Questões - IME | Gabarito e resoluções

(IME - 2016/2017 - 1 fase) Sejam os pontos , , , e .A reta r passa por A e corta o lado CD, dividindo o pentgono ABCDE em dois polgonos de mesma rea. Determine a soma das coordenadas do ponto de interseo da reta r com a reta que liga C e D.

(IME - 2016/2017 - 2 FASE) TEXTO 2 O HOMEM: AS VIAGENS Carlos Drummond de Andrade O homem, bicho da terra to pequeno Chateia-se na terra Lugar de muita misria e pouca diverso, Faz um foguete, uma cpsula, um mdulo Toca para a lua Desce cauteloso na lua Pisa na lua Planta bandeirola na lua Experimenta a lua Coloniza a lua Civiliza a lua Humaniza a lua. Lua humanizada: to igual terra. O homem chateia-se na lua. Vamos para marte - ordena a suas mquinas. Elas obedecem, o homem desce em marte Pisa em marte Experimenta Coloniza Civiliza Humaniza marte com engenho e arte. Marte humanizado, que lugar quadrado. Vamos a outra parte? Claro - diz o engenho Sofisticado e dcil. Vamos a vnus. O homem pe o p em vnus, V o visto - isto? Idem Idem Idem. O homem funde a cuca se no for a jpiter Proclamar justia junto com injustia Repetir a fossa Repetir o inquieto Repetitrio. Outros planetas restam para outras colnias. O espao todo vira terra-a-terra. O homem chega ao sol ou d uma volta S para tever? No-v que ele inventa Roupa insidervel de viver no sol. Pe o p e: Mas que chato o sol, falso touro Espanhol domado. Restam outros sistemas fora Do solar a col- Onizar. Ao acabarem todos S resta ao homem (estar equipado?) A dificlima dangerosssima viagem De si a si mesmo: Pr o p no cho Do seu corao Experimentar Colonizar Civilizar Humanizar O homem Descobrindo em suas prprias inexploradas entranhas A perene, insuspeitada alegria De con-viver. ANDRADE, Carlos Drummond. Nova reunio: 19 livros de poesia 3 ed. Rio de Janeiro: Jos Olympio, 1978, pp. 448-450. O sentido do verbo que constitui o ltimo verso do Texto 2 refere-se a/ao

(IME - 2016/2017 - 1 fase) Dado um quadrado ABCD, de lado a, marcam-se os pontos E sobre o lado AB, F sobre o lado BC, G sobre o lado CD e H sobre o lado AD, de modo que os segmentos formados AE, BF, CG e DH tenham comprimento igual a. A rea do novo quadriltero formado pelas intersees dos segmentos AF, BG, CH, e DE mede:

(IME - 2016/2017 - 2 FASE) TEXTO 2 O HOMEM: AS VIAGENS Carlos Drummond de Andrade O homem, bicho da terra to pequeno Chateia-se na terra Lugar de muita misria e pouca diverso, Faz um foguete, uma cpsula, um mdulo Toca para a lua Desce cauteloso na lua Pisa na lua Planta bandeirola na lua Experimenta a lua Coloniza a lua Civiliza a lua Humaniza a lua. Lua humanizada: to igual terra. O homem chateia-se na lua. Vamos para marte - ordena a suas mquinas. Elas obedecem, o homem desce em marte Pisa em marte Experimenta Coloniza Civiliza Humaniza marte com engenho e arte. Marte humanizado, que lugar quadrado. Vamos a outra parte? Claro - diz o engenho Sofisticado e dcil. Vamos a vnus. O homem pe o p em vnus, V o visto - isto? Idem Idem Idem. O homem funde a cuca se no for a jpiter Proclamar justia junto com injustia Repetir a fossa Repetir o inquieto Repetitrio. Outros planetas restam para outras colnias. O espao todo vira terra-a-terra. O homem chega ao sol ou d uma volta S para tever? No-v que ele inventa Roupa insidervel de viver no sol. Pe o p e: Mas que chato o sol, falso touro Espanhol domado. Restam outros sistemas fora Do solar a col- Onizar. Ao acabarem todos S resta ao homem (estar equipado?) A dificlima dangerosssima viagem De si a si mesmo: Pr o p no cho Do seu corao Experimentar Colonizar Civilizar Humanizar O homem Descobrindo em suas prprias inexploradas entranhas A perene, insuspeitada alegria De con-viver. ANDRADE, Carlos Drummond. Nova reunio: 19 livros de poesia 3 ed. Rio de Janeiro: Jos Olympio, 1978, pp. 448-450. Assinale a alternativa em que a substituio da palavra perene (verso 61, Texto 2) acarretaria mudana de sentido:

