Questões - ITA 2018 | Gabarito e resoluções

(ITA - 2018 - 2 FASE) A aresta lateral de uma pirmide reta de base quadrada mede 13 cme a rea do crculo inscrito na base mede .Dois planos, e paralelos base, decompem a pirmide em trs slidos de mesmo volume. Determine a altura de cada um desses slidos.

(ITA - 2018 - 2 FASE) Considere a reao genrica equimolar: X + YZsendo que: I. as concentraes iniciais de Xe de Zso iguais. II. a reao direta apresenta lei de velocidade de 2 ordem. III. a energia de ativao da reao inversa 2,49 kJ mol-1a 300 K Considere dados o fator pr-exponencial da reao inversa, A-1= 2,72 X 105L mol-1s-1e a constante de equilbrio da reao direta, K1= 4,0 Com base nessas informaes, determine o valor numrico da velocidade da reao direta, quando a concentrao de Zfor 0,5 molL-1o que corresponde a 25% de rendimento da reao.

(ITA - 2018 - 1 FASE) As razes do polinmio 1 + z + z2+ z3+ z4+ z5+ z6+ z7, quando representadas no plano complexo, formam os vrtices de um polgono convexo cuja rea

(ITA - 2018 - 2 FASE) Na figura, presa a um fio de comprimento de 1,0 m,uma massa de 1,0 kggira com uma certa velocidade angular num plano vertical sob a ao da gravidade, com eixo de rotao a h = 6,0 mdo piso. Determine a velocidade angular mnima dessa massa para a ruptura do fio que suporta no mximo a trao de 46 N,bem como a distncia ao ponto P do ponto em que, nesse caso, a massa tocar o solo.

(ITA - 2018 - 1 FASE) Se log2 = a e log5 = b, ento

(ITA - 2018 - 2 FASE) Considere os experimentos abaixo, executados consecutivamente: I. Uma pea polida de cobre metlico completamente mergulhada em um bquer que contm uma soluo aquosa concentrada de sulfato de zinco e tambm aparas polidas de zinco metlico no fundo do bquer. A pea permanece completamente mergulhada na soluo e em contato com as aparas de zinco, enquanto a soluo mantida em ebulio durante 50minutos. Aps transcorrido esse tempo, a pea de cobre adquire uma colorao prateada. II. A seguir, a pea de cobre com colorao prateada removida do bquer, enxaguada com gua destilada e colocada em um forno a 300Cpor dez minutos, adquirindo uma colorao dourada. Com base nesses experimentos, a) explique o fenmeno qumico que provoca a mudana de colorao da pea de cobre no item I. b) explique o fenmeno qumico que provoca a mudana de colorao da pea de cobre no item II.

(ITA - 2018 - 2 FASE) Um tomo de Hidrognio emite um fton de energia 2,55 eV na transio entre dois estados estacionrios. A razo entre as velocidades dos eltrons nesses dois estados 1/2. Determine a energia potencial do eltron no estado final desse tomo, sabendo que energia total no estado n e o raio , em que o raio de Bohr e n = 1, 2, 3, ...

(ITA - 2018 - 2 FASE) Seja p(x) um polinmio no nulo. Se e so divisores de p(x), determine o menor grau possvel de p(x).

(ITA - 2018 - 2 FASE) No plano cartesiano so dados o ponto e o tringulo de vrtices , e . Determine um ponto sobre o eixo dos de modo que a reta que passa pore divida o tringulo em duas regies de mesma rea.

(ITA - 2018 - 2 FASE) A figura mostra um fio por onde passa uma corrente l conectado a uma espira circular de raio a. A semicircunferncia superior tem resistncia igual a 2 R e a inferior, igual a R. Encontre a expresso para o campo magntico no centro da espira em termos da corrente l.

