Questões - FUVEST | Gabarito e resoluções

(FUVEST- 2022 - 1 fase) Os funcionrios de um salo de beleza compraram um presente no valor de R$ 200,00 para a recepcionista do estabelecimento. No momento da diviso igualitria do valor, dois deles desistiram de participar e, por causa disso, cada pessoa que ficou no grupo precisou pagar R$ 5,00 a mais que a quantia originalmente prevista. O valor pago por pessoa que permaneceu na diviso do custo do presente foi:

(FUVEST - 2022 - 1 fase) Uma empresa construiu um poo para armazenar gua de reso. O custo para construir o primeiro metro foi de R$ 1.000,00, e cada novo metro custou R$ 200,00 a mais do que o imediatamente anterior. Se o custo total da construo foi de R$ 48.600,00, a profundidade do poo :

(FUVEST - 2022 - 1 fase) Um deltaedro um poliedro cujas faces so todas tringulos equilteros. Se um deltaedro convexo possui 8 vrtices, ento o nmero de faces desse deltaedro : Note e adote: Em poliedros convexos, vale a relao de Euler , em que o nmero de faces, o nmero de arestas e o nmero de vrtices do poliedro.

(FUVEST- 2022 - 1 fase) A figura mostra um quadrado e um crculo, ambos com centro no ponto 𝑂. O quadrado tem lado medindo 1 unidade de medida (u.m.) e o crculo tem raio igual a 2 u.m. O ponto 𝐴 est sobre o contorno do quadrado, o ponto 𝐵 est sobre o contorno do crculo, e o segmento 𝐴𝐵 tem tamanho 2 u.m. Quando o ngulo for mximo, seu cosseno ser:

(FUVEST- 2022 - 1 fase) Suponha que o polinmio , em que 𝑚 um nmero real, tenha uma raiz real dupla 𝑎 e uma raiz real simples 𝑏. O valor da soma de 𝑚 com 𝑎 :

(FUVEST - 2022 - 1 fase) Quatro tanques cilndricos so vistos de cima (em planta baixa) conforme a figura. Todos tm 10 m de raio e seus centros se posicionam em vrtices dos dois quadrados tracejados adjacentes, ambos com 30 m de lado. Uma fita de isolamento, esticada e paralela ao solo, envolve os 4 tanques, dando uma volta completa (linha em laranja na figura). O comprimento da fita, em metros, :

(FUVEST- 2022 - 1 fase) Em fevereiro de 2021, um grupo de fsicos da Universidade Federal de Minas Gerais (UFMG) publicou um artigo que foi capa da importante revista Nature. O texto a seguir foi retirado de uma reportagem do site da UFMG sobre o artigo: O nanoscpio, prossegue Ado Jorio (professor da UFMG), ilumina a amostra com um microscpio ptico usual. O foco da luz tem o tamanho de um crculo de 1 micrmetro de dimetro. O que o nanoscpio faz inserir uma nanoantena, que tem uma ponta com dimetro de 10 nanmetros, dentro desse foco de 1 micrmetro e escanear essa ponta. A imagem com resoluo nanomtrica formada por esse processo de escaneamento da nanoantena, que localiza o campo eletromagntico da luz em seu pice, afirma o professor. Itamar Rigueira Jr. Nanoscpio da UFMG possibilita compreender estrutura que torna grafeno supercondutor. Adaptado. Disponvel em https://ufmg.br/comunicacao/noticias/. Gadelha A C et al. (2021), Nature, 590, 405-409, doi: 10.1038/s41586-021-03252-5. Com base nos dados mencionados no texto, a razo entre o dimetro do foco da luz de um microscpio ptico usual e o dimetro da ponta da nanoantena utilizada no nanoscpio da ordem de:

(FUVEST- 2022 - 1 fase) A quantidade de bactrias em um lquido diretamente proporcional medida da turbidez desse lquido. O grfico mostra, em escala logartmica, o crescimento da turbidez 𝑥 de um lquido ao longo do tempo 𝑡 (medido em minutos), isto , mostra log10𝑥 em funo de 𝑡. Os dados foram coletados de 30 em 30 minutos, e uma curva de interpolao foi obtida para inferir valores intermedirios. Com base no grfico, em quantas vezes a populao de bactrias aumentou, do instante 𝑡0para o instante 𝑡1?

