(FUVEST 2020 1ª FASE) A função E de Euler determina, para cada número natural n, a quantidade de números naturais menores do que n cujo máximo divisor comum com n é igual a 1. Por exemplo, E(6) = 2 pois os números menores do que 6 com tal propriedade

são 1 e 5. Qual o valor máximo de E(n), para n de 20 a 25?

Todas as atividades celulares dependem, de certa forma, da ação de proteínas, entre as quais, algumas são especiais e denominadas enzimas, cuja função é:

(PUC-RJ) TEXTO: Driverless automobiles - The car that parks itself

CARS that need no driver are just around the corner according to researchers who have been testing vehicles bristling with aerials and cameras on public roads in America. However, researchers do not make cars, so it will be up to firms that do to bring the technology to market. And carmakers are a conservative bunch. Still, slowly and steadily the autonomous car will arrive, with the help of an increasing number of automated driving aids. A Swedish carmaker has recently demonstrated one such feature: a car that really does park itself.

Some cars already have systems that assist with parking, but these are not completely autonomous. They can identify an empty parallel-parking space and steer into it while the driver uses the brake. The Swedish system, however, lets the driver get out and use a smartphone application to instruct the vehicle to park. The car then ¹trundles off, manoeuvres into a parking place and sends a message to the driver to inform him where it is. The driver can collect the car in person or use his phone to call it back to where he dropped it off. Autonomous parking could thus be provided at places like shopping centers and airports, which are controlled areas in which automated vehicles can be managed more easily than on open highways.  In the past, designs for doing this have relied on car parks being fitted with buried guide wires that a vehicle can follow to an empty bay. That, though, creates ²a chicken-and-egg problem: car-park operators will not invest in such infrastructure until there is a sufficient number of suitably equipped cars on the road. Drivers, conversely, will not want to buy self-parking cars if there is nowhere to use them.

This means, as a safety engineer working on the project observes, that for autonomous parking to work most of the technology will have to be in the car itself. The test car, which looks like a normal car, therefore uses on-board GPS mapping, cameras with image-recognition software, and radar sensors to find its own way around a car park and avoid pedestrians and non-autonomous vehicles. The same engineer says the system is five to ten years from commercial deployment. If it proves a success then infrastructure might adapt to it, for instance by packing cars into tighter spaces. If there is no one in them there is no need to make room for their doors to open.

Driverless cars would also need to communicate with one another, to enhance safety. That, too, is coming. ³A number of carmakers are developing wireless networking systems through which vehicles can exchange data, such as their speed, their steering angle and even their weight, to forewarn anti-collision systems and safety devices if an accident looks likely.

In the USA, for example, a carmaker recently tested a brake light that can provide an early warning to other motorists. If the brakes are applied hard in an emergency, a signal is broadcast. This illuminates a warning light in the dashboard of suitably equipped following vehicles, even if they are out of sight around a bend or not immediately behind the vehicle doing the braking.

The American company has been testing this system as part of a collaborative research project with several European carmakers. ⁴They have put a fleet of 150 experimental vehicles on the roads. When they tested a group of these, the Americans found the technology let drivers brake much earlier, helping avoid collisions. A driverless car would be able to react even faster.

Another member of the research group has been testing driverless cars on roads around Munich— including belting down some of Germany’s high-speed autobahns. ⁵The ordinary-looking models use a variety of self-contained guidance systems. These include cameras mounted on the upper windscreen, which can identify road markings, signs and various obstacles likely to be encountered on roads.

The German cars also use a radar, to gauge how far the vehicle is from other cars and potential obstacles, and a lidar, which works like a radar but at optical frequencies. The lidar employs laser beams to scan the road ahead and builds up from the reflections a three-dimensional image of what this looks like. The image is processed by a computer in the vehicle, which also collects and compares data from a high-accuracy GPS unit. A series of ultrasonic sonars similar to those used in vehicles to provide parking assistance are placed around the car to add to the virtual picture. And just to make sure, a set of accelerometers provide an inertial navigation system that double-checks the vehicle’s position on the road.

⁶Although these cars can be switched to an autonomous driving mode, they are still required to have someone in the driving seat who can take over in the event of any difficulty. Some cars can steer themselves, slow down, brake and accelerate, even changing lanes to overtake slower vehicles.

From the print edition: Science and Technology Jun 29^th 2013

The word “Although” (ref. 6) introduces 

Texto I

Eu amo a rua. Esse sentimento de natureza toda íntima não vos seria revelado por mim se não julgasse, e razões não tivesse para julgar, que este amor assim absoluto e assim exagerado é partilhado por todos vós.  Nós somos irmãos, nós nos sentimos parecidos e iguais; nas cidades, nas aldeias, nos povoados, não porque soframos, com a dor e os desprazeres, a lei e a polícia, mas porque nos une, nivela e agremia o amor da rua.  É este mesmo o sentimento imperturbável e indissolúvel, o único que, como a própria vida, resiste às idades e às épocas.

RIO, J. A rua. In: A alma encantadora das ruas. São Paulo: Companhia das Letras, 2008 (fragmento).

Texto II

A rua dava-lhe uma força de fisionomia, mais consciência dela. Como se sentia estar no seu reino, na região  em que era rainha e imperatriz. O olhar cobiçoso dos homens e o de inveja das mulheres acabavam o  sentimento de sua personalidade, exaltavam-no até. Dirigiu-se para a rua do Catete com o seu passo miúdo e  sólido. [...] No caminho trocou cumprimento com as raparigas pobres de uma casa de cômodos da vizinhaça.

[...] E debaixo dos olhares maravilhados das pobres raparigas, ela continuou o seu caminho, arrepanhando a saia, satisfeita que nem uma duquesa atravessando os seus domínios.

BARRETO, L. Um e outro. In: Clara dos anjos. Rio de Janeiro: Editora Mérito (fragmento).

A experiência urbana é um tema recorrente em crônicas, contos e romances do final do século XIX  e início do XX, muitos dos quais elegem a rua para explorar essa experiência. Nos fragmentos I e II, a rua é vista, respectivamente, como lugar que:

(UNINORTE) O corpo humano é composto por algumas centenas de trilhões de células, mas se desenvolve a partir de uma única célula, o zigoto, resultante da fusão de um espermatozoide e um óvulo. Os estágios iniciais no desenvolvimento de um embrião são caracterizados pela rápida divisão celular e pela diferenciação de células nos tecidos.

LODISH, H.; et al. Biologia Celular e Molecular. Porto Alegre: Artmed, 2014, p.18. Adaptado.

Sobre o desenvolvimento dos animais, inclusive os seres humanos, é correto afirmar: