Intramurals Reflection Essay

Intramurals 2012 had the theme of: â€Å"Four Teams. One Goal. One Epic Olympics.† This years event marks my first Intramurals as a student of UP Cebu. I was so excited for this event because in my previous school we didn’t have the facilities for sports so, our intramurals had very limited activities. Unfortunately I didn’t get to participate in any of the sports this year but, I did participate during the parade as a flag bearer. Although the sun was burning, the practices were early, and it took away a part of my free time, it was all worth while when Ms. Empleo told us that the flags looked really nice during the parade. During the succeeding days, I watched most of the games and cheered for my division. I also helped with the preparations of the candidates for â€Å"Mister and Miss Fitness†. I had so much fun watching the teachers dance ballroom! It just goes to show that our teachers can do a whole lot more than just teach inside the classroom. After a whole week of cheering, screaming, and yelling for my division, I can say that its a miracle I didn’t loose my voice. In my opinion and based on my experience, Intramurals is the time where you get to know other people better and where you get to make new friends in your division or cluster because earlier during the semester as a freshman, you aren’t really given the chance to do so. Also, during the events, your inner determination is being brought out, as well as teamwork and cooperation. I noticed that there were some controversies and the competition was very heated. This cannot be avoided in any competition. It just shows how much school spirit we have, and how determined we are to win. It also shows that if your team is still standing strong despite the controversies, it means that your team has truly captured the essence of unity. Being a Management student, there was a great deal of pressure for my division to defend their title as overall champions, and champions for the cheer dance competition. I saw how sad everyone was, when the results of the cheer dance competition were announced. Sadly, this year we lost our title as champs .A lot of tears were shed but, eventually we all accepted it and moved on. Not winning just gives us the opportunity to try harder next year in order to redeem ourselves. Intramurals was a week of fun for me. It was nice to have a break from schoolwork and exams. It also gave me the opportunity to have fun with my fellow school mates. I’m hoping that next year, I will be able to participate more and be able to contribute a greater deal to my cluster, and maybe the Management Division will gain back their title as champs. Overall, So many lessons and values can be learned from intramurals. I am glad that most if not all schools practice this event annually. It not only promotes health and fitness but values as well. We learn values such as: teamwork, unity, loyalty, cooperation, school spirit, humility, determination and many more. I look forward for next year’s intramurals, and I’m excited with what it has in store for us.

