FUVEST 2001

Questão 52415

(UNICAMP - 2001 - 2 FASE) O sistema de numeração na base 10 utiliza, normalmente, os dígitos de 0 a 9 para representar os números naturais, sendo que o zero não é aceito como o primeiro algarismo da esquerda. Pergunta-se:

a) Quantos são os números naturais de cinco algarismos formados por cinco dígitos diferentes?

b) Escolhendo-se ao acaso um desses números do item a, qual a probabilidade de que seus cinco algarismos estejam em ordem crescente?

Questão 52416

(UNICAMP - 2001 - 2 FASE) Considere, no plano xy, as retas y =1, y = 2x - 5 e x - 2y + 5 = 0 .

a) Quais são as coordenadas dos vértices do triângulo ABC formado por essas retas?

b) Qual é a área do triângulo ABC ?

Questão 52418

(UNICAMP - 2001 - 2 FASE) As populações de duas cidades, A e B, são dadas em milhares de habitantes pelas funções   e   onde a variável t representa o tempo em anos.

a) Qual é a população de cada uma das cidades nos instantes t = 1 e t = 7 ?

b) Após certo instante t, a população de uma dessas cidades é sempre maior que a da outra. Determine o valor mínimo desse instante t e especifique a cidade cuja população é maior a partir desse instante.

Questão 52420

(UNICAMP - 2001 - 2 FASE) Considere a equação trigonométrica 

a) Mostre que não são soluções dessa equação os valores de  para os quais 

b) Encontre todos os valores de  que são soluções da equação.

Questão 52423

(UNICAMP - 2001 - 2 FASE) Considere o polinômio p(x )= x³+2x²+5x+26

a) Verifique se o número complexo 2 + 3i é raiz desse polinômio.

b) Prove que p(x) > 0 para todo número real x > – 2.

Questão 52425

(UNICAMP - 2001 - 2 FASE) A base de uma pirâmide é um triângulo eqüilátero de lado L = 6cm e arestas laterais das faces A = 4cm.

a) Calcule a altura da pirâmide.

b) Qual é o raio da esfera circunscrita à pirâmide?

Questão 52427

(UNICAMP - 2001 - 2 FASE) Responda a questão em português.

No diálogo apresentado no quadrinho abaixo, o que a mãe quer salientar para a criança e o que a criança entende?

Questão 52430

(UNICAMP - 2001 - 2 FASE) Responda a questão em português.

The surprising truth about women's hearts

WHILE women are less likely to suffer heart attacks than men, once a woman
suffers her first attack she is 70 per cent more likely to die from it than a
man. These surprising new findings highlight the need for medical staff to be
more vigilant against heart disease in women.

Researchers at the Municipal Institute of Medical Research in Barcelona
studied 331 women and 1129 men who had suffered their first heart attack. The
researchers report in The Journal of the American Medical Association
(vol 280, p 1405) that women were 72 per cent more likely to die within the
first 28 days, and 73 per cent more likely to die within the first six months.
“We were surprised that women were so much more at risk,” says Jaume Marrugat,
who led the Spanish team.

Marrugat notes that women were less likely to get clot-busting treatment than
men, and that they generally took more time getting to hospital—problems
that may reflect the low priority doctors put on heart disease in women. Heart
specialist Graham McGregor of St George’s Hospital Medical School in London also
notes that women tend to be older than men at their first heart attack because
they have some hormonal protection against heart disease until menopause. On
average, women in the Spanish study were five years older than the men.

“These are important factors to consider but they can’t account for the whole
difference,” says Marrugat. “Women have more complications in the first six
months and their initial heart attacks may be more severe.” He speculates that
narrower coronary vessels in women may be a factor. Nonetheless, heart disease
remains a bigger killer of men than women.

Michael Day

Considerando as razões apresentadas pelos pesquisadores, qual é the surprising truth about women’s hearts?

Questão 52432

(UNICAMP - 2001 - 2 FASE) Responda a questão em português.

The surprising truth about women's hearts

WHILE women are less likely to suffer heart attacks than men, once a woman
suffers her first attack she is 70 per cent more likely to die from it than a
man. These surprising new findings highlight the need for medical staff to be
more vigilant against heart disease in women.

Researchers at the Municipal Institute of Medical Research in Barcelona
studied 331 women and 1129 men who had suffered their first heart attack. The
researchers report in The Journal of the American Medical Association
(vol 280, p 1405) that women were 72 per cent more likely to die within the
first 28 days, and 73 per cent more likely to die within the first six months.
“We were surprised that women were so much more at risk,” says Jaume Marrugat,
who led the Spanish team.

Marrugat notes that women were less likely to get clot-busting treatment than
men, and that they generally took more time getting to hospital—problems
that may reflect the low priority doctors put on heart disease in women. Heart
specialist Graham McGregor of St George’s Hospital Medical School in London also
notes that women tend to be older than men at their first heart attack because
they have some hormonal protection against heart disease until menopause. On
average, women in the Spanish study were five years older than the men.

“These are important factors to consider but they can’t account for the whole
difference,” says Marrugat. “Women have more complications in the first six
months and their initial heart attacks may be more severe.” He speculates that
narrower coronary vessels in women may be a factor. Nonetheless, heart disease
remains a bigger killer of men than women.

Michael Day

Por que, segundo Graham McGregor, as mulheres tendem a sofrer seus primeiros ataques cardíacos em idade mais avançada que os homens?

Questão 52434

(UNICAMP - 2001 - 2 FASE) Responda a questão em português.

Como o poema de Carroll Arnettjustifica que Your problem is not my problem?