Questões - IME 2017 | Gabarito e resoluções

(IME - 2017/2018 - 2 FASE) HYPATIA OF ALEXANDRIA Hypatia of Alexandria (c. 370 CE March 415 CE) was a female philosopher and mathematician, born in Alexandria, Egypt possibly in 370 CE (although some scholars cite her birth as c. 350 CE). She was the daughter of the mathematician Theon, the last Professor at the University of Alexandria, who tutored her in math, astronomy, and the philosophy of the day which, in modern times, would be considered science. Nothing is known of her mother and there is little information about her life. As the historian Deakin writes, The most detailed accounts we have of Hypatias life are the records of her death. We learn more about her death from the primary sources than we do about any other aspect of her life. She was murdered in 415 CE by a Christian mob who attacked her on the streets of Alexandria. The primary sources, even those Christian writers who were hostile to her and claimed she was a witch, portray her as a woman who was widely known for her generosity, love of learning, and expertise in teaching in the subjects of Neo-Platonism, mathematics, science, and philosophy in general. In a city which was becoming increasingly diverse religiously (and had always been so culturally) Hypatia was a close friend of the pagan prefect Orestes and was blamed by Cyril, the Christian Archbishop of Alexandria, for keeping Orestes from accepting the true faith. She was also seen as a stumbling block to those who would have accepted the truth of Christianity were it not for her charisma, charm, and excellence in making difficult mathematical and philosophical concepts understandable to her students; concepts which contradicted the teachings of the relatively new church. Alexandria was a great seat of learning in the early days of Christianity but, as the faith grew in adherents and power, steadily became divided by fighting among religious factions. It is by no means an exaggeration to state that Alexandria was destroyed as a centre of culture and learning by religious intolerance, and 1Hypatia has come to symbolize this tragedy to the extent that her death has been cited as the end of the classical world. 2By all accounts, Hypatia was an extraordinary woman __________. Theon refused to impose upon his daughter the traditional role assigned to women and raised her as one would have raised a son in the Greek tradition; by teaching her his own trade. The historian Slatkin writes, Greek women of all classes were occupied with the same type of work, mostly centered around the domestic needs of the family. Women cared for young children, nursed the sick, and prepared food. Hypatia, on the other hand, led the life of a respected academic at Alexandrias university; a position to which, as far as the evidence suggests, only males were entitled previously. She never married and remained celibate throughout her life, devoting herself to learning and teaching. The ancient writers are in agreement that she was a woman of enormous intellectual power. Deakin writes: The breadth of her interests is most impressive. Within mathematics, she wrote or lectured on astronomy (including its observational aspects - the astrolabe), geometry (and for its day advanced geometry at that) and algebra (again, for its time, difficult algebra), and made an advance in computational technique - all this as well as engaging in religious philosophy and aspiring to a good writing style. 3Her writings were, as best we can judge, an outgrowth of her teaching in the technical areas of mathematics. In effect, she was continuing a program initiated by her father: a conscious effort to preserve and to elucidate the great mathematical works of the Alexandrian heritage. CE = Common Era, the same as AD, Anno Domini. MARK, Joshua J. Hypatia of Alexandria. In: Ancient History Encyclopedia, 2017. Disponvel em: http://www.ancient.eu/Hypatia_of_Alexandria/. Acesso em: 20/06/2017. Choose the correct option.

(IME - 2017/2018 - 1 FASE ) O sistema mostrado na figura gira em torno de um eixo central em velocidade angular constante . Dois cubos idnticos, de massa uniformemente distribuda, esto dispostos simetricamente a uma distncia r do centro ao eixo, apoiados em superfcies inclinadas de ngulo . Admitindo que no existe movimento relativo dos cubos em relao s superfcies, a menor velocidade angular para que o sistema se mantenha nessas condies : Dados: - acelerao da gravidade: g; - massa de cada cubo: m; - aresta de cada cubo: a;e - coeficiente de atrito entre os cubos e as superfcies inclinadas:.

(IME - 2017/2018 - 2 FASE ) EXAUSTO Eu quero uma licena de dormir, perdo pra descansar horas a fio, sem ao menos sonhar a leve palha de um pequeno sonho. Quero o que antes da vida foi o sono profundo das espcies, a graa de um estado. Semente. Muito mais que razes. PRADO, Adlia. Exausto. Disponvel em http://byluleoa-tecendopalavras.blogspot.com.br/. Acesso em 31/07/17. A respeito da forma verbal quero (versos 1 e 5), podemos afirmar que

(IME - 2017/2018 - 1 FASE ) Seja um heptgono regular de lado cuja menor diagonal vale d. O valor da maior diagonal satisfaz a qual das expresses?

