Matemática
- Circunferências e Círculos
- Prova de 2022
- UFPR
- Dificuldade: Fácil
- Com imagem
- Código da questão: 87A3ECDC-0B

Instituição
460 questões de Universidade Federal do Paraná (UFPR), de 2010 a 2024. Cada uma tem página própria, com enunciado completo, alternativas e gabarito — e dá para responder na própria página.


O texto a seguir é referência para a questão.
Do que tanto ri esse tal de Scorsese?
Sergio Del Molino


O texto a seguir é referência para a questão.
Do que tanto ri esse tal de Scorsese?
Sergio Del Molino


O texto a seguir é referência para a questão.

(Peter Burke. Quando foi a globalização? In: O historiador como colunista: ensaios da Folha. RJ: Civilização Brasileira, 2009. Adaptado.)
O texto a seguir é referência para a questão.
How the American Dream has changed
The phrase ‘American Dream’ was officially coined just under 90 years ago in a book called The Epic of America by James Truslow Adams. He argued it was “that dream of a land in which life should be better and richer and fuller for everyone, with opportunity for each according to ability or achievement.”
Today: No single American Dream?
For some today the American Dream means a chance for fame and celebrity, while for others it means succeeding through the old adage of family values and hard work. Still others believe that the American Dream just represents a world closed to all but the elite with their wealth and contacts […]. Meanwhile, surveys have found that almost half of all millennials believe the American Dream is dead. In an ever-changing country, the idea of what the American Dream means to different people is changing too.
(Disponível em: https://www.msn.com/en-us/news/other/what-the-american-dream-looked-like-the-decade-you-were-born/ss-AABbxjy)
According to the text, it is correct to say that James Truslow Adams:O texto a seguir é referência para a questão.
More Than Just Children's Books
Krumulus, a small bookstore in Germany, has everything a kid could want: parties, readings, concerts, plays, puppet shows, workshops and book clubs.
“I knew it was going to be very difficult to open a bookstore, everyone tells you you're crazy, there will be no future,” says Anna Morlinghaus, Krumulus's founder. Still, she wanted to try. A month before her third son was born, she opened the store in Berlin's Kreuzberg district.
BERLIN — On a recent Saturday afternoon, a hush fell in the bright, airy “reading-aloud” room at Krumulus, a small children's bookstore in Berlin, as Sven Wallrodt, one of the store's employees, stood up to speak. Brandishing a newly published illustrated children's book about the life of Johannes Gutenberg, the inventor of the printing press, he looked at the crowd of eager, mo stly school-aged children and their parents. “Welcome to this book presentation”, he said. “If you fall asleep, snore quietly”. Everyone laughed, but no one fell asleep. An hour later, the children followed Wallrodt down to the bookstore's basement workshop, whe re he showed them how Gutenberg fit leaden block letters into a metal plate. Then the children printed their own bookmark using a technique similar to Gutenberg's, everyone was thrilled.
(Disponível em: https://www.nytimes.com/2019/05/20/books/berlin-germany-krumulus.html)
O texto a seguir é referência para a questão.
More Than Just Children's Books
Krumulus, a small bookstore in Germany, has everything a kid could want: parties, readings, concerts, plays, puppet shows, workshops and book clubs.
“I knew it was going to be very difficult to open a bookstore, everyone tells you you're crazy, there will be no future,” says Anna Morlinghaus, Krumulus's founder. Still, she wanted to try. A month before her third son was born, she opened the store in Berlin's Kreuzberg district.
BERLIN — On a recent Saturday afternoon, a hush fell in the bright, airy “reading-aloud” room at Krumulus, a small children's bookstore in Berlin, as Sven Wallrodt, one of the store's employees, stood up to speak. Brandishing a newly published illustrated children's book about the life of Johannes Gutenberg, the inventor of the printing press, he looked at the crowd of eager, mo stly school-aged children and their parents. “Welcome to this book presentation”, he said. “If you fall asleep, snore quietly”. Everyone laughed, but no one fell asleep. An hour later, the children followed Wallrodt down to the bookstore's basement workshop, whe re he showed them how Gutenberg fit leaden block letters into a metal plate. Then the children printed their own bookmark using a technique similar to Gutenberg's, everyone was thrilled.
(Disponível em: https://www.nytimes.com/2019/05/20/books/berlin-germany-krumulus.html)

