6/18/2023 0 Comments Character isadora moon![]() ![]() But will they be able to resist adding a sprinkling of magic to their creation. When Isadora is invited to stay at her friend Zoe's house she's so excited she hasn't been to a sleepover before! There will be midnight feasts, and staying up all night, it's going to be so much fun! And while she's there, Isadora and Zoe are going to work on their cake for a baking competition at school. Her mum is a fairy and her dad is a vampire and she's a bit of both. Language eng Summary Isadora Moon is special because she's different. Moon, Isadora, (Fictitious character) - Juvenile fiction.The four-year-old from Barnsley thinks the character is funny because he wears saucepans and kettles.Label Isadora Moon has a sleepover Title Isadora Moon has a sleepover Statement of responsibility Harriet Muncaster Creator His favourite book is The Magic Faraway Tree, which was published in 1943. The Saucepan Man, from Enid Blyton’s series The Faraway Tree has been the inspiration for Isaac Levick’s costume. The Saucepan Man Isaac is The Saucepan Man from The Faraway Tree series (Photo: Glev Levick/Twitter) Aryan Uzzaman loves playing with his Incredible Hulk action figure and dressing up as the Marvel Comics character.ĭad Rashid says Aryan, from London, would prefer to celebrate World Book Day at school today “but he is still glad he gets to dress up and see his friends all dressed up too in their online lessons”. It wouldn’t be World Book Day without a superhero costume. “She just loved Katie Taylor and loved the fact she pretended to be a boy as girls were not allowed to fight in Ireland.” The Hulk Aryan Uzzaman, 9, is happy he got to dress up for World Book Day despite being at home (Photo: Rashid Uzzaman/Twitter) Mum Catherine, from County Derry, says: “Santa brought her this book at Christmas and we read a few pages a night – we have been through the book twice now. Jacqui Hurley’s book highlights the achievements of Irish sportswomen. Katie Taylor Caitlin Bradley decided to dress up as Katie Taylor (Photo: Catherine Mullan/Twitter)Ĭaitlin Bradley, 7, decided to dress up as Irish professional boxer Katie Taylor after reading about her in Girls Play Too. Mum Tenika says he likes “their witty, relatable topics about school and friendships”. Greg Heffley, the main character from the much loved Diary of a Wimpy Kid series by Jeff Kinney, is a favourite for World Book Day.Ĭaelan Blake, 9, from London, is a big fan of the book series. This afternoon William is doing some maths with The Very Hungry Caterpillar and this evening Daddy has promised to help them make a den to read their bedtime story in.” Wimpy Kid Caelan, 9, is Greg Heffley from Diary of a Wimpy Kid (Photo: Tenika Blake) ![]() “This morning we went on little walk pretending we were going on a bear hunt, we read The Tiger Who Came To Tea and recreated the tea party for our lunch. The children were fascinated, which gave me the idea of making one for Isadora Moon. At my last school visit I took in a couple of 3D sets I had made for I am a Witch’s Cat. ![]() “They are some of their favourite bedtime stories to read with Mummy and Daddy,” says mum Samantha. This 3D illustration scene of Isadora Moon’s kitchen is coming on tour with me. It's almost time for the vampire ball, and Isadora can't wait There's just one problem: she's got to compete in a talent show with the other vampire children. The Coleman brothers, from Doncaster, have chosen their favourite picture books for their World Book Day costumes.įour-year-old William is Max from Where the Wild Things Are, published in 1963 by Maurice Sendak, and 18-month-old Finn is Elmer the Patchwork Elephant from David McKee. Isadora Moon is special because she's different. Where the Wild Things Are and Elmer Brothers William and Finn have celebrated World Book Day at home (Photo: Samantha Coleman/Twitter) “The plan is to celebrate World Book Day again when they’re back at school,” adds David. ![]()
