weren't stupid, you just saw life at a different angle,† I say. â€Å"I've always envied you for it. Like when you used to dance in a room where no one was dancing or how you stuck up for people. But there was always that wall you put up. You would never let anyone completely through.† She's soundless for a while and I expect for her to push me away. But she sits up and hovers over me, her hair veiling our faces. Her breath is ragged, like she's terrified out of her mind. â€Å"I opened up to you once,† she whispers. â€Å"When we were here in this spot doing this same thing.† I can't take my eyes off her lips. â€Å"I'm not sure what you're talking about.† She licks her lips. â€Å"I told you I didn't want you dating Cassandra.† â€Å"Cassandra†¦ Oh, was that what that was about?† I start to laugh. â€Å"What's so funny?† she asks, but I can't stop laughing. She pinches my nipple and I jerk upward, smacking my forehead against hers. â€Å"Ow.† She blinks, rubbing her forehead and a laugh escapes her lips. â€Å"Tell me what's so funny.† She looks beautiful, trying to be pissed, when deep down she's relishing the moment. I'm enjoying myself, which I didn't envisage tonight, but if anyone can cheer me up, it's her. Like when my dad left and she caught me in the garage, clutching onto his tool box crying like a baby. She gave me her Popsicle and then just sat there with me until I ran out of tears. I eye her over and she fusses with her hair self-consciously. With one quick movement, I flip us over so my body is covering hers. â€Å"When I told Ethan about that day when you told me not to see Cassandra, he told me you had a thing for me. He's usually not right about those things.† â€Å"I didn't have a thing for you,† she argues. â€Å"I just didn't want anyone else to have a thing for you.† â€Å"You're adorable when you deny the truth. You always have been.† â€Å"Micha, I used to have studs on every item of clothing I owned and enough black eyeliner to make an entire sketch. That's not adorable.† â€Å"It is on you.† I wink at her. She shakes her head and pokes a finger at my chest. â€Å"Don't try and use your player moves on me.† We remain silent, frozen in the moment, until I finally speak again. â€Å"I have an idea.† Curiosity slowly takes over her face as I shift over her body. My arms are at the side of her head, barely holding my weight up. My face hovers above hers, our lips only an inch apart, and she lies perfectly still. â€Å"I want to kiss you.† She shakes her head promptly. â€Å"I don't think that's a good idea.† I trace one of my fingers over her lips. I've been going about this all wrong. I can't force myself on her. I have to move slow and think of her as a skittish cat that needs to be approached cautiously. â€Å"Just kiss. I swear to God that's all we'll do.† I move my finger away from her lips. â€Å"And kissing's not that scary, right?† â€Å"With you it is,† she says truthfully. â€Å"If you want me not to, just say it.† Taking my time, I leisurely lower my lips toward hers. She stays stationary, her big green eyes targeted on my mouth. Slowly, so she has time to let her thoughts slow down, I caress my lips across hers. A small gasp flees from her lips and I slip my tongue into her mouth. Her hands glide up my back and into my hair. My body conforms to hers as I explore her mouth with my tongue. She bites down on my bottom lip, sucking my lip ring into her mouth before releasing it. Fuck. She's making this hard. I intensify the kiss as my body becomes more impatient, but I keep my promise and only kiss her, even when she fastens her legs around my waist and rubs up against me. Ella He said just kiss and it seemed okay, but now my body has developed a mind of its own. I'm writhing my hips against him enjoying the pleasure erupting inside me. He's hard between my legs as he kisses me so fiercely that my lips are swollen. His fingers tangle in my hair and his tongue plunges deeper and deeper into my mouth the more I rock against him. My head falls back and my eyes open to the stars shining in the sky. It feels like I'm falling or flying†¦ I'm not sure, but whatever it is I can't seem to control it. For a second, I want to capture the moment, put it in a jar, and always have it with me, but panic seizes my mind and I jerk away from his lips. His eyes snap open and his pupils are vast. â€Å"What's wrong?† â€Å"Nothing†¦ It's just†¦ I have to calm down.† I take a deep breath, my skin still tingling in the spots his hands touched. Micha nods, breathless. Carefully, he moves off of me and leans back against the window, securing his hand around mine. We don't speak as we stare up at the sky. He traces his finger along the folds between my fingers and my eyelids drift shut. I feel a wall crumble, leaving behind dust, debris, and pieces that desperately need to be put back together. *** â€Å"Are you okay?† I ask Micha when we pull into my driveway. He's been quiet the whole drive home and I can tell something's bothering him. â€Å"Yeah, I'm fine,† he says with a shrug and then his gaze darts to the back window as headlights shine up behind us. â€Å"Although, you might not be.† My eyebrows furrow. â€Å"Why? What's wrong?† He points a finger at a car parking at the curb in front of my house; a shiny black Mercedes with a familiar blonde-haired driver sitting in it. â€Å"Oh my God, is that Lila's car?