Questões - AFA | Gabarito e resoluções

(AFA - 2021) The End of life on Earth It weighted about 10,000 tons, entered the atmosphere at a speed of 64,000 km/h and exploded over a city with a blast of 500 kilotons. But on 15 February 2013, we were lucky. The meteorite that 5showered pieces of rock over Chelyabinsk, Russia, was relatively small, at only about 17 metres wide. Although many people were injured by falling glass, the damage was nothing compared to what had happened in Siberia neraly one hundred years ago, when a relatively small 10object (approximately 50 metres in diameter) exploded in mid-air over a forest region, flattening about 80 million trees. If it had exploded over a city such as Moscow or London, millions of people would have been killed. By a strange coincidence, the same day that the 15meteorite terrified the people of Chelyabinsk, another 50m-wide asteroid passed relatively close to Earth. Scientists were expecting that visit and know that the asteroid will return to fly close by us in 2046, but the Russian meteorite earlier in the day had been too small 20for anyone to spot. Most scientists agree that comets and asteroids pose the biggest natural threat to human existence. It was probably a large asteroid or comet collinding with Earth which wiped out the dinosaurs about 65 million 25years ago. An enormous object, 10 to 16 km in diameter, struck the Yucatan region in Mexico with the force of 100 megatons. That is the equivalent of one Hiroshima bomb for every peerson alive on Earth today. Many scientists, including the late Stephen 30Hawking, say that any comet or asteroid greater than 20km in diameter that hits Earth will result in the complete destruction of complex life, including all animals and most plants. As we have seen even a much smaller asteroid can cause great damage. 35The Earth has been kept fairly safe for the last 65 million years by good fortune and the massive gravitational field of the planet Jupiter. Our cosmic guardian, with its stable circular orbit far from the sun, sweeps up and scatters away most of the dangerous 40comets and asteroids which might cross Earths orbit. After the Chelyabinsk meteorite, scientists are now monitoring potential hazards even more carefully but, as far as they know, there is no danger in the foreseeable future. 45Types of space rocks Comet - a ball of rock and ice that sends out a tail of gas and dust behind it. Bright comets only appear in our visible night sky about once every ten years. Asteroid - a rock a few feet to several kms in 50diameter. Unlike comets, asteroids have no tail. Most are to small to cause any damage and burn up in the atmosphere. Meteoroid - part of an asteroid or comet. Meteorite - what a meteoroid is called when it 55hits Earth. Taken from: http://learningenglishteens.britishcouncil.org - Access on 29/06/2020 The Russian meteorite

(AFA - 2021 - Modelo C - Questo 26) Sejam as curvas : x2+ y2= r2e:y2- x2= 4 tangentes em dois pontos distintos do plano cartesiano. ConsidereSo conjunto de pontos P(x, y) tais que x2+ y2 r2. Se for realizada uma rotao de 90 dos pontos deSem torno de uma das assntonas de, ento o slido formado tem uma superfcie cuja rea total, em unidade de rea, mede