Bloodsucking Fiends: A Love Story Chapter 13~14

Chapter 13 To-Do List of the Fashionably Doomed When you know the future is grim, there is no need for speed. Tommy decided to walk to the financial district. He shuffled along with the hang-dog look of the cosmically fucked. He walked through Chinatown, spotted three of the Wongs buying lottery tickets at a liquor store, and headed up to the room to get his typewriter and clothes before they returned. His spirits lifted a little when he climbed down the narrow stairway for the last time, but Madame Natasha's words came back to dump on him again: â€Å"I don't see a woman in your near future.† It had been one of the reasons he had come to San Francisco – to find a girlfriend. Someone who would see him as an artist. Not like the girls back home, who saw him as a bookish freak. It was all part of the plan: live in the City, write stories, look at the bridge, ride cable cars, eat Rice-A-Roni, and have a girlfriend – someone he could tell his thoughts to, preferably after hours of godlike sex. He wasn't looking for perfection, just someone who made him feel secure enough to be insecure around. But not now. Now he was doomed. He looked up at the skyline and realized that he had navigated wrong, arriving in the financial district, several blocks from the Pyramid. He zigzagged from block to block, avoiding eye contact with the men and women in business suits, who avoided eye contact in turn by checking their watches every few steps. Sure, he thought, they can check their watches. They have a future. He arrived at the foot of the Pyramid a little breathless, his arms aching from carrying his belongings. He sat on a concrete bench at the edge of a fountain and watched people for a while. They were all so determined. They had places to go, people to see. Their hair was perfect. They smelled good. They wore nice shoes. He looked at his own worn leather sneakers. Fucked. Someone sat down next to him on the bench and he avoided looking up, thinking that it would just be another person who would make him feel inferior. He was staring at a spot on the concrete by his feet when a Boston terrier appeared on the spot and blew a jet stream of dog snot on his pant leg. â€Å"Bummer, that's rude,† the Emperor said. â€Å"Can't you see that our friend is sulking?† Tommy looked up into the face of the Emperor. â€Å"Your Highness. Hello.† The man had the wildest eyebrows Tommy had ever seen, as if two gray porcupines were perched on his brow. The Emperor tipped his crown, a fedora made of panels cut from beer cans and laced together with yellow yarn. â€Å"Did you get the job?† â€Å"Yes, they hired me that day. Thanks for the tip.† â€Å"It's honest work,† the Emperor said. â€Å"There's a certain grace in that. Not like this tragedy.† â€Å"What tragedy?† â€Å"These poor souls. These poor pathetic souls.† The Emperor gestured toward the passersby. â€Å"I don't understand,† Tommy said. â€Å"Their time has passed and they don't know what to do. They were told what they wanted and they believed it. They can only keep their dream alive by being with others like themselves who will mirror their illusions.† â€Å"They have really nice shoes,† Tommy said. â€Å"They have to look right or their peers will turn on them like starving dogs. They are the fallen gods. The new gods are producers, creators, doers. The new gods are the chinless techno-children who would rather eat white sugar and watch science-fiction films than worry about what shoes they wear. And these poor souls desperately push papers around hoping that a mystical message will appear to save them from the new, awkward, brilliant gods and their silicon-chip reality. Some of them will survive, of course, but most will fall. Uncreative thinking is done better by machines. Poor souls, you can almost hear them sweating.† Tommy looked at the well-dressed stream of business people, then at the Emperor's tattered overcoat, then at his own sneakers, then at the Emperor again. For some reason, he felt better than he had a few minutes before. â€Å"You really worry about these people, don't you?† â€Å"It is my lot.† An attractive woman in a gray suit and heels approached the Emperor and handed him a five-dollar bill. She wore a silk camisole under her jacket and Tommy could make out the top of her lace bra when she bent over. He was mesmerized. â€Å"Your Highness,† she said, â€Å"there's a Chinese chicken salad on special at the Cafe Suisse today. I think Bummer and Lazarus would love it.† Lazarus wagged his tail. Bummer yapped at the mention of his name. â€Å"Very thoughtful of you, my child. The men will enjoy it.† â€Å"Have a good day,† she said, and walked away. Tommy watched her calves as she went. Two men who were passing by, embroiled in an argument about prices and earnings, stopped their conversation and nodded to the Emperor. â€Å"Go with God,† the Emperor said. He turned back to Tommy. â€Å"Are you still looking for a domicile, or just a woman now?† â€Å"I don't understand.† â€Å"You wear your loneliness like a badge.† Tommy felt as if his ego had just taken a right to the jaw. â€Å"Actually, I met a girl and I'm going to rent us a place this afternoon.† â€Å"My mistake,† the Emperor said. â€Å"I misread you.† â€Å"No, you didn't. I'm fucked.† â€Å"Pardon?† â€Å"A fortune-teller told me that there was no woman in my future.† â€Å"Madame Natasha?† â€Å"How did you know?† â€Å"You mustn't give too much credence to Madame Natasha's predictions. He's dying and it darkens his vision. The plague.† â€Å"I'm sorry,† Tommy said. In fact, he felt relieved, then guilty for the reason behind it. He had no right to feel sorry for himself. The Emperor had nothing except his dogs, yet his sympathy was all directed toward his fellowman. I'm scum, Tommy thought. He said, â€Å"Your Highness, I have a little money now, if you need†¦Ã¢â‚¬  The Emperor held up the bill the woman had given him. â€Å"We have all that we need, my son.† He stood and tugged on the ropes that held Bummer and Lazarus. â€Å"And I should be off before the men revolt from hunger.† â€Å"Me, too, I guess.† Tommy stood and made as if to shake hands, then bowed instead. â€Å"Thanks for the company.† The Emperor winked, spun on one heel, and started to lead his troops away, then stopped and turned back. â€Å"And, son, don't touch anything with an edge while you're in the building? Scissors, letter openers, anything.† â€Å"Why?† Tommy asked. â€Å"It's the shape of the building, a pyramid. They'd rather people not know about it, but they have a full-time employee who just goes around dulling the letter openers.† â€Å"You're kidding.† â€Å"Safety first,† the Emperor said. â€Å"Thanks.† Tommy took a deep breath and steeled himself for his assault on the Pyramid. As he walked out of the sun and under the massive concrete buttresses, he could feel a chill through his flannel shirt, as if the concrete had stored the damp cold of the night fog and was radiating it like a refrigerator coil. He was shivering by the time he reached the information desk. A guard eyed him suspiciously. â€Å"Can I help you?† â€Å"I'm looking for the Transamerica personnel department.† The guard made a face as if Tommy had been dipped in sewage. â€Å"Do you have an appointment?† â€Å"Yes.† Tommy waved Jody's papers under the guard's nose. The guard picked up a phone and was punching numbers when a second guard came up behind him and took the receiver. â€Å"He's fine,† the second guard said. â€Å"Send him up.† â€Å"But – â€Å" â€Å"He's a friend of the Emperor.† The first guard hung up the phone and said, â€Å"Twenty-first floor, sir.† He pointed to the elevators. Tommy took an elevator to the twenty-first floor, then followed the signs until he found the right department. An officious-looking older woman told him to have a seat in the reception room, she would be right with him. Then she took great pains to act as if he had been sucked off the planet. Tommy sat on a black leather sofa that sighed with his weight, chose a magazine from the black stone coffee table, and waited. During the next hour he read a household-hints column (â€Å"Coffee grounds in that cat box will fill your house with the delightful aroma of brewing espresso every time kitty heeds the call†); an article on computer junkies (â€Å"Bruce has been off the mouse for six months now, but he says he takes life one byte at a time†); and a review of the new musical Jonestown! (â€Å"Andrew Lloyd Webber's version of the Kool-Aid jingle is at once chilling and evocative. Donny Osmond is brilliant as Jim Jones.†) He borrowed some whiteout from the officious-looking woman and touched up the finish on his sneakers, then dried them under a halogen reading light that looked like a robot's arm holding the sun. When he started pulling cologne sample cards out of GQ and rubbing them on his socks, the woman told him he could go on in. He picked up his shoes and walked into the office in his stocking feet. Another officious-looking woman, who looked remarkably like the first officious-looking woman, down to the little chain on her reading glasses, had him sit down across from her while she looked at Jody's papers and ignored him. She consulted a computer screen, tapped on a few keys, then waited while the computer did something. Tommy put his shoes on and waited. She didn't look up. He cleared his throat. She tapped on the keys. He reached down, opened his suitcase, and took out his portable typewriter. She didn't look up. She tapped and looked at the screen. He opened the typewriter case, rolled a piece of paper in the machine, and tapped on a few keys. She looked up. He tapped a few more keys. â€Å"What are you doing?† she asked. Tommy tapped. He didn't look up. The woman raised her voice. â€Å"I said, what are you doing?† Tommy kept typing and looked up. â€Å"Pardon me, I was ignoring you. What did you say?† â€Å"What are you doing?† She repeated. â€Å"It's a note. Let me read it for you. ‘Couldn't anyone else see that they were all slaves of Satan? I had to cleanse the world of their evil. I am the hand of God. Why else would security have let me into the building with an assault rifle in my suitcase? I am a divine instrument. † Tommy paused and looked up. â€Å"That's all I have so far, but I'll guess I end it with an apology to my mom. What do you think?† She smiled as if hiding gas pains and handed him an envelope. â€Å"This is Jody's final paycheck. Give her our best. And you have a nice day now, young man.† â€Å"You too,† Tommy said. He gathered up his stuff and left the office whistling. Fashionable SOMA looked to Tommy an awful lot like a light industrial area: two- and three-story buildings with steel roll-up doors and steel-framed windows. The bottom floors housed ethnic restaurants, underground dance clubs, auto-repair shops, and the occasional foundry. Tommy paused outside of one to watch two long-haired men pouring bronze into a mold. Artists, Tommy thought. He had never seen a real artist, and although these guys looked more like bikers, he wanted to talk to them. He took a tentative step through the doorway. â€Å"Hi,† he said. The men were wrestling with a huge ladle, the two of them gripping the long metal handle with asbestos gloves. One looked up. â€Å"Out!† he said. Tommy said, â€Å"Okay, I can see you guys are busy. ‘Bye.† He stood on the sidewalk and checked his map. He was supposed to meet the rental agent somewhere around here. He looked up and down the street. Except for a guy passed out on the corner, the street was empty. Tommy was thinking about waking the guy up and asking him if this was, indeed, the fashionable part of SOMA, when a green Jeep pulled up beside him and skidded to a stop. The driver, a woman in her forties with wild gray hair, rolled down the window. â€Å"Mr. Flood?† She said. Tommy nodded. â€Å"I'm Alicia DeVries. Let me park and I'll show you the loft.† She backed the Jeep into a spot that seemed too short for it by six inches, running the wheels up over the curb, then she jumped out, dragging after her a purse roughly the size of Tommy's suitcase. She wore sandals, a dashiki, and multicolored Guatemalan cotton pants. There were chopsticks stuck here and there in her hair, as if she were prepared at any minute to deal with an emergency stir-fry. She looked at Tommy's suitcase. â€Å"You look like you're ready to move in today. This way.† She breezed by Tommy to a fire door beside the foundry. Tommy could smell the patchouli in her wake. She said, â€Å"This area is just like Soho was twenty years ago. You're lucky to have a shot at one of these lofts now, before they go co-op and start selling for a million dollars.† She unlocked the door and started up the steps. â€Å"This place has incredible energy,† she said, without looking back. â€Å"I'd love to live here myself, except the market's down right now and I'd have to sell my place in the Heights.† Tommy dragged his suitcase up the steps after her. â€Å"Do you paint, Mr. Flood?† â€Å"I'm a writer.† â€Å"Oh, a writer! I do a little writing myself. I'd like to write a book myself some weekend, if I can find the time. Something about female circumcision, I think. Maybe something about marriage. But what's the difference, right?† She stopped at a landing at the top of the stairs and unlocked another fire door. â€Å"Here it is.† She threw the door open and gestured for Tommy to enter. â€Å"A nice work area and a bedroom in the back. There are two sculptors that work downstairs and a painter next door. A writer would really round the building out. What's your take on female circumcision, Mr. Flood?† Tommy was still about three topics behind her, so he stood on the landing while his brain caught up. People like Alicia were the reason God made decaf. â€Å"I think everyone should have a hobby,† he said, taking a shot in the dark. Alicia jammed like an overheated machine gun. She seemed to look at him for the first time, and did not seem to like what she saw. â€Å"You are aware that we'll need a significant security deposit, if your application is accepted?† â€Å"Okay,† Tommy said. He entered the loft, leaving her standing on the landing. The loft was roughly the size of a handball court. It had an island kitchen in the middle, and windows ran along one wall from floor to ceiling. There was an old rug, a futon, and a low plastic coffee table in the open area near the kitchen. The back wall was lined with empty bookshelves, broken only by a single door to the bedroom. The bookshelves did it. Tommy wanted to live here. He could see the shelves filled with Kerouac, and Kesey, and Hammett, and Ginsberg, and Twain, and London, and Bierce, and every other writer who had lived and written in the City. One shelf would be for the books he was going to write: hardbacks in thirty languages. There would be a bust of Beethoven on that shelf. He didn't really like Beethoven, but he thought he should have a bust of him. He resisted the urge to shout, â€Å"I'll take it!† It was Jody's money. He had to check the bedroom for windows. He opened the door and went in. The room was as dark as a cave. He flipped the light switch and track lighting along one wall came on. There was an old mattress and box springs on the floor. The walls were bare brick. No windows. Through another door was a bathroom with a freestanding sink and a huge claw-foot tub that was stained with rust and paint. No windows. He was so excited, he thought he would wet himself. He ran out into the main living area where Alicia was standing with her hand on her hip, mentally shoving him into the pigeonhole of abusive barbarism she had made for him. â€Å"I'll take it,† Tommy said. â€Å"You'll have to fill out an – â€Å" â€Å"I'll give you four thousand dollars in cash, right now.† He pulled the wad of bills out of his jeans. â€Å"How many keys will you need?† Chapter 14 Two Losts Do Not Make a Found Consciousness went off like a flashbulb of pain: a dull ache in her head, sharp daggers in her knees and her chin. Jody was slumped in the shower. The water was still running – had been running on her all day. She crawled out of the shower stall on her hands and knees and pulled towels out of the rack. She sat on the bathroom floor and dried herself, blotting away the water with rough terry cloth. Her skin felt tender, almost raw. The towels were damp from fourteen hours of steam. The ceiling dripped and the walls ran with condensation. She braced herself against the sink and climbed to her feet, then opened the door and stumbled through the room to the bed. Be careful what you ask for, she thought. All the regret about waking up a little too alert, coming out of sleep like a gunshot, came back on her. She hadn't thought about falling asleep in the same way. She must have been in the shower at sunup, dropped to the shower floor, and stayed there throughout the day. She sat up on the bed and gently touched her chin. Pain shot up her jaw. She must have hit it on the soap dish when she went out. Her knees were bruised as well. Bruised? Something was wrong. She jumped to her feet and went to the dresser. She turned on the light and leaned into the mirror, then yelped. Her chin was bruised blue, with a corona of yellow. Her hair was hopelessly tangled and she now had a small bald spot where the water had worn away at her scalp. She backed away and sat back on the bed, stunned. Something was wrong, seriously wrong, beyond her injuries. It was the light. Why had she turned on the light? The night before she would have been able to see herself in the mirror by the light filtering in under the bathroom door. But it was more than that. It was a tightness in her mouth, pressure, like when she had first gotten braces as a child. She ran her tongue over her teeth and felt the points breaking through the roof of her mouth just behind her eyeteeth. She thought, I'm breaking down from lack of†¦ She couldn't even make herself think it. This will get worse. Much worse. Now she could feel the hunger, not in her stomach, but in her entire body, as if her veins were going to collapse on themselves. And there was a tension in her muscles, as if piano strings were tightening inside her body, sharpening her movements, making her feel as if she would jump through a window any second. I've got to calm down. Calm down. Calm down. Calm down. She repeated the mantra to herself as she got up and walked to the phone. It seemed to take an incredible effort to push the zero button and wait for the desk clerk to come on. â€Å"Hi, this is room two-ten. Is there a guy in the lobby waiting? Yes, that's him. Would you tell him I'll be down in a few minutes?† She put down the phone and went to the bathroom, where she turned off the shower and wiped down the mirror. She looked at herself in the mirror and fought the urge to burst into tears. This is a project, she thought. She turned her head and looked at her bald spot. It was small enough that she could cover it with a new part held by a couple of hairpins. Her bruised chin might require some explaining. She started to run her fingers though her hair to facilitate the preliminary untangle, fighting the tension in her arms that seemed to be increasing every second. A large moth buzzed into the bathroom and went for the light above the mirror. Before she knew what had happened, she snatched it out of the air and ate it. She stared at her reflection and was horrified by the red-haired stranger who had just eaten a moth. Even so, a warmth ran though her like good brandy. The bruise on her chin faded as she watched. The first thing she saw when she turned the corner at the lobby was Tommy's grin. â€Å"Good,† he said. â€Å"You're dressed for moving. I like your hair pinned up like that.† Jody smiled, and stood awkwardly in front of him, thinking she should greet him with a hug, but afraid to get too close to him. She could smell him and he smelled like food. â€Å"You found a place?† â€Å"An incredible loft, south of Market. It's even furnished.† He seemed as if he would burst with excitement. â€Å"I used all the money; I hope that's okay.† â€Å"Fine,† Jody said. She just wanted to get him alone. â€Å"Get your stuff,† he said. â€Å"I want to show it to you.† Jody nodded. â€Å"I'll be just a minute. Have the desk clerk call a cab.† She turned to leave. Tommy caught her by the arm. â€Å"Hey, are you okay?† She motioned for him to move within whisper range. â€Å"I want you so badly I can hardly stand it.† She pulled away and ran up the steps to her room. Inside she gathered what few belongings she had and checked herself in the mirror one last time. She was wearing jeans and the chambray blouse from the night before. She unbuttoned her blouse and did a straitjacket escape from her bra, then buttoned the blouse halfway up. She stuffed the bra into her day pack and locked the room for the last time. When she returned to the lobby, Tommy was waiting outside by a blue DeSoto cab. He opened the door for her, climbed in, and gave the driver the address. â€Å"You're going to love it,† he said. â€Å"I know you are.† She moved closer to him and held his arm tightly between her breasts. â€Å"I can't wait,† she said. A tiny voice in her head asked, What are you doing? What are you going to do to him? It was so faint and foreign that it might have come from someone outside on the street. Tommy pulled away from her and dug into his jeans pocket, coming out with an envelope. â€Å"Your check's in here. I didn't open it.† She took it and put it in her day pack, then moved on him again. He scooted to the door and nodded toward the driver, who was watching them in the rearview mirror. â€Å"Forget him,† Jody whispered. She licked Tommy neck and shuddered with the taste and warmth of his flesh. â€Å"I couldn't get your car out of impound. It has to be the owner.† â€Å"Doesn't matter,† she said, nuzzling into the space under his jaw. The cab stopped and the driver turned to them. â€Å"Six-ten,† he said. Jody threw a twenty over the seat, reached over Tommy and opened the door, dived out and dragged him out of the cab after her. â€Å"Where is it?† Tommy just had time to point to the door before she pushed him at it. She climbed on his back as he unlocked the door, then bolted past him and dragged him up the steps. â€Å"You're really excited about this, aren't you?† he asked. â€Å"It's great.† She stopped at the fire door at the top of the stairs. â€Å"Open it,† she commanded. Tommy unlocked the door and threw it open. â€Å"This is it!† She went through, catching the front of his shirt and pulling him in. â€Å"Look at all these bookshelves,† he said. She ripped his shirt off and kissed him hard. He pulled up for air and said, â€Å"The bedroom doesn't have any windows, just like you wanted.† â€Å"Where?† she demanded. He pointed to the open door and she pushed him through it. He fell face down on the bare mattress. She flipped him over, hooked her hands into the waist of his jeans and ripped them off him. â€Å"So you like it?† he asked. She ripped her shirt open and held him to the bed, one hand on his chest while she took off her own jeans. She climbed on him and muffled his next question with a kiss. He finally got the message and returned her kiss and tried to match her urgency, then didn't have to try at all. She pulled away from the kiss as her fangs unsheathed, then guided him into her as he moaned. Jody growled deep in her chest, pushed his head to the side and bit him on the neck. â€Å"Ouch!† Tommy shouted. She held him down and snarled into his neck. Dust from the old mattress filled the air and was stirred by the movement of their bodies. â€Å"Oh jeez!† Tommy shouted, digging his fingers into her bottom. Jody answered him with a catlike scream as she came, then fell on his chest and licked the blood that dribbled from the punctures on his neck. She twitched and shuddered while he repeated, â€Å"Oh jeez,† over and over again between gasps. After a few minutes she rolled off him and lay on the bed feeling the warm nourishment running though her. Tommy rubbed his neck. â€Å"That was great,† he said. â€Å"That was incredible. You are – â€Å" Jody rolled over. â€Å"Tommy, I have to tell you something.† â€Å"You're beautiful,† he said. Jody smiled at him. The urgency was gone now and she was feeling guilty. I could have killed him, she thought. Tommy reached over and touched her lips. â€Å"What's that on your teeth? Did you hurt yourself?† â€Å"It's blood, Tommy. It's your blood.† He felt his neck again, which was completely healed. â€Å"My blood?† â€Å"Tommy, I've never done anything like that before. I've never been that way before.† â€Å"Me either. It was great!† â€Å"I'm a vampire.† â€Å"That's okay,† Tommy said. â€Å"I knew this girl in high school who gave me a hickey that covered the whole side of my neck.† â€Å"No, Tommy. I'm really a vampire.† She looked him in the eye and did not smile or look away. She waited. He said, â€Å"Don't goof on me, okay?† â€Å"Tommy, have you ever seen anyone tear a pair of jeans like that before?† â€Å"That was my animal attraction, right?† Jody got out of bed, went to the bedroom door and closed it, shutting out the light from the living area. â€Å"Can you see anything?† â€Å"No,† he said. â€Å"Hold up a number of fingers. Don't tell me how many.† He did. â€Å"Three,† Jody said. â€Å"Try again.† He did. â€Å"Seven.† â€Å"Jeez,† he said. â€Å"Are you psychic?† She opened the door. Light spilled in. â€Å"You have an incredible body,† Tommy said. â€Å"Thanks. I need to lose five pounds.† â€Å"Let's do it again, without our shoes on this time.† â€Å"Tommy, you have to listen to me. This is important. I'm not kidding you. I am a vampire.† â€Å"C'mon, Jody, come over here. I'll take your shoes off for you.† Jody looked up at the ceiling. There were open steel beams twenty feet above. â€Å"Watch.† She jumped up and grabbed on to a beam and hung. â€Å"See?† â€Å"Jeez,† Tommy said. â€Å"Do you have a book here?† â€Å"In my suitcase.† â€Å"Go get it.† â€Å"Be careful. You could fall.† â€Å"Get the book, Tommy.† Tommy went into the living area, looking up at her as he walked under. He returned with a volume of Kerouac. â€Å"Now what? Come down from there. You're making me nervous.† â€Å"Close the door and open the book.† He closed the door and the room went dark again. Jody read a half page aloud before he opened the door again. â€Å"Jeez,† he said. She let go of the beam and dropped to the floor. Tommy backed away from her to the bed and sat down. â€Å"If you want to leave, I'll understand,† she said. â€Å"When we were making love†¦ you were cold inside.† â€Å"Look, I didn't mean to hurt you.† Tommy's eyes were wide. â€Å"You really are a vampire, aren't you?† â€Å"I'm sorry. I needed help. I needed someone.† â€Å"You really are a vampire.† It was a statement this time. â€Å"Yes, Tommy. I am.† He paused for a second to think, then said, â€Å"That's the coolest thing I've ever heard. Let's do it with our shoes off.†