† I ask. â€Å"I'm guessing yes, since I doubt anyone around here owns a Mercedes.† Lila climbs out of the car and it's clear that she's been crying. Her eyes are swollen and her cheeks are red. She has her pajama bottoms on and a hoodie pulled over her head. The last time she walked around in an outfit like that she'd just broken up with her boyfriend. â€Å"I think she might have some issues at home,† I tell him, grabbing the door handle. â€Å"She acted like she didn't want to go home.† â€Å"But you didn't ask her about it?† he questions with an arch of his eyebrow. I bite my lip guiltily. â€Å"I wasn't sure I wanted to know the answer.† God, I'm a terrible friend. Lila heads up the driveway and we get out to meet her around the back. Before I can say anything, she hugs me and starts to sob. I tense, not used to being hugged, except by Micha. â€Å"I didn't want to go back there,† she cries. â€Å"I knew this was going to happen.† I look over Lila's head at Micha for help. â€Å"It'll be okay.† He gives me a sympathetic look and mouths, take her inside. I nod and he waves at me, getting back into his car. I guide Lila into the house holding her weight up for her like she's ill. When I get her into my room, she curls up on my bed and hugs a pillow. I wait a minute before I speak. â€Å"Do you want to talk about it?† She shakes her head. â€Å"I just want to go to sleep.† â€Å"Alright.† I turn off the light and collapse onto the trundle. I need to get into my pajamas, but it's been an exhausting day. â€Å"My dad hates me,† Lila whispers through sobs. I freeze and then sit up, squinting at her through the dark. â€Å"I'm sure he doesn't hate you.† â€Å"Yes, he does,† she says. â€Å"He always says so – that he wished he had sons instead of daughters because they're easier to deal with.† â€Å"Are you going to be okay?† I ask, unsure what else to say. â€Å"I will be. It'll just take some time.† Was that the magical cure? Time. I flop back down and fall asleep to the murmur of her sobs.

8 Unique Nursing Careers You Didnt Know Existed

8 Unique Nursing Careers You Didnt Know Existed There are a thousand nursing specialties out there, but most people only know of a handful. If you want to choose nursing as your career, but you want to do something a little different than working in a hospital or office setting, then you might want to consider a few of these more obscure nursing positions. Think outside the hospital! 1. Legal Nursing ConsultantIf you have an interest in law as well as nursing, you could consider becoming certified as an LNC. You’ll work with lawsuits and worker’s comp cases, or as a sort of in-house medical expert as the go-to on terminology, medical practices, and health care. Certification isn’t always required, but it will certainly give you a boost.2. Forensic NursingYou’ll still be treating patients and dressing wounds, but you’ll also be assessing patients to determine whether or not a crime has been committed and collecting evidence. This job might even involve identifying bodies. It’s likely not as glamorous as T.V. shows make it out to be, but still very cool, and you get to play your part in making sure justice is served.3. Cruise Ship NursingSee the world, sail the seas, and live your life where others only vacation. All you have to do is treat the thousands of patients sailing around with you at any given time. The workload is diverse, the people are from all over, the perks are undeniable: you’ll get free room and board plus good vacation time after long stretches of work.4. Camp NursingLove the great outdoors? Were you a camp kid back in the day? Sign up to be the nurse at a summer or wilderness camp to deal with sick campers. You won’t make that much money, comparatively speaking, but you will lead a much more relaxed life (and work life) and get to work with kids, if that’s your preference.5. Flight/Transport NursingRural areas don’t have the kinds of medical resources for emergencies that larger metropolitan areas do. The long ambulance ri des or helicopter flights often require a nurse to ride along to help. Get yourself certified as a CFRN (Certified Flight Registered Nurse) for this always exciting gig. And bonus: the money is pretty great!6. Nursing InformaticsWant to be a nurse but find that you also really love geeking out about technology? You could work in large medical facilities or private consulting firms, keeping up with the newest technology to optimize patient care.7. Parish NursingBring your spirituality and faith to work as a parish nurse, where you can help your patients improve their physical health as well as their overall spiritual well-being. This can be a very rewarding career for the right kind of nurse who wants to serve a specific community. This type of nursing is most common in Christian denominations, but others are starting to pop up as well.8. Hyperbaric NursingThis field is in surprisingly high demand. Hyperbaric nurses treat patients in decompression chambers to relieve multiple kinds o f very serious symptoms. You’ll work with cutting-edge treatments and be at the forefront of helping with this growing medical practice, but this job does come with some physical risk, given how much exposure you’ll have to the decompression chambers.

The 13 Hardest SAT Math Questions Ever

The 13 Hardest SAT Math Questions Ever SAT / ACT Prep Online Guides and Tips Want to test yourself against the most difficult SAT math questions? Want to know what makes these questions so difficult and how best to solve them? If you’re ready to really sink your teeth into the SAT math section and have your sights set on that perfect score, then this is the guide for you. We’ve put together what we believe to be the 13 most difficult questions for the new 2016 SAT, with strategies and answer explanations for each. These are all hard SAT Math questions from College Board SAT practice tests, which means understanding them is one of the best ways to study for those of you aiming for perfection. Image: Sonia Sevilla/Wikimedia Brief Overview of SAT Math The third and fourth sections of the SAT will always be math sections. The first math subsection (labeled "3") does not allow you to use a calculator, while the second math subsection (labeled as "4") does allow the use of a calculator. Don't worry too much about the no-calculator section, though: if you're not allowed to use a calculator on a question, it means you don’t need a calculator to answer it. Each math subsection is arranged in order of ascending difficulty (where the longer it takes to solve a problem and the fewer people who answer it correctly, the more difficult it is). On each subsection, question 1 will be â€Å"easy† and question 15 will be considered â€Å"difficult.† However, the ascending difficulty resets from easy to hard on the grid-ins. Hence, multiple choice questions are arranged in increasing difficulty (questions 1 and 2 will be the easiest, questions 14 and 15 will be the hardest), but the difficulty level resets for the grid-in section (meaning questions 16 and 17 will again be â€Å"easy† and questions 19 and 20 will be very difficult). With very few exceptions, then, the most difficult SAT math problems will be clustered at the end of the multiple choice segments or the second half of the grid-in questions. In addition to their placement on the test, though, these questions also share a few other commonalities. In a minute, we'll look at example questions and how to solve them, then analyze them to figure out what these types of questions have in common. But First: Should You Be Focusing on the Hardest Math Questions Right Now? If you’re just getting started in your study prep (or if you’ve simply skipped this first, crucial step), definitely stop and take a full practice test to gauge your current scoring level. Check out our guide to all the free SAT practice tests available online and then sit down to take a test all at once. The absolute best way to assess your current level is to simply take the SAT practice test as if it were real, keeping strict timing and working straight through with only the allowed breaks (we know- probably not your favorite way to spend a Saturday). Once you’ve got a good idea of your current level and percentile ranking, you can set milestones and goals for your ultimate SAT Math score. If you’re currently scoring in the 200-400 or the 400-600 range on SAT Math, your best bet is first to check out our guide to improving your math score to be consistently at or over a 600 before you start in trying to tackle the most difficult math problems on the test. If, however, you're already scoring above a 600 on the Math section and want to test your mettle for the real SAT, then definitely proceed to the rest of this guide. If you’re aiming for perfect (or close to), then you’ll need to know what the most difficult SAT math questions look like and how to solve them. And luckily, that’s exactly what we’ll do. WARNING: Since there are a limited number of official SAT practice tests, you may want to wait to read this article until you've attempted all or most of the first four official practice tests (since the questions below were taken from those tests). If you're worried about spoiling those tests, stop reading this guide now; come back and read it when you've completed them. Now let's get to our list of questions (whoo)! Image: Niytx/DeviantArt The 13 Hardest SAT Math Questions Now that you’re sure you should be attempting these questions, let’s dive right in! We've curated 13 of the most difficult SAT Math questions for you to try below, along with walkthroughs of how to get the answer (if you're stumped). No Calculator SAT Math