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No ano de 2024, na sua aula de Divertimentos Matemáticos, o Professor Numerisvaldo Perplexo, levando em consideração que todos os seus alunos nasceram depois dos anos 2000, propôs o seguinte problema:
Seja 
o conjunto de todos os pontos 
que satisfazem
= AAAA,
em que cada aluno que estava na aula deveria substituir AAAA pelo ano do seu
nascimento. O que se pode afirmar a respeito dos pontos
Após analisar o problema, três dos alunos expuseram suas conclusões:
I- Zé Gauss disse que
é sempre diferente do conjunto vazio.
II- Chico Euler disse que os pontos de , quando este conjunto é diferente do vazio, estão sempre sobre uma circunferência.
II- Tião Argand disse que para alguns valores de AAAA o conjunto é vazio.
É CORRETO o que se afirma apenas em:
O enunciado a seguir deve ser usado para a questão.
Na figura a seguir, ACDB é um retângulo de lados medindo 
= 
= 1cm e 
= 
= 4cm. O ponto E pertence ao segmento AC e é tal que 
= 1cm.
Considere todos os quadrados contidos no interior do retângulo ACDB e com as seguintes características: E é um de seus vértices; um de seus lados está contido no segmento BE; e outro de seus lados está contido na reta r que passa por E e é perpendicular à reta 
.
Chamemos de F o ponto de interseção de r com a reta 
. Introduzimos um sistema cartesiano de coordenadas no plano de modo que A = (0,0), a semirreta 
coincide com o semieixo positivo dos y e a semirreta 
coincide com o semieixo positivo dos x. Partindo destes pressupostos, assinale a alternativa cujas desigualdades lineares simultâneas descrevem o conjunto de todos os pontos na fronteira e no interior do trapézio ECDF.
Dado um número racional positivo x, é sempre possível escrevê-lo da única forma x
seguinte:
,
Em que α ∈ ℤ, α ≥ 0, β ∈ ℤ , β ≥ 1, y ∈ ℤ, y ≥ 1, m.d.c.(2α β, y) = 1 e m.d.c.(2, β) = 1. Denotando por ℚ>0 e ℤ≥0 o conjunto de todos os racionais positivos e o conjunto de todos os inteiros não negativos, respectivamente, e supondo x ∈ ℚ>0 escrito na forma anteriormente descrita, a esse x associamos o número α ∈ ℤ≥0.
A respeito dessa regra de correspondência, é CORRETO afirmar que:
Read the text III to answer the question.
TEXT III
A new report into world education shows Finland has the best system. The global study is called "The Learning Curve" and is from the British magazine "The Economist". It aims to help governments provide a better education to students. The 52-page report looked at the education system in 50 countries. Researchers analysed millions of statistics on exam grades, literacy rates, attendance, and university graduation rates. Asia did well in the report, with South Korea, Hong Kong, Japan and Singapore finishing second, third, fourth and fifth. The United States came 17th in the study, while Mexico, Brazil and Indonesia filled the bottom three positions in the top 50.
The Learning Curve reported on five things that education leaders should remember. The first is that spending lots of money on schools and teachers does not always mean students will learn. Second is that "good teachers are essential to high-quality education". The report said teachers should be "treated as the valuable professionals they are, not as technicians in a huge, educational machine". Numbers three and four are that a country's culture must have a strong focus on the importance of education, and parents have a key part to play. Finally, countries need to "educate for the future, not just the present." The report said: "Many of today's job titles…simply did not exist 20 years ago."
Sources:
http://www.timeshighereducation.co.uk/story.asp?sectioncode=26&storycode=421944&c=1
http://thelearningcurve.pearson.com/content/download/bankname/components/filename/FINAL%20LearningCurve_Final.pdf
3
Read the text III to answer the question.
TEXT III
A new report into world education shows Finland has the best system. The global study is called "The Learning Curve" and is from the British magazine "The Economist". It aims to help governments provide a better education to students. The 52-page report looked at the education system in 50 countries. Researchers analysed millions of statistics on exam grades, literacy rates, attendance, and university graduation rates. Asia did well in the report, with South Korea, Hong Kong, Japan and Singapore finishing second, third, fourth and fifth. The United States came 17th in the study, while Mexico, Brazil and Indonesia filled the bottom three positions in the top 50.
The Learning Curve reported on five things that education leaders should remember. The first is that spending lots of money on schools and teachers does not always mean students will learn. Second is that "good teachers are essential to high-quality education". The report said teachers should be "treated as the valuable professionals they are, not as technicians in a huge, educational machine". Numbers three and four are that a country's culture must have a strong focus on the importance of education, and parents have a key part to play. Finally, countries need to "educate for the future, not just the present." The report said: "Many of today's job titles…simply did not exist 20 years ago."
Sources:
http://www.timeshighereducation.co.uk/story.asp?sectioncode=26&storycode=421944&c=1
http://thelearningcurve.pearson.com/content/download/bankname/components/filename/FINAL%20LearningCurve_Final.pdf
3
Read the text III to answer the question.
TEXT III
A new report into world education shows Finland has the best system. The global study is called "The Learning Curve" and is from the British magazine "The Economist". It aims to help governments provide a better education to students. The 52-page report looked at the education system in 50 countries. Researchers analysed millions of statistics on exam grades, literacy rates, attendance, and university graduation rates. Asia did well in the report, with South Korea, Hong Kong, Japan and Singapore finishing second, third, fourth and fifth. The United States came 17th in the study, while Mexico, Brazil and Indonesia filled the bottom three positions in the top 50.
The Learning Curve reported on five things that education leaders should remember. The first is that spending lots of money on schools and teachers does not always mean students will learn. Second is that "good teachers are essential to high-quality education". The report said teachers should be "treated as the valuable professionals they are, not as technicians in a huge, educational machine". Numbers three and four are that a country's culture must have a strong focus on the importance of education, and parents have a key part to play. Finally, countries need to "educate for the future, not just the present." The report said: "Many of today's job titles…simply did not exist 20 years ago."
Sources:
http://www.timeshighereducation.co.uk/story.asp?sectioncode=26&storycode=421944&c=1
http://thelearningcurve.pearson.com/content/download/bankname/components/filename/FINAL%20LearningCurve_Final.pdf
3
Read the text II to answer the question.
TEXT II
JOHN LAURENS:
The ten-dollar Founding Father without a father
Got a lot farther by workin' a lot harder
By bein' a lot smarter
By bein' a self-starter
By fourteen, they placed him in charge of a trading charter
THOMAS JEFFERSON:
And every day while slaves were being slaughtered and carted
Away across the waves, he struggled and kept his guard up
Inside, he was longing for something to be a part of
The brother was ready to beg, steal, borrow, or barter
[…]
AARON BURR:
Well, the word got around, they said, "This kid is insane, man!"
Took up a collection just to send him to the mainland
"Get your education, don't forget from whence you came, and
The world's gonna know your name! What's your name, man?"
Excerpt from the musical Hamilton, with lyrics by Lin-Manuel Miranda.
Read the text II to answer the question.
TEXT II
JOHN LAURENS:
The ten-dollar Founding Father without a father
Got a lot farther by workin' a lot harder
By bein' a lot smarter
By bein' a self-starter
By fourteen, they placed him in charge of a trading charter
THOMAS JEFFERSON:
And every day while slaves were being slaughtered and carted
Away across the waves, he struggled and kept his guard up
Inside, he was longing for something to be a part of
The brother was ready to beg, steal, borrow, or barter
[…]
AARON BURR:
Well, the word got around, they said, "This kid is insane, man!"
Took up a collection just to send him to the mainland
"Get your education, don't forget from whence you came, and
The world's gonna know your name! What's your name, man?"
Excerpt from the musical Hamilton, with lyrics by Lin-Manuel Miranda.
Read the text I to answer the question.
TEXT I
IS BURNOUT REAL?