Avalon Essay Example | Topics and Well Written Essays - 3000 words

Avalon - Essay Example Census Bureau 2000). The city's population is only about 3,500 according to the US population census in 2000. About 719 families live in the city composed of about 1,158 households at an average density of 252.7/km (654.2/mi) and 1,839 housing units. Population density is estimated at 429.7/km (1,112.4/mi). The racial composition of the city includes 71.63% White, 0.74% Black 1.02% Native American, 0.61% Asian, 0.22% Pacific Islander, 20.37% from other races, and 5.40% from two or more races. 45.95% of the population are of Hispanic or Latino background. Out of 1,158 households, 38.3% had children below the age of 18 residing with them; 44.0% of these are married couples; 11.2% had a single female householder, and 37.9% are considered non-families. Of these households, 31.3% are individuals living independently and 10.3% are 65 years of age or older living alone. The estimated average household size is about 2.65 and the average family size is about 3.38 (U.S. Census Bureau 2000). Avalon City's population is quite diffused with 30.3% of the population below 18 years of age. 7.7% are from the age of 18 to 24. The population is also comprised of 30.2% of individuals ages 25 to 44, 21.7% of these are aged 45 to 64, and only about 10.1% are 65 years of age or older. 34 years old is the median age. ... The city's per capita income is recorded at about $21,032. 9.2% of families and 10.4% of the population live below the poverty line, which includes 11.5% of the residents under the age of 18. About 4.6% of individuals age of 65 or above live under the poverty level (U.S. Census Bureau 2000). There are various factors that will clearly affect both the expenses and revenues of the city of Avalon. First, it is apparent that about 4.5 percent to 10 percent of the ageing population is dependent on the city's health care systems. Second, employed residents constitute about 74.5. This percentage is high as compared to the national employment of about 63 percent. However, the city needs to consider the population living below the poverty level, which comprise mostly of the younger individuals. The city government then, needs prudence on planning which type of program to implement as the pattern of population is quite diffused and spread out. The target of poverty alleviation measures would be the young mostly, comprising of about 11.5 percent. Families who live below poverty level are estimated at 9.2 and individuals below poverty level, 10.4. The unemployment rate in Avalon is quite high at about 5.20 percent as compared to the US average of 4.60%. About 50 percent of the unemp loyed are of African descent and 8 percent are Hispanics. Although Avalon jobs have augmented by 3.35 percent, per capita is lower compared to the national figures. As of the last census, Avalon per capita stands at $21,032 dollars as compared with $21,587 national per capita. Hence, the Avalon government must increase its efforts to curb unemployment and increase income of the population. Job generation

The effects of Asda's Social Responsibility Policy on the business Dissertation

The effects of Asda's Social Responsibility Policy on the business Practice - Dissertation Example The study adopted a qualitative approach and this study was based purely on secondary data. Secondary data was obtained through different sources which helped in triangulating the data and in conducting the analysis. The study finds that CSR has a major role in enhancing corporate performance which stretches beyond financial performance. Corporations, by addressing their duties towards all the stakeholders, fulfill their legal responsibilities and duties as corporate citizens. ASDA too has been able to achieve this because of its CSR strategy which is sustainable. They have integrated and embedded CSR into their overall business right and it is not implemented for the purpose of public relations or with selfish motives. CSR plays a critical role in bringing continuous improvement in Asda’s market performance. ASDA has been able to bring change in its organizational practices, change in managerial attitude which has helped them demonstrate their readiness to respond to the chan ging business environment. ASDA does have self-motivating reasons for making environmental and social contributions, but these do not impact the quality of contribution to the society and the planet. The study concluded by highlighting the limitations of the study and by making recommendations for further study on the subject. Table of Contents Chapter I Introduction 1.1 Background 1 1.2 Rationale for the Study 3 1.3 Research Aims and Objectives 3 1.4 Research Questions 4 1.5 Structure of the Study 4 Chapter II Literature Review 2.1 Definitions 6 2.2 Advantages of CSR and Corporate Citizenship 11 2.3 CSR in Retail Sector in Europe 12 2.4 CSR in Food Retail 13 2.5 Stakeholders’ Theory 14 2.6 Corporate Ethics 15 2.7 Sustainability 16 2.8 Chapter Summary 16 Chapter III Methodology 3.1 Research Philosophy 17 3.2 Research Phenomenon 17 3.3 Research Design 17 3.4 Choice of Method 18 3.5 Research Approach 18 3.6 Data Collection 19 3.7 Justification for Literature Review 19 3.8 Justi fication for Secondary Research 20 3.9 Sources of Secondary Data 21 3.10 Data Analysis 22 3.11 Reliability & Validity 23 3.12 Ethical Concerns 23 Chapter IV Findings & Discussions 4.1 Findings 24 4.2 Discussion 31 Chapter V Conclusion and Recommendations 5.1 Conclusion 37 5.2 Limitations of the Study 39 5.3 Recommendations for further study 40 5.4 Reflective Thinking 40 References 41 Figure 2.1 Carroll's Pyramid 9 Table 2.1 The Grid of Corporate Citizenship Values 9 Figure 2.1 The ‘Rationale Triangle’ 10 Table 2.2 CSR initiatives by large Corporations 13 Chapter I Introduction 1.1 Background Companies are individual legal entities and hence can be considered to be corporate citizens with legal rights and duties (Marsden and Andriof, 1998). Citizenship entails active commitment and responsibility. It means to make a difference in the society, in the community or the world in which one lives. Good corporate citizenship, therefore, requires understanding and managing the o rganization’s influences on and relationship with the rest of the society so as to minimize the negative impacts and maximize the positive impacts. Organizations hence need to have self-motivating reasons for making environmental and social contributions. Mounting pressure from people, individuals and groups have urged businesses to be economically, environmentally and socially sustainable, to be transparent in their dealings and to be ethical and more equitable (Batten and Brich, 2005). Corporate citizenshi

Life is college Essay Example | Topics and Well Written Essays - 750 words

Life is college - Essay Example I further hoped that, through healthy relationships both with fellow students and the faculty, I would acquire great approach in learning and handling major courses in my field of choice. To me, being able to value relations with people, time, energy, besides personal abilities is an important duty if one aims for achieving real success. It was in my hope to meet different kinds of people with whom to share ideas or insights for I hoped as well to develop my communication skills and become an assertive and competent student through the span of my college life. Aside from fruitful interactions with other individuals, friends and colleagues alike, I also expected to have a rewarding experience with the academic facilities and resources of ISU, thinking of the possible ways I could utilize them to be equipped with adequate skills and knowledge toward scholastic excellence. On the other hand, however, I was anxious of encountering difficult subjects and instructors who might fall short at teaching the class with efficient tools and methods. I know the subject areas I am often weak at and I normally struggle to cope with subject matters that seem too technical or too analytical to comprehend. Inasmuch as I can, I would typically go an extra mile of studying and asking for all the help I can obtain to prepare myself for major exams and presentations. One of my greatest fears before was being left behind and failing to get by with the mental and emotional challenge of tertiary level studies. I feared loads of curricular assignments and take-home projects that could set me in conflict with time management and especially the potential to produce something that deserves an A. I thought that if I would not be able to interact sufficiently with people due to language barrier and other factors, I might find it hard to pass and finish college with grades that mu st make my parents proud. Now that I am in the eighth week of college at ISU, I must confess

Wind Load Effects on Skyscrapers Essay Example | Topics and Well Written Essays - 3750 words

