Se ( 1 + i) !$ \left ( cos{ \large \pi \over 12} + isen { \large \pi \over 12} = x + iy \right ) !$ , em que i é a unidade imaginária e x e y são números reais, o valor de !$ \sqrt{3}. x + y !$ é

Considerando a função real definida por !$ { \begin{cases} 2 - | x -3|,se\,x > 2 \\-x^2 + 2 x+ 1,se x \le 2 \end{cases}} !$ , o valor de f(0)+f(4) é

Em uma cidade, a distância entre as localidades X e Y é de 16 Km e entre as localidades X e Z é de 28 Km. A distância no mapa entre X e Y é de 4 cm e entre X e Z é de 7 cm. A escala desse mapa é de:

Considere o polinômio p(x)=x⁶-2x⁵+2x^4-4x³+x^2-2x. Sobre as raízes de p(x)=0, podemos afirmar que

No circuito elétrico desenhado acima, todos os resitores ôhmicos são iguais e têm resistência R=1,0 Ω. Ele é alimentado por uma fonte ideal de tensão contínua de E=5,0 V. A diferença de potencial entre os pontos A e B é de:

Leia a perguntas e respostas a seguir e responda à questão.

Frequently Asked Questions – Instagram

What is Instagram?
It’s an application for your mobile phone that enables you to edit pictures you have taken with your mobile phone camera using built-in filters and share them with others. If you have an Instagram account you can tag pictures, rate and comment on other people’s pictures and follow other users.

How much is your app?
$0.00

Where does the name come from?
When we were kids we loved playing around with cameras. We loved how different types of old cameras marketed themselves as “instant” - something we take for granted today. We also felt that the snapshots people were taking were like telegrams in that they got sent over the wire to others - so we figured why not combine the two?

How did the idea come about?
We love taking photos. We always assumed taking interesting photos required a big bulky camera and a couple years of art school. But as mobile phone cameras got better and better, we decided to challenge that assumption. We created Instagram to solve three simple problems:

- Mobile photos always come out looking mediocre. Our awesome looking filters transform your photos into professional-looking snapshots.

- Sharing on multiple platforms is a pain - we help you take a picture once, then share it (instantly) on multiple services.

- Most uploading experiences are clumsy and take forever - we’ve optimized the experience to be fast and efficient.

How does privacy work?
We have adopted a follower model that means if you’re “public” on Instagram, anyone can subscribe to follow your photos. We do, however, have a special private option. In this mode, a user can make sure he/she must approve all follow requests before they go through.

Who can see my photos?
All photos are public by default which means they are visible to anyone who has an account. If you choose to make your account private, then only people who follow you on Instagram will be able to see your photos.

Adapted from https://instagram.com/about/faq/#

In the sentence “We loved how different types of old cameras marketed themselves as “instant” - something we take for granted today.”, the expression something we take for granted means

Escolha a única alternativa correta, dentre as opções apresentadas, que responde ou completa a questão, assinalando-a.

Leia o texto a seguir, extraído do livro He knows too much, e responda à questão.

Chapter 1 - Madras 1986

“He knows too much. I must ask you to do nothing.”

“But this time I caught him in the act. I have proof, witnesses, everything. There is no possible doubt.”

“I said he knows too much! The company can’t afford to have any problems. Our position is very sensitive in this country. We can’t afford to take risks. I am telling you once again – you will do nothing. And if there is any trouble, I’m afraid I shall have to hold you personally responsible. So be sensible for once in your life.”

“I see. So you are telling me to close my eyes to corruption and behave as if nothing has happened. Is that right?”

“I didn’t put it quite like that. But, if you insist, yes. What Vish does or doesn’t do is a minor matter compared with the company’s global strategy. Just try to get things in perspective. After all, you won’t be stuck in Madras for ever – I’ll make sure that you are not. So just go with the flow for a bit longer. When you’re in your next post this will all seem a very long way away, I can assure you. But meantime, no trouble. I hope I’ve made myself clear. Oh, and, by the way, I advise you to forget that we have had this conversation. Goodbye.”

Dick Sterling put the phone down. His hands were trembling. He was furious with himself for failing to persuade his boss in Delhi, Keith Lennox, to support him, and was disgusted at the mixture of veiled threats and vague promises Lennox had made.

Adapted from MALEY, Alan. He knows too much. Cambridge University Press, 1999. p.6

According to the text, Keith Lennox and Dick Sterling are

Considere o seguinte procedimento: em uma circunferência de diâmetro 2R, inscreve-se um hexágono regular para, em seguida, inscrever neste polígono uma segunda circunferência. Tomando esta nova circunferência, o processo é repetido gerando uma terceira circunferência. Caso este procedimento seja repetido infinitas vezes, a soma dos raios de todas as circunferências envolvidas nesse processo é igual a:

Um recipiente cilíndrico, cujo raio da base tem medida R, contém água até uma certa altura. Uma esfera de aço é mergulhada nesse recipiente ficando totalmente submersa, sem haver transbordamento de água. Se a altura da água subiu !$ { \large 9 \over 16} !$ R, então o raio da esfera mede

Escolha a única alternativa correta, dentre as opções apresentadas, que responde ou completa a questão, assinalando-a.

Fazendo x=ln5 temos que !$ y = e^x - e^{-x} = { \large a \over b} !$, a !$ \in\,z !$ e !$ b\,\in\,z^* !$, a e b primos entre si. Logo a+b é igual a