Muitos processos fisiológicos e bioquímicos, tais como batimentos cardíacos e taxa de respiração, apresentam escalas construídas a partir da relação entre superfície e massa (ou volume) do animal. Uma dessas escalas, por exemplo, considera que “o cubo da área S da superfície de um mamífero é proporcional ao quadrado de sua massa M”.

HUGHES-HALLETT, D. et al. Cálculo e aplicações. São Paulo: Edgard Blücher, 1999 (adaptado).

Isso é equivalente a dizer que, para uma constante k > 0, a área S pode ser escrita em função de M por meio da expressão:

(FGV-SP) The road to hell

(1) Bringing crops from one of the futuristic new farms in Brazil’s central and northern plains to foreign markets means taking a journey back in time. Loaded onto lorries, most are driven almost 2,000km south on narrow, potholed roads to the ports of Santos and Paranaguá. In the 19th and early 20th centuries they were used to bring in immigrants and ship out the coffee grown in the fertile states of São Paulo and Paraná, but now they are overwhelmed. Thanks to a record harvest this year, Brazil became the world’s largest soya producer, overtaking the United States. The queue of lorries waiting to enter Santos sometimes stretched to 40km.

(2) No part of that journey makes sense. Brazil has too few crop silos, so lorries are used for storage as well as transport, causing a crush at ports after harvest. Produce from so far north should probably not be travelling to southern ports at all. Freight by road costs twice as much as by rail and four times as much as by water. Brazilian farmers pay 25% or more of the value of their soya to bring it to port; their competitors in Iowa just 9%. The bottleneck at ports pushes costs higher still. It also puts off customers. In March Sunrise Group, China’s biggest soya trader, cancelled an order for 2m tonnes of Brazilian soya after repeated delays.

(3) All of Brazil’s infrastructure is decrepit. The World Economic Forum ranks it at 114th out of 148 countries. After a spate of railway-building at the turn of the 20th century, and road- and dam-building 50 years later, little was added or even maintained. In the 1980s infrastructure was a casualty of slowing growth and spiralling inflation. Unable to find jobs, engineers emigrated or retrained. Government stopped planning for the long term. According to Contas Abertas, a public-spending watchdog, only a fifth of federal money budgeted for urban transport in the past decade was actually spent. Just 1.5% of Brazil’s GDP goes on infrastructure investment from all sources, both public and private. The long-run global average is 3.8%. The McKinsey Global Institute estimates the total value of Brazil’s infrastructure at 16% of GDP. Other big economies average 71%. To catch up, Brazil would have to triple its annual infrastructure spending for the next 20 years.

(4) Moreover, it may be getting poor value from what little it does invest because so much goes on the wrong things. A cumbersome environmental-licensing process pushes up costs and causes delays. Expensive studies are required before construction on big projects can start and then again at various stages along the way and at the end. Farmers and manufacturers spend heavily on lorries because road transport is their only option. But that is working around the problem, not solving it.

(5) In the 1990s Mr Cardoso’s government privatized state-owned oil, energy and telecoms firms. It allowed private operators to lease terminals in public ports and to build their own new ports. Imports were booming as the economy opened up, so container terminals were a priority. The one at the public port in Bahia’s capital, Salvador, is an example of the transformation wrought by private money and management. Its customers used to rate it Brazil’s worst port, with a draft too shallow for big ships and a quay so short that even smaller vessels had to unload a bit at a time. But in the past decade its operator, Wilson & Sons, spent 260m reais on replacing equipment, lengthening the quay and deepening the draft. Capacity has doubled. Land access will improve, too, once an almost finished expressway opens. Paranaguá is spending 400m reais from its own revenues on replacing outdated equipment, but without private money it cannot expand enough to end the queues to dock. It has drawn up detailed plans to build a new terminal and two new quays, and identified 20 dockside areas that could be leased to new operators, which would bring in 1.6 billion reais of private investment. All that is missing is the federal government’s permission. It hopes to get it next year, but there is no guarantee.

(6) Firms that want to build their own infrastructure, such as mining companies, which need dedicated railways and ports, can generally build at will in Brazil, though they still face the hassle of environmental licensing. If the government wants to hand a project to the private sector it will hold an auction, granting the concession to the highest bidder, or sometimes the applicant who promises the lowest user charges. But since Lula came to power in 2003 there have been few infrastructure auctions of any kind. In recent years, under heavy lobbying from public ports, the ports regulator stopped granting operating licences to private ports except those intended mainly for the owners’ own cargo. As a result, during a decade in which Brazil became a commodity-exporting powerhouse, its bulk-cargo terminals hardly expanded at all.

(7) At first Lula’s government planned to upgrade Brazil’s infrastructure without private help. In 2007 the president announced a collection of long-mooted public construction projects, the Growth Acceleration Programme (PAC). Many were intended to give farming and mining regions access to alternative ports. But the results have been disappointing. Two-thirds of the biggest projects are late and over budget. The trans-north-eastern railway is only half-built and its cost has doubled. The route of the east-west integration railway, which would cross Bahia, has still not been settled. The northern stretch of the BR-163, a trunk road built in the 1970s, was waiting so long to be paved that locals started calling it the “endless road”. Most of it is still waiting.

(8) What has got things moving is the prospect of disgrace during the forthcoming big sporting events. Brazil’s terrible airports will be the first thing most foreign football fans see when they arrive for next year’s World Cup. Infraero, the state-owned company that runs them, was meant to be getting them ready for the extra traffic, but it is a byword for incompetence. Between 2007 and 2010 it managed to spend just 800m of the 3 billion reais it was supposed to invest. In desperation, the government last year leased three of the biggest airports to private operators.

(9) That seemed to break a bigger logjam. First more airport auctions were mooted; then, some months later, Ms Rousseff announced that 7,500km of toll roads and 10,000km of railways were to be auctioned too. Earlier this year she picked the biggest fight of her presidency, pushing a ports bill through Congress against lobbying from powerful vested interests. The new law enables private ports once again to handle third-party cargo and allows them to hire their own staff, rather than having to use casual labour from the dockworkers’ unions that have a monopoly in public ports. Ms Rousseff also promised to auction some entirely new projects and to re-tender around 150 contracts in public terminals whose concessions had expired.

(10) Would-be investors in port projects are hanging back because of the high chances of cost overruns and long delays. Two newly built private terminals at Santos that together cost more than 4 billion reais illustrate the risks.  Both took years to get off the ground and years more to build. Both were finished earlier this year but remained idle for months. Brasil Terminal Portuário, a private terminal within the public port, is still waiting for the government to dredge its access channel. At Embraport, which is outside the public-port area, union members from Santos blocked road access and boarded any ships that tried to dock. Rather than enforcing the law that allows such terminals to use their own workers, the government summoned the management to Brasília for some arm-twisting. In August Embraport agreed to take the union members “on a trial basis”.

(11) Given such regulatory and execution risks, there are unlikely to be many takers for either rail or port projects as currently conceived, says Bruno Savaris, an infrastructure analyst at Credit Suisse. He predicts that at most a third of the planned investments will be auctioned in the next three years: airports, a few simple port projects and the best toll roads. That is far short of what Brazil needs. The good news, says Mr Savaris, is that the government is at last beginning to understand that it must either reduce the risks for private investors or raise their returns. Private know-how and money will be vital to get Brazil moving again.

(www.economist.com/news/special-report. Adapted)

In the sentence fragment from the last paragraph – it must either reduce the risks for private investors or raise their returns – the use of either ... or indicates an idea of

(UCS) Quando um jogador de futebol é muito veloz, uma forma divertida de se referir a essa qualidade é dizer que ele é capaz de cobrar escanteio para a área adversária e ele mesmo correr e conseguir chutar a bola antes de ela tocar o chão. Suponha um jogador ficcional que seja capaz de fazer isso. Se ele cobrar o escanteio para dentro da área fornecendo à bola uma velocidade inicial de 20 m/s, fazendo um ângulo de 60° com a horizontal, qual distância o jogador precisa correr, em linha reta, saindo praticamente de forma simultânea à cobrança de escanteio, para chutar no gol sem deixar a bola tocar no chão? Para fins de simplificação, considere que a altura do chute ao gol seja desprezível, que sen 60°= 0,8; cos 60°= 0,5 e que a aceleração da gravidade seja 10m/s²

Texto base:    Disponível em: <http://www.estudopratico.com.br/o-que-foi-o-tratado-de-tordesilhas/>. Acesso em: 06 nov. 2015.  

Enunciado:

O mapa ilustra a linha imaginária traçada nas terras do chamado “Novo Mundo” que deu forma a um acordo assinado entre Portugal e Espanha denominado Tratado de Tordesilhas. O principal motivo que levou à assinatura desse tratado foi

(UFIJ)  O selênio quando combinado com enxofre forma o sulfeto de selênio, substância que apresenta propriedades antifúngicas e está presente na composição de xampus anticaspa. Qual o tipo de ligação química existente entre os átomos de enxofre e selênio?