Wind Load Effects on Skyscrapers - Essay Example These devices are utilised in high-rise buildings reaching above 50 storeys. The TMDs enhance strength of the building while increasing comfort of residents. The Taipei 101 structure remains the building with the largest TMD weighing over six tons. This massive structure was constructed using advanced technology providing a significant breakthrough for the engineering industry. The massive structure has contributed towards the capacity for the building to withstand numerous typhoons, common in Asia. In many modern cities around the world, skyscrapers have continued to dominate the skylines. The construction of these structures continues to define the element of modernisation and evolvement of modern city designs. These magnificent structures decorating the skylines of major cities require a considerable amount of planning before commencing construction. The planning for construction of skyscrapers begins with consideration of various elements among them cost, economic efficiency and strength of the structure(Chew, 2001). The element of strength remains most important as it relates to safety of the tenants and other occupants of the building. The strength of a skyscraper remains the determinant element for the successful construction of these high rise structures. These structures remain highly susceptible to natural calamities like earth quakes and hurricanes, among others. During the planning phase for the construction of these high rise structures, those designing components seek to ensure the structure becomes sufficiently resistant to any forces that might arise. The consideration of these wind forces makes the designing phase most important. The forces exerted by winds on the structures remain fundamental for designing of high-rise structures. WIND AND TUNED MASS DAMPER Wind remains a complex phenomenon because of the variations in wind speeds resulting from interaction with the structures surrounding the wind. Wind comprises of numerous particles moving in different directions. The speed and direction of wind contributes immensely towards the effects produced by the wind(Holmes, 2007). During construction of tall structures, engineers and architects must consider the expected wind effects upon the intended structure. While normal wind force could be resisted by many structures, extreme cases like tornadoes, hurricanes present great challenges as they create massive forces, capable of collapsing entire buildings. The resulting effects of wind damage can cause massive destruction as have been recorded. Hurricanes, for example, are some of the most feared winds across the globe. Some hurricanes have enough strength to even uproot trees and destroy even the shortest of structures. During these extreme wind cases, like winds measuring 10 or higher on the Beaufort scale, the wind load affecting tall buildings is normally higher

Outsourcing the positive and negative affects; purchasing and supply Research Paper

Outsourcing the positive and negative affects; purchasing and supply chain management - Research Paper Example Although, the argument that denies the inevitability of phenomenon claims it to be a major cause of unemployment in America, but the positive impact of outsourcing on the economy cannot be rejected altogether. As a matter of fact, there is a fair amount of subjectivity in the questions like where, when and how outsourcing should be employed and the detrimental effects of outsourcing on US job market are a reality but another reality is the importance of these outsourcing companies to the US economy. Although cost is the key factor while making a decision of outsourcing, it must also be a strategic decision at the same time. A strategic decision takes into account the capabilities of companys resources, challenges at hand, benefits and key factors that favor outsourcing. The strategic outsourcing prevents the outsourcing of goods, services and labor that are critically important to the function of the company. At the same time, strategic outsourcing can take into account the expected impact of an outsourcing decision on national economy. The establishment of a separate formal Officials authority might be a good idea to evolve a regulating mechanism and to strike a balance in outsourcing decisions. Nevertheless, purging it altogether is not an option. Pacing with rapid changes in business dimensions has become a demanding challenge for business leaders in diminishing geographical limitations. Technology in general and cutting edge communications in particular drastically redefines business operations in terms of resources. The globalization has vast and vivid repercussions on business domains and business leaders have to be very knowledgeable and current on prevailing trends in human resources, purchases and supplies to manage these effects in their specific domain. The globalization of businesses and advancement in technologies to support these global business operations have reduced the geographical limitation of

Effect of Immigration on New York City Research Paper

Effect of Immigration on New York City - Research Paper Example Writing about New York City's population, Nathan Glazer noted, "If the United States remains the permanently unfinished country, to an even greater degree the same is true for New York City" (Vecoli, 567). Various reports show that immigration continues to shape the city. Immigrant flows are at an all time high since the peaks at the turn of the century. Immigration to the city in the 1990-2000 periods stood at approx 13,000 annually, a 32 percent increase over the average of 86,000 in the 1980s. (Lobo, 12) This growth mirrored the increasing flow of immigrants to the country as a whole; as a result, immigrants to the city constituted nearly 15 percent of all immigrants to the U.S. in both the 1980s and 2000s. (Martin, 02) This article examines the nature of these recent immigrant flows and their impact on the city's population. Traditionally, immigrants to the city have been disproportionately from the Caribbean and South America relative to the nation, which has been more likely to get immigrants from Asia and Mexico. The Caribbean comprised 33 percent of the flow of immigrants to the city, but only 12 percent of the flow to the nation in the 2005-2009 periods. ... Likewise, Asians were 26 percent of the city's flow but comprised 42 percent of entering immigrants to the nation. (Martin, 5) The 2000s marked resurgence in European immigration to New York City, and a decline in the share of Caribbean flows. Immigration from Europe stood at 22 percent, more than twice the level of 9 percent in the 1990s. (Vecoli, 562) Caribbean immigration, which stood at 40 percent of the total in the 1990s, dropped 7 points in the 2000s. However, the share of the Hispanic Caribbean (primarily the Dominican Republic) actually increased while there was a decline in flows from non-Hispanic Caribbean nations such as Jamaica, Haiti, and Barbados. Flows from Guyana, an English-speaking South American nation with a heavy Caribbean influence, also declined. The number of African immigrants to the city, while small, has been increasing steadily over the past three decades and comprised just over two percent of entering immigrants. The reason that immigrants are able to find jobs in the New York City and put a lot of people out of work is because they often take the low-paying jobs that most Americans don't want to do. Even though a lot of people may not like immigrants because they are putting them out of jobs, immigrants in this economy today are helping to keep inflation low, improve housing values, and benefit taxpayers (Martin, par. 12). In other words, immigration helps provide an increase to the U.S. economy. The only people that are really being hurt right now by immigrants are those people without high school degrees (Gelfand and Yee, par. 10). Every year they fight against immigrants for jobs and their wages just seem to keep getting lower. Immigrants who see their relatives and friends leading a better life

Discrimination - Thought Essay Example for Free

Discrimination Thought Essay 1. What do you consider to be the most valuable information you got from this class? Why do you consider this most valuable? I think that the most valuable thing that I took from this class is the fact that racism is still very much a major part of our society. Growing up in rural Iowa I always new that there were racist people, but I never knew how the racism actually affected our society and how strongly it influences such things as government funding for education and housing developments. Racism and prejudice always seemed secondary to me. I always knew that this country had issues with racism, but I never imagined that it affected serious issues so heavily. Minorities in this country are put at a greater disadvantage then whites. Many minorities especially those that do not speak English as their primary language have to deal with inadequate housing, under funded school districts and the everyday struggle of discrimination for their differences and beliefs. 2. To what extent, if any, has your thought process about race relations change as a result of this class? Explain your answer. I wouldnt say that my personal beliefs have changed due to this class, because I feel that I have always been open-minded and treated everyone with equal respect. I would however say that my thought process has changed slightly. My thought process has been altered because I always looked at racism as a problem, but not my problem. I was never directly involved in racism, and I thought that there was nothing that I could do to change the views of others. After this class I have realized that if you are not part of the solution then you are ultimately part of the problem. Many people turn their head when they are around a situation of discrimination, saying nothing. People have the misconception that just because you didnt say anything negative or directly discriminate against another person that there is nothing else that they can do to fix the problem. The only way for racism and discrimination to disappear in this country is for us to admit that they exist and they are a major problem. 3. What will you do differently as a result of what you learned? After taking this course it opened my eyes and really made me think in a different light. Since the course began in August I have accepted new concepts and have decided for myself which ones that I choose to follow and which ones I have chosen to ignore. I feel that my mindset involving racism has changed and because of that I will attempt to get more involved and stop ignoring racist comments and gestures. I have never been a person to treat people differently based on their beliefs, race and/or ethic backgrounds, but that doesnt mean that I have done anything to help get rid of the problem. I believe that people can make very small steps to correct racism and it will indeed make a huge difference. Some people feel that their individual efforts will make little, if any, difference in the overall scheme of things. If only one person from each group friends changes their mindset about racism then they can begin to reverse the situation. If that one person educates themselves about the issues involving racism and practices their beliefs then they will ultimately begin to change the minds of many of their friends. Obviously this will not work to change everyones mindset, as some people are set in their ways and due to ignorance will never change or even attempt to broaden their views and beliefs.

Insecure, Pressured, Over-taxed and Debt-ridden Youth (IPOD)

Insecure, Pressured, Over-taxed and Debt-ridden Youth (IPOD) THE IPOD GENERATION The young adults of today, the under-35s, are often referred to as the IPOD generation. This both connects them with the latest technology and design that the sleek IPOD represents, and according to David Smith in a recent article in the Sunday Times, stands as an acronym for insecure, pressured, overtaxed, and debt-ridden. Labels such as these designate a generation that is experiencing and environment and reaction both negative to itself and to the future prosperity of Britain. They call to question both whether the current situation could have been avoided, and what can be done to more fully integrate the IPOD generation into British prosperity now. It is perhaps easiest to consider the four labels of the IPOD acronym in reverse order. First, the generation is debt-ridden. This is due not only to an increase in ease of acquiring consumer credit, but also to changing attitudes about debt and an increase in educational costs. Credit is easier to obtain than ever before, with many if the IPOD generation having multiple credit cards and getting them whilst still in school. Various banks and lending institutions, who make high profits from consumers carrying credit balances on such cards, often target young adults who may not be ready to responsibly manage debt. Where once young adults assumed they would need to work and save to emulate their parents standards of living, todays young adults are encouraged towards immediate gratification. They can buy a car on credit, fill the tank on credit, furnish their first place on credit, and so on until their credit limits are reached. Then they are strapped, spending years paying off a quick path to a â€Å"higher† standard of living. Additionally, many young adults leave university with high student loan debt. This reflects both a change in education and a change in the overall British economy. At one time there were well-paying jobs for those chose not to attend university. Many could enter into manufacturing and similar positions with an expectation of job stability and reasonable pay and job security. However, in the past twenty years the British economy has shifted. Many of these â€Å"secure† manufacturing jobs have been transferred to Asia and similar countries, where companies can secure workers for much lower wages. Computers and technology have changed the face of many of the jobs that remain, requiring a higher educational level for those wanting a reasonable wage. As a result, the number of young adults going on to university has increased eight times over since the 1960s. Although they feel it necessary to extend their education to have any shot at a well-paying job, this has made university ed ucation more commonplace and therefore worth less in the marketplace. Most students have responsibility for some or all of their educational expenses, and resort to loans. Many of the IPOD generation are therefore leaving university having pounds ten or twenty thousand or more in student debt without the job prospects previous generations enjoyed. They spend years in unstable positions, combating their acquired debt and high rents. The property ladder is not even a consideration, at least not for many years. To make matters more difficult, the IPOD generation is also over-taxed. This is the first generation who is on the losing end of the welfare bargain, who will pay more into the system than they receive from it. First, the large number of aging baby boomers require greater expenditures by the government on health care and pensions. This requires current workers, including young adults, to shoulder a greater share of the tax burden. This is likely to only become worse over the next two decades, and politicians continue to be slow to cater to the needs of young adults, as the IPOD generation is both fewer and less likely to vote than their older counterparts. Young adults also receive fewer benefits from the state. They are not only expected to pay for their own education, as mentioned above, but health care and pension costs previously mentioned leave less money for other government programmes that might benefit them. Their tax burden, therefore, is disproportionate and a great hampera nce to their full integration into and enjoyment of economic opportunities. A combination of these high taxes and debt leave the IPOD generation pressured. There is a societal expectation that they should be exceeding their parents in lifestyle and success, yet good jobs are few and they have greater obligations from society economically. They must learn to juggle high debt and high taxes at increasingly an young age, often with little hope of escape from such a situation. For example, moving to another part of the country with lower taxes also typically means fewer job prospects and those jobs having lower wages. In addition, some believe the integration of the UK into the European Union also puts pressure on the IPOD generation. On one hand, British participation opens the opportunities for companies to sell product in a wider market. However, this is more likely to benefit business owners, whom are typically of the older generations, rather than entry-level workers. Increased opening of British job markets to other Europeans actually increases the number of potential workers. This also disproportionately affects younger adults, as workers from some other countries will compete for entry-level and less-skilled jobs, and are often willing to work at much lower wages. This means young adults from Poland, for example, can compete for British jobs, although British young adults are unlikely to benefit similarly from job opportunities in Poland. Such political changes in the both the UK and global environment put additional pressure on the IPOD generation. All the above leaves the young adults of today increasingly insecure. They can no longer count on job opportunities, even if they have invested the time and expense in additional education. Debt and high tax burdens leave todays young adults with less available capital, and less prospect of available capital. This makes them less inclined to risk or to venture into entrepreneurial activity. The IPOD generation in Britain are not only less likely to engage in entrepreneurial pursuits than previous generations, but, according to Smiths report in the Sunday Times, less likely than youth in America, Australia, New Zealand, or Ireland. This indicates such insecurity is particularly a British phenomena, even with the number of wider economic shifts that contribute. Concerns are rising of the impact of all of this on the future of the British economy. An insecure generation that does not create business also does not create jobs or a tax base. Over time, this further opens British markets to competition from non-British firms. The economy begins to slide, increasing the tax burden on those who are working or trying to develop business pursuits, which hampers their success and makes other potential British entrepreneurs even more insecure and adverse to risk. This has the potential to become a downward circle, with continuing negative impact on the UK economy as a whole and the IPOD generation in particular. Whilst there are certainly steps that could have been undertaken to lessen the pressure on the IPOD generation, as noted above some of the impact is simply the result of economic and demographic shifts in the economy. In regard to debt, tighter government regulation of credit and tighter credit requirements would reduce debt in the IPOD generation, as would increased government investment in higher education, and programmes to provide other job skills as an alternative to university. Certainly the government could have also anticipated rising health and pension costs and taken steps to alleviate some of tax burden on todays young adults. Instead, the government appears to be making decisions based on current votes, rather than future economic needs. Increasing affordable housing or programmes for new businesses would additionally address the pressure and insecurity experienced by the IPOD generation. However, all these require both advance planning and the willingness of the governme nt to make difficult decisions that will be also undoubtedly unpopular to older people. Politically, this appears unlikely, although such steps could still be undertaken now. Some possible avenues to address the needs of the IPOD generation, however, are being considered. A Reform study of the problems facing the IPOD generation contradict Tony Blairs agenda to increase school leavers who pursue additional education to fifty percent. That plan, the study contends, would flood the job market with over-educated workers who will not be able to get ample return on their educational investment. The Reform study instead recommends focusing on increasing job skills based on the countrys economic needs. Suggestions include changing recruitment of school leavers and job seekers to assist young adults in securing stable, reasonably paying employment, and implementing apprenticeship plans where young adults can develop job skills needed by the current and future economy without incurring high debt or investing potential earning years in university education that may not provide the same return that it did for previous generations. Both these suggestions would be a step towards assisting the IPOD generation in becoming more economically viable, but larger issues requiring government intervention, as discussed above, are additionally needed to truly address the situation.

