Questões - ITA 2016 | Gabarito e resoluções

(ITA - 2016 - 1 FASE) Considere as seguintes afirmaes: I. A funo f(x) = log10 estritamente crescente no intervalo ]1, + [. II. A equao 2x+2 = 3x1 possui uma nica soluo real. III. A equao (x + 1)x = x admite pelo menos uma soluo real positiva. (so) verdadeira(s)

(ITA - 2016 - 1 Fase) Considerando condies ambientes, assinale a opo ERRADA.

(ITA - 2016 - 1 FASE) Marque a opo cujo assunto no mencionado no texto.

(ITA - 2016 - 1 FASE) Considere um corpo esfrico de raio r totalmente envolvido por um fluido de viscosidade com velocidade mdia v. De acordo com a lei de Stokes, para baixas velocidades, esse corpo sofrer a aode uma fora de arrasto viscoso dada por F= 6rv. A dimenso de dada por:

(ITA - 2016 - 1 FASE) Se x um nmero natural com 2015dgitos, ento o nmero de dgitos da parte inteira de igual a

(ITA - 2016 - 1 FASE) Trs barras de peso desprezvel, articuladas nos pinos P, Q e R, constituem uma estrutura vertical em forma de tringulo issceles, com 6,0 m de base e 4,0 m de altura, que sustenta uma massa M suspensa em Q em equilbrio esttico. O pino P tambm e articulado no seu apoio fixo, e o pino R apoia-se verticalmente sobre o rolete livre. Sendo de 1,5 104 N e 5,0 103 N os respectivos valores mximos das foras de trao e compresso suportveis por qualquer das barras, o mximo valor possvel para M de:

(ITA - 2016 - 1 Fase) Assinale a opo que apresenta o sal solvel em gua a 25 oC.

(ITA - 2016 - 1 FASE) Brazils business Belindia Why the country produces fewer world-class companies than it should BRAZILIANS make up almost of the planets population and produce about of its output. Yet of the firms in Fortune magazines 2014 Global 500 ranking of the biggest companies by revenue only seven, or were from Brazil, down from eight in 2013. And on Forbess list of the most highly valued firms worldwide just 25, or were Brazilian. The countrys biggest corporate star, Petrobras, is mired in scandals, its debt downgraded to junk status. 1In 1974 Edmar Bacha, an economist, described its economy as Belindia, a Belgium-sized island of prosperity in a sea of India-like poverty. Since then Brazil has done far better than India in alleviating poverty, but in business terms it still has a Belindia problem: a handful of world-class enterprises in a sea of poorly run ones. 2Brazilian businesses face a litany of obstacles: bureaucracy, complex tax rules, shoddy infrastructure and a shortage of skilled workers to say nothing of a stagnant economy. But a big reason for Brazilian firms underperformance is less well rehearsed: poor management. Since 2004 John van Reenen of the London School of Economics and his colleagues have surveyed midsized firms in 34 countries, grading them on a five-point scale based on how well they monitor their operations, set targets and reward performance. Brazilian firms average score, at is similar to that of Chinas and a bit above that of Indias. But Brazil ranks below Chile (2.8) and Mexico (2.9); America leads the pack with 3.3. 3The best Brazilian firms score as well as the best American ones, but its long tail of badly run ones is fatter. Part of the explanation is that medium and large firms tend to be better-organised than small ones, and not only because well-run ones are likelier to grow. 4Brazil offers incentives aplenty to stay bitty, such as preferential tax treatment for firms with a turnover of no more than reais As they expand, many firms split rather than face increased scrutiny from the taxman. According to the World Bank, a midsized Brazilian firm spends hours filing taxes each year. In Mexico, it is hours. 5Ownership patterns play a part too. 6Many Brazilian concerns are controlled by an individual shareholder, or one or two families. 7Two-thirds of those with sales of more than $1 billion a year are family-owned, notes Heinz-Peter Elstrodt of McKinsey, a consulting firm. That is less than in Mexico or South Korea but more than in America or Europe. Mr Van Reenens research shows that where family owners plump for outside chief executives, their firms do no worse than similarly sized ones with more diverse shareholders. But all too often they pick kin over professional managers and performance suffers. 8This is particularly true in low-trust societies like Brazil, where bosses hire relatives instead of better-qualified strangers to avoid being robbed or sued for falling foul of overly worker-friendly labour laws. 9Decades of economic turmoil 10which ended when hyperinflation was vanquished in 1994 meant that companies were managed from crisis to crisis. 11This forced Brazilian firms to be nimble. But it also encouraged short-termism, which management consultants and academics finger as Brazilian managers number-one sin. Faced with a record drought in 2014, 12and a subsequent spike in energy prices in a hydropower-dependent country, Usiminas, a steelmaker, stopped smelting and started selling power it had bought on cheap long-term contracts. Energy sales made up most of its operating profits that year. 13Such short-term stunts are hardly the path to long-term greatness. Worse, crisis management all too often consists of going cap in hand to the government. 14Brazilian bosses continue to waste hours in meetings with politicians that could be better spent improving their businesses. 15In January 2014, as vehicle sales flagged, 16the automotive industrys reflex reaction was to descend on the capital, Braslia, and demand an extension of its costly tax breaks. Thanks to lifelines cast by the state, feeble firms stay afloat rather than sink and make room for more agile competitors. Shielded from competition by tariffs, subsidies and local-content rules, they have little reason to innovate. A locally invented gizmo which lets cars run on both petrol and biodiesel is nifty. But, asks Marcos Lisboa of Insper, a business school, does that really justify six decades of public support for the motor industry? The dead hand of government Indeed, a glance at the Belgian end of Brazils corporate landscape suggests that successful firms cluster in sectors the state has not tried desperately to help, such as retail or finance. 17Bradesco, a big lender, is internationally praised as a pioneer of automated banking. Each month Arezzo creates new models of womens shoes, and picks 170-odd to sell in its shops. Brazils other world-beaters are in industries like agriculture and aerospace, which are free to compete at home and abroad, and in which the government sticks to its proper role. In 1990 farms were allowed to consolidate and to buy foreign machines, pesticides and fertiliser. Efforts by Brazils trade negotiators opened up export markets. JBS, a meat giant, can slaughter head of cattle a day, selling more beef than any rival worldwide. Thanks in part to Embrapa, the national agriculture-research agency, Brazilian farms have been raising productivity by about a year for two decades. Similarly, a supply of skilled engineers and know-how from the governments Technological Institute of Aeronautics has helped turn Embraer, privatised in 1994, into one of the worlds most successful aircraft-makers. The success of businesses such as these offers a lesson for the state. The best way to make Brazils underperforming firms more competitive would be to make them compete more. 18Coddling by the state can be more a curse than a blessing. Ronald Reagans dictum that the nine most terrifying words in the English language are, Im from the government and Im here to help, translates well into Flemish, Hindi and Brazilian Portuguese. By Schumpeter. In: The Economist. Feb 28th, 2015. De acordo com o texto,

