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Conforme a figura acima, um corpo, cuja velocidade é nula no ponto A da superfície circular de raio R, é atingido por um projétil, que se move verticalmente para cima, e fica alojado no corpo. Ambos passam a deslizar sem atrito na superfície circular, perdendo o contato com a superfície no ponto B. A seguir, passam a descrever uma trajetória no ar até atingirem o ponto C, indicado na figura. Diante do exposto, a velocidade do projétil é:
Dados:
• massa do projétil: m ;
• massa do corpo: 9m ; e
• aceleração da gravidade: g .
As fibras ópticas funcionam pelo Princípio da Reflexão Total, que ocorre quando os raios de luz que seguem determinados percursos dentro da fibra são totalmente refletidos na interface núcleo-casca, permanecendo no interior do núcleo. Considerando apenas a incidência de raios meridionais e que os raios refratados para a casca são perdidos, e ainda, sabendo que os índices de refração do ar, do núcleo e da casca são dados, respectivamente, por n0, n1; e n2 ( n1 > n2 > n0), o ângulo máximo de incidência θa , na interface ar-núcleo, para o qual ocorre a reflexão total no interior da fibra é:
Considerações:
• raios meridionais são aqueles que passam pelo centro do núcleo; e
• todas as opções abaixo correspondem a números reais.
A menor raiz real positiva da equação
encontra-se no intervalo:
onde Z é um número complexo que satisfaz a equação:
24033 Z2 - 22017 Z + 1 = 0.
Obs: Im(Z) é a parte imaginária do número complexo Z.
Seja o seguinte sistema de equações, em que s é um número real:
Escolha uma faixa de valores de s em que as soluções do sistema são todas negativas.
Seja a função H: ℂ → ℂ definida por
com aj e bk reais, para j = 0,1,2,3 e k = 0,1,2. Seja a função ƒ: ℝ → ℝ em que ƒ(w ) é a parte real de H (iw) em que i = √-1 é a unidade imaginária e w ∈ ℝ. A afirmação correta a respeito de ƒ(w ) é:
Sejam X1, X2, X3 e X4 os quatro primeiros termos de uma P.A. com X1 = x e razão r, com x, r ∈ ℜ. O determinante de 
é:
Seja f(x) uma função definida nos conjunto dos números reais, de forma que f(1) = 5 e para qualquer x pertencente aos números reais f(x+4) ≥ f(x) + 4 e f(x+1) ≤ f(x) + 1.
Se g(x) = f(x) + 2 - x, o valor de g(2017) é:
Considere as alternativas:
I. O inverso de um irracional é sempre irracional.
II. Seja a função f: A → B e X e Y dois subconjuntos quaisquer de A, então f(X ∩ Y)= f(X) ∩ f(Y).
III. Seja a função f: A → B e X e Y dois subconjuntos quaisquer de A, então f(X ∪ Y)= f(X) ∪ f(Y).
IV. Dados dois conjuntos A e B não vazios, então A ∩ B = A se, e somente se, B ⊂ A.
São corretas:
Obs: f(Z) é a imagem de f no domínio Z.
Woman who rescued Nigerian 'witch-child' beats Obama and Pope Francis to top list of world's most inspiring people
A woman who rescued a two-year-old boy who had been cast out by his own community for being a "witch-child" has been recognised in an international list of the most inspiring people of the year. Anja Ringgren Lovén, a Danish care worker who rescued the young Nigerian boy back in February 2016, beat the likes of Pope Francis, Barack Obama and the Dalai Lama to top the list of 100 inspiring individuals compiled by German-language OOOM Magazine.
An image of Ms Lovén giving the two-year-old boy (now called Hope) some water was shared around the world, and served to highlight the work she was doing to help orphan children in Nigeria. Witch accusations is a growing problem in many African countries, especially in Nigeria, where Anja's charity African Children's Aid Education and Development Foundation cares for other children like Hope.
"When she saw the starving child, she acted like a human being and became an inspiration for millions," said Georg Kindel, OOOM's editor-in-chief, who led the jury that chose the list. Speaking today about the experience, she said: "He was the size of a little baby, my whole body froze. I was thinking of my own son when I saw the boy. For me it was clear at that moment that I would fight with all my strength for him to survive."
Adapted from http://www.independent.co.uk/news/people/
worlds-most-inspiring-person-2016-ooom-anja-ringgren-lovennigeria-witch-child-a7460976.html
According to the text, read the statements and choose the correct alternative.
I - Hope's community didn't want him because of a superstition.
II - Ms Lovén started helping orphan children after she met Hope.
III - Anja's foundation cares for poor parents who have many children.
IV - George Kindel was the only person who voted for Ms Lovén.
V - Ms Lovén has a child of her own and it's a boy.
Woman who rescued Nigerian 'witch-child' beats Obama and Pope Francis to top list of world's most inspiring people
A woman who rescued a two-year-old boy who had been cast out by his own community for being a "witch-child" has been recognised in an international list of the most inspiring people of the year. Anja Ringgren Lovén, a Danish care worker who rescued the young Nigerian boy back in February 2016, beat the likes of Pope Francis, Barack Obama and the Dalai Lama to top the list of 100 inspiring individuals compiled by German-language OOOM Magazine.
An image of Ms Lovén giving the two-year-old boy (now called Hope) some water was shared around the world, and served to highlight the work she was doing to help orphan children in Nigeria. Witch accusations is a growing problem in many African countries, especially in Nigeria, where Anja's charity African Children's Aid Education and Development Foundation cares for other children like Hope.
"When she saw the starving child, she acted like a human being and became an inspiration for millions," said Georg Kindel, OOOM's editor-in-chief, who led the jury that chose the list. Speaking today about the experience, she said: "He was the size of a little baby, my whole body froze. I was thinking of my own son when I saw the boy. For me it was clear at that moment that I would fight with all my strength for him to survive."
Adapted from http://www.independent.co.uk/news/people/
worlds-most-inspiring-person-2016-ooom-anja-ringgren-lovennigeria-witch-child-a7460976.html
Woman who rescued Nigerian 'witch-child' beats Obama and Pope Francis to top list of world's most inspiring people
A woman who rescued a two-year-old boy who had been cast out by his own community for being a "witch-child" has been recognised in an international list of the most inspiring people of the year. Anja Ringgren Lovén, a Danish care worker who rescued the young Nigerian boy back in February 2016, beat the likes of Pope Francis, Barack Obama and the Dalai Lama to top the list of 100 inspiring individuals compiled by German-language OOOM Magazine.
An image of Ms Lovén giving the two-year-old boy (now called Hope) some water was shared around the world, and served to highlight the work she was doing to help orphan children in Nigeria. Witch accusations is a growing problem in many African countries, especially in Nigeria, where Anja's charity African Children's Aid Education and Development Foundation cares for other children like Hope.
"When she saw the starving child, she acted like a human being and became an inspiration for millions," said Georg Kindel, OOOM's editor-in-chief, who led the jury that chose the list. Speaking today about the experience, she said: "He was the size of a little baby, my whole body froze. I was thinking of my own son when I saw the boy. For me it was clear at that moment that I would fight with all my strength for him to survive."
Adapted from http://www.independent.co.uk/news/people/
worlds-most-inspiring-person-2016-ooom-anja-ringgren-lovennigeria-witch-child-a7460976.html
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