(AFA - 2021) The End of life on Earth It weighted about 10,000 tons, entered the atmosphere at a speed of 64,000 km/h and exploded over a city with a blast of 500 kilotons. But on 15 February 2013, we were lucky. The meteorite that 5showered pieces of rock over Chelyabinsk, Russia, was relatively small, at only about 17 metres wide. Although many people were injured by falling glass, the damage was nothing compared to what had happened in Siberia neraly one hundred years ago, when a relatively small 10object (approximately 50 metres in diameter) exploded in mid-air over a forest region, flattening about 80 million trees. If it had exploded over a city such as Moscow or London, millions of people would have been killed. By a strange coincidence, the same day that the 15meteorite terrified the people of Chelyabinsk, another 50m-wide asteroid passed relatively close to Earth. Scientists were expecting that visit and know that the asteroid will return to fly close by us in 2046, but the Russian meteorite earlier in the day had been too small 20for anyone to spot. Most scientists agree that comets and asteroids pose the biggest natural threat to human existence. It was probably a large asteroid or comet collinding with Earth which wiped out the dinosaurs about 65 million 25years ago. An enormous object, 10 to 16 km in diameter, struck the Yucatan region in Mexico with the force of 100 megatons. That is the equivalent of one Hiroshima bomb for every peerson alive on Earth today. Many scientists, including the late Stephen 30Hawking, say that any comet or asteroid greater than 20km in diameter that hits Earth will result in the complete destruction of complex life, including all animals and most plants. As we have seen even a much smaller asteroid can cause great damage. 35The Earth has been kept fairly safe for the last 65 million years by good fortune and the massive gravitational field of the planet Jupiter. Our cosmic guardian, with its stable circular orbit far from the sun, sweeps up and scatters away most of the dangerous 40comets and asteroids which might cross Earths orbit. After the Chelyabinsk meteorite, scientists are now monitoring potential hazards even more carefully but, as far as they know, there is no danger in the foreseeable future. 45Types of space rocks Comet - a ball of rock and ice that sends out a tail of gas and dust behind it. Bright comets only appear in our visible night sky about once every ten years. Asteroid - a rock a few feet to several kms in 50diameter. Unlike comets, asteroids have no tail. Most are to small to cause any damage and burn up in the atmosphere. Meteoroid - part of an asteroid or comet. Meteorite - what a meteoroid is called when it 55hits Earth. Taken from: http://learningenglishteens.britishcouncil.org - Access on 29/06/2020 Experts maintain that comets and asteroids could

(AFA - 2021) The End of life on Earth It weighted about 10,000 tons, entered the atmosphere at a speed of 64,000 km/h and exploded over a city with a blast of 500 kilotons. But on 15 February 2013, we were lucky. The meteorite that 5showered pieces of rock over Chelyabinsk, Russia, was relatively small, at only about 17 metres wide. Although many people were injured by falling glass, the damage was nothing compared to what had happened in Siberia neraly one hundred years ago, when a relatively small 10object (approximately 50 metres in diameter) exploded in mid-air over a forest region, flattening about 80 million trees. If it had exploded over a city such as Moscow or London, millions of people would have been killed. By a strange coincidence, the same day that the 15meteorite terrified the people of Chelyabinsk, another 50m-wide asteroid passed relatively close to Earth. Scientists were expecting that visit and know that the asteroid will return to fly close by us in 2046, but the Russian meteorite earlier in the day had been too small 20for anyone to spot. Most scientists agree that comets and asteroids pose the biggest natural threat to human existence. It was probably a large asteroid or comet collinding with Earth which wiped out the dinosaurs about 65 million 25years ago. An enormous object, 10 to 16 km in diameter, struck the Yucatan region in Mexico with the force of 100 megatons. That is the equivalent of one Hiroshima bomb for every peerson alive on Earth today. Many scientists, including the late Stephen 30Hawking, say that any comet or asteroid greater than 20km in diameter that hits Earth will result in the complete destruction of complex life, including all animals and most plants. As we have seen even a much smaller asteroid can cause great damage. 35The Earth has been kept fairly safe for the last 65 million years by good fortune and the massive gravitational field of the planet Jupiter. Our cosmic guardian, with its stable circular orbit far from the sun, sweeps up and scatters away most of the dangerous 40comets and asteroids which might cross Earths orbit. After the Chelyabinsk meteorite, scientists are now monitoring potential hazards even more carefully but, as far as they know, there is no danger in the foreseeable future. 45Types of space rocks Comet - a ball of rock and ice that sends out a tail of gas and dust behind it. Bright comets only appear in our visible night sky about once every ten years. Asteroid - a rock a few feet to several kms in 50diameter. Unlike comets, asteroids have no tail. Most are to small to cause any damage and burn up in the atmosphere. Meteoroid - part of an asteroid or comet. Meteorite - what a meteoroid is called when it 55hits Earth. Taken from: http://learningenglishteens.britishcouncil.org - Access on 29/06/2020 A relatively small asteroid