(IME - 2017/2018 - 1 FASE ) Uma partcula eltrica de carga unitria, dotada de massa e inicialmente parada, sofre a ao de um impulso, entrando imediatamente em uma regio do espao na qual o campo magntico uniforme, passando a realizar um movimento no sistema de coordenadas XYZ,descrito pelas seguintes funes do tempo t: Considerando todas as grandezas no Sistema Internacional de Unidades, o mdulo do campo magntico : Dado: - impulso: 10. Observao: despreze a fora gravitacional.

(IME - 2017/2018 - 2 FASE ) EXAUSTO Eu quero uma licena de dormir, perdo pra descansar horas a fio, sem ao menos sonhar a leve palha de um pequeno sonho. Quero o que antes da vida foi o sono profundo das espcies, a graa de um estado. Semente. Muito mais que razes. PRADO, Adlia. Exausto. Disponvel em http://byluleoa-tecendopalavras.blogspot.com.br/. Acesso em 31/07/17. O vocbulo razes (verso 9) se contrape a

(IME - 2017/2018 - 2 FASE) HYPATIA OF ALEXANDRIA Hypatia of Alexandria (c. 370 CE March 415 CE) was a female philosopher and mathematician, born in Alexandria, Egypt possibly in 370 CE (although some scholars cite her birth as c. 350 CE). She was the daughter of the mathematician Theon, the last Professor at the University of Alexandria, who tutored her in math, astronomy, and the philosophy of the day which, in modern times, would be considered science. Nothing is known of her mother and there is little information about her life. As the historian Deakin writes, The most detailed accounts we have of Hypatias life are the records of her death. We learn more about her death from the primary sources than we do about any other aspect of her life. She was murdered in 415 CE by a Christian mob who attacked her on the streets of Alexandria. The primary sources, even those Christian writers who were hostile to her and claimed she was a witch, portray her as a woman who was widely known for her generosity, love of learning, and expertise in teaching in the subjects of Neo-Platonism, mathematics, science, and philosophy in general. In a city which was becoming increasingly diverse religiously (and had always been so culturally) Hypatia was a close friend of the pagan prefect Orestes and was blamed by Cyril, the Christian Archbishop of Alexandria, for keeping Orestes from accepting the true faith. She was also seen as a stumbling block to those who would have accepted the truth of Christianity were it not for her charisma, charm, and excellence in making difficult mathematical and philosophical concepts understandable to her students; concepts which contradicted the teachings of the relatively new church. Alexandria was a great seat of learning in the early days of Christianity but, as the faith grew in adherents and power, steadily became divided by fighting among religious factions. It is by no means an exaggeration to state that Alexandria was destroyed as a centre of culture and learning by religious intolerance, and 1Hypatia has come to symbolize this tragedy to the extent that her death has been cited as the end of the classical world. 2By all accounts, Hypatia was an extraordinary woman __________. Theon refused to impose upon his daughter the traditional role assigned to women and raised her as one would have raised a son in the Greek tradition; by teaching her his own trade. The historian Slatkin writes, Greek women of all classes were occupied with the same type of work, mostly centered around the domestic needs of the family. Women cared for young children, nursed the sick, and prepared food. Hypatia, on the other hand, led the life of a respected academic at Alexandrias university; a position to which, as far as the evidence suggests, only males were entitled previously. She never married and remained celibate throughout her life, devoting herself to learning and teaching. The ancient writers are in agreement that she was a woman of enormous intellectual power. Deakin writes: The breadth of her interests is most impressive. Within mathematics, she wrote or lectured on astronomy (including its observational aspects - the astrolabe), geometry (and for its day advanced geometry at that) and algebra (again, for its time, difficult algebra), and made an advance in computational technique - all this as well as engaging in religious philosophy and aspiring to a good writing style. 3Her writings were, as best we can judge, an outgrowth of her teaching in the technical areas of mathematics. In effect, she was continuing a program initiated by her father: a conscious effort to preserve and to elucidate the great mathematical works of the Alexandrian heritage. CE = Common Era, the same as AD, Anno Domini. MARK, Joshua J. Hypatia of Alexandria. In: Ancient History Encyclopedia, 2017. Disponvel em: http://www.ancient.eu/Hypatia_of_Alexandria/. Acesso em: 20/06/2017. Choose the correct option.