(FUVEST - 2022 - 1 fase) Fatbergs are a growing scourge infesting cities around the world some are more than 800 feet long and weigh more than four humpback whales. These gross globs, which can cause sewer systems to block up and even overflow, have been plaguing the U.S., Great Britain and Australia for the past decade, forcing governments and utilities companies to send workers down into the sewers armed with water hoses, vacuums and scrapers with the unenviable task of prying them loose. It is hard not to think of [fatbergs] as a tangible symbol of the way we live now, the ultimate product of our disposable, out of sight, out of mind culture, wrote journalist Tim Adams in The Guardian. At their core, fatbergs are the accumulation of oil and grease thats been poured down the drain, congealing around flushed nonbiological waste like tampons, condoms and baby wipes. When fat sticks to the side of sewage pipes, the wipes and other detritus get stuck, accumulating layer upon layer of gunk in a sort of slimy snowball effect. Fatbergs also collect other kinds of debrisLondon fatbergs have been cracked open to reveal pens, false teeth and even watches. Restaurants are a big contributor to fatbergs: Thames Water, the London utilities company, found nine out of 10 fast-food eateries lacked adequate grease traps to stop fat from entering the sewers. Homeowners also contribute to the problem by pouring grease and fat down the sink. Even though its component materials are soft, fatbergs themselves can be tough as rocks. Researchers have found a host of dangerous bacteria in fatbergs, including listeria and e.coli. Fatbergs are notorious for their fetid smell, which can make even the hardiest sewer workers gag, and chipping away at one can release noxious gases. The key to fatberg prevention is remembering the four Ps: Pee, poo, puke and (toilet) paper are the only things that should be flushed. Newsweek, 14 March, 2019. Adaptado. O texto informa que, na opinio do jornalista Tim Adams, os fatbergs

(FUVEST - 2022 - 1 fase) Fatbergs are a growing scourge infesting cities around the world some are more than 800 feet long and weigh more than four humpback whales. These gross globs, which can cause sewer systems to block up and even overflow, have been plaguing the U.S., Great Britain and Australia for the past decade, forcing governments and utilities companies to send workers down into the sewers armed with water hoses, vacuums and scrapers with the unenviable task of prying them loose. It is hard not to think of [fatbergs] as a tangible symbol of the way we live now, the ultimate product of our disposable, out of sight, out of mind culture, wrote journalist Tim Adams in The Guardian. At their core, fatbergs are the accumulation of oil and grease thats been poured down the drain, congealing around flushed nonbiological waste like tampons, condoms and baby wipes. When fat sticks to the side of sewage pipes, the wipes and other detritus get stuck, accumulating layer upon layer of gunk in a sort of slimy snowball effect. Fatbergs also collect other kinds of debrisLondon fatbergs have been cracked open to reveal pens, false teeth and even watches. Restaurants are a big contributor to fatbergs: Thames Water, the London utilities company, found nine out of 10 fast-food eateries lacked adequate grease traps to stop fat from entering the sewers. Homeowners also contribute to the problem by pouring grease and fat down the sink. Even though its component materials are soft, fatbergs themselves can be tough as rocks. Researchers have found a host of dangerous bacteria in fatbergs, including listeria and e.coli. Fatbergs are notorious for their fetid smell, which can make even the hardiest sewer workers gag, and chipping away at one can release noxious gases. The key to fatberg prevention is remembering the four Ps: Pee, poo, puke and (toilet) paper are the only things that should be flushed. Newsweek, 14 March, 2019. Adaptado. De acordo com o texto, o processo de bloqueio do fluxo de esgoto, provocado pelos fatbergs, ocorre

(FUVEST - 2022 - 1 fase) Fatbergs are a growing scourge infesting cities around the world some are more than 800 feet long and weigh more than four humpback whales. These gross globs, which can cause sewer systems to block up and even overflow, have been plaguing the U.S., Great Britain and Australia for the past decade, forcing governments and utilities companies to send workers down into the sewers armed with water hoses, vacuums and scrapers with the unenviable task of prying them loose. It is hard not to think of [fatbergs] as a tangible symbol of the way we live now, the ultimate product of our disposable, out of sight, out of mind culture, wrote journalist Tim Adams in The Guardian. At their core, fatbergs are the accumulation of oil and grease thats been poured down the drain, congealing around flushed nonbiological waste like tampons, condoms and baby wipes. When fat sticks to the side of sewage pipes, the wipes and other detritus get stuck, accumulating layer upon layer of gunk in a sort of slimy snowball effect. Fatbergs also collect other kinds of debrisLondon fatbergs have been cracked open to reveal pens, false teeth and even watches. Restaurants are a big contributor to fatbergs: Thames Water, the London utilities company, found nine out of 10 fast-food eateries lacked adequate grease traps to stop fat from entering the sewers. Homeowners also contribute to the problem by pouring grease and fat down the sink. Even though its component materials are soft, fatbergs themselves can be tough as rocks. Researchers have found a host of dangerous bacteria in fatbergs, including listeria and e.coli. Fatbergs are notorious for their fetid smell, which can make even the hardiest sewer workers gag, and chipping away at one can release noxious gases. The key to fatberg prevention is remembering the four Ps: Pee, poo, puke and (toilet) paper are the only things that should be flushed. Newsweek, 14 March, 2019. Adaptado. Considerado o contexto, os quatro elementos associados preveno dos fatbergs tm em comum o fato de