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![]() ![]() Larger driveshafts and wheel bearings have been fitted to cope with the upgrade.ĮPA estimates say the '08 Cobalt SS gets 22 mpg city/30 mpg highway. Compare this to 205 hp at 5,600 rpm and 200 lb-ft of torque way up at 4,000 for the supercharged Ecotec in the '07 Cobalt SS. The 2.0-liter turbo develops 260 horsepower at 5,300 rpm and 260 pound-feet of torque at only 2,000 rpm. The output gains over the former supercharged Ecotec are substantial. This turbocharged, intercooled Ecotec with direct fuel injection is the same engine introduced by the 2008 Chevy HHR SS. In addition, the 2.0-liter Ecotec four-cylinder gets continuously variable timing for its intake and exhaust valves this year. Of course, then we go poking around under the Cobalt's hood and find the turbocharger that engineers from the GM Performance Division (GMPD) have secreted away in the back, which replaces the supercharger that used to be under the SS's hood. The only hard visual evidence that we're driving a 2008 Chevrolet Cobalt SS is a set of new 18-by-7.5-inch wheels (0.5 inch wider than before). But give this 2008 Chevrolet Cobalt SS Coupe an hour of your time on a good road and it takes you somewhere completely different. It's an odd feeling, because with that familiar Chevy face and Pro Stock-size rear wing, you wonder if you're getting behind the wheel of last year's car. It's an old-school touch in a car full of new-school kit, and you realize there's quite a bit going on with the 2008 Chevrolet Cobalt SS. The sounds are distinct even to the distracted ear, and they refuse to harmonize. We hear the euphoric sigh of the turbocharger, followed by a throbbing exhaust note out the back. Instead of savoring the moment, we get back on the throttle. Perhaps most surprising of all, it gives the impression of being happy to do it. It turns into a tight left-hander with the haste and hunger of an import sport compact. We come to our first serious corner on Glendora Mountain Road, and the 2008 Chevrolet Cobalt SS Coupe delivers the unexpected. ![]() ![]() ![]() See Also: Get to know Mendeecees from Love and Hip Hop ATL View this post on Instagram A post shared by C.E. Rich Dollaz has earned a decent income from his career as an entrepreneur, music executive and reality television star and is alleged to have an estimated net worth of $2. Her net worth is estimated at over 1m as per Page Six in 2020. Only one of his children, Ashley Trowers is known as she appeared on Love & Hip Hop with her mother Miracle Kay Hall. He has four children but he keeps their identities private. ![]() Rich Dollaz is currently not married but has had several celebrity ex-girlfriends like Erica Mena, Diamond Strawberry, Jade Wifey, Miracle Kay Hall, Tiffany Lewis, and others. His uncle and grandmother died of the same disease. ![]() He made this known in the season 8 premiere of Love and Hip Hop: New York. Rich Dollaz gained his major recognition after joining Love & Hip Hop: New York in 2011 as a manager of Olivia Longott. From 2015 to early 2017, she appeared as a regular cast member on the VH1 reality television series Love and Hip Hop in New York, which depicted her. The music executive left Bad Records and joined Universal Music and is now the head of radio promotion and experience in the New York club scene.ĭue to his friendship with Sean Combs, Rich Dollaz because a brand ambassador for Ciroc and has also been working as the Senior Director of Promotions at Power Moves, Inc with Shawn Prez.Īside from this, he is the CEO of Dollaz Unlimited, a record label launched in 2009 with artists like Erica Mena, Helen Little, Jasmeen Christian, and others. ![]() 6/17/2023 0 Comments Pasta e fagioli![]() ![]() Reheat soup in a pot on the stovetop over medium heat, stirring occasionally. Thaw overnight in the refrigerator before reheating. I usually store the soup and cooked pasta (tossed with a little olive oil) separately in the freezer. It freezes really well for about 3 month in an airtight container (be sure to allow about 3/4-inch for liquid to expand at top of container). I like to store in individual microwave safe containers to I can reheat individual portions straight from the fridge. Store pasta e fagioli soup (separate from pasta) for up to 3 days in the refrigerator in an airtight container. Add beans and parsley to soup and serve warm.Cook pasta separately on stovetop near the end of cooking. Add remaining ingredients up to and including salt and pepper.Saute onion then garlic and add to crock pot. Add pasta and