[IME 2016/2017 - 1 fase] Um projtil lanado obliquamente de um canho, atingindo um alcance igual a 1000 m no plano horizontal que contm a boca do canho. Nesse canho, o projtil parte do repouso executando um movimento uniformemente variado dentro do tubo at sair pela boca do canho. Ademais, a medida que o projtil se desloca no interior do tubo, ele executa um movimento uniformemente variado de rotao, coaxial ao tubo. Tendo sido o projtil rotacionado de 1 rad durante seu deslocamento dentro do canho, sua acelerao angular, em rad/s2, ao deixar o canho : Dados: ngulo do tubo do canho em relao horizontal: 45; comprimento do tubo: 2 m; acelerao da gravidade: C = 10 m/s2. Considerao:despreze a resistncia do ar.

(IME - 2016/2017 - 1 fase) Um tronco de pirmide regular possui 12 vrtices. A soma dos permetros das bases 36 cm, a soma das reas das bases cm2 e sua alturamede 3 cm. Calcule o volume do tronco de pirmide.

[IME 2016/2017 - 1 fase] Considere um feixe homogneo de pequenos projteis deslocando-se na mesma direo e na mesma velocidade constante at atingir a superfcie de uma esfera que est sempre em repouso. A esfera pode ter um ou dois tipos de superfcies: uma superfcie totalmente refletora (coliso perfeitamente elstica entre a esfera e o projtil) e/ou uma superfcie totalmente absorvedora (coliso perfeitamente inelstica entre a esfera e o projtil). Em uma das superfcies (refletora ou absorvedora), o nguloda figura pertence ao intervalo , enquanto na outra superfcie (absorvedora ou refletora)pertence ao intervalo. Para que a fora aplicada pelos projteis sobre a esfera seja mxima, o(s) tipo(s) de superfcie(s) (so):

(IME - 2016/2017 - 2 FASE) TEXTO 2 O HOMEM: AS VIAGENS Carlos Drummond de Andrade O homem, bicho da terra to pequeno Chateia-se na terra Lugar de muita misria e pouca diverso, Faz um foguete, uma cpsula, um mdulo Toca para a lua Desce cauteloso na lua Pisa na lua Planta bandeirola na lua Experimenta a lua Coloniza a lua Civiliza a lua Humaniza a lua. Lua humanizada: to igual terra. O homem chateia-se na lua. Vamos para marte - ordena a suas mquinas. Elas obedecem, o homem desce em marte Pisa em marte Experimenta Coloniza Civiliza Humaniza marte com engenho e arte. Marte humanizado, que lugar quadrado. Vamos a outra parte? Claro - diz o engenho Sofisticado e dcil. Vamos a vnus. O homem pe o p em vnus, V o visto - isto? Idem Idem Idem. O homem funde a cuca se no for a jpiter Proclamar justia junto com injustia Repetir a fossa Repetir o inquieto Repetitrio. Outros planetas restam para outras colnias. O espao todo vira terra-a-terra. O homem chega ao sol ou d uma volta S para tever? No-v que ele inventa Roupa insidervel de viver no sol. Pe o p e: Mas que chato o sol, falso touro Espanhol domado. Restam outros sistemas fora Do solar a col- Onizar. Ao acabarem todos S resta ao homem (estar equipado?) A dificlima dangerosssima viagem De si a si mesmo: Pr o p no cho Do seu corao Experimentar Colonizar Civilizar Humanizar O homem Descobrindo em suas prprias inexploradas entranhas A perene, insuspeitada alegria De con-viver. ANDRADE, Carlos Drummond. Nova reunio: 19 livros de poesia 3 ed. Rio de Janeiro: Jos Olympio, 1978, pp. 448-450. Assinale a alternativa em que os versos do Texto 2 e suas leituras abaixo fogem ideia de tdio e de colonizao do cosmos exteriorizadas no poema.

(IME - 2016/2017 - 1 fase) O polinmio P(x) = x3 - bx2 + 80x - c possui trs razes inteiras positivas distintas. Sabe-se que duas das razes do polinmio so divisoras de 80 e que o produto dos divisores positivos de c menores do que c c2. Qual o valor de b?