(ITA - 2018 - 2 FASE) O tetraetilchumbo era adicionado gasolina na maioria dos pases at cerca de 1980. a) Escreva a equao qumica balanceada que representa a reao de combusto do composto tetraetilchumbo, considerando que o chumbo elementar o nico produto formado que contm chumbo. b) O 238Udecai a 206Pbcom tempo de meia-vida de 4,5 x 109anos. Uma amostra de sedimento colhida em 1970 continha 0,119 mgde 238Ue 2,163 mgde 206Pb.Assumindo que todo o 206Pb formado somente pelo decaimento do 238Ue que o 206Pb no sofre decaimento, estime a idade do sedimento. c) Justifique o resultado obtido no item b) sabendo que a idade do Universo de 13,7bilhes de anos. Dados: ln = 0,693; ln22 = 3,091

(ITA - 2018 - 1 FASE) O lugar geomtrico das solues da equao x2+ bx + 1 = 0, quando 2, b , representado no plano complexo por

(ITA - 2018 - 1 FASE) Em um tringulo de vrtices A, B e C so dados = /2, = /3 e o lado BC = 1 cm. Se o lado o dimetro de uma circunferncia, ento a rea da parte do tringulo ABC externa circunferncia, em cm2,

(ITA - 2018 - 1 FASE) WE RECORDED VCs CONVERSATIONS AND ANALYZED HOW DIFFERENTLY THEY TALK ABOUT FEMALE ENTREPRENEURS When venture capitalists (VCs) evaluate investment proposals, the language they use to describe the entrepreneurs who write them plays an important but often hidden role in shaping who is awarded funding and why. [] We were given access to government venture capital decision making meetings in Sweden and were able to observe the types of language that VCs used over a two-year period. One major thing stuck out: The language used to describe male and female entrepreneurs was radically different. And these differences have very real consequences for those seeking funding and for society in general. [] Worldwide, government venture capital is important for bridging significant financial gaps and supporting innovation and growth, as VCs can take risks where banks are not allowed to. When uncertainty is high regarding assessment of product and market potential, for example, the assessment of the entrepreneurs potential becomes highly central in government VCs decision making. In Sweden, about one-third of businesses are owned and run by women, 1although they are not granted a corresponding proportion of government funding. In fact, women-owned businesses receive much less only 13%18%, the rest going to male-owned companies. This brings us back to our research. From 2009 to 2010 we were invited to silently observe governmental VC decision-making meetings and, more important, the conversations they had about entrepreneurs applying for funding. [] We observed closed-room, face-to-face discussions leading final funding decisions for 125 venture applications. Of these, 99 (79%) were from male entrepreneurs and 26 (21%) were from female entrepreneurs. The group of government venture capitalists observed included seven individuals: two women and five men. [] 2Aside from a few exceptions, the financiers rhetorically produce stereotypical images of women as having qualities opposite to those considered important to being an entrepreneur, with VCs questioning their credibility, trustworthiness, experience, and knowledge. 3Conversely, when assessing male entrepreneurs, financiers leaned on stereotypical beliefs about men that reinforced their entrepreneurial potential. Male entrepreneurs were commonly described as being assertive, innovative, competent, experienced, knowledgeable, and having established networks. We developed male and female entrepreneur personas based on our findings []. These personas highlight a few key differences in how the entrepreneurs were perceived depending on their gender. Men were characterized as having entrepreneurial potential, while the entrepreneurial potential for women was diminished. Many of the young men and women were described as being young, though youth for men was viewed as promising, while young women were considered inexperienced. Men were praised for being viewed as aggressive or arrogant, while womens experience and excitement were tempered by discussions of their emotional shortcomings. Similarly, cautiousness was viewed very differently depending on the gender of the entrepreneur. Unsurprisingly, these stereotypes seem to have played a role in who got funding and who didnt. Women entrepreneurs were only awarded, on average, 25% of the applied-for amount, 4whereas men received, on average, 52% of what they asked for. Women were also denied financing to a greater extent than men, with close to 53% of women having their applications dismissed, compared with 38% of men. [] Such stereotyping will inevitably influence the distribution of financing, but could also have other major consequences. 5Because the purpose of government venture capital is to use tax money to stimulate growth and value creation for society as a whole, gender bias presents the risk that the money isnt being invested in businesses that have the highest potential. This isnt only damaging for women entrepreneurs; its potentially damaging for society as a whole. Fonte: Adaptado de Harvard Business Review https://hbr.org/2017/05/we-recorded-vcs-conversations-and-analyzedhow-differently-they-talk-about-female-entrepreneurs. Acesso em: 17 mai. 2017. A expresso sublinhada na primeira coluna pode ser substituda pela expresso que segue em todas as opes, EXCETO em

(ITA - 2018 - 1 Fase) O composto 3,3-dimetil-1-penteno reage com gua em meio cido e na ausncia de perxidos, formando um composto X que, a seguir, oxidado para formar um composto Y. Os compostos X e Y formados preferencialmente so, respectivamente,