Water Temperature And Evaporation Rate

Water Temperature And Evaporation Rate This report details the scientific method used to investigate the effects of water temperature on the rate at which the water will evaporate. Project design plan: Problem statement The purpose of this experiment was to compare the effect of temperature on the evaporation rate of water. The vision was to establish three containers of water. Each container contains the same amount of water. Surrounding air and humidity are kept consistent. One container is kept at a consistent room temperature; one container is kept at a heated consistent temperature; one container is kept at a cooled consistent temperature. The issue being examined is how the three different water temperatures impacts the rate at which the water evaporates from the container. The experiment was conceived as part of an effort to learn more about Global Warming. Since the world is made up of approximately 75% water, there is a desire to understand how increases in water temperature impacted the evaporation of water and if Global Warming could impact the worlds water base. Relevance of the question evaporation is the scientific process where a liquid is converted to a gas state by increasing the speed of its moleculars which causes a release in energy. Water evaporates faster at higher temperatures although any amount of heat resulting from the release of this energy will cause water to evaporate. Literature review http://www.engineeringtoolbox.com/evaporation-water-surface-d_690.html this site provides a detailed process and mathematical equations for calculating the amount of evaporated water from a water surfaces. The amount of evaporation depends on the temperature in the water and in the air, and the humidity and velocity of the air above the surface. This site can be used as a reference to determine the level at which evaporation will occur in the experiment. http://www.usc.edu/CSSF/History/2002/Projects/J0615.pdf this site provides the results of an experiment that measured which factor had the greatest effect on the rate of evaporation of water. The factors tested were surface area, wind speed, air temperature and water temperature. The results of this experiment validated the hypothesis for this experiment. Experimental design The constants in this experiment were: à ¢Ã¢â€š ¬Ã‚ ¢ The type of water (tap) à ¢Ã¢â€š ¬Ã‚ ¢ The amount of water à ¢Ã¢â€š ¬Ã‚ ¢ The location where the water is placed à ¢Ã¢â€š ¬Ã‚ ¢ The size of the container à ¢Ã¢â€š ¬Ã‚ ¢ The number of test conducted à ¢Ã¢â€š ¬Ã‚ ¢ The type of the container à ¢Ã¢â€š ¬Ã‚ ¢ The length of time the water has to evaporate Materials Used Quantity Item Description 1 Small home humidifier 1 Gallon jug of tap water 1 Graduated measuring cup 1 Digital wall mounted temperature and humidity gauge 3 8 ounce glass glasses 1 Digital thermometer 1 4 foot square, 3 foot high table 1 4 inch circular electrical heating plate 1 Thermos 1 Digital timer 1 1212 terry cloth cooling towel Steps executed in the experimental procedure 1. Collect all required materials 2. Stabilize and maintain the humidity in testing room using a small home air humidifier. For the testing, the humidity was stabilized at 40%. 3. Stabilize and maintain the temperature in testing room using the home HVAC system. For the testing, the room temperature was stabilized at 70 °. 4. Stabilize and maintain the air speed in testing room using isolated room. For the testing, the air speed was essentially dead calm. Note: no special equipment was used to stabilize the air speed. The test was conducted in an isolated room. There was some air movement introduced into the room through stabilizing the room temperature and humidity but was considered not significant enough to impact the tests. 5. Place a gallon jug of tap water in the testing room for 3 days so it adjusts to the room temperature and humidity. 6. Pour 100 ml. of tap water from the gallon jug stabilized to testing room temperature into each of 3 identical 8 ounce glass glasses using a graduated measuring cup. 7. Place the glasses into the center of the room on a table 3 feet off the floor so they are being equally affected by room temperature, humidity, and air movement. 8. Using a 4 inch, circular heating plate, place one of the glasses on the heating plate. The heating plate will raise the temperature of the water in the glass to 140 degrees. Note: it takes 30 minutes for the heating plate to heat the water in this glass to the 140 degree mark. Once this consistent temperature is reached, the volume of the water in this glass is rechecked to make sure the testing starting point is 100 ml. 9. Using a thermos, cooled via keeping it in a refrigerator for 24 hours, insert one of the glasses inside the thermos. The thermos will lower the temperature of the water in the glass to 35 degrees. Note: it takes 30 minutes for the thermos to cool the water in this glass to the 35 degree mark. Once this consistent temperature is reached, the volume of the water in this glass is rechecked to make sure the testing starting point is 100 ml. 10. Place a glass on the table and let it stabilize to the room temperature. Note: it takes 30 minutes for the water in this glass to stabilize to the room temperature degree mark. Once this consistent temperature is reached, the volume of the water in this glass is rechecked to make sure the testing starting point is 100 ml. 11. Using the timer, let the water sit in the testing room at the 3 different temperatures for 180 minutes. 12. Using a graduated measuring cup, measure the remaining water in milliliters from each glass. 13. Record how many milliliters remained after evaporation for each temperature for each test. 14. Repeat steps 11-12 for 2 more cycles. Total evaporation time is 9 hours. 15. Wait 24 hours from the start of the test. Repeat steps 1-14. 16. Repeat steps 14 one more time. Reason for choosing this particular experimental design plan the reason for this particular experimental design plan was to provide 3 water sources maintained at 3 different temperatures kept in a controlled humidity, room temperature and air rate environment. This environment was expected to provide a static environment to allow water evaporation to progress solely based on the temperature of the 3 water sources. Using identical starting water amounts and a graduated measuring cup to measure the resulting water amounts was expected to provide the most accurate results. Sequence of events used to collect quantitative data 1. Using the timer, let the water sit in the testing room at the 3 different temperatures for 180 minutes. 2. Using a graduated measuring cup, measure the remaining water in milliliters from each glass. 3. Record how many milliliters remained after evaporation for each temperature for each test. 4. Repeat steps 1-3 for 3 more cycles. Total evaporation time is 9 hours. 5. Wait 24 hours from the start of the test. Repeat steps 1-4. 6. Repeat steps 5 two more times. Tools, technologies, and measurement units used to collect quantitative data The recorded variable was the amount of water in milliliters that remained after evaporation was allowed to occur over in 180 minutes. The water in the 3 glass glasses was measured in milliliters using a graduated measuring cup before and after the evaporation occurred. Dependent, independent, and controlled variables Dependent variables the observed result of the independent variable being manipulated was the resulting water amount in each glass after evaporation has occurred Independent variables the value being manipulated or changed in this experiment was the water temperature of the water contained in the 3 glass glasses. Controlled variables the controlled variables were the air humidity, the air speed, the room temperature, the type of water (tap), the amount of water, the location where the water was placed, the size of the containers used, the number of tests conducted, the type of the containers used, and the length of time the water had to evaporate. Threat reduction to internal validity To reduce the threats to internal validity the following steps were taken: 1. Stabilize and maintain the humidity in testing room using a small home air humidifier. For the testing, the humidity was stabilized at 40%. 2. Stabilize and maintain the air speed in testing room using isolated room. For the testing, the air speed was essentially dead calm. Note: no special equipment was used to stabilize the air speed. The test was conducted in an isolated room. There was some air movement introduced into the room through stabilizing the room temperature and humidity but was considered not significant enough to impact the tests. 3. Stabilize and maintain the room temperature in testing room using the home HVAC system. For the testing, the room temperature was stabilized at 70 °. 4. Stabilize the water used by placing a gallon jug of tap water in the testing room for 3 days so it adjusts to the room temperature and humidity. 5. Stabilize the test environment by placing the glasses into the center of the room on a table 3 feet off the floor so they are being equally affected by room temperature, humidity, and air movement. Hypothesis The hypothesis was that the temperature of the water would affect the evaporation rate of the water the most and that the higher the water temperature, the more evaporation that would occur. The hypothesis proposed that the warmer the water, the more molecules escaped as vapor, and thus evaporated. The hypothesis theorized that the warmer the waters molecules were the more energy that would be produced and the amount of molecules escaping as vapor would occur at a much faster pace than molecules at lower temperatures. Process of data collection: At the end of each evaporation cycle of 180 minutes, the contents of each glass were poured into the graduated measuring cup and the resulting water in milliliters was measured and recorded. The data below shows the resulting milliliters for each sample for each test cycle as well as the percentage of evaporation that occurred which was determined by subtracting the resulting value from the original 100 milliliters and dividing by 100 to result in a percentage. Evaporation Test #1 Sample Resulting milliliters Sample Percentage of water evaporation Hours 3 6 9 3 6 Heated water 70 42 5 Heated water 0.3 0.58 Room temperature water 99 98 97 Room temperature water 0.01 0.02 Cooled water 91 80 68 Cooled water 0.09 0.2 Evaporation Test #2 Hours 3 6 9 3 6 Heated water 73 48 10 Heated water 0.27 0.52 Room temperature water 98 97 96 Room temperature water 0.02 0.03 Cooled water 99 98 97 Cooled water 0.01 0.02 Evaporation Test #3 Hours 3 6 9 3 6 Heated water 78 48 11 Heated water 0.22 0.52 Room temperature water 99 98 97 Room temperature water 0.01 0.02 Cooled water 96 88 86 Cooled water 0.04 0.12 Results of experiment: The original purpose of this experiment was to compare the effect of temperature on the evaporation rate of water. The results for the heated sample were as hypothesized. The highest rate of evaporation occurred in the heated sample. Also as the amount of water source decreased from previous evaporations, the subsequent evaporations were larger. The room temperature sample had marginal evaporation as expected. The results of the cooled sample were somewhat surprising, especially in the first test. It was assumed that the rate of evaporation would have been slowed down due to the cooler temperature and it would take longer for the evaporation to occur since the water source would have to warm over time for the molecules to excite and turn into vapor and evaporate. In researching this, it was discovered that these results might have been caused by the perspiration effect on cold water. It was noticed that there was a great deal of perspiration on the outside of the glass when the measurements were taken. After the first test, in an attempt to control this perspiration factor, the thermos was wrapped in the cooling towel. This did have an effect of the readings but the cooled sample results were still inconsistent and not what was expected. The results of the 3 separate tests showed consistency in the rate of evaporation across the both the heated and room temperature sources. This satisfies my goal of having a controlled environment in which to perform the tests. Conclusion: The results of the experiment confirmed the hypothesis in terms of heat having the largest impact on the evaporation rate of water. The heated sample had the greatest rate of evaporation. The hypothesis was that the temperature of the water would affect evaporation rate most. The results indicate that this hypothesis should be accepted, because the heated water source had the greatest rate of evaporation. The experimental design was a key factor in the success of the scientific inquiry. By controlling the air humidity, the air speed, the room temperature, the type of water (tap), the amount of water, the location where the water was placed, the size of the containers used, the number of tests conducted, the type of the containers used, and the length of time the water had to evaporate variables, enabled a controlled environment and allowed the focus of the experiment to be on the variable being manipulated which was the resulting water amount in each glass after evaporation has occurred. If the experimental design was faulty and the controlled environment was not established, other variables may have impacted the results. Humidity, air rate and air speed are factors in the rate of evaporation. If they were not controlled, the results of the experiment would have most likely been inconsistent. This experiment is valid since the test environment was controlled and only one variable was impacted by the test. Having multiple uncontrolled variable can invalidate an experiment in most cases. The experimental design and execution steps listed above would allow anyone to execute this experiment. If the tests were to be re-executed, the perspiration effect of the cooled sample needs to be taken into account and included in the measurements. Re-execution of the experiment described above and resulting similar results validates the experiment.