(IME - 2016/2017 - 2 FASE) Texto 1 LANDFILLS AND THE INTRODUCTION OF NANOMATERIALS IN WASTE Waste disposal on land (dumping) and landfilling remain the most prominent waste management techniques used ___(16)___. The standards and practices for this type of waste disposal vary greatly ranging from uncontrolled sites to highly specialised and controlled engineered landfills. The potential ___(17)___ of contaminants through landfill gas and leachate is largely dependent on landfill design, site conditions and the sophistication of the control measures in place, ___(18)___ landfill gas recovery and leachate collection and treatment systems. Modern engineered landfills use ___(19)___ barriers, with few relying on natural barriers, to line the bottom of a landfill and incorporate collection systems for both leachate and landfill gas. The purpose of these collection systems is to capture and treat leachate and landfill gas; __(20)____ preventing the migration of leachate into ground/surface water and the release of untreated landfill gases to the atmosphere. An un-engineered landfill would be considered an uncontrolled system due to the lack of environmental controls, potentially resulting in significant environmental exposure of contaminants. Because of widespread use of ENMs in a broad range of products, it is possible that some ENMs ___(21)___ through landfill gases; however this report will primarily focus on ENMs that may be present in landfill leachate, as this is considered to be the primary means by which ENMs could be transported___(22)___ a landfill. Characterisation of landfill gases to identify the presence of ENMs __(23)____ an important area for further research. Landfill leachate is generated when rain passes through the waste mass and by the liquid generated due to the breakdown of waste ___(24)___ the landfill. The composition of leachate is extremely ___(25)___ depending on the type of waste landfilled, the quantity of precipitation, the construction and operation of the landfill, the age of the landfill and other factors such as pH, temperature and microbial populations. () ENMs = engineered nanomaterials. Organisation for Economic Co-operation and Development. Landfills and the introduction of nanomaterials in waste. In: Landfilling of waste containing nanomaterials and nanowaste, 2015. Disponvel em: http://www.oecd.org/officialdocuments/ publicdisplaydocumentpdf/? cote=ENV/EPOC/WPRPW(2014)5/FINALdocLanguage=En. Acesso em: 22/04/2015. ESCOLHA A ALTERNATIVA QUE COMPLETA O TEXTO 1 CORRETAMENTE (lacuna 16).

(IME - 2016/2017 - 2 FASE) Texto 1 LANDFILLS AND THE INTRODUCTION OF NANOMATERIALS IN WASTE Waste disposal on land (dumping) and landfilling remain the most prominent waste management techniques used ___(16)___. The standards and practices for this type of waste disposal vary greatly ranging from uncontrolled sites to highly specialised and controlled engineered landfills. The potential ___(17)___ of contaminants through landfill gas and leachate is largely dependent on landfill design, site conditions and the sophistication of the control measures in place, ___(18)___ landfill gas recovery and leachate collection and treatment systems. Modern engineered landfills use ___(19)___ barriers, with few relying on natural barriers, to line the bottom of a landfill and incorporate collection systems for both leachate and landfill gas. The purpose of these collection systems is to capture and treat leachate and landfill gas; __(20)____ preventing the migration of leachate into ground/surface water and the release of untreated landfill gases to the atmosphere. An un-engineered landfill would be considered an uncontrolled system due to the lack of environmental controls, potentially resulting in significant environmental exposure of contaminants. Because of widespread use of ENMs in a broad range of products, it is possible that some ENMs ___(21)___ through landfill gases; however this report will primarily focus on ENMs that may be present in landfill leachate, as this is considered to be the primary means by which ENMs could be transported___(22)___ a landfill. Characterisation of landfill gases to identify the presence of ENMs __(23)____ an important area for further research. Landfill leachate is generated when rain passes through the waste mass and by the liquid generated due to the breakdown of waste ___(24)___ the landfill. The composition of leachate is extremely ___(25)___ depending on the type of waste landfilled, the quantity of precipitation, the construction and operation of the landfill, the age of the landfill and other factors such as pH, temperature and microbial populations. () ENMs = engineered nanomaterials. Organisation for Economic Co-operation and Development.Landfills and the introduction of nanomaterials in waste.In: Landfilling of waste containing nanomaterials and nanowaste, 2015. Disponvel em: http://www.oecd.org/officialdocuments/ publicdisplaydocumentpdf/? cote=ENV/EPOC/WPRPW(2014)5/FINALdocLanguage=En. Acesso em: 22/04/2015. ESCOLHA A ALTERNATIVA QUE COMPLETA O TEXTO 1 CORRETAMENTE (lacuna 17).