beans to soup warm briefly then stir in parsley.Add broth, tomato sauce, canned tomatoes, sugar, dried herbs and beef.Cook beef in a pot, drain and transfer beef.In a pinch another small pasta will work fine here like macaroni or even orzo. Dried oregano, basil, thyme, marjoram. If you don’t have all the different dried herbs then you can just use an Italian seasoning blend.This very small amount just balances the acidity of the canned tomatoes. These canned ingredients make this a weeknight friendly recipe cutting way down on prep. Canned tomato sauce, diced tomatoes, kidney beans, great northern beans, and low-sodium chicken broth.Yellow onion, carrots, celery, garlic and parsley. These fresh vegetables add layers of flavor.This is used for sauteing the veggies so you won’t need much. You can also try it with half Italian sausage. It’s a hearty soup consisting of plenty of the two. The Italian term “pasta e fagoili” translates in English to pasta and beans. Plus this is super easy to make, nothing complicated here and it all comes together in one pot!Īll around win! Try it and let me know how you like it. You’ll love that it uses ingredients that are commonly kept on hand (do you store ground beef in the freezer like I do?), it has such a delicious satisfying flavor, it’s so hearty and it’s a dinner everyone agree on. And of course a family favorite too – everyone in my family loves this soup! Since sharing this soup 6 years ago it has become a reader favorite recipe. It’s one of the ultimate comfort food and truly one of the best soups you’ll make! This pasta fagioli recipe is a MUST that you can’t miss out on. ![]() This Italian style soup is loaded with hearty ground beef, fresh vegetables, creamy beans, tender pasta and delicious herbs all in a rich and savory broth. The BEST Pasta e Fagioli Soup! And yes, it’s even better than Olive Garden’s! ![]() 6/17/2023 0 Comments Starfront collision galaxy s5![]() ![]() Enjoy unlimited replayability thanks to Multiplayer mode.Choose between 5 multiplayer maps, each corresponding to one of the 5 environments in the game.Confront your friends in epic and challenging Local and Online Multiplayer battles.Gaze upon top-notch 3D-rendered environments, buildings and units.Discover the deep and engaging story of a war for resources, told throughout the solo campaign.Wage war across five gorgeous environments: ice, badlands, a jungle, an underground reactor and a destroyed alien city.Gather resources to build 24 different buildings and recruit 30 different units.Complete 20 missions and create your own battles thanks to Skirmish mode.Hone your strategy with three different factions - The Consortium, Wardens and Myriad - each with unique tech trees and tactics.The entire interface has been redesigned for the iPad to ensure a perfectly ergonomic handling of the game.At last, an RTS with intuitive touch controls that give you total control over your forces.THE DEEPEST, MOST BALANCED RTS GAMEPLAY ON iPAD Once you’ve mastered the solo campaign, put your skills to the test in exciting multiplayer battles. Each faction can construct 8 different buildings and over 10 destructive units to build up their base and mount an unstoppable assault on adversaries. Whose side will you choose?With Starfront: Collision HD, choose from 3 unique but balanced races and deploy your strategy for victory in this battle. To add to the chaos, a sentient robot race called the Wardens is trying to turn the war in their favor. The Myriad, an indigenous race of aliens, is addicted to Xenodium and will do everything they can to prevent the Consortium from plundering their resources. However, they are not the only ones after the rare mineral. Summary: The best real-time strategy is now at your fingertips! Starfront: Collision HD, the epitome of RTS gameplay with gorgeous HD graphics and a competitive 4-player multiplayer, finally hits the App Store! Welcome to planet Sinistral, where rare Xenodium crystals are coveted by a human mining The best real-time strategy is now at your fingertips! Starfront: Collision HD, the epitome of RTS gameplay with gorgeous HD graphics and a competitive 4-player multiplayer, finally hits the App Store! Welcome to planet Sinistral, where rare Xenodium crystals are coveted by a human mining