Questions Question 1 $$C=5/9(F-32)$$ The equation above shows how temperature $F$, measured in degrees Fahrenheit, relates to a temperature $C$, measured in degrees Celsius. Based on the equation, which of the following must be true? A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of $5/9$ degree Celsius. A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit. A temperature increase of $5/9$ degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius. A) I onlyB) II onlyC) III onlyD) I and II only ANSWER EXPLANATION:Think of the equation as an equation for a line $$y=mx+b$$ where in this case $$C= {5}/{9} (F−32)$$ or $$C={5}/{9}F −{5}/{9}(32)$$ You can see the slope of the graph is ${5}/{9}$, which means that for an increase of 1 degree Fahrenheit, the increase is ${5}/{9}$ of 1 degree Celsius. $$C= {5}/{9} (F)$$ $$C= {5}/{9} (1)= {5}/{9}$$ Therefore, statement I is true. This is the equivalent to saying that an increase of 1 degree Celsius is equal to an increase of ${9}/{5}$ degrees Fahrenheit. $$C= {5}/{9} (F)$$ $$1= {5}/{9} (F)$$ $$(F)={9}/{5}$$ Since ${9}/{5}$ = 1.8, statement II is true. The only answer that has both statement I and statement II as true is D, but if you have time and want to be absolutely thorough, you can also check to see if statement III (an increase of ${5}/{9}$ degree Fahrenheit is equal to a temperature increase of 1 degree Celsius) is true: $$C= {5}/{9} (F)$$ $$C= {5}/{9} ({5}/{9})$$ $$C= {25} /{81} (\which \is ≠  1)$$ An increase of $5/9$ degree Fahrenheit leads to an increase of ${25}/{81}$, not 1 degree, Celsius, and so Statement III is not true. The final answer is D. Question 2 The equation ${24x^2 + 25x -47}/{ax-2} = -8x-3-{53/{ax-2}}$ is true for all values of $x≠ 2/a$, where $a$ is a constant. What is the value of $a$? A) -16B) -3C) 3D) 16 ANSWER EXPLANATION: There are two ways to solve this question. The faster way is to multiply each side of the given equation by $ax-2$ (so you can get rid of the fraction). When you multiply each side by $ax-2$, you should have: $$24x^2 + 25x - 47 = (-8x-3)(ax-2) - 53$$ You should then multiply $(-8x-3)$ and $(ax-2)$ using FOIL. $$24x^2 + 25x - 47 = -8ax^2 - 3ax +16x + 6 - 53$$ Then, reduce on the right side of the equation $$24x^2 + 25x - 47 = -8ax^2 - 3ax +16x - 47$$ Since the coefficients of the $x^2$-term have to be equal on both sides of the equation, $−8a = 24$, or $a = −3$. The other option which is longer and more tedious is to attempt to plug in all of the answer choices for a and see which answer choice makes both sides of the equation equal. Again, this is the longer option, and I do not recommend it for the actual SAT as it will waste too much time. The final answer is B. Question 3 If $3x-y = 12$, what is the value of ${8^x}/{2^y}$? A) $2^{12}$B) $4^4$C) $8^2$D) The value cannot be determined from the information given. ANSWER EXPLANATION: One approach is to express $${8^x}/{2^y}$$ so that the numerator and denominator are expressed with the same base. Since 2 and 8 are both powers of 2, substituting $2^3$ for 8 in the numerator of ${8^x}/{2^y}$ gives $${(2^3)^x}/{2^y}$$ which can be rewritten $${2^3x}/{2^y}$$ Since the numerator and denominator of have a common base, this expression can be rewritten as $2^(3x−y)$. In the question, it states that $3x − y = 12$, so one can substitute 12 for the exponent, $3x − y$, which means that $${8^x}/{2^y}= 2^12$$ The final answer is A. Question 4 $${8-i}/{3-2i}$$ If the expression above is rewritten in the form $a+bi$, where $a$ and $b$ are real numbers, what is the value of $a$? (Note: $i=√{-1}$) ANSWER EXPLANATION: To rewrite ${8-i}/{3-2i}$ in the standard form $a + bi$, you need to multiply the numerator and denominator of ${8-i}/{3-2i}$ by the conjugate, $3 + 2i$. This equals $$({8-i}/{3-2i})({3+2i}/{3+2i})={24+16i-3+(-i)(2i)}/{(3^2)-(2i)^2}$$ Since $i^2=-1$, this last fraction can be reduced simplified to $$ {24+16i-3i+2}/{9-(-4)}={26+13i}/{13}$$ which simplifies further to $2 + i$. Therefore, when${8-i}/{3-2i}$ is rewritten in the standard form a + bi, the value of a is 2. The final answer is A. Question 5 In triangle $ABC$, the measure of $∠ B$ is 90 °, $BC=16$, and $AC$=20. Triangle $DEF$ is similar to triangle $ABC$, where vertices $D$, $E$, and $F$ correspond to vertices $A$, $B$, and $C$, respectively, and each side of triangle $DEF$ is $1/3$ the length of the corresponding side of triangle $ABC$. What is the value