Um poliedro convexo de 32 arestas tem apenas 8 faces triangulares e x faces quadrangulares. Dessa forma, o valor de x é

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Diplomat

There are three main aspects to this profession: a diplomat has to keep his country informed about pertinent international events, promote a favorable image of his country and protect his country’s interests.

Whoever is interested in a diplomatic career has to be extremely familiar with political, economical, scientific, cultural and administrative issues. To be a diplomat, it is essential to have a good knowledge of English, not only the conversational language, but also the technical terms in international law and diplomacy itself.

To follow this career, besides being fluently bilingual, one needs a standard college education and has to take and do well in the Rio Branco Institute examination in Brasilia.

English is so important in this career that in the first part of this selection exam, the applicant has to demonstrate his or her proficiency in the English language. Then, during the course, foreign language classes become a priority, giving future diplomats the necessary expertise to deal with the areas of official correspondences, diplomatic negotiation and international media.

Adapted from Inglês no mundo do trabalho.

In...“giving future diplomats the necessary expertise to deal with”, the underlined word in the text is closest in meaning to, EXCEPT:

Uma amostra de um gás ideal realiza uma sequência de transformações termodinâmicas (AB, BC, CD e DA) conforme o gráfico pressão (P) em função do volume (V) a seguir.

Assinale a alternativa que indica corretamente as transformações termodinâmicas pelas quais a energia interna da amostra aumentou.

Os pontos O e P são os centros de duas circunferências que possuem raios medindo, respectivamente, 8 cm e 3 cm, conforme a figura. Se !$ OP=5\sqrt {37}cm !$ e se !$ \overline{AB} !$ é tangente a essas circunferências, em A e B, então AB = cm.

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An e-mail to Mary

Hi, Mary!

How are you? I miss you so much!

I arrived in Rome last week and I’m having a lot of fun. This morning my parents and I woke up at 8:00 and had a great breakfast at the hotel. Afterwards, I walked a little and saw many tourists (many from Russia and China) and even some famous people!

Now we are going to Venice.

How are things in Las Vegas? Come meet us!

See you soon!

Paul.

Where did Paul go on his vacation?

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The words “bite” and “net”, in the comic strip, are, respectively:

Sejam as matrizes !$ A^t= \begin{bmatrix}2 & 4 \\ x+1 & 3 \end{bmatrix} !$ e !$ \color{red}{B^t}=\begin{bmatrix} 1 & 2y-3 \\ -3 & 1 \end{bmatrix} !$.

Se !$ A+B=\begin{bmatrix} 3 & 2 \\ 5 & 4 \end{bmatrix} !$, então !$ x+y !$ é

Uma mola ideal está presa a parede e apoiada sobre um plano inclinado. Quando um bloco de massa igual a 5 kg é preso a extremidade dessa mola, esta sofre uma distensão de 20 cm, conforme o desenho. Considerando que o módulo da aceleração da gravidade no local vale 10 m/s² e desprezando qualquer tipo de atrito, qual o valor da constante elástica da mola em N/m?

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Mandela

Nelson Mandela has achieved many things, but his greatest influence may be for something he didn’t do: run for a second term as South Africa’s leader. As the first President of a post-apartheid South Africa, he was, like George Washington, aware that everything he did would be a model for those who would follow. He once said, “I don’t want to be an octogenarian President.”

What he really meant was that no man - not even one unfairly imprisoned for 27 years - should be above the law or the people. Mandela will remain perhaps the only figure on the world stage who has been an unambiguous moral giant. He could be considered a hero precisely because he always admitted his errors and then tried to rise above them. And never stop learning. He had to catch up on almost three decades of social change, and one of the things he had to learn about was AIDS. At first, this man didn’t have the most enlightened view. But within a year-long before other, younger South African leaders - he understood that AIDS was an enormous tragedy for his country and his continent, and he saw it as another moral challenge in a life of facing up to them. That’s a moral leadership.

Adapted from Grad Two.

In... “he had to catch up on almost three decades of social change...”, we can infer that Mandela had to .

Em um prisma hexagonal regular de !$ 4\sqrt3 cm !$ de altura, a aresta da base mede 4 cm. As bases desse sólido foram pintadas de branco e 4 faces laterais pintadas de preto. Se SB e SP são as medidas das áreas pintadas de branco e preto, respectivamente, então !$ S_p-S_B= !$ !$ cm^2 !$.