conglomerate called the Consortium. ![]() ![]() ![]() 5 were the reason for the band switching from MySpace Records to A&M/Octone for their label, as MySpace wanted to censor or remove these songs from the tracklisting. This song and other party-oriented songs such as Los Angeles, Everywhere I Go, and No. Despite the song's initial success and its intended release for the album Hollywood Undead, it was never re-recorded for their debut album Swan Songs. Some tracks on this album include “California Dreaming”, “Whatever It Takes”, “Renegade” or “We Own The Night”.This song was one of the major reasons for the band's success, since guest vocalist Jeffree Star had a huge fanbase on MySpace that later became fans of the band after Jeffree did this song with them. The band states that it is “ their best album so far”. On October 27th, 2017 the album Five was released. In 2015 they released their fourth album entitled Day of the Dead where you can find songs like “Day of the Dead”, “Disease” or “Fuck the World”. Songs from this album included “We Are”, “From the Ground”, “Outside” and many others. Third album was titled Notes From The Underground. American Tragedy features songs such as “Been to Hell”, “S.C.A.V.A.”, “Bullet”. On this album, the main vocals are sung by Danny rather than Deuce. Second studio album was called American Tragedy and was released in 2011. It was called Swan Songs and includes songs like “City”, “Black Dahlia” and “Everywhere I Go”. Their first album was released on September 2nd, 2008. J-Dog liked the way it sounded, and the name stuck. ![]() The neighbor didn’t read it correctly, and thought that both of those words were the name of the band. J-Dog wrote the band name and name of the song on a small CD and showed it to his neighbor. ![]() The name “Hollywood Undead” was introduced by J-Dog when he and Deuce wrote a song called “Hollywood,” and at the time called the band “Undead” (this designation comes from the times when they used to call people who lived in Hollywood “undead” because they were partying all the time and that is why they thought they looked like zombies). Some of their songs are about partying, drinking, taking drugs, girls but also about love, feelings, being heartless, having a broken heart and similar things. They are well known for their sarcastic and accurate lyrics. All members wear masks and use nicknames. There are also three past members Da Kurlzz (vocals, drums, percussion, left in June 2017) Deuce (vocals, left in 2009 for an unconfirmed reason) and Shady Jeff (vocals, left in 2007 because of disagreement with other members). Nowadays there are five members J-Dog (vocals, guitar, bass guitar, keyboards, synthesizer), Charlie Scene (vocals, lead guitar), Johnny 3 Tears (vocals, bass guitar), Funny Man (vocals) and Danny (vocals, keyboards, guitar). All of the members have grown up in LA, California. UNDEAD You better get up out the way Tomorrow we'll rise so let's fight todayĮdit bioHollywood Undead was formed in June/July 2005 by J-Dog and Deuce (past member). That's when we turn off the lights, undead You think that's funny? Watch me eat ForBiddeN's fat pussy Let's play Barbie and shove Ken's dick in my assĪnd then I'll beat you like I did that bitch, Stevie Then he'll cum on my face before I go on MySpaceĪnd every guy wants my lipstick smeared on his nut-sack ![]() Wanna give me a hand? 'Cause I'll deep-throat your dad Hey, what is that? Dude, is that a guy or a girl?īitches get mad that I swallow more cum than they can That's when we, that's when we turn off the lights That's when we, that's when we turn off the lights, Undead Or I'll do the Michael Jackson and I'mma rape you! You better put out, don't make me hate you Rub it on your butt cheeks and watch it transform I pull out my skin sword on the dance floor "Beep-beep! Hey, you girls need a ride? Get inside!" My dick's sinned so much it should be crucified "Hey, Charlie, how many girls you taking home tonight?" It's Charlie Scene, let me drink from your flask I get drunk and touch Tila in her hot spot I get pissed when the haters try to cock-block Sad boobies, bad boobies, clean boobies, mean boobies Take off that shirt and let me see them B boobies That's when we turn off the lights, Undead "Fuck girls deep, stick it in their