of $sinF$? ANSWER EXPLANATION: Triangle ABC is a right triangle with its right angle at B. Therefore, $\ov {AC}$ is the hypotenuse of right triangle ABC, and $\ov {AB}$ and $\ov {BC}$ are the legs of right triangle ABC. According to the Pythagorean theorem, $$AB =√{20^2-16^2}=√{400-256}=√{144}=12$$ Since triangle DEF is similar to triangle ABC, with vertex F corresponding to vertex C, the measure of $\angle ∠  {F}$ equals the measure of $\angle ∠  {C}$. Therefore, $sin F = sin C$. From the side lengths of triangle ABC, $$sinF ={\opposite \side}/{\hypotenuse}={AB}/{AC}={12}/{20}={3}/{5}$$ Therefore, $sinF ={3}/{5}$. The final answer is ${3}/{5}$ or 0.6. Calculator-Allowed SAT Math Questions Question 6 The incomplete table above summarizes the number of left-handed students and right-handed students by gender for the eighth grade students at Keisel Middle School. There are 5 times as many right-handed female students as there are left-handed female students, and there are 9 times as many right-handed male students as there are left-handed male students. if there is a total of 18 left-handed students and 122 right-handed students in the school, which of the following is closest to the probability that a right-handed student selected at random is female? (Note: Assume that none of the eighth-grade students are both right-handed and left-handed.) A) 0.410B) 0.357C) 0.333D) 0.250 ANSWER EXPLANATION: In order to solve this problem, you should create two equations using two variables ($x$ and $y$) and the information you’re given. Let $x$ be the number of left-handed female students and let $y$ be the number of left-handed male students. Using the information given in the problem, the number of right-handed female students will be $5x$ and the number of right-handed male students will be $9y$. Since the total number of left-handed students is 18 and the total number of right-handed students is 122, the system of equations below must be true: $$x + y = 18$$ $$5x + 9y = 122$$ When you solve this system of equations, you get $x = 10$ and $y = 8$. Thus, 5*10, or 50, of the 122 right-handed students are female. Therefore, the probability that a right-handed student selected at random is female is ${50}/{122}$, which to the nearest thousandth is 0.410. The final answer is A. Questions 7 8 Use the following information for both question 7 and question 8. If shoppers enter a store at an average rate of $r$ shoppers per minute and each stays in the store for average time of $T$ minutes, the average number of shoppers in the store, $N$, at any one time is given by the formula $N=rT$. This relationship is known as Little's law. The owner of the Good Deals Store estimates that during business hours, an average of 3 shoppers per minute enter the store and that each of them stays an average of 15 minutes. The store owner uses Little's law to estimate that there are 45 shoppers in the store at any time. Question 7 Little's law can be applied to any part of the store, such as a particular department or the checkout lines. The store owner determines that, during business hours, approximately 84 shoppers per hour make a purchase and each of these shoppers spend an average of 5 minutes in the checkout line. At any time during business hours, about how many shoppers, on average, are waiting in the checkout line to make a purchase at the Good Deals Store? ANSWER EXPLANATION: Since the question states that Little’s law can be applied to any single part of the store (for example, just the checkout line), then the average number of shoppers, $N$, in the checkout line at any time is $N = rT$, where $r$ is the number of shoppers entering the checkout line per minute and $T$ is the average number of minutes each shopper spends in the checkout line. Since 84 shoppers per hour make a purchase, 84 shoppers per hour enter the checkout line. However, this needs to be converted to the number of shoppers per minute (in order to be used with $T = 5$). Since there are 60 minutes in one hour, the rate is ${84 \shoppers \per \hour}/{60 \minutes} = 1.4$ shoppers per minute. Using the given formula with $r = 1.4$ and $T = 5$ yields $$N = rt = (1.4)(5) = 7$$ Therefore, the average number of shoppers, $N$, in the checkout line at any time during business hours is 7. The final answer is 7. Question 8 The owner of the Good Deals Store opens a new store across town. For the new store, the owner estimates that, during