(AFA - 2021 - Modelo C - Questo 27) O jogo rabe chamadoQuirkatouAl- Quirg semelhante ao jogo de damas moderno, no qual h um tabuleiro de 25 casas (5x5). Esse jogo foi mencionado na obra Kitab Al-Aghannido sculo X. OAl-Quirgera tambm o nome para o jogo que atualmente conhecido como trilha. Certo dia, uma caixeiro viajante apresentou esse jogo a um rei que ficou encantado com ele e decidiu que iria compr-lo. Pediu ao viajante que colocasse preo no produto. O caixeiro disse: - Vossa Majestade, posso lhe vender o jogo por uma simples barganha! Basta me dar 1 gro de milho para a 1 casa do jogo, 2 gros de milho para a 2 casa do jogo, 4 gros de milho para a 3 casa do jogo, 8 gros de milho para a 4 casa do jogo e assim por diante at a 25 casa do tabuleiro! O rei, imediatamente, ordenou o pagamento para o caixeiro viajante em troca do jogo que tannto lhe agradou. Levando em considerao que o peso mdio de um gro de milho seja de 0,30g pode-se afirmar que

(AFA - 2021) The End of life on Earth It weighted about 10,000 tons, entered the atmosphere at a speed of 64,000 km/h and exploded over a city with a blast of 500 kilotons. But on 15 February 2013, we were lucky. The meteorite that 5showered pieces of rock over Chelyabinsk, Russia, was relatively small, at only about 17 metres wide. Although many people were injured by falling glass, the damage was nothing compared to what had happened in Siberia neraly one hundred years ago, when a relatively small 10object (approximately 50 metres in diameter) exploded in mid-air over a forest region, flattening about 80 million trees. If it had exploded over a city such as Moscow or London, millions of people would have been killed. By a strange coincidence, the same day that the 15meteorite terrified the people of Chelyabinsk, another 50m-wide asteroid passed relatively close to Earth. Scientists were expecting that visit and know that the asteroid will return to fly close by us in 2046, but the Russian meteorite earlier in the day had been too small 20for anyone to spot. Most scientists agree that comets and asteroids pose the biggest natural threat to human existence. It was probably a large asteroid or comet collinding with Earth which wiped out the dinosaurs about 65 million 25years ago. An enormous object, 10 to 16 km in diameter, struck the Yucatan region in Mexico with the force of 100 megatons. That is the equivalent of one Hiroshima bomb for every peerson alive on Earth today. Many scientists, including the late Stephen 30Hawking, say that any comet or asteroid greater than 20km in diameter that hits Earth will result in the complete destruction of complex life, including all animals and most plants. As we have seen even a much smaller asteroid can cause great damage. 35The Earth has been kept fairly safe for the last 65 million years by good fortune and the massive gravitational field of the planet Jupiter. Our cosmic guardian, with its stable circular orbit far from the sun, sweeps up and scatters away most of the dangerous 40comets and asteroids which might cross Earths orbit. After the Chelyabinsk meteorite, scientists are now monitoring potential hazards even more carefully but, as far as they know, there is no danger in the foreseeable future. 45Types of space rocks Comet - a ball of rock and ice that sends out a tail of gas and dust behind it. Bright comets only appear in our visible night sky about once every ten years. Asteroid - a rock a few feet to several kms in 50diameter. Unlike comets, asteroids have no tail. Most are to small to cause any damage and burn up in the atmosphere. Meteoroid - part of an asteroid or comet. Meteorite - what a meteoroid is called when it 55hits Earth. Taken from: http://learningenglishteens.britishcouncil.org - Access on 29/06/2020 Earth has been relatively save thanks to

(AFA - 2021 - Modelo C - Questo 28) Sequncias tm relevncia para estudos em matemtica, mas atmbm habitem o imaginrio das pessoas na observao de possveis coincidncias. Um exemplo doi a data de 02 de fevereiro deste ano de 2020. Esse foi o 33 dia de ano e estava a 333 dias do fim de 2020. Alm disso, 02/02/2020 uma capicua, ou seja, uma sequencia de nmeros que tanto pode ser lida da direita para a esquerda como da esquerda para a direita sem alterao de significado. Considere todas as combinaes numricas capicuas no formato DD/MM/AAAA, em que DD dia com dois algarismos, MM ms com dois algarismos e AAAA ano com quatro algarismos. A diferena entre o nmero de capicuas possveis de 01 de janeiro de 2000 a 31 de dezembro de 2999 e de 01 de janeiro de 3000 a 31 de dezembro de 3999, nessa ordem, um nmero do intervalo