Good God Essay -- essays research papers

Good God When one walks through the streets of humanity, one must choose their destiny. Is it to believe in God, or to become conservative and choose not to believe? Well, the people of the world should all just creep within their minds, and choose not to follow the Messiah onto the deceptive fields of love. These people become sicken with doubt, and unleashing them are quite easy. But the world may never know, for the fools that are blinded with salvation still wander in oblivion. Objection number one is that, can one actually prove the â€Å"existence† of God? How can one experience divinity, without experiencing death first? No men on this earth can! Not the Pope, Saint Anselm, nor William Paley, who actually tired to prove the existence of God. William Paley once said , â€Å"If a man wandered upon a hill, and discovered a watch; who would question the fact, that the watch was created by a designer?† It's possible that the statement is true, but a watch can't be compared to a universe's creation. Paley would later say that the world must have a designer, meaning a God. The watch of coarse must of been created by a designer, but the world is totally different. It's more like a carpenter building a house or building. People can relate more to a building than a universe, cause it's possible that one can experience living within a house. It's not possible for anyone to live among the outside world, and think that God created everything. This only proves Paley's downfall, and ideas ... Good God Essay -- essays research papers Good God When one walks through the streets of humanity, one must choose their destiny. Is it to believe in God, or to become conservative and choose not to believe? Well, the people of the world should all just creep within their minds, and choose not to follow the Messiah onto the deceptive fields of love. These people become sicken with doubt, and unleashing them are quite easy. But the world may never know, for the fools that are blinded with salvation still wander in oblivion. Objection number one is that, can one actually prove the â€Å"existence† of God? How can one experience divinity, without experiencing death first? No men on this earth can! Not the Pope, Saint Anselm, nor William Paley, who actually tired to prove the existence of God. William Paley once said , â€Å"If a man wandered upon a hill, and discovered a watch; who would question the fact, that the watch was created by a designer?† It's possible that the statement is true, but a watch can't be compared to a universe's creation. Paley would later say that the world must have a designer, meaning a God. The watch of coarse must of been created by a designer, but the world is totally different. It's more like a carpenter building a house or building. People can relate more to a building than a universe, cause it's possible that one can experience living within a house. It's not possible for anyone to live among the outside world, and think that God created everything. This only proves Paley's downfall, and ideas ...

The Postal Acceptance Rule Essay -- Business Law

Contractual agreement has always been viewed in terms of offer and acceptance. The universal principle to contract law has always been parties may get into an agreement in whichever way they deem fit and they are subject to certain terms as they choose. As far as legal requirements vital to their formation are binding contracts may be formed. Moreover a binding agreement may be manifested in terms of writing or in verbal form. One of the controversial issues in the law of contract formation has always been the issue of distance contracts. Matters regarding to the types of rules that should be used to govern this type of contracts have always been a topic of debate. One of these rules includes the age old Postal acceptance rule also known as the â€Å"postal rule† or the â€Å"Mailbox rule†. This paper seeks to examine the justification of the postal acceptance rule and its place in the modern world with the emergence of electronic means of communication Background Postal acceptance rule dates back in 1818 when it was established in a court case of (adam v lindsell) In this case the code had to reach a verdict on the moment of contract formation by post. Apparently the courts found out that the parties communicating acceptance through post office were never certain at the exact time the acceptance had been sent. Since postal communication is subject to delay, the involved parties could never be simultaneously aware of the acceptance of the communication, that is, the communication was non instantaneous. As a result this created a series of problems that in turn led to the formation of the postal acceptance rule that still is in so much use today The postal acceptance rule The postal acceptance rule as accepted in the law legal systems... ... Journal (1997): 13. poggi, chrisopher T. "Electronic commerce legislation :An analysis of European and American approaches to contract formation." Virginia journal of international (n.d.). rule", The electronic formation of contracts and the common law: "mailbox. baylor law review. 8 april 2004. scott, Dave. Should the postal acceptance rule be applied t email. 8 april 2012 . T, Poggi and Christopher. "Electronic Commerce Legislation: An analysis of European and American Approaches to Contract Formation." Virginia Journal OF International Law (2000): 224. watnick, valerie. THE ELECTRONIC FORMATION OF CONTRACTS AND THECOMMON LAW "mailbox rule". 6 november 2004. Yamaguchi, mikio. "The problem of delay in the Contract formation Process: A comparative study of contract law' ." cornell international law (2004): 357.

A person I would like to become

Everybody goes about life being whatever he is or doing whatever he is supposed to be, but in the heart of hearts, everyone has a longing – a longing to be someone else other than being himself. ‘What do you want to be’ is an often-asked question. If I were to be asked whom I want to be, at least for as brief a time as one day, my answer would be Mother Teresa. Mother Teresa’s life is what I would call a perfect life. To leave one’s own country and people and go to a totally alien county at a tender age to serve the underprivileged people requires tremendous strength and faith. Mother Teresa was an embodiment of purity, love, and selflessness. Mother Teresa, as everyone knows, had to endure a lot of tribulations because she started from absolutely nothing.   Yet her love and compassion for the poor and neglected made her stick to her task. Nobody can imagine the strength and determination housed in the fragile body. She was a blessed soul with a vision, and it was her faith in God and humanity that kept her going ahead with her noble task. It is a boon to even know her. So, if there is one person who I would want to be, then without any doubt, it would be Mother Teresa. Even at the peak of her popularity, Mother Teresa was simple and modest.   That a person can still be so simple in the midst of all the popularity baffles me. Her life had a purpose.   Mother Teresa has made the lives of countless people worth living.   Known also as â€Å"Saint of the Gutters,† Mother Teresa started an order of nuns, the Missionaries of Charity in Calcutta and the strength grew from 12 sisters to over 3000 in just 50 years. To see God in all His creation, especially the poor, the underprivileged, the neglected, is something very rare, and it is this rarity in her which inspired me all the more, and I would embrace any opportunity to be Mother Teresa, at least for a brief   period. Reference The Mother Teresa of Calcutta Memorial page, [Electronic Version] Retrieved on June 4, 2005, from http://www.catholic.net                                    