business hours, an average of 90 shoppers per hour enter the store and each of them stays an average of 12 minutes. The average number of shoppers in the new store at any time is what percent less than the average number of shoppers in the original store at any time? (Note: Ignore the percent symbol when entering your answer. For example, if the answer is 42.1%, enter 42.1) ANSWER EXPLANATION: According to the original information given, the estimated average number of shoppers in the original store at any time (N) is 45. In the question, it states that, in the new store, the manager estimates that an average of 90 shoppers per hour (60 minutes) enter the store, which is equivalent to 1.5 shoppers per minute (r). The manager also estimates that each shopper stays in the store for an average of 12 minutes (T). Thus, by Little’s law, there are, on average, $N = rT = (1.5)(12) = 18$ shoppers in the new store at any time. This is $${45-18}/{45} x 100 = 60$$ percent less than the average number of shoppers in the original store at any time. The final answer is 60. Question 9 A grain silo is built from two right circular cones and a right circular cylinder with internal measurements represented by the figure above. Of the following, which is closest to the volume of the grain silo, in cubic feet? A) 261.8B) 785.4C) 916.3D) 1047.2 ANSWER EXPLANATION: The volume of the grain silo can be found by adding the volumes of all the solids of which it is composed (a cylinder and two cones). The silo is made up of a cylinder (with height 10 feet and base radius 5 feet) and two cones (each with height 5 ft and base radius 5 ft). The formulas given at the beginning of the SAT Math section: Volume of a Cone $$V={1}/{3}Ï€r^2h$$ Volume of a Cylinder $$V=Ï€r^2h$$ can be used to determine the total volume of the silo. Since the two cones have identical dimensions, the total volume, in cubic feet, of the silo is given by $$V_{silo}=Ï€(5^2)(10)+(2)({1}/{3})Ï€(5^2)(5)=({4}/{3})(250)Ï€$$ which is approximately equal to 1,047.2 cubic feet. The final answer is D. Question 10 If $x$ is the average (arithmetic mean) of $m$ and $9$, $y$ is the average of $2m$ and $15$, and $z$ is the average of $3m$ and $18$, what is the average of $x$, $y$, and $z$ in terms of $m$? A) $m+6$B) $m+7$C) $2m+14$D) $3m + 21$ ANSWER EXPLANATION: Since the average (arithmetic mean) of two numbers is equal to the sum of the two numbers divided by 2, the equations $x={m+9}/{2}$, $y={2m+15}/{2}$, $z={3m+18}/{2}$are true. The average of $x$, $y$, and $z$ is given by ${x + y + z}/{3}$. Substituting the expressions in m for each variable ($x$, $y$, $z$) gives $$[{m+9}/{2}+{2m+15}/{2}+{3m+18}/{2}]/3$$ This fraction can be simplified to $m + 7$. The final answer is B. Question 11 The function $f(x)=x^3-x^2-x-{11/4}$ is graphed in the $xy$-plane above. If $k$ is a constant such that the equation $f(x)=k$ has three real solutions, which of the following could be the value of $k$? ANSWER EXPLANATION: The equation $f(x) = k$ gives the solutions to the system of equations $$y = f(x) = x^3-x^2-x-{11}/{4}$$ and $$y = k$$ A real solution of a system of two equations corresponds to a point of intersection of the graphs of the two equations in the $xy$-plane. The graph of $y = k$ is a horizontal line that contains the point $(0, k)$ and intersects the graph of the cubic equation three times (since it has three real solutions). Given the graph, the only horizontal line that would intersect the cubic equation three times is the line with the equation $y = −3$, or $f(x) = −3$. Therefore, $k$ is $-3$. The final answer is D. Question 12 $$q={1/2}nv^2$$ The dynamic pressure $q$ generated by a fluid moving with velocity $v$ can be found using the formula above, where $n$ is the constant density of the fluid. An aeronautical engineer users the formula to find the dynamic pressure of a fluid moving with velocity $v$ and the same fluid moving with velocity 1.5$v$. What is the ratio of the dynamic pressure of the faster fluid to the dynamic pressure of the slower fluid? ANSWER EXPLANATION: To solve this problem, you need to set up to equations with variables. Let $q_1$ be the dynamic pressure of the slower fluid moving with velocity $v_1$, and let $q_2$ be the dynamic pressure of the faster fluid moving with velocity $v_2$. Then $$v_2 =1.5v_1$$ Given the equation $q = {1}/{2}nv^2$, substituting the dynamic pressure and velocity of the faster