pooper" I'm a sex robot sent back from the fa-fa-fucking future Your boyfriend's gay, got his trunk raised I got a dick like Kareem Abdul-J-J-Jabbarie What a change 'cause I fuck g-g-girls in alleysīehind the beauty bar, let's see how far we can go on a sexual safari Uh, I be the J to the D, girls call from O.C Girl, if you're from Orange County, I'll fuck you right Let's have a pillow fight, I know you're tight Girl, your boobies look real nice to me tonight ![]() 6/17/2023 0 Comments 2017 ammo stockpile![]() ![]() The MEICO documents obtained by OCCRP show that nearly 110 tons of the RDX were sold in 2010. ![]() (The RDX had been stored at a separate site.) However, the cable notes that US diplomats had already heard rumors that an unnamed Czech company had attempted buy the explosives. ![]() US officials had asked Albanian authorities to destroy – and not export – its stockpile of 150 tons of RDX following the Gërdec disaster, according to the cable. ![]() The potential sale of the RDX explosive was being carefully watched by US diplomats in Albania as early as 2009, according to a State Department cable from July that year released by WikiLeaks. The remaining rounds – nearly 17 million – were also sold by MEICO to the Czech Republic, but it is not clear which company bought them. These cost a total of $920,160 – about three cents per round. Drda’s rival STV Group imported about another 31 million rounds of 7.62x39 mm ammunition, the type used in AK-47 assault rifles and other Soviet-style guns. Of the 81 million rounds, Real Trade Praha, a firm from Strnad’s portfolio, imported nearly 34 million in various calibers (as well as the 358 mortar rounds). It also sold 358 mortar rounds and nearly 110 tons of RDX explosive. They show that, between 20, MEICO sold a total of over 81 million rounds of ammunition – most of it Chinese-made and mostly of types used for Soviet-style rifles and machine guns – to the Czech Republic. The MEICO documents reveal specific details about nine deals the Albanian arms exporter made with the Czech companies. They show that, in seeking to smooth the movement of one shipment, the company sought help from Petar Crnogorac, a Serbian businessman previously investigated for attempting to sell weapons to Islamist fighters in Libya. “Yemen or an impoverished and conflict-ridden African country, like South Sudan, could also be a possible destination.”Ī separate set of leaked emails obtained by reporters throw more light on Real Trade’s deals. Georges Berghezan, a researcher for the Group for Research and Information on Peace and Security (GRIP), said it was likely that “the Czech firms re-exported the Chinese-Albanian ammunition to third parties and that the ammo finally ended up in the hands of Syrian rebels, Iraqi Kurds or central government forces, or Afghan security forces.” Instead, he said, typical purchasers of such ammunition might be “countries have relatively little money to spend which are in urgent need because they have a conflict ongoing and which have a procurement system which is not functioning particularly well.” Wezeman, senior researcher at the Stockholm International Peace Research Institute (SIPRI). “There will not be any interest from the military or police side ,” said Pieter D. But, along with old Czech rounds, decades-old Chinese ammunition frequently makes its way onto battlefields in Africa and the Middle East. It is not used by NATO member states’ armies, including that of the Czech Republic. Decrepit and unreliable, Chinese ammunition of the sort kept in Albanian stockpiles is difficult to sell on the international market. The ammunitions purchases raise questions about what the firms did with their tens of millions of rounds. The documents also show that over 100 tons of RDX, an explosive, was sold from Albanian stockpiles to buyers in the Czech Republic, in spite of alarm by US diplomats over the instability of the material. Between 20, Real Trade Praha – the Strnad-linked firm – and the Drda-controlled STV Group bought tens of millions of rounds of old Chinese munitions between them, according to internal documents from Albania’s state-owned Military Export Import Company (MEICO). ![]() 6/17/2023 0 Comments Galavant richard and tad cooper![]() Then, as the monks sang of