Integration

http://sahatmozac. blogspot. com ADDITIONAL MATHEMATICS FORM 5 MODULE 4 INTEGRATION http://mathsmozac. blogspot. com http://sahatmozac. blogspot. com CHAPTER 3 : INTEGRATION Content Concept Map page 2 3–4 5 6 7 8–9 10 – 11 12 4. 1 Integration of Algebraic Functions Exercise A 4. 2 The Equation of a Curve from Functions of Gradients. Exercise B SPM Question Assessment Answer http://mathsmozac. blogspot. com 1 http://sahatmozac. blogspot. com Indefinite Integral a) o o a x n a dx = ax + c. xn+ 1 + c. n+ 1 b) x n dx = c ) o d x = a o x n d x = a n x + n + 1 1 + c . Integration of Algebraic Functions ) ) The [f (x)  ± g(x) ]dx = o f (x) dx  ± d o Equation of a Curve from Functions of Gradients o g(x)dx y = y = o f ‘( x ) d x c, f (x) + http://mathsmozac. blogspot. com 2 http://sahatmozac. blogspot. com INTEGRATION 1. Integration is the reverse process of differentiation. dy 2. If y is a function of x and = f ‘( x) then o f ‘( x)dx = y + c, c = c onstant. dx If dy = f ( x ), then dx o f ( x)dx = y 4. 1. Integration of Algebraic Functions Indefinite Integral a) b) o o a dx = ax + c. n a and c are constants xn+ 1 x dx = + c. n+ 1 n c is constant, n is an integer and n ? – c) o ax dx = a o ax n + 1 x dx = + c. n+ 1 n and c are constants n is an d) o [f ( x )  ± g ( x ) ]dx = o f ( x) dx  ± o g ( x)dx http://mathsmozac. blogspot. com 3 http://sahatmozac. blogspot. com Find the indefinite integral for each of the following. a ) ? 5dx b) ? x 3 dx c) ? 2 x dx 5 d) ? ( x ? 3x 2 )dx Always remember to include ‘+c’ in your answers of indefinite integrals. Solution : a) ? 5dx ? 5x ? c b) 3 ? x dx ? x3? 1 ? c 3 ? 1 x4 = ? c 4 2 c) 5 ? 2 x dx ? 2 x5? 1 ? c 5 ? 1 2 x6 = ? c 6 1 = x6 ? c 3 d) ? ( x ? 3x )dx ? ? xdx ? ? 3x 2 dx = x 2 3 x3 ? ?c 2 3 x2 = ? x3 ? c 2 Find the indefinite integral for each of the following. a) ? ? x ? 3x ? dx 2 x 4 b) ?x ? x 2 4 ? ? ? 3 ? ? dx x ? ? a) Solution : x ? 3Ãâ€"2 ? ? x 4 ?dx ? ? x 3Ãâ€"2 ? ? ? x4 ? x4 ? dx ? ? b) 2 4? ? ? 2 4? ? 3 ? 4 ? dx = ? ? 3x ? 2 ? dx x ? x ? ? ? = ? 3Ãâ€"2 ? 4 x ? 2 dx ? x ? 1 ? 3x 3 = ? 4? c 3 ? ?1 ? 4 = x3 ? ? c x ? ? x? 3 ? 3x? 2 dx ? x? 1 ? x? 2 = ? 3? c ? 2 ? ?1 ? 1 3 =? 2 ? ?c 2x x ? ? ? ? http://mathsmozac. blogspot. com 4 http://sahatmozac. blogspot. com 1. Find ? ? 3x 2 ? 4 x ? 10 dx. ? [3m] 2. Find ? ? x 2 ? 1 ? 2 x ? 3 ? dx. ? [3m] 1? ? 3. Find ? ? 2 x ? ? dx. x? ? 2 [3m] 4. Find ? ? 2x ? ? 3 ?x? 3 ? ? 2 ? dx. 4 x ? [3m] 6x ? 5 5. Integrate with respect to x. x3 [3m] 6. Find ? ?x 5 ? 4Ãâ€"2 2x 4 ? dx [3m] 3 ? ? 7. Find ? x ? 6 ? 6 ? x . x ? ? 2 [3m] 8. Integrate x 2 ? 3x ? 2 with respect to x. x ? 1 [3m] http://mathsmozac. blogspot. com 5 http://sahatmozac. blogspot. com The Equation of a Curve from Functions of Gradients dy ? f ‘( x), then the equation of the curve is dx If the gradient function of the curve is y ? ? f ‘( x ) dx c is constant. y ? f ( x) ? c, Find the equation of the curve that has the gradient function 3x ? 2 and passes through the point (2, ? 3). Solution The gradient function is 3x ? 2. dy ? 3x ? 2 dx y ? ? (3x ? 2)dx y? 3Ãâ€"2 ? 2x ? c 2 The curve passes through the point (2, ? 3). Thus, x = 2, y = ? 3. 3(2) 2 ? 3 ? ? 2x ? c 2 ? 3 ? 6 ? 4 ? c c ? 5 Hence, the equation of curve is y? 3x 2 ? 2x ? 5 2 http://mathsmozac. blogspot. com 6 http://sahatmozac. blogspot. com 1. Given that dy ? 6 x ? 2 , express y in terms of x if y = 9 when x = 2. dx 2. Given the gradient function of a curve is 4x ? 1. Find the equation of the curve if it passes through the point (? 1, 6). 3. The gradient function of a curve is given by dy 48 ? kx ? 3 , where k is a constant. dx x Given that the tangent to the curve at the point (-2, 14) is parallel to the x-axis, find the equation of the curve. http://mathsmozac. blogspot. com 7 http://sahatmozac. blogspot. com SPM 2003- Paper 2 :Question 3 (a) Given that y ? 2 x ? 2 and y = 6 when x = ? 1, find y in terms of x. dx [3 marks] SPM 2004- Paper 2 :Question 5(a) The gradient function of a curve which passes through A(1, ? 12) is 3 x 2 ? 6 x. Find the equation of the curve. [3 marks] http://mathsmozac. blogspot. com 8 http://sahatmozac. blogspot. com SPM 2005- Paper 2 :Question 2 A curve has a gradient function px 2 ? 4 x , where p is a constant. The tangent to the curve at the point (1, 3) is parallel to the straight line y + x ? 5 =0. Find (a) the value of p, [3 marks] (b) the equation of the curve. [3 marks] http://mathsmozac. blogspot. com 9 http://sahatmozac. blogspot. com 1.Find the indefinite integral for each of the following. (a) ? ? 4x 3 ? 3 x ? 2 dx ? (b) 3? x ? ? 2 2 ? 6? ? dx x3 ? 1 ? 2 ( c) (c) ? ? x 5 + 5 6x ? 3 ? ? dx ? ? x2 ? 3 (d) ? ? ? x2 ? ? ? 2 ? ? dx ? ? 2. If dy ? 4 x3 ? 4 x, and y = 0 when x = 2, find y in terms of x. dx http://mathsmozac. blogspot. com 10 http://sahatmozac. blogspot. com 3. If dp v3 ? 2v ? , and p = 0 when v = 0, find the value of p when v = 1. dv 2 4. Find the equation of th e curve with gradient 2 x 2 ? 3 x ? 1, which passes through the origin. 5. d2y dy dy Given that ? 4 x, and that ? 0, y = 2 when x = 0. Find and y in terms 2 dx dx dx of x. http://mathsmozac. blogspot. om 11 http://sahatmozac. blogspot. com EXERCISE A 1) 2) 3) 4) 5) 6) 7) 8) x ? 2 x ? 10 x ? c 3 2 SPM QUESTIONS 1) y ? x2 ? 2x ? 7 2) y ? x3 ? 3 x 2 ? 10 3) p ? 3, y ? x3 ? 2 x 2 ? 4 x4 ? x3 ? 3x ? c 2 4 3 1 x ? 4x ? ? c 3 x 4 2 x x 1 ? ? 3 ? 2x ? c 2 2 x 6 5 ? ? 2 x 2x 2 x 2 ? ?c 4 x 1 2 x3 ? 3 ? c x 2 x ? 2x ? c 2 ASSESSMENT 1) (a ) x 4 ? 3 2 x ? 2x ? c 2 2 3 (b) 3x ? ? 2 ? c x x 6 x 1 (c ) ? ?c 9 24 x 4 x3 9 (d ) ? 6x ? ? c 3 x y ? x4 ? 2 x2 ? 8 p? 7 8 2 3 3 2 x ? x ? x 3 2 2 3 x ? 2 3 EXERCISE B 1) y ? 3x 2 ? 2 x ? 1 3 x 2 24 ? 2 ? 2 2 x 2) 2) y ? 2 x 2 ? x ? 3 3) y ? 3) 4) y? 5) y? http://mathsmozac. blogspot. com 12 http://sahatmozac. logspot. com ADDITIONAL MATHEMATICS FORM 5 MODULE 5 INTEGRATION http://mathsmozac. blogspot. com 13 http://sahatmozac. blogspot. com CONTENT CONCEPT MAP INTEGRATION BY SUBSTITUTION DEFINITE INTEGRALS EXERCISE A EXERCISE B ASSESSMENT SPM QUESTIOS ANSWERS 2 3 5 6 7 8 9 10 http://mathsmozac. blogspot. com 14 http://sahatmozac. blogspot. com CONCEPT MAP INTEGRATION BY SUBSTITUTION un ? ax ? b ? dx ? ? du ? a n DEFINITE INTEGRALS If b d g(x) ? f (x) then dx b where u = ax + b, a and b are constants, n is an integer and n ? -1 OR (a) ? f (x)dx g(x)? ? g(b) ? g(a) a a (b) ? f (x)dx f (x)dx a a b b (c) ? f (x)dx f (x)dx ? ? f (x)dx a b a b c ? ax ? b ? ? ? ax ? b ? dx ? a ? n ? 1? n n ? 1 ? c, where a, b, and c are constants, n is integer and n ? -1 http://mathsmozac. blogspot. com 15 http://sahatmozac. blogspot. com INTEGRATION BY SUBSTITUTION un ? ? ax ? b ? dx ? ? a du n where u = ax + b, a and b are constants, n is an integer and n ? -1 O R ? ax ? b ? ? ? ax ? b ? dx ? a ? n ? 1? n n ? 1 ? c, where a, b, and c are constants, n is integer and n ? -1 Find the indefinite integral for each of the following. (a) ? ? 2 x ? 1? dx 3 (b) ? 4(3 x ? 5)7 dx 2 (c) ? dx (5 x ? 3)3 SOLUTION (a) ? ? 2 x ? 1? dx 3 Let u = 2x +1 du du ? 2 ? dx ? dx 2 3 3 ? du ? ? (2 x ? 1) dx ? ? u ? ? ? ? u3 = ? du 2 u 3 ? 1 = ? c 2(3 ? 1) u4 +c 8 (2 x ? 1) = +c 8 = Substitute 2x+1 and substitute dx with du dx = 2 OR (2 x ? 1) 4 ? c ? (2 x ? 1) dx ? 2(4) 3 = ? 2 x ? 1? 8 4 ?c Substitute u = 2x +1 http://mathsmozac. blogspot. com 16 http://sahatmozac. blogspot. com (b) ? 4(3 x ? 5) dx 7 (c) Let u ? 3 x ? 5 du du ? 3 ? dx ? dx 3 7 4u 7 du ? 4(3 x ? 5) dx ? ? 3 4u 8 = ? c 3(8) u8 ? c 6 (3u ? 5)8 = ? c 6 = 2 dx ? ? 2(5 x ? 3) ? 3 dx (5 x ? 3)3 Let u ? 5 x ? 3 du du ? 5 ? dx ? dx 5 ? 3 2u ? 3 du ? 2(5 x ? 3) dx ? ? 5 2u ? 3 = ? c 5(? 2) ? OR 4(3 x ? 5)8 ? c ? 4(3 x ? 5) dx ? 3(8) 7 u ? 2 ? c ? 5 1 = ? 2 5u 1 =? ?c 5(5 x ? 3)2 = = (3x ? 5)8 ? 6 DEFINITE INTEGRALS If d g ( x) ? f ( x) then dx b (a) (b) ? b a b f ( x)dx ? ? g ( x) ? ? g (b) ? g (a) a ? (c ) ? a b f ( x)dx ? ? ? f ( x)dx a b a f ( x)dx ? ? f ( x)dx ? ? f ( x)dx b a c c http://maths mozac. blogspot. com 17 http://sahatmozac. blogspot. com Evaluate each of the following ( x ? 3)( x ? 3) (a) ? 12 dx x4 1 1 (b) ? 0 dx (2 x ? 1) 2 SOLUTION (a) x2 ? 9 2 ( x ? 3)( x ? 3) ? c ? ?12 4 dx ? 1 x4 x 2 9 ? 2? x = ? 1 ? 4 ? 4 ? dx x ? ?x = ? 12 ( x ? 2 ? 9 x ? 4 )dx ? x ? 1 ? x ? 3 ? ? =? ? 9? ? ? 3 ? ?1 ? ?1 2 2 (b) ?0 1 1 1 dx ? ?0 (2 x ? 1)? 2 dx 2 (2 x ? 1) 1 = ? 0 (2 x ? 1) ? 2 dx ? (2 x ? 1) ? 1 ? =? ? ? ?1(2) ? 0 ? 1 = ? ? 2(2 x ? 1) ? 0 =? ? ? 1 1 ? 2[2(1) ? 1] ? 2[2(0) ? 1] ? 1 1 ? 1 3? = ? 3 ? ? x x ? 1 ? 1 3 ? ? 1 3? = ? 3 ? ? 3 ? ? 2 2 ? ? 1 1 ? 1 3 = ? ? ? (? 1 ? 3) 2 8 1 =? ?2 8 1 =? 2 8 1 ? 