(IME - 2016/2017 - 2 FASE) Texto 1 LANDFILLS AND THE INTRODUCTION OF NANOMATERIALS IN WASTE Waste disposal on land (dumping) and landfilling remain the most prominent waste management techniques used ___(16)___. The standards and practices for this type of waste disposal vary greatly ranging from uncontrolled sites to highly specialised and controlled engineered landfills. The potential ___(17)___ of contaminants through landfill gas and leachate is largely dependent on landfill design, site conditions and the sophistication of the control measures in place, ___(18)___ landfill gas recovery and leachate collection and treatment systems. Modern engineered landfills use ___(19)___ barriers, with few relying on natural barriers, to line the bottom of a landfill and incorporate collection systems for both leachate and landfill gas. The purpose of these collection systems is to capture and treat leachate and landfill gas; __(20)____ preventing the migration of leachate into ground/surface water and the release of untreated landfill gases to the atmosphere. An un-engineered landfill would be considered an uncontrolled system due to the lack of environmental controls, potentially resulting in significant environmental exposure of contaminants. Because of widespread use of ENMs in a broad range of products, it is possible that some ENMs ___(21)___ through landfill gases; however this report will primarily focus on ENMs that may be present in landfill leachate, as this is considered to be the primary means by which ENMs could be transported___(22)___ a landfill. Characterisation of landfill gases to identify the presence of ENMs __(23)____ an important area for further research. Landfill leachate is generated when rain passes through the waste mass and by the liquid generated due to the breakdown of waste ___(24)___ the landfill. The composition of leachate is extremely ___(25)___ depending on the type of waste landfilled, the quantity of precipitation, the construction and operation of the landfill, the age of the landfill and other factors such as pH, temperature and microbial populations. () ENMs = engineered nanomaterials. Organisation for Economic Co-operation and Development.Landfills and the introduction of nanomaterials in waste.In: Landfilling of waste containing nanomaterials and nanowaste, 2015. Disponvel em: http://www.oecd.org/officialdocuments/ publicdisplaydocumentpdf/? cote=ENV/EPOC/WPRPW(2014)5/FINALdocLanguage=En. Acesso em: 22/04/2015. ESCOLHA A ALTERNATIVA QUE COMPLETA O TEXTO 1 CORRETAMENTE (lacuna 18).

(IME - 2016/2017 - 2 FASE) Texto 1 LANDFILLS AND THE INTRODUCTION OF NANOMATERIALS IN WASTE Waste disposal on land (dumping) and landfilling remain the most prominent waste management techniques used ___(16)___. The standards and practices for this type of waste disposal vary greatly ranging from uncontrolled sites to highly specialised and controlled engineered landfills. The potential ___(17)___ of contaminants through landfill gas and leachate is largely dependent on landfill design, site conditions and the sophistication of the control measures in place, ___(18)___ landfill gas recovery and leachate collection and treatment systems. Modern engineered landfills use ___(19)___ barriers, with few relying on natural barriers, to line the bottom of a landfill and incorporate collection systems for both leachate and landfill gas. The purpose of these collection systems is to capture and treat leachate and landfill gas; __(20)____ preventing the migration of leachate into ground/surface water and the release of untreated landfill gases to the atmosphere. An un-engineered landfill would be considered an uncontrolled system due to the lack of environmental controls, potentially resulting in significant environmental exposure of contaminants. Because of widespread use of ENMs in a broad range of products, it is possible that some ENMs ___(21)___ through landfill gases; however this report will primarily focus on ENMs that may be present in landfill leachate, as this is considered to be the primary means by which ENMs could be transported___(22)___ a landfill. Characterisation of landfill gases to identify the presence of ENMs __(23)____ an important area for further research. Landfill leachate is generated when rain passes through the waste mass and by the liquid generated due to the breakdown of waste ___(24)___ the landfill. The composition of leachate is extremely ___(25)___ depending on the type of waste landfilled, the quantity of precipitation, the construction and operation of the landfill, the age of the landfill and other factors such as pH, temperature and microbial populations. () ENMs = engineered nanomaterials. Organisation for Economic Co-operation and Development.Landfills and the introduction of nanomaterials in waste.In: Landfilling of waste containing nanomaterials and nanowaste, 2015. Disponvel em: http://www.oecd.org/officialdocuments/ publicdisplaydocumentpdf/? cote=ENV/EPOC/WPRPW(2014)5/FINALdocLanguage=En. Acesso em: 22/04/2015. ESCOLHA A ALTERNATIVA QUE COMPLETA O TEXTO 1 CORRETAMENTE (lacuna 19)