what may be should there be a Season 3, we got a glimpse into the future, where Roberta sent Richard to feed Tad Cooper - who now apparently is a full-grown fire-breather who snacks on sheep: “I’ve got a dragon,” the True King boasts to the camera. Madalena though was last seen arriving on the doorstep of the DEL (Dark Evil Lord), to complete her training (after being properly accessorized by his manservant, of course). Gareth was determined to find his love and rescue from herself, and to that end enlisted Sid for an adventure. Richard found his own happy ending as well, racing to stop Roberta from boarding the boat to the Island of Spinsters, cat and chocolate in hand. Gal meanwhile had a promise to make good on, having quasi-proposed to Isabella mid-melee, so the two married with Weird Al and the other jazz-handing monks officiating. a tear in my eye when it was revealed that (SPOILER) Tad Cooper is really a dragon. With the zombie horde powered down by Wormwood’s vanquishing, Gareth reached out to Madalena to share a life together, but she explained that she had tasted total power and liked it, so she D’DEW’d herself away. Galavant, Richard, and the rest of the cast join forces to take down. Wielding the sword of the One True King to Unite Them All - and motivated by the seeming death of Tad Cooper! - Richard easily dispatched with Wormwood, while Isabella fought hard against Mad for the happy ending she deserves (after wearing pretty much the same outfit for two years). ![]() Mad’s magic trapped Galavant and Gareth inside Hortensia, but Richard and Isabella escaped to face off against Wormwood and the increasingly evil queen, respectively. With that finished and doom knock-knocking on their door, Sid arrived on the scene with an army of his own, cobbled together from Enchanted Forest beefcakes, giants, dwarves and Princess Jubilee’s posse - though, Sid explained, the budget prohibited including any of the recognizable guest actors. The shift from our title character to Richard having the most important plot arc becomes more or less official, as the former king finally becomes The One True King, gallops off to keep Roberta from going to Spinster Island, and watches Tad Cooper grow into a dragon. Galavant is an American musical fantasy comedy television series, created and written by Dan Fogelman, with music and lyrics by Alan Menken and Glenn Slater.Episode 2 opened with the wonderful number that Timothy Omundson told us about, in which Richard dueted with his younger self, lamenting their sad lot in life. In an interview about the show, actress Mallory Jansen described Galavant as, "the bastard child of Monty Python and The Princess Bride." Fogelman, Menken and Slater also serve as executive producers alongside Chris Koch, Kat Likkel and John Hoberg. The series premiered on January 4, 2015, with its first season consisting of eight episodes which aired over four weeks. The series was renewed for a second season of ten episodes on May 7, 2015, which premiered on January 3, 2016, following the same airing scheme as the first season. On May 12, 2016, the series was canceled after two seasons. Galavant is a dashing knight, down on his luck, determined to reclaim his reputation and his "happily ever after" by going after the evil King Richard, who ruined it the moment he kidnapped the love of Galavant's life, Madalena, who then decided to stay with Richard for his money and power. Galavant is assisted by his faithful squire, Sid, and the lovely Princess Isabella, whose kingdom of Valencia has been conquered by Richard. Meanwhile, the malevolent but weak-willed Richard tries to win over the scheming Madalena and seeks help from his brawny henchman, Gareth, and his chef, Vincenzo. The episodes chronicle Galavant's journeys (and the twists and turns that go along with them) through musical numbers composed and written by Menken and Slater. They participate in a joust, visit Sid's hometown, are captured by shipwrecked pirates, and make a stop with a band of singing monks before finally being captured by Richard and Gareth as they try to infiltrate the castle to rescue Madalena, who, it turns out, doesn't want or need to be rescued as Isabella had told the group. Richard is knocked off the throne when his older brother, Kingsley, shows up and claims it, and everyone finds themselves locked in the dungeon together. Richard's brother orders the captives executed. ![]() Gareth refuses and sets them all free but Sid, but before the new king can retaliate he is stabbed in the back and Madalena puts Gareth on the throne of Valencia beside her. ![]() Isabella and crew seek shelter with her cousin Harry in Hortensia, where she is locked away until they can marry, and Richard and Galavant (who, it turns out, is more than a little fickle) set sail with the pirates to rescue her. ![]() 6/17/2023 0 Comments Autocad 2021 download student![]()