1? = ? ? 6 ? 2? 1 = 3 http://mathsmozac. blogspot. com 18 Distributed:18. 1. 09 Return:20. 1. 09 INTEGRATE THE FOLLOWING USING SUBSTITUTION METHOD. (1) ? ( x ? 1)3dx (2) ? ?4 ? 3 x ? 5 ? dx ? 5 (3) ? 1 ? 5 x ? 3? dx 4 1 ? ? (4) ? ? 5 ? x ? dx 2 ? ? ?3 1 ? ? (5) ? 5 ? 4 ? y ? dy 2 ? ? 4 3? 2 ? (6) ? ? 5 ? u ? du 2? 3 ? 5 19 http://sahatmozac. blogspot. com EXERCISE B 8 1. Evaluate ? 3 ( x3 ? 4)dx Answer : 1023. 75 2. Evaluate Answer: 3 ? ?3 1 2 x( x ? x ? 5)dx 8 83 96 ?2 ? 3. Integrate ? x ? 5 ? with respect to x ? 3 ? 4 4. Evaluate ? 1 3 1 ? ? ? 2 ? 3x ? 4 ? dx ? 1 x ? ? 1 Answer: 3 ? 2 ? ? x ? 5? ? c 10 ? 3 ? 5 Answer : 3 5. Evaluate ? 3 1 ? 2 x ? 1 2 x ? 1? dx 4 x2 6. Given that of 2 5 ? 5 2 f ( x)dx ? 10 , find the value 5 Answer: 1 6 ? ? 1 ? 2 f ( x)? dx Answer :17 http://mathsmozac. blogspot. com 20 http://sahatmozac. blogspot. com ASSESSMENT ?6 and 2. (a) ? 5(2 ? 3v) dv 4 (b) ? dx 5 3 ? 1 ? 5 x ? 1. Given that ? 2 2 1 f ( x)dx ? 3 ? 2 3 f ( x)dx ? ?7 . Find (a) the value of k if (b) ? ? kx ? f ( x)? dx ? 8 1 ? ? 5 f ( x) ? 1? dx 3 1 Answer : (a) k = (b) 48 22 3 3.Show that d ? x 2 ? 2 x 2 ? 6 x 4. . ? dx ? 3 ? 2 x ? ? 3 ? 2 x ? 2 4 Given that ? 4 0 f ( x)dx ? 3 and Hence, find the value of Answer : 1 10 ? ? 3 ? 2x ? 0 1 x ? x ? 3? ? 0 g ( x)dx ? 5 . Find 4 0 2 dx . ? f ( x)dx ? ? g ( x)dx (b) ? ?3 f ( x) ? g ( x)? dx (a) 0 4 0 4 Answer: (a) – 15 (b) 4 http://mathsmozac. blogspot. com 21 http://sahatmozac. blogspot. com SPM QUESTIONS SPM 2003 – PAPER 1, QUESTION 17 1. Given that ? SPM 2004 – PAPER 1, QUESTION 22 k n dx ? k ? 1 ? x ? ? c , 2. Given that 1 ? 2 x ? 3? dx ? 6 , where k ; -1 , find the value of k. [4 marks] ? 1 ? x ? find the value of k and n [3 marks] Answer: k = 5 5 Answer: k = ? =-3 3 5 4 SPM 2005 – PAPER 1, QUESTION 21 6 6 3. Given that ? 2 f ( x)dx ? 7 and ? 2 (2 f ( x) ? kx)dx ? 10 , find the value of k. Answer: k = 1 4 http://mathsmozac. blogspot. com 22 http://sahatmozac. blogspot. com ANSWERS EXERCISE A 1. 3 ( x + 1)4 + c 2. 60 (3 x +5) – 4 + c 3. ?20 EXERCISE B 1. 1023. 75 ? 5 x ? 3? 3 ?c 2. 3 83 96 5 4. 3? 1 ? ?5 ? x? ? c 2? 2 ? ? y? ?c ? 6 4 ?2 3 ? 2 ? 3. ? x ? 5? ? c 10 ? 3 ? 1 3 5 5. 1 6 6. 17 1 ? 5. ?10 ? 4 ? 2 ? 6. 4. 3 2 ? ? ? 5 ? 5 ? u ? ? c 3 ? ? ASSESSMENT 22 1. (a) k = 3 (b) 48 2. (a) 90(2 – 3v) +c ? 100 (b) (1 ? 5 x) ? 4 ? c 3 3. 1 10 -5 SP M QUESTIONS 1. k = ? 2. k = 5 3. = 1 4 5 3 n=-3 4. (a) – 15 (b) 4 http://mathsmozac. blogspot. com 23 http://sahatmozac. blogspot. com ADDITIONAL MATHEMATICS MODULE 6 INTEGRATION http://mathsmozac. blogspot. com 24 http://sahatmozac. blogspot. com CHAPTER 3 : INTEGRATION Content Concept Map 9. 1 Integration as Summation of Areas page 2 3 4–6 7–8 9 – 11 12 – 14 15 Exercise A 9. 2 Integration as Summation of Volumes Exercise B SPM Question Answer http://mathsmozac. blogspot. com 25 http://sahatmozac. blogspot. com a) The area under a curve which enclosed by x-axis, x = a and x = b is a) The volume generated when a curve is rotated through 360? bout the x-axis is ? ? b a y dx b) The area under a curve which enclosed by y-axis, y = a and y = b is b a Vx ? ? ? y 2 dx a b x dy b) The volume generated when a curve is rotated through 360? about the y-axis is c) The area enclosed by a curve and a straight line ? ? f ( x) ? g ( x)? dx b a Vy ? ? ? x 2 dy a b http://mathsmozac. blogspot. com 26 http://sahatmozac. blogspot. com 3. INTEGRATION 3. 1 Integration as Summation of Area y y = f(x) b a a b 0 The area under a curve which enclosed by x = a and x = b is x 0 x y = f(x) ? b a ydx The area under a curve which is enclosed by y = a and y = b isNote : The area is preceded by a negative sign if the region lies below the x – axis. ? b a xdy Note : The area is preceded by a negative sign if the region is to the left of the y – axis. The area enclosed by a curve and a straight line y y = g (x) y = f (x) a The area of the shaded region = = b b x ? ? ? f ( x) ? g ( x)? dx a b a a b f ( x)dx ? ? g ( x) http://mathsmozac. blogspot. com 27 http://sahatmozac. blogspot. com 1. Find the area of the shaded region in the diagram. y y = x2 – 2x 2. Find the area of the shaded region in the diagram. y y = -x2 + 3x+ 4 x -1 0 4 0 x http://mathsmozac. blogspot. com 28 http://sahatmozac. logspot. com 3. Find the area of the shaded region y y=2 4. Find the area of the shaded region in the diagram. y y = x2 + 4x + 4 0 x = y2 x -2 -1 0 2 x http://mathsmozac. blogspot. com 29 http://sahatmozac. blogspot. com 5. Find the area of the shaded region in the diagram y 1 x = y3 – y x 6. y y = ( x – 1)2 0 0 x x=k -1 Given that the area of the shaded region in 28 the diagram above is units2. Find the 3 value of k. http://mathsmozac. blogspot. com 30 http://sahatmozac. blogspot. com 3. 2 Integration as Summation of Volumes y y=f(x) The volume generated when a curve is rotated through 360? about the x-axis is 0 a b xVx ? ? ? y 2 dx a b y y=f(x) The volume generated when a curve is rotated through 360? about the y-axis is b a 0 x Vy ? ? ? x 2 dy a b http://mathsmozac. blogspot. com 31 http://sahatmozac. blogspot. com y y=x(x+1) Find the volume generated when the shaded region is rotated through 360? about the x-axis. x 0 Answer : x=2 ? ? ? y 2 dx 0 2 Volume generated ? ? ? x 2 ? x ? 1? dx 2 2 0 ? ? ? ( x 4 ? 2 x3 ? x 2 )dx 0 2 ? x 5 2 x 4 x3 ? ? ? ? ? 4 3 ? 0 ? 5 2 25 2(2)4 23 ? ? ? ? ? ? ? ? 0? 5 4 3? ? 256 1 ? ? @ 17 ? units 3 . 15 15 y y ? 6 ? x2 The figure shows the shaded region that is enclosed by the curve y ? ? x 2 , the x-axis and the y-axis. Calculate the volume generated when the shaded region is revolved through 360? about y-axis. 0 Answer : Given y ? 6 ? x 2 substitute x ? 0 into y ? 6 ? x Then, y ? 6? 0 y? 6 2 x Volume generated ? ? ? x 2 dy 0 6 ? ? ? ? 6 ? y ? dx 6 0 ? y2 ? ? ? ?6 y ? ? 2 ? 0 ? 62 ? ? 6(6) ? 2 ? 18? units 3 . ? ? ? ? 0? ? ? 6 http://mathsmozac. blogspot. com 32 http://sahatmozac. blogspot. com 1. y y = x (2 – x) 0 x The above figure shows the shaded region that is enclosed by the curve y = x (2 – x) and x-axis. Calculate the volume generated when the shaded region is revolved through 360? bout the y-axis. [4 marks] http://mathsmozac. blogspot. com 33 http://sahatmozac. blogspot. com 2. y R (0, 4) Q (3, 4) P (0, 2) y? = 4 (x + 1) 0 x=3 x The f igure shows the curve y ? ( x ? 2) 2 . Calculate the volume generated when the shaded region is revolved through 360? about the x-axis. http://mathsmozac. blogspot. com 34 http://sahatmozac. blogspot. com 3. y R (0, 4) x y ? ? 3? x 0 x=k The above figure shows part of the curve y ? ? 3 ? x and the straight line x = k. If the volume generated when the shaded region is revolved through 1 360? about the x-axis is 12 ? units3 , find the value of k. 2 http://mathsmozac. logspot. com 35 http://sahatmozac. blogspot. com SPM 2003- Paper 2 :Question 9 (b) Diagram 3 shows a curve x ? y 2 ? 1 which intersects the straight line 3 y ? 2 x at point A. y 3 y ? 2x 3y ? 2x x ? y2 ? 1 ?1 0 x Diagram 3 Calculate the volume generated when the shaded region is involved 360? about the y-axis. [6 marks] http://mathsmozac. blogspot. com 36 http://sahatmozac. blogspot. com SPM 2004- Paper 2 :Question 10 Diagram 5 shows part of the curve y ? y 3 ? 2 x ? 1? 2 which passes through A(1, 3). A(1,3) y? 0 a) b) Di agram 5 3 ? 2 x ? 1? 2 x Find the equation of the tangent to the curve at the point A. [4 marks] A egion is bounded by the curve, the x-axis and the straight lines x=2 and x= 3. i) Find the area of the region. ii) The region is revolved through 360? about the x-axis. Find the volume generated, in terms of ? . [6 marks] http://mathsmozac. blogspot. com 37 http://sahatmozac. blogspot. com SPM 2005- Paper 2 :Question 10 In Diagram 4, the straight line PQ is normal to the curve y ? straight line AR is parallel to the y-axis. y x2 ? 1 at A(2, 3). The 2 y? x2 ? 1 2 A(2, 3) 0 R Diagram 4 Find (a) (b) (c) Q(k, 0) x the value of k, [3 marks] the area of the shaded region, [4 marks] the volume generated, in terms of ? when the region bounded by the curve, the y-axis and the straight line y = 3 is revolved through 360? about y-axis. [3 marks] http://mathsmozac. blogspot. com 38 http://sahatmozac. blogspot. com EXERCISE A EXERCISE B 1. 1 1 ? unit 2 15 1. 1 1 units 2 3 5 units 2 6 2. 2. 20 3 6 ? unit 3 5 k ? ?2 3. 3. 2 2 units 2 3 2 units 2 3 SPM QUESTIONS SPM 2003 Volume Generated ? 52 ? units3 15 4. 24 SPM 2004 i) Area ? 1 units 2 5 49 ? units3 1125 5. 1 units 2 2 k? 4 ii) Volume Generated ? 6. SPM 2005 a) k ? 8 1 b) Area ? 12 units2 3 c) Volume Generated ? 4? units? http://mathsmozac. blogspot. com 39