(IME - 2016/2017 - 2 FASE) Texto 1 LANDFILLS AND THE INTRODUCTION OF NANOMATERIALS IN WASTE Waste disposal on land (dumping) and landfilling remain the most prominent waste management techniques used ___(16)___. The standards and practices for this type of waste disposal vary greatly ranging from uncontrolled sites to highly specialised and controlled engineered landfills. The potential ___(17)___ of contaminants through landfill gas and leachate is largely dependent on landfill design, site conditions and the sophistication of the control measures in place, ___(18)___ landfill gas recovery and leachate collection and treatment systems. Modern engineered landfills use ___(19)___ barriers, with few relying on natural barriers, to line the bottom of a landfill and incorporate collection systems for both leachate and landfill gas. The purpose of these collection systems is to capture and treat leachate and landfill gas; __(20)____ preventing the migration of leachate into ground/surface water and the release of untreated landfill gases to the atmosphere. An un-engineered landfill would be considered an uncontrolled system due to the lack of environmental controls, potentially resulting in significant environmental exposure of contaminants. Because of widespread use of ENMs in a broad range of products, it is possible that some ENMs ___(21)___ through landfill gases; however this report will primarily focus on ENMs that may be present in landfill leachate, as this is considered to be the primary means by which ENMs could be transported___(22)___ a landfill. Characterisation of landfill gases to identify the presence of ENMs __(23)____ an important area for further research. Landfill leachate is generated when rain passes through the waste mass and by the liquid generated due to the breakdown of waste ___(24)___ the landfill. The composition of leachate is extremely ___(25)___ depending on the type of waste landfilled, the quantity of precipitation, the construction and operation of the landfill, the age of the landfill and other factors such as pH, temperature and microbial populations. () ENMs = engineered nanomaterials. Organisation for Economic Co-operation and Development.Landfills and the introduction of nanomaterials in waste.In: Landfilling of waste containing nanomaterials and nanowaste, 2015. Disponvel em: http://www.oecd.org/officialdocuments/ publicdisplaydocumentpdf/? cote=ENV/EPOC/WPRPW(2014)5/FINALdocLanguage=En. Acesso em: 22/04/2015. ESCOLHA A ALTERNATIVA QUE COMPLETA O TEXTO 1 CORRETAMENTE (lacuna 20).

(IME - 2016/2017 - 2 FASE) Texto 1 LANDFILLS AND THE INTRODUCTION OF NANOMATERIALS IN WASTE Waste disposal on land (dumping) and landfilling remain the most prominent waste management techniques used ___(16)___. The standards and practices for this type of waste disposal vary greatly ranging from uncontrolled sites to highly specialised and controlled engineered landfills. The potential ___(17)___ of contaminants through landfill gas and leachate is largely dependent on landfill design, site conditions and the sophistication of the control measures in place, ___(18)___ landfill gas recovery and leachate collection and treatment systems. Modern engineered landfills use ___(19)___ barriers, with few relying on natural barriers, to line the bottom of a landfill and incorporate collection systems for both leachate and landfill gas. The purpose of these collection systems is to capture and treat leachate and landfill gas; __(20)____ preventing the migration of leachate into ground/surface water and the release of untreated landfill gases to the atmosphere. An un-engineered landfill would be considered an uncontrolled system due to the lack of environmental controls, potentially resulting in significant environmental exposure of contaminants. Because of widespread use of ENMs in a broad range of products, it is possible that some ENMs ___(21)___ through landfill gases; however this report will primarily focus on ENMs that may be present in landfill leachate, as this is considered to be the primary means by which ENMs could be transported___(22)___ a landfill. Characterisation of landfill gases to identify the presence of ENMs __(23)____ an important area for further research. Landfill leachate is generated when rain passes through the waste mass and by the liquid generated due to the breakdown of waste ___(24)___ the landfill. The composition of leachate is extremely ___(25)___ depending on the type of waste landfilled, the quantity of precipitation, the construction and operation of the landfill, the age of the landfill and other factors such as pH, temperature and microbial populations. () ENMs = engineered nanomaterials. Organisation for Economic Co-operation and Development.Landfills and the introduction of nanomaterials in waste.In: Landfilling of waste containing nanomaterials and nanowaste, 2015. Disponvel em: http://www.oecd.org/officialdocuments/ publicdisplaydocumentpdf/? cote=ENV/EPOC/WPRPW(2014)5/FINALdocLanguage=En. Acesso em: 22/04/2015. ESCOLHA A ALTERNATIVA QUE COMPLETA O TEXTO 1 CORRETAMENTE (lacuna 21)