![]() ![]() In other words, the surface is given by a vector-valued function P (encoding the x, y, and z coordinates of points on the surface) depending on two parameters, say u and v. Recall that a surface is an object in 3-dimensional space Downloaded by Fares Amzarih ( ) lOMoARcPSD|23476781 Uploaded by ChiefHedgehog3111 on coursehero.In this lesson, we will study integrals over parametrized surfaces. We have z x = y and z y = x, so dS = p y 2 + x 2 +1. Solution: The surface S sits above the region D in the xy -plane defined in polar coordinates by 1 ≤ r ≤ 2, 0 ≤ t ≤ 2 π. Let S be the portion of the surface z = xy that is inside the cylinder x 2 + y 2 =4 but outside the cylinder x 2 + y 2 =1. We parametrize this circle by x ( t ) = √ 3cos( - t ), y ( t ) = √ 3sin( - t ), z ( t ) = 3 for 0 ≤ t ≤ 2 π. ![]() The boundary of S is the upper rim, which is the circle C defined by x 2 + y 2 = 3 and z = 3, oriented clockwise so that the outer side of S is on the left as we move around the circle. We observe that if G ( x,y,z )= - y i - z j - 2 x k then curl( G )=(0+1) i +(2+0) j +(0+1) k = F so we may apply Stokes' Theorem. The surface S 2 sits above the region D in the xy -plane defined in polar form by 1 ≤ r ≤ √ 3, 0 ≤ θ ≤ 2 π. Downloaded by Fares Amzarih ( ) lOMoARcPSD|23476781įor the side S 2, we use the outward normal n =. ![]() n dS = ZZ S 1 - dS = - (area of S 1 )= - π.Since S is oriented outward, we use the normal n = and obtain ZZ S 1 F The bottom of the bowl is the disc S 1 defined by z =1 and x 2 + y 2 ≤ 1. The top of the bowl is open, and S is oriented outwards. Let S be the bowl having a flat base in the plane z = 1 and whose sides are the part of the paraboloid z = x 2 + y 2 between z =1 and z =3. ![]() Parametrize the line C 3 from (2, 2) to (1, 1) by x =2 - t, y =2 - t, 0 ≤ t ≤ 1. Parametrize the line C 2 from (3, 1) to (2, 2) by x =3 - t, y =1+ t, 0 ≤ t ≤ 1. Parametrize the line C 1 from (1, 1) to (3, 1) by x = t, y = 1, 1 ≤ t ≤ 3. d r = ZZ T (2 x - 2) dA = Z 2 1 Z 4 - y y (2 x - 2) dxdy = Z 2 1 ( x 2 - 2 x ) vextendsingle vextendsingle 4 - y y dy = Z 2 1 ((4 - y ) 2 - 2(4 - y ) - y 2 +2 y ) dy = Z 2 1 (8 - 4 y ) dy = (8 y - 2 y 2 ) vextendsingle vextendsingle 2 1 =16 - 8 - 8+2= 2.Theleftsideof T istheline y = x andtherightsideistheline x + y =4. If C is the closed path around T in the counter-clockwise direction and F =2 y i + x 2 j, evaluate the line integral Z C F Let T be the triangle with vertices at (1, 1), (3, 1), and (2, 2). Downloaded by Fares Amzarih ( ) lOMoARcPSD|23476781ģ. I = Z 1 0 Z 2 x x p 1+ x 2 dydx = Z 1 0 (2 x p 1+ x 2 - x p 1+ x 2 ) dx = Z 1 0 x p 1+ x 2 dx = 1 3 (1+ x 2 ) 3 / 2 vextendsingle vextendsingle vextendsingle vextendsingle 1 0 = 1 3 (2 √ 2 - 1). 0.2 0.4 0.6 0.8 1.0 0.5 1.0 1.5 2.0 We change the order of integration to dydx and evaluate. The dashed line is y =2 x, the solid line is y = x. Solution: The region of integration is shown below. Evaluate Z 1 0 Z y y/ 2 p 1+ x 2 dxdy + Z 2 1 Z 1 y/ 2 p 1+ x 2 dxdy. Then the mass is, using polar coordinates, ZZ D ρ ( x,y ) dA = Z 2 π 0 Z 1 0 (2+ r 2 ) r drd θ = Z 2 π 0 ✓ r 2 + r 4 4 ◆vextendsingle vextendsingle vextendsingle vextendsingle 1 0 =2 π ✓ 1+ 1 4 ◆ = 5 π 2 g. Solution: Let D be the region x 2 + y 2 ≤ 1. Suppose a lamina L (flat plate) occupies the region defined by x 2 + y 2 ≤ 1 and has density ρ ( x,y )=2+ x 2 + y 2, with ρ in g/cm 2 and x, y in cm. A formula sheet appears on the back of this page. Only ENCS approved calculators are permitted. Answers should be given as exact values (e.g. Macdonald Time: 90 minutes MaAll solutions must include a carefully written explanation. ENGR 233-S Midterm 2 Concordia University Instructor: J. ![]() |