(AFA - 2021) The End of life on Earth It weighted about 10,000 tons, entered the atmosphere at a speed of 64,000 km/h and exploded over a city with a blast of 500 kilotons. But on 15 February 2013, we were lucky. The meteorite that 5showered pieces of rock over Chelyabinsk, Russia, was relatively small, at only about 17 metres wide. Although many people were injured by falling glass, the damage was nothing compared to what had happened in Siberia neraly one hundred years ago, when a relatively small 10object (approximately 50 metres in diameter) exploded in mid-air over a forest region, flattening about 80 million trees. If it had exploded over a city such as Moscow or London, millions of people would have been killed. By a strange coincidence, the same day that the 15meteorite terrified the people of Chelyabinsk, another 50m-wide asteroid passed relatively close to Earth. Scientists were expecting that visit and know that the asteroid will return to fly close by us in 2046, but the Russian meteorite earlier in the day had been too small 20for anyone to spot. Most scientists agree that comets and asteroids pose the biggest natural threat to human existence. It was probably a large asteroid or comet collinding with Earth which wiped out the dinosaurs about 65 million 25years ago. An enormous object, 10 to 16 km in diameter, struck the Yucatan region in Mexico with the force of 100 megatons. That is the equivalent of one Hiroshima bomb for every peerson alive on Earth today. Many scientists, including the late Stephen 30Hawking, say that any comet or asteroid greater than 20km in diameter that hits Earth will result in the complete destruction of complex life, including all animals and most plants. As we have seen even a much smaller asteroid can cause great damage. 35The Earth has been kept fairly safe for the last 65 million years by good fortune and the massive gravitational field of the planet Jupiter. Our cosmic guardian, with its stable circular orbit far from the sun, sweeps up and scatters away most of the dangerous 40comets and asteroids which might cross Earths orbit. After the Chelyabinsk meteorite, scientists are now monitoring potential hazards even more carefully but, as far as they know, there is no danger in the foreseeable future. 45Types of space rocks Comet - a ball of rock and ice that sends out a tail of gas and dust behind it. Bright comets only appear in our visible night sky about once every ten years. Asteroid - a rock a few feet to several kms in 50diameter. Unlike comets, asteroids have no tail. Most are to small to cause any damage and burn up in the atmosphere. Meteoroid - part of an asteroid or comet. Meteorite - what a meteoroid is called when it 55hits Earth. Taken from: http://learningenglishteens.britishcouncil.org - Access on 29/06/2020 Which (line 40) refers to

(AFA - 2021) The End of life on Earth It weighted about 10,000 tons, entered the atmosphere at a speed of 64,000 km/h and exploded over a city with a blast of 500 kilotons. But on 15 February 2013, we were lucky. The meteorite that 5showered pieces of rock over Chelyabinsk, Russia, was relatively small, at only about 17 metres wide. Although many people were injured by falling glass, the damage was nothing compared to what had happened in Siberia neraly one hundred years ago, when a relatively small 10object (approximately 50 metres in diameter) exploded in mid-air over a forest region, flattening about 80 million trees. If it had exploded over a city such as Moscow or London, millions of people would have been killed. By a strange coincidence, the same day that the 15meteorite terrified the people of Chelyabinsk, another 50m-wide asteroid passed relatively close to Earth. Scientists were expecting that visit and know that the asteroid will return to fly close by us in 2046, but the Russian meteorite earlier in the day had been too small 20for anyone to spot. Most scientists agree that comets and asteroids pose the biggest natural threat to human existence. It was probably a large asteroid or comet collinding with Earth which wiped out the dinosaurs about 65 million 25years ago. An enormous object, 10 to 16 km in diameter, struck the Yucatan region in Mexico with the force of 100 megatons. That is the equivalent of one Hiroshima bomb for every peerson alive on Earth today. Many scientists, including the late Stephen 30Hawking, say that any comet or asteroid greater than 20km in diameter that hits Earth will result in the complete destruction of complex life, including all animals and most plants. As we have seen even a much smaller asteroid can cause great damage. 35The Earth has been kept fairly safe for the last 65 million years by good fortune and the massive gravitational field of the planet Jupiter. Our cosmic guardian, with its stable circular orbit far from the sun, sweeps up and scatters away most of the dangerous 40comets and asteroids which might cross Earths orbit. After the Chelyabinsk meteorite, scientists are now monitoring potential hazards even more carefully but, as far as they know, there is no danger in the foreseeable future. 45Types of space rocks Comet - a ball of rock and ice that sends out a tail of gas and dust behind it. Bright comets only appear in our visible night sky about once every ten years. Asteroid - a rock a few feet to several kms in 50diameter. Unlike comets, asteroids have no tail. Most are to small to cause any damage and burn up in the atmosphere. Meteoroid - part of an asteroid or comet. Meteorite - what a meteoroid is called when it 55hits Earth. Taken from: http://learningenglishteens.britishcouncil.org - Access on 29/06/2020 In the sentence the dangerous comets and asteroids whichmightcross Earths orbit(lines 39 and 40), the underlined word is similar to