(IME - 2017/2018 - 1 FASE) Um prisma retangular reto possui trs arestas que formam uma progresso geomtrica de razo 2. Sua rea total de 28 cm2. Calcule o valor da diagonal do referido prisma.

(IME - 2017/2018 - 2 FASE) HYPATIA OF ALEXANDRIA Hypatia of Alexandria (c. 370 CE March 415 CE) was a female philosopher and mathematician, born in Alexandria, Egypt possibly in 370 CE (although some scholars cite her birth as c. 350 CE). She was the daughter of the mathematician Theon, the last Professor at the University of Alexandria, who tutored her in math, astronomy, and the philosophy of the day which, in modern times, would be considered science. Nothing is known of her mother and there is little information about her life. As the historian Deakin writes, The most detailed accounts we have of Hypatias life are the records of her death. We learn more about her death from the primary sources than we do about any other aspect of her life. She was murdered in 415 CE by a Christian mob who attacked her on the streets of Alexandria. The primary sources, even those Christian writers who were hostile to her and claimed she was a witch, portray her as a woman who was widely known for her generosity, love of learning, and expertise in teaching in the subjects of Neo-Platonism, mathematics, science, and philosophy in general. In a city which was becoming increasingly diverse religiously (and had always been so culturally) Hypatia was a close friend of the pagan prefect Orestes and was blamed by Cyril, the Christian Archbishop of Alexandria, for keeping Orestes from accepting the true faith. She was also seen as a stumbling block to those who would have accepted the truth of Christianity were it not for her charisma, charm, and excellence in making difficult mathematical and philosophical concepts understandable to her students; concepts which contradicted the teachings of the relatively new church. Alexandria was a great seat of learning in the early days of Christianity but, as the faith grew in adherents and power, steadily became divided by fighting among religious factions. It is by no means an exaggeration to state that Alexandria was destroyed as a centre of culture and learning by religious intolerance, and 1Hypatia has come to symbolize this tragedy to the extent that her death has been cited as the end of the classical world. 2By all accounts, Hypatia was an extraordinary woman __________. Theon refused to impose upon his daughter the traditional role assigned to women and raised her as one would have raised a son in the Greek tradition; by teaching her his own trade. The historian Slatkin writes, Greek women of all classes were occupied with the same type of work, mostly centered around the domestic needs of the family. Women cared for young children, nursed the sick, and prepared food. Hypatia, on the other hand, led the life of a respected academic at Alexandrias university; a position to which, as far as the evidence suggests, only males were entitled previously. She never married and remained celibate throughout her life, devoting herself to learning and teaching. The ancient writers are in agreement that she was a woman of enormous intellectual power. Deakin writes: The breadth of her interests is most impressive. Within mathematics, she wrote or lectured on astronomy (including its observational aspects - the astrolabe), geometry (and for its day advanced geometry at that) and algebra (again, for its time, difficult algebra), and made an advance in computational technique - all this as well as engaging in religious philosophy and aspiring to a good writing style. 3Her writings were, as best we can judge, an outgrowth of her teaching in the technical areas of mathematics. In effect, she was continuing a program initiated by her father: a conscious effort to preserve and to elucidate the great mathematical works of the Alexandrian heritage. CE = Common Era, the same as AD, Anno Domini. MARK, Joshua J. Hypatia of Alexandria. In: Ancient History Encyclopedia, 2017. Disponvel em: http://www.ancient.eu/Hypatia_of_Alexandria/. Acesso em: 20/06/2017. Choose a synonym for the expression toto the extent that in the sentence () Hypatia has come to symbolize this tragedy to the extent that her death has been cited as the end of the classical world. in reference 1

(IME - 2017/2018 - 1 FASE ) A figura acima mostra dois geradores de corrente contnua, denominados G1e G2que possuem resistncias internas R1 e R2e a mesma tenso induzida E. Os geradores esto conectados a uma resistncia R por meio de uma chave S. A resistncia R1 um cilindro no condutor que possui um mbolo condutor em sua parte superior e que se encontra, inicialmente, totalmente preenchido por um liquido condutor. O mbolo desce junto com o nvel do lquido condutor no interior do cilindro, mantendo a continuidade do circuito. No instante em que a chave S fechada, o lquido comea a escoar pelo registro cuja vazo volumtrica Q. Diante do exposto, o instante de tempo t, no qual o gerador G1fornece 40% da corrente demandada pela carga : Dados: - antes do fechamento da chave S: R1 = 4R2; - resistividade do lquido condutor: ; e - rea da base do cilindro: A.