fluid gives $q_2 = {1}/{2}n(v_2)^2$. Since $v_2 =1.5v_1$, the expression $1.5v_1$ can be substituted for $v_2$ in this equation, giving $q_2 = {1}/{2}n(1.5v_1)^2$. By squaring $1.5$, you can rewrite the previous equation as $$q_2 = (2.25)({1}/{2})n(v_1)^2 = (2.25)q_1$$ Therefore, the ratio of the dynamic pressure of the faster fluid is $${q2}/{q1} = {2.25 q_1}/{q_1}= 2.25$$ The final answer is 2.25 or 9/4. Question 13 For a polynomial $p(x)$, the value of $p(3)$ is $-2$. Which of the following must be true about $p(x)$? A) $x-5$ is a factor of $p(x)$.B) $x-2$ is a factor of $p(x)$.C) $x+2$ is a factor of $p(x)$.D) The remainder when $p(x)$ is divided by $x-3$ is $-2$. ANSWER EXPLANATION: If the polynomial $p(x)$ is divided by a polynomial of the form $x+k$ (which accounts for all of the possible answer choices in this question), the result can be written as $${p(x)}/{x+k}=q(x)+{r}/{x+k}$$ where $q(x)$ is a polynomial and $r$ is the remainder. Since $x + k$ is a degree-1 polynomial (meaning it only includes $x^1$ and no higher exponents), the remainder is a real number. Therefore, $p(x)$ can be rewritten as $p(x) = (x + k)q(x) + r$, where $r$ is a real number. The question states that $p(3) = -2$, so it must be true that $$-2 = p(3) = (3 + k)q(3) + r$$ Now we can plug in all the possible answers. If the answer is A, B, or C, $r$ will be $0$, while if the answer is D, $r$ will be $-2$. A. $-2 = p(3) = (3 + (-5))q(3) + 0$$-2=(3-5)q(3)$$-2=(-2)q(3)$ This could be true, but only if $q(3)=1$ B. $-2 = p(3) = (3 + (-2))q(3) + 0$$-2 = (3-2)q(3)$$-2 = (-1)q(3)$ This could be true, but only if $q(3)=2) C. $-2 = p(3) = (3 + 2)q(3) + 0$$-2 = (5)q(3)$ This could be true, but only if $q(3)={-2}/{5}$ D. $-2 = p(3) = (3 + (-3))q(3) + (-2)$$-2 = (3 - 3)q(3) + (-2)$$-2 = (0)q(3) + (-2)$ This will always be true no matter what $q(3)$ is. Of the answer choices, the only one that must be true about $p(x)$ is D, that the remainder when $p(x)$ is divided by $x-3$ is -2. The final answer is D. Want to improve your SAT score by 160 points? We've written a guide about the top 5 strategies you must be using to have a shot at improving your score. Download it for free now: You deserve all the naps after running through those questions. What Do the Hardest SAT Math Questions Have in Common? It’s important to understand what makes these hard questions â€Å"hard.† By doing so, you’ll be able to both understand and solve similar questions when you see them on test day, as well as have a better strategy for identifying and correcting your previous SAT math errors. In this section, we’ll look at what these questions have in common and give examples of each type. Some of the reasons why the hardest math questions are the hardest math questions is because they: #1: Test Several Mathematical Concepts at Once Here, we must deal with imaginary numbers and fractions all at once. Secret to success: Think of what applicable math you could use to solve the problem, do one step at a time, and try each technique until you find one that works! #2: Involve a Lot of Steps Remember: the more steps you need to take, the easier to mess up somewhere along the line! We must solve this problem in steps (doing several averages) to unlock the rest of the answers in a domino effect. This can get confusing, especially if you're stressed or running out of time. Secret to success: Take it slow, take it step by step, and double-check your work so you don't make mistakes! #3: Test Concepts That You Have Limited Familiarity With For example, many students are less familiar with functions than they are with fractions and percentages, so most function questions are considered â€Å"high difficulty† problems. If you don't know your way around functions, this would be a tricky problem. Secret to success: Review math concepts that you don't have as much familiarity with such as functions. We suggest using our great free SAT Math review guides. #4: Are Worded in Unusual or Convoluted Ways It can be difficult to figure out exactly what some questions are asking, much less figure out how to solve them. This is especially true when the question is located at the end of the section, and you are running out of time. Because this question provides so much information without a diagram, it can be difficult to puzzle through in the limited time allowed. Secret to success: Take your time, analyze what is being asked of you, and draw a