(AFA - 2021 - Modelo C - Questo 30) Considere a figura a seguir. Nela est representada a inscrio de uma esfera num cubo que, por sua vez, est inscrito num cone equiltero, de tal forma que uma de suas faces est apoiada na base do cone e os vrtices da face oposta esto na lateral do cone. A projeo ortogonal do vrtice do cone sua base contm dois pontos de tangncia da esfera com o cubo. Se R e r so, respectivamente, as medidas do raio da base do cone e do raio da esfera, em cm, ento

(AFA - 2021 - Modelo C - Questo 31) Considere as funes f: IR* IR - {2} e g: IR* IR - {2} definidas por e e, tambm, a funo real h definida por. correto afirmar que

(AFA - 2021) The End of life on Earth It weighted about 10,000 tons, entered the atmosphere at a speed of 64,000 km/h and exploded over a city with a blast of 500 kilotons. But on 15 February 2013, we were lucky. The meteorite that 5showered pieces of rock over Chelyabinsk, Russia, was relatively small, at only about 17 metres wide. Although many people were injured by falling glass, the damage was nothing compared to what had happened in Siberia neraly one hundred years ago, when a relatively small 10object (approximately 50 metres in diameter) exploded in mid-air over a forest region, flattening about 80 million trees. If it had exploded over a city such as Moscow or London, millions of people would have been killed. By a strange coincidence, the same day that the 15meteorite terrified the people of Chelyabinsk, another 50m-wide asteroid passed relatively close to Earth. Scientists were expecting that visit and know that the asteroid will return to fly close by us in 2046, but the Russian meteorite earlier in the day had been too small 20for anyone to spot. Most scientists agree that comets and asteroids pose the biggest natural threat to human existence. It was probably a large asteroid or comet collinding with Earth which wiped out the dinosaurs about 65 million 25years ago. An enormous object, 10 to 16 km in diameter, struck the Yucatan region in Mexico with the force of 100 megatons. That is the equivalent of one Hiroshima bomb for every peerson alive on Earth today. Many scientists, including the late Stephen 30Hawking, say that any comet or asteroid greater than 20km in diameter that hits Earth will result in the complete destruction of complex life, including all animals and most plants. As we have seen even a much smaller asteroid can cause great damage. 35The Earth has been kept fairly safe for the last 65 million years by good fortune and the massive gravitational field of the planet Jupiter. Our cosmic guardian, with its stable circular orbit far from the sun, sweeps up and scatters away most of the dangerous 40comets and asteroids which might cross Earths orbit. After the Chelyabinsk meteorite, scientists are now monitoring potential hazards even more carefully but, as far as they know, there is no danger in the foreseeable future. 45Types of space rocks Comet - a ball of rock and ice that sends out a tail of gas and dust behind it. Bright comets only appear in our visible night sky about once every ten years. Asteroid - a rock a few feet to several kms in 50diameter. Unlike comets, asteroids have no tail. Most are to small to cause any damage and burn up in the atmosphere. Meteoroid - part of an asteroid or comet. Meteorite - what a meteoroid is called when it 55hits Earth. Taken from: http://learningenglishteens.britishcouncil.org - Access on 29/06/2020 Scientists support the idea that