(FUVEST - 2022 - 1 fase) If you take a look at my smartphone, youll know that I like to order out. But am I helping the small local businesses? You would think that if you own a restaurant youd be thrilled to have an outsourced service that would take care of your delivery operations while leveraging their marketing might to expand your businesses brand. However, restaurant owners have complained of lack of quality control once their food goes out the door. They dont like that the delivery people are the face of their product when it gets into the customers hand. Some of the delivery services have been accused of listing restaurants on their apps without the owners permission, and oftentimes publish menu items and prices that are incorrect or out of date. But there is another reason why restaurant owners arent fond of delivery services. Its the costs, which, for some, are becoming unsustainable. Even with the increased revenues from the delivery services, the fees wind up killing a restaurants margins to the extent that its at best marginally profitable. Therefore, some restaurants are pushing harder to drive orders from their own websites and offering special deals for customers that use their in-house delivery people. The simple fact is that these delivery apps are here to stay. They are enormously popular and have significantly grown. I believe that restaurant owners that resist these apps are hurting their brands by missing out on potential customers. The good news is that the delivery platforms are not as evil as some would portray them. They have some skin in the game. They are competing against other services. They want their listed restaurants to profit. Maybe instead of fighting, the nations restaurant industry needs to proactively embrace the delivery service industry and figure out ways to profitably work together. The Guardian. 02 December, 2020. Adaptado. De acordo com o texto, para os proprietrios de restaurante, a principal vantagem dos aplicativos de entrega de comida que eles

(FUVEST- 2022 - 1 fase) If you take a look at my smartphone, youll know that I like to order out. But am I helping the small local businesses? You would think that if you own a restaurant youd be thrilled to have an outsourced service that would take care of your delivery operations while leveraging their marketing might to expand your businesses brand. However, restaurant owners have complained of lack of quality control once their food goes out the door. They dont like that the delivery people are the face of their product when it gets into the customers hand. Some of the delivery services have been accused of listing restaurants on their apps without the owners permission, and oftentimes publish menu items and prices that are incorrect or out of date. But there is another reason why restaurant owners arent fond of delivery services. Its the costs, which, for some, are becoming unsustainable. Even with the increased revenues from the delivery services, the fees wind up killing a restaurants margins to the extent that its at best marginally profitable. Therefore, some restaurants are pushing harder to drive orders from their own websites and offering special deals for customers that use their in-house delivery people. The simple fact is that these delivery apps are here to stay. They are enormously popular and have significantly grown. I believe that restaurant owners that resist these apps are hurting their brands by missing out on potential customers. The good news is that the delivery platforms are not as evil as some would portray them. They have some skin in the game. They are competing against other services. They want their listed restaurants to profit. Maybe instead of fighting, the nations restaurant industry needs to proactively embrace the delivery service industry and figure out ways to profitably work together. The Guardian. 02 December, 2020. Adaptado. Segundo o texto, uma das solues encontradas pelos donos de restaurante para amenizar os problemas com os servios de entrega

(FUVEST - 2022 - 1 fase) If you take a look at my smartphone, youll know that I like to order out. But am I helping the small local businesses? You would think that if you own a restaurant youd be thrilled to have an outsourced service that would take care of your delivery operations while leveraging their marketing might to expand your businesses brand. However, restaurant owners have complained of lack of quality control once their food goes out the door. They dont like that the delivery people are the face of their product when it gets into the customers hand. Some of the delivery services have been accused of listing restaurants on their apps without the owners permission, and oftentimes publish menu items and prices that are incorrect or out of date. But there is another reason why restaurant owners arent fond of delivery services. Its the costs, which, for some, are becoming unsustainable. Even with the increased revenues from the delivery services, the fees wind up killing a restaurants margins to the extent that its at best marginally profitable. Therefore, some restaurants are pushing harder to drive orders from their own websites and offering special deals for customers that use their in-house delivery people. The simple fact is that these delivery apps are here to stay. They are enormously popular and have significantly grown. I believe that restaurant owners that resist these apps are hurting their brands by missing out on potential customers. The good news is that the delivery platforms are not as evil as some would portray them. They have some skin in the game. They are competing against other services. They want their listed restaurants to profit. Maybe instead of fighting, the nations restaurant industry needs to proactively embrace the delivery service industry and figure out ways to profitably work together. The Guardian. 02 December, 2020. Adaptado. Em I believe that restaurant owners that resist these apps are hurting their brands by missing out on potential customers (3 pargrafo), a expresso sublinhada pode ser substituda, sem prejuzo de sentido, por:

(FUVEST - 2022 - 1 fase) Lying, thinking Last night How to find my soul a home Where water is not thirsty And bread loaf is not stone I came up with one thing And I dont believe Im wrong That nobody, But nobody Can make it out here alone Alone - Maya Angelou Os versos do poema