(ITA - 2016 - 1 FASE) No sistema de sinalizao de trnsito urbano chamado de onda verde, h semforos com dispositivos eletrnicos que indicam a velocidade a ser mantida pelo motorista para alcanar o prximo sinal ainda aberto. Considere que de incio o painel indique uma velocidade de 45 km/h. Alguns segundos depois ela passa para 50 km/h e, finalmente, para 60 km/h. Sabendo que a indicao de 50 km/h no painel demora 8,0 s antes de mudar para 60 km/h, ento a distncia entre os semforos de:

QUESTO ANULADA!! (ITA - 2016 - 1 FASE) QUESTO ANULADA!! Escolhendo-se, aleatoriamente, trs nmeros inteiros distintos no intervalo [1, 20], a probabilidade de que eles estejam, em alguma ordem, em progresso geomtrica igual a *Devido impreciso no enunciado a questo foi considerada correta para todos os candidatos.

(ITA - 2016 - 1 FASE) Marque a opo em que a(s) vrgula(s) sublinhada(s) no demarca(m) um termo ou expresso explicativa.

QUESTO ANULADA!! (ITA - 2016 - 1 Fase) A constante ebulioscpica da gua 0,51 Kkgmol1. Dissolve-se em gua 15,7 g de um composto solvel, no voltil e no eletrlito, cuja massa molar de 157 gmol1 . Assinale a alternativa que corresponde variao na temperatura de ebulio desta soluo aquosa, em kelvin. QUESTO ANULADA!! *Devido impreciso no enunciado a questo foi considerada correta para todos os candidatos.

(ITA - 2016 - 1 FASE) Se e , ento sen3x igual a

(ITA - 2016 - 1 FASE) Os termos sublinhados nas oraes abaixo podem ser substitudos, respectivamente, sem que haja prejuzo do sentido, por: I. Ownership patterns play a part too (linha 23) as well. II. Decades of economic turmoil... (linha 30) growth. III. Brazilian bosses continue to waste hours in meetings with politicians(linhas 36/37) findings. IV. In January 2014, as vehicle sales flagged (linha 37/38) dropped. Esto corretas:

(ITA - 2016 - 1 Fase) A respeito de reaes qumicas descritas pela equao de Arrhenius, so feitas as seguintes proposies: I. Para reaes bimoleculares, o fator pr-exponencial na equao de Arrhenius proporcional frequncia de colises, efetivas ou no, entre as molculas dos reagentes. II. O fator exponencial na equao de Arrhenius proporcional ao nmero de molculas cuja energia cintica relativa maior ou igual energia de ativao da reao. III. Multiplicando-se o negativo da constante dos gases (R) pelo coeficiente angular da reta ln k versus 1/T obtm-se o valor da energia de ativao da reao. IV. O fator pr-exponencial da equao de Arrhenius determinado pela interseco da reta ln k versus 1/T com o eixo das abscissas. Das proposies acima, esta(ao) ERRADA(S)