diagram if it's helpful to you. #5: Use Many Different Variables With so many different variables in play, it is quite easy to get confused. Secret to success: Take your time, analyze what is being asked of you, and consider if plugging in numbers is a good strategy to solve the problem (it wouldn't be for the question above, but would be for many other SAT variable questions). The Take-Aways The SAT is a marathon and the better prepared you are for it, the better you'll feel on test day. Knowing how to handle the hardest questions the test can throw at you will make taking the real SAT seem a lot less daunting. If you felt that these questions were easy, make sure not underestimate the effect of adrenaline and fatigue on your ability to solve problems. As you continue to study, always adhere to the proper timing guidelines and try to take full tests whenever possible. This is the best way to recreate the actual testing environment so that you can prepare for the real deal. If you felt these questions were challenging, be sure to strengthen your math knowledge by checking out our individual math topic guides for the SAT. There, you'll see more detailed explanations of the topics in question as well as more detailed answer breakdowns. What’s Next? Felt that these questions were harder than you were expecting? Take a look at all the topics covered in the SAT math section and then note which sections were particular difficulty for you. Next, take a gander at our individual math guides to help you shore up any of those weak areas. Running out of time on the SAT math section? Our guide will help you beat the clock and maximize your score. Aiming for a perfect score? Check out our guide on how to get a perfect 800 on the SAT math section, written by a perfect-scorer. Want to improve your SAT score by 160 points? Check out our best-in-class online SAT prep classes. We guarantee your money back if you don't improve your SAT score by 160 points or more. Our classes are entirely online, and they're taught by SAT experts. If you liked this article, you'll love our classes. Along with expert-led classes, you'll get personalized homework with thousands of practice problems organized by individual skills so you learn most effectively. We'll also give you a step-by-step, custom program to follow so you'll never be confused about what to study next. Try it risk-free today:

Read attachment Essay Example | Topics and Well Written Essays - 1000 words

Read attachment - Essay Example In his thesis, Turner points out that America is unique due to a number of reasons that include the settlement by White people, the existence of large areas of free land and its continuous recession as well as the Westward advancement of American settlement. He further argues that it is these three attributes that are the central story of American history. A number of historical events can be noted to arguably support this thesis. One of these events is the Bacon’s rebellion. The Bacon’s rebellion is noted to have occurred over a period of several months in Tidewater Virginia. The rebellion was brought about by a rapidly growing shortage of available land as well as the colony’s relatively complicated relations with both the hostile and friendly tribes of Native Americans. Noble (42), points out that in one of his essays, Turner points out that the Bacon’s rebellion was essentially the first attempt of the American people to attempt to throw out both the British authority as well as the colonial aristocracy. As is characteristic of Turner’s thesis, the eastern authority was able to gradually push inland into the American frontier to the fall line of the rivers that served to end the existence of this first frontier. Turner’s thesis is also noted to be supported by the ideology behind Manifest Destiny. The ideology behind this phrase was that it was indeed the providential mission of the United States to ensure that it extends itself over the frontier as this was essentially a God-given national right. In this regard, the American frontier is noted to have quickly moved across the nation although this was not done in a uniform manner. Americans believed that all the land spanning form the Pacific to the Atlantic should be filled. When all this area was eventually filled in 1893, Turner proclaimed that the American Frontier was closed. It was during this time that the United States started moving towards a