Last week, the World Health Organization upgraded Burnout from a “state” of exhaustion to “a syndrome” resulting from “chronic workplace stress” in its International Disease Classification. That is such a broad definition that it could well apply to most people at some point in their working lives. When a disorder is reportedly so widespread, it makes me wonder whether we are at risk of medicalizing everyday distress. If almost everyone suffers from Burnout, then no one does, and the concept loses all credibility.
By Richard A. Friedman
I'm sure the author's generation also experienced workplace stress. However, his generation also experienced real economic stability and socioeconomic gains. There was a light at the end of the tunnel. Currently, we are working tirelessly towards what ends? There doesn't seem to be a light at the end of the tunnel. The Burnout is psychological and existential as much as it is physical.
Anna B. – New York, June 4, 2019.
(Adaptado de https://www.nytimes.com/2019/06/03/opinion/burnout-stress.html. Acessado em 16/09/2020.)
Read the text I to answer the question.
TEXT I
IS BURNOUT REAL?
Last week, the World Health Organization upgraded Burnout from a “state” of exhaustion to “a syndrome” resulting from “chronic workplace stress” in its International Disease Classification. That is such a broad definition that it could well apply to most people at some point in their working lives. When a disorder is reportedly so widespread, it makes me wonder whether we are at risk of medicalizing everyday distress. If almost everyone suffers from Burnout, then no one does, and the concept loses all credibility.
By Richard A. Friedman
I'm sure the author's generation also experienced workplace stress. However, his generation also experienced real economic stability and socioeconomic gains. There was a light at the end of the tunnel. Currently, we are working tirelessly towards what ends? There doesn't seem to be a light at the end of the tunnel. The Burnout is psychological and existential as much as it is physical.
Anna B. – New York, June 4, 2019.
(Adaptado de https://www.nytimes.com/2019/06/03/opinion/burnout-stress.html. Acessado em 16/09/2020.)
“A Colônia se diversificava. As formas de ocupação que haviam garantido a presença portuguesa entre os séculos XVI e XVII, ou seja, o latifúndio e a monocultura, passaram a conviver crescentemente com outras atividades econômicas.” (Del priore, Mary. Venâncio, Renato. Uma breve história do Brasil. São Paulo. Planeta. 2010. p. 135).
Avalie as proposições a seguir, considerando a realidade sócio-economica da América portuguesa.
I- A vida urbana trouxe para a cena vários atores, entre eles os ciganos. Só não há registro, neste espaço, de artesãos, devido à proibição da metrópole da colônia ter sua própria produção.
II- Um intricado mundo de comerciantes dominava as várias áreas da América portuguesa. Sua imensidão territorial gerou, contudo, o aparecimento de comerciantes volantes, gente acostumada a percorrer grandes distâncias levando seus produtos em uma ou outra direção. A maioria branca, nascida no Brasil.
III- Em Salvador, no início do século XIX, um dado digno de registro é que não há na capital baiana a presença de indigentes mendigando em suas ruas devido a ser um centro administrativo onde centralizava recursos.
É CORRETO o que se afirma apenas em:
“Além de suas renovadoras críticas à racionalidade moderna, ao autoritarismo e ao totalitarismo político (inclusive a vertente stalinista da época) os temas privilegiados (...) e que interessam mais propriamente a uma História Cultural voltam-se para a cultura de massas, para o papel da ciência e da tecnologia na sociedade moderna , para a família e a sexualidade. Aparece ainda um especial interesse pelos problemas relacionados à alienação, à perda de autonomia do sujeito na sociedade industrializada.” (Barros, José D'Assunção. O campo da história: especialidades e abordagens. Petrópolis. Vozes 2004. P. 71)
Estamos falando da tendência do Materialismo Histórico que propôs uma radical renovação do marxismo e que incorporou diálogos com a Psicanálise e com as teorias da Comunicação. Este grupo de intelectuais que muito contribuiu para um tratamento mais diversificado da cultura é a:
Conheça nossos planos