Ao se lançar uma moeda de raio r (variável) sobre o chão coberto por ladrilhos quadrados de lado l (fixo), com l > 2r, qual deverá ser o diâmetro d (aproximado) da moeda que daria 60% de chances de vitória ao seu lançador, se o piso do chão fosse coberto por ladrilhos quadrados de 30 cm de lado?

Dado: !$ \sqrt{0,6}\cong !$ 0,7746

Seja n um número natural de 3 algarismos. Se, ao multiplicar-se n por 7 obtém-se um número terminado em 373, é correto afirmar que

Sobre o tratamento dispensado aos índios no período colonial, pode-se afirmar que

O dióxido de carbono tem diversas e importantes aplicações. No estado gasoso, é utilizado no combate a incêndios, em especial quando envolvem materiais elétricos; no estado sólido, o denominado gelo seco é utilizado na refrigeração de produtos perecíveis, entre outras aplicações. A figura apresenta um esboço do diagrama de fases para o CO₂.

The Revivals of the fittest

Jeremy McCarter

One compensation of New York City life is that even the unpleasant parts come wrapped in legend. Your commute to Brooklyn might be a drag, but hey, Walt Whitman did it before you, and immortalized it in a poem. For generations, no art form has done more to make the city a place of fables than the Broadway musical. From Rodgers and Hart's “Manhattan” in 1925 to “Christopher Street” in “Wonderful Town” to “Another Hundred People” in “Company”, songwriters haven't just reflected their madcap city – they've helped to define it.

Now, just when New Yorkers are in the midst of a spiritual flogging – upstaged by Obama's Washington, humbled by Wall Street's collapse, perplexed by real estate prices that are almost reasonable – the two greatest New York musicals have returned. If staged well, “West Side Story”, with its native-born and Puerto Rican gang warfare, distills the violence, frustrated dreams and tragic undertow of this immigrant town. And “Guys and Dolls”, with its hustlers and zealous (though badly outnumbered) religious believers, captures the ingenuity of New York's street poetry, the hard-edged sense of humor that is constantly demanded of people forced to navigate these sidewalks every day. Both of the revivals take liberties with the material, in hopes of speaking more directly to our vexed moment. Each tells a very different story about the way we live in the nation's artistic capital now.

The chief novelty of the revival of “West Side Story” directed by Arthur Laurents, the show's 91-year old librettist, is that considerable chuncks of the sad tale of Tony and Maria are now spoken and sung in Spanish. When this happens the first time, in a scene between Maria (Josefina Scaglione) and Anita (Karen Olivo, who just became a great big star), your eyes flick instinctively to the proscenium arch for a translation to appear. It doesn't. This prompts two thoughts in quick succession: (1) Hey, you have to know Spanish to understand what they're saying. (2) Wait – why don't I know Spanish?

(Newsweek, March 30, 2009)

Ecological Intelligence

Bryan Walsh

When it comes to going green, intention can be easier than action. Case in point: you decide to buy a T shirt made from 100% organic cotton, because everyone knows that organic is better for Earth. And in some ways it is; in conventional cotton-farming, pesticides strip the soil of life. But that green label doesn't tell the whole story – like the fact that even organic cotton requires more than 2,640 gal. (10,000 L) of water to grow enough fiber for one T shirt. Or the possibility that the T shirt may have been dyed using harsh industrial chemicals, which can pollute local groundwater. If you knew all that, would you possibly consider the T shirt green? Would you still buy it?

Scanning the supermarket aisles, we lack the data to understand the full impact of what we choose – and probably couldn't make sense of the information even if we had it.

But what if we could seamlessly calculate the full lifetime effect of our actions on the earth and on our bodies? Not just carbon footprints but social and biological footprints as well? What if we could think ecologically? That's what psychologist Daniel Goleman describes in his forthcoming book, Ecological Intelligence. Using a young science called industrial ecology, businesses and green activists alike are beginning to compile the environmental and biological impact of our every decision – and delivering that information to consumers in a user-friendly way. That's thinking ecologically – understanding the global environmental consequences of our local choices.

(Time, March.12, 2009)

macacas uma substância capaz de evitar o contágio por via sexual de um vírus similar ao HIV. Eles acompanharam atentamente os primeiros dias depois do contágio e descreveram como uma infecção localizada no útero progride até espalhar-se para o organismo. Nas primeiras horas, apenas um pequeno grupo de células do aparelho reprodutor é invadido pelo vírus. O tecido prejudicado inflama e o sistema imunológico recruta células de defesa para debelar a infecção incipiente. A reação, no entanto, beneficia o vírus, que procurava justamente células de defesa para infectar e, assim, se espalhar pelo organismo.

Testaram, então, um gel com monolaurato de glicerol, aplicado na vagina de cinco macacas. Depois, simularam o contágio por via sexual inoculando até quatro doses de soluções ricas em vírus. O gel diminuiu a produção de proteínas responsáveis pelo processo inflamatório no corpo. Nenhuma fêmea desenvolveu a doença. Para controle do teste, realizaram o mesmo procedimento em cinco macacas que não usaram o gel: quatro contraíram a infecção.

“O trabalho mostra que você não precisa atacar diretamente o vírus para impedir que ele infecte as células”, explica o infectologista Esper Kallás, da Universidade de São Paulo. “Você pode atuar no processo inflamatório que beneficia o vírus.”

(O Estado de S.Paulo, 04.03.2009. Adaptado)