O texto a seguir é referência para as questão.
O jogo do salário mínimo

Diverti-me imensamente com a história dos imbecis da web. Para quem não acompanhou, foi publicado em alguns jornais e também on-line que no curso de uma chamada lectio magistralis em Turim eu teria dito que a web está cheia de imbecis. É falso. A lectio era sobre um tema completamente diferente, mas isso mostra como as notícias circulam e se deformam entre os jornais e a web. A história dos imbecis surgiu numa conferência de imprensa durante a qual, respondendo a uma pergunta que não me lembro mais, fiz uma observação de puro bom senso. Admitindo que em 7 bilhões de habitantes exista uma taxa inevitável de imbecis, muitíssimos deles costumavam comunicar seus delírios aos íntimos ou aos amigos do bar - e assim suas opiniões permaneciam limitadas a um círculo restrito. Hoje uma parte consistente dessas pessoas tem a possibilidade de expressar as próprias opiniões nas redes sociais e, portanto, tais opiniões alcançam audiências altíssimas e se misturam com tantas outras ideias expressas por pessoas razoáveis.
[...]
É justo que a rede permita que mesmo quem não diz coisas sensatas se expresse, mas o excesso de besteira congestiona as linhas. E algumas reações descompensadas que vi na internet confirmam minha razoabilíssima tese. Alguém chegou a dizer que, para mim, as opiniões de um tolo e aquelas de um ganhador do prêmio Nobel têm a mesma evidência e não demorou para que se difundisse viralmente uma inútil discussão sobre o fato de eu ter ou não recebido um prêmio Nobel - sem que ninguém consultasse sequer a Wikipédia.
(Umberto Eco - Os imbecis e a imprensa responsável, 2017.)
Um objeto de massa m = 10 kg está suspenso por dois cabos que exercem
trações
de mesma intensidade T, de modo que
. As
trações exercidas pelos cabos estão dispostas conforme mostra a figura ao lado,
fazendo um ângulo de 30° com a direção horizontal. O objeto está em equilíbrio
estático e sujeito à atração gravitacional da Terra. Nesse local, a aceleração
gravitacional é g = 10 m/s2.
As medições no local são executadas por um observador inercial. Sabe-se que 1 V3 sen 30° = cos 60° = 1/2 , e que sen 60° = cos 30° = √3/2.
Levando em consideração os dados apresentados, assinale a alternativa que apresenta corretamente o valor do módulo da tração exercida por cada cabo.

Um objeto de massa m = 500 g recebe uma certa quantidade de calor Q e, com isso, sofre uma variação de temperatura ΔT. A relação entre ΔT e Q está representada no gráfico ao lado. (abaixo)

Assinale a alternativa que apresenta corretamente o valor do calor específico c desse objeto.
Ancient dreams of intelligent machines: 3,000 years of robots
The French philosopher René Descartes was reputedly fond of automata: they inspired his view that living things were biological machines that function like clockwork. Less known is a strange story that began to circulate after the philosopher’s death in 1650. This centred on Descartes’s daughter Francine, who died of scarlet fever at the age of five.
According to the tale, a distraught Descartes had a clockwork Francine made: a walking, talking simulacrum. When Queen Christina invited the philosopher to Sweden in 1649, he sailed with the automaton concealed in a casket. Suspicious sailors forced the trunk open; when the mechanical child sat up to greet them, the horrified crew threw it overboard.
The story is probably apocryphal. But it sums up the hopes and fears that have been associated with human-like machines for nearly three millennia. Those who build such devices do so in the hope that they will overcome natural limits – in Descartes’s case, death itself. But this very unnaturalness terrifies and repulses others. In our era of advanced robotics and artificial intelligence (AI), those polarized responses persist, with pundits and the public applauding or warning against each advance. Digging into the deep history of intelligent machines, both real and imagined, we see how these attitudes evolved: from fantasies of trusty mechanical helpers to fears that runaway advances in technology might lead to creatures that supersede humanity itself.
(Disponível em: <https://www.nature.com/articles/d41586-018-05773-y)
A partir das informações apresentadas no texto, considere as seguintes afirmativas:
1. Descartes viajou para a Suécia com um robô escondido.
2. Os marinheiros abriram à força um baú que continha o simulacro de uma criança.
3. A tripulação fez uma apresentação do robô para os passageiros do navio.
4. Chocados com o que viram, os marinheiros jogaram o humanoide ao mar.
Assinale a alternativa correta.
More than 100 South African gold miners
treated for smoke inhalation
JOHANNESBURG (Reuters) – Hundreds of South African gold mine workers were rescued and over 100 treated for smoke inhalation after an underground fire, the National Union of Mineworkers (NUM) said on Thursday.
Safety is a huge issue in South Africa’s dangerous deep-level mines and a focus for investors. A spate of deaths at SibanyeStillwater’s gold operations, including a seismic event that killed seven miners in early May, has highlighted the risks.
In the latest incident, more than 600 miners were initially trapped after a fire broke out at a mine east of Johannesburg operated by unlisted Gold One, NUM said.
This comes almost two weeks after five miners died in an underground fire at a South African copper mine operated by unlisted Palabora Mining Company in Limpopo.
Company officials could not immediately be reached for comment.
“As the NUM, we vehemently condemn this kind of incident as it is becoming a trend”, the union said in a statement.
(Disponível em:<https://www.reuters.com/article/us-safrica-mining-fire/more-than-100-south-african-gold-miners-treated-for-smoke-inhalation-idUSKBN1KG294 .)