(IME - 2017/2018 - 2 FASE ) EXAUSTO Eu quero uma licena de dormir, perdo pra descansar horas a fio, sem ao menos sonhar a leve palha de um pequeno sonho. Quero o que antes da vida foi o sono profundo das espcies, a graa de um estado. Semente. Muito mais que razes. PRADO, Adlia. Exausto. Disponvel em http://byluleoa-tecendopalavras.blogspot.com.br/. Acesso em 31/07/17. Nas opes abaixo, encontram-se cinco afirmaes sobre o poema. Qual delas est estritamente relacionada escolha lexical feita pela autora?

(IME- 2017/2018 - 2 FASE ) EXAUSTO Eu quero uma licena de dormir, perdo pra descansar horas a fio, sem ao menos sonhar a leve palha de um pequeno sonho. Quero o que antes da vida foi o sono profundo das espcies, a graa de um estado. Semente. Muito mais que razes. PRADO, Adlia. Exausto. Disponvel em http://byluleoa-tecendopalavras.blogspot.com.br/. Acesso em 31/07/17. A respeito dos versos abaixo (versos 3 e 4), sem ao menos sonhar a leve palha de um pequeno sonho. podemos afirmar que

(IME - 2017/2018 - 2 FASE) HYPATIA OF ALEXANDRIA Hypatia of Alexandria (c. 370 CE March 415 CE) was a female philosopher and mathematician, born in Alexandria, Egypt possibly in 370 CE (although some scholars cite her birth as c. 350 CE). She was the daughter of the mathematician Theon, the last Professor at the University of Alexandria, who tutored her in math, astronomy, and the philosophy of the day which, in modern times, would be considered science. Nothing is known of her mother and there is little information about her life. As the historian Deakin writes, The most detailed accounts we have of Hypatias life are the records of her death. We learn more about her death from the primary sources than we do about any other aspect of her life. She was murdered in 415 CE by a Christian mob who attacked her on the streets of Alexandria. The primary sources, even those Christian writers who were hostile to her and claimed she was a witch, portray her as a woman who was widely known for her generosity, love of learning, and expertise in teaching in the subjects of Neo-Platonism, mathematics, science, and philosophy in general. In a city which was becoming increasingly diverse religiously (and had always been so culturally) Hypatia was a close friend of the pagan prefect Orestes and was blamed by Cyril, the Christian Archbishop of Alexandria, for keeping Orestes from accepting the true faith. She was also seen as a stumbling block to those who would have accepted the truth of Christianity were it not for her charisma, charm, and excellence in making difficult mathematical and philosophical concepts understandable to her students; concepts which contradicted the teachings of the relatively new church. Alexandria was a great seat of learning in the early days of Christianity but, as the faith grew in adherents and power, steadily became divided by fighting among religious factions. It is by no means an exaggeration to state that Alexandria was destroyed as a centre of culture and learning by religious intolerance, and 1Hypatia has come to symbolize this tragedy to the extent that her death has been cited as the end of the classical world. 2By all accounts, Hypatia was an extraordinary woman __________. Theon refused to impose upon his daughter the traditional role assigned to women and raised her as one would have raised a son in the Greek tradition; by teaching her his own trade. The historian Slatkin writes, Greek women of all classes were occupied with the same type of work, mostly centered around the domestic needs of the family. Women cared for young children, nursed the sick, and prepared food. Hypatia, on the other hand, led the life of a respected academic at Alexandrias university; a position to which, as far as the evidence suggests, only males were entitled previously. She never married and remained celibate throughout her life, devoting herself to learning and teaching. The ancient writers are in agreement that she was a woman of enormous intellectual power. Deakin writes: The breadth of her interests is most impressive. Within mathematics, she wrote or lectured on astronomy (including its observational aspects - the astrolabe), geometry (and for its day advanced geometry at that) and algebra (again, for its time, difficult algebra), and made an advance in computational technique - all this as well as engaging in religious philosophy and aspiring to a good writing style. 3Her writings were, as best we can judge, an outgrowth of her teaching in the technical areas of mathematics. In effect, she was continuing a program initiated by her father: a conscious effort to preserve and to elucidate the great mathematical works of the Alexandrian heritage. CE = Common Era, the same as AD, Anno Domini. MARK, Joshua J. Hypatia of Alexandria. In: Ancient History Encyclopedia, 2017. Disponvel em: http://www.ancient.eu/Hypatia_of_Alexandria/. Acesso em: 20/06/2017. Choose the appropriate continuation for the sentence By all accounts, Hypatia was an extraordinary woman __________ in reference 2.

(IME - 2017/2018 - 2 FASE ) EXAUSTO Eu quero uma licena de dormir, perdo pra descansar horas a fio, sem ao menos sonhar a leve palha de um pequeno sonho. Quero o que antes da vida foi o sono profundo das espcies, a graa de um estado. Semente. Muito mais que razes. PRADO, Adlia. Exausto. Disponvel em http://byluleoa-tecendopalavras.blogspot.com.br/. Acesso em 31/07/17. Qual das palavras a seguir substituindo a palavra semente no verso 8, acarretaria mudana de sentido?

(IME - 2017/2018 - 2 FASE) HYPATIA OF ALEXANDRIA Hypatia of Alexandria (c. 370 CE March 415 CE) was a female philosopher and mathematician, born in Alexandria, Egypt possibly in 370 CE (although some scholars cite her birth as c. 350 CE). She was the daughter of the mathematician Theon, the last Professor at the University of Alexandria, who tutored her in math, astronomy, and the philosophy of the day which, in modern times, would be considered science. Nothing is known of her mother and there is little information about her life. As the historian Deakin writes, The most detailed accounts we have of Hypatias life are the records of her death. We learn more about her death from the primary sources than we do about any other aspect of her life. She was murdered in 415 CE by a Christian mob who attacked her on the streets of Alexandria. The primary sources, even those Christian writers who were hostile to her and claimed she was a witch, portray her as a woman who was widely known for her generosity, love of learning, and expertise in teaching in the subjects of Neo-Platonism, mathematics, science, and philosophy in general. In a city which was becoming increasingly diverse religiously (and had always been so culturally) Hypatia was a close friend of the pagan prefect Orestes and was blamed by Cyril, the Christian Archbishop of Alexandria, for keeping Orestes from accepting the true faith. She was also seen as a stumbling block to those who would have accepted the truth of Christianity were it not for her charisma, charm, and excellence in making difficult mathematical and philosophical concepts understandable to her students; concepts which contradicted the teachings of the relatively new church. Alexandria was a great seat of learning in the early days of Christianity but, as the faith grew in adherents and power, steadily became divided by fighting among religious factions. It is by no means an exaggeration to state that Alexandria was destroyed as a centre of culture and learning by religious intolerance, and 1Hypatia has come to symbolize this tragedy to the extent that her death has been cited as the end of the classical world. 2By all accounts, Hypatia was an extraordinary woman __________. Theon refused to impose upon his daughter the traditional role assigned to women and raised her as one would have raised a son in the Greek tradition; by teaching her his own trade. The historian Slatkin writes, Greek women of all classes were occupied with the same type of work, mostly centered around the domestic needs of the family. Women cared for young children, nursed the sick, and prepared food. Hypatia, on the other hand, led the life of a respected academic at Alexandrias university; a position to which, as far as the evidence suggests, only males were entitled previously. She never married and remained celibate throughout her life, devoting herself to learning and teaching. The ancient writers are in agreement that she was a woman of enormous intellectual power. Deakin writes: The breadth of her interests is most impressive. Within mathematics, she wrote or lectured on astronomy (including its observational aspects - the astrolabe), geometry (and for its day advanced geometry at that) and algebra (again, for its time, difficult algebra), and made an advance in computational technique - all this as well as engaging in religious philosophy and aspiring to a good writing style. 3Her writings were, as best we can judge, an outgrowth of her teaching in the technical areas of mathematics. In effect, she was continuing a program initiated by her father: a conscious effort to preserve and to elucidate the great mathematical works of the Alexandrian heritage. CE = Common Era, the same as AD, Anno Domini. MARK, Joshua J. Hypatia of Alexandria. In: Ancient History Encyclopedia, 2017. Disponvel em: http://www.ancient.eu/Hypatia_of_Alexandria/. Acesso em: 20/06/2017. Choose the correct meaning of outgrowth in the sentence Her writings were, as best we can judge, an outgrowth of her teaching () in reference 3.