(AFA - 2021) The End of life on Earth It weighted about 10,000 tons, entered the atmosphere at a speed of 64,000 km/h and exploded over a city with a blast of 500 kilotons. But on 15 February 2013, we were lucky. The meteorite that 5showered pieces of rock over Chelyabinsk, Russia, was relatively small, at only about 17 metres wide. Although many people were injured by falling glass, the damage was nothing compared to what had happened in Siberia neraly one hundred years ago, when a relatively small 10object (approximately 50 metres in diameter) exploded in mid-air over a forest region, flattening about 80 million trees. If it had exploded over a city such as Moscow or London, millions of people would have been killed. By a strange coincidence, the same day that the 15meteorite terrified the people of Chelyabinsk, another 50m-wide asteroid passed relatively close to Earth. Scientists were expecting that visit and know that the asteroid will return to fly close by us in 2046, but the Russian meteorite earlier in the day had been too small 20for anyone to spot. Most scientists agree that comets and asteroids pose the biggest natural threat to human existence. It was probably a large asteroid or comet collinding with Earth which wiped out the dinosaurs about 65 million 25years ago. An enormous object, 10 to 16 km in diameter, struck the Yucatan region in Mexico with the force of 100 megatons. That is the equivalent of one Hiroshima bomb for every peerson alive on Earth today. Many scientists, including the late Stephen 30Hawking, say that any comet or asteroid greater than 20km in diameter that hits Earth will result in the complete destruction of complex life, including all animals and most plants. As we have seen even a much smaller asteroid can cause great damage. 35The Earth has been kept fairly safe for the last 65 million years by good fortune and the massive gravitational field of the planet Jupiter. Our cosmic guardian, with its stable circular orbit far from the sun, sweeps up and scatters away most of the dangerous 40comets and asteroids which might cross Earths orbit. After the Chelyabinsk meteorite, scientists are now monitoring potential hazards even more carefully but, as far as they know, there is no danger in the foreseeable future. 45Types of space rocks Comet - a ball of rock and ice that sends out a tail of gas and dust behind it. Bright comets only appear in our visible night sky about once every ten years. Asteroid - a rock a few feet to several kms in 50diameter. Unlike comets, asteroids have no tail. Most are to small to cause any damage and burn up in the atmosphere. Meteoroid - part of an asteroid or comet. Meteorite - what a meteoroid is called when it 55hits Earth. Taken from: http://learningenglishteens.britishcouncil.org - Access on 29/06/2020 According to the text

(AFA - 2021) Numa partida de vlei, certo atleta d um mergulho na quadra,a uma distncia x=2,5m da rede, defendendo um ataque adversrio, conforme figura a seguir. Aps essa defesa, considere que a bola lanada de uma altura desprezvel em relao ao cho, de forma que sua velocidade faz um ngulo de 45 com a direo horizontal. Ao longo de sua trajetria, essa bola toca a fita da rede caindo, posteriormente, do outro lado da quadra. Imediatamente antes e imediatamente aps tocar a fita, a velocidade da bola tem direo horizontal. A distncia x, onde a bola cai na quadra, igual metade da altura h da fita. Despreze a resistncia do ar e considere a bola uma partcula de massa 200g, cujo movimento se d no plano da figura. O mdulo do impulso, aplicado pela fita sobre a bola, em N . s, vale

(AFA - 2021) Uma partcula de massa M lanada obliquamente com sua velocidade incialfazendo um ngulo de 30 com a direo horizontal, conforme indica figura a seguir. Ao atingir a altura mxima de sua trajetria parablica, essa partcula colide inelasticamente com um bloco de massa 5M. Esse blobo, de dimenses desprezveis, est preso ao teto por um fio ideal, de comprimento 1,2m, formando um pndulo balstico. Inicialmente o fio do pndulo est na vertical. Aps a coliso, o pndulo atinge uma altura mxima, na qual o fio tem uma inclinao de 30 em relao direo horizontal. Desprezando a resistncia do ar, o mdulo da velocidade inicial da partcula,, em m/s, igual a