Note the following sentences:

i. They planned to reduce staff and thus to cut costs.

ii. We were unable to get funding and therefore had to abandon the project.

iii. I was lost so I bought a street map.

Select the alternative that brings a connector that has the same meaning those highlighted in the above sentences.

The following text is part of the article Principles of Instructed Second Language Acquisition of professor Rod Ellis who formulated a set of general principles for instructed language acquisition. Principle 8 will be used for the next question.

TEXT - Principle 8: The opportunity to interact in the second language is central to developing second
language proficiency
While it is useful to consider the relative contributions of input and output to acquisition, it is also important to acknowledge that both occur in oral interaction and that this plays a central role in second language acquisition. As Hatch (1978) famously put it, “One learns how to do conversation, one learns how to interact verbally, and out of the interaction syntactic structures are developed” (p. 404). Thus, interaction is not just a means of automatizing what the learners already know but also about helping them to acquire new language. According to the Interaction Hypothesis (Long, 1996), interaction fosters acquisition when a communication problem arises and learners are engaged in negotiating for meaning. The interactional modifications that arise help to make input comprehensible, provide corrective feedback, and push learners to modify their own output by repairing their own errors. According to sociocultural theory, interaction serves as a form of mediation, enabling learners to construct new forms and perform new functions collaboratively (Lantolf, 2000). According to this view, learning is first evident on the social plane and only later on the psychological plane. In both theories, social interaction is viewed as a primary source of learning. Figure 5 identifies five key requirements for interaction to create an acquisition-rich classroom. Creating the right kind of interaction for acquisition constitutes a major challenge for teachers. One solution is to incorporate small group work into a lesson. When students interact among themselves, acquisition-rich discourse is more likely to ensue. However, there are also dangers in group work (e.g., excessive use of the native language in monolingual groups) that teachers need to guard against.

To create an acquisition-rich classroom, teachers need to:
- create contexts of language use where students have a reason to attend to language,
- allow students to initiate topics and to control topic development,
- provide opportunities for learners to use the language to express their own personal meanings,
- help students to participate in language-related activities that are beyond their current level of proficiency,
- and offer a full range of contexts that provide opportunities for students to engage in a full performance in the language.
(Ellis, 1999; Johnson 1995).

Seja C o trecho da parábola y²=4x que vai de x = 3 a x = 15. Calcule !$ \int_C y \ ds !$, nesse trecho.

Sabendo que !$ \vec F (x, y) = (2y^2 + 2xe^y)\hat i + (x^z e^y + 4xy + 1)\hat j !$ é um campo vetorial conservativo, podemos afirmar que a !$ \int_C \vec F ⋅ d\vec r !$ , onde C é a curva parametrizada por !$ \vec r(t) = (t + sen(\pi t), t - cos (\pi t)) !$ vale:

A porta de um bar possui uma dobradiça de tal modo que ela permita sua abertura tanto para dentro, quanto para fora do ambiente. Um dos frequentadores do bar é um matemático bastante conceituado. Em uma de suas visitas ao bar, ele formulou que o movimento desta porta é descrito pela equação diferencial !$ \ddot y + 3 \dot y +2 = 0 !$. Sabendo que inicialmente a porta encontra-se em 0,2 metros afastada em relação à posição de equilíbrio e parada. Pode-se afirmar que a solução da equação do movimento é dada por:

A figura a seguir ilustra o diagrama de Venn de quatro conjuntos A, B, C e D, onde é possível observar as intersecções desses conjuntos. Escolhendo aleatoriamente um elemento que pertence à interseção dos conjuntos B e C, a probabilidade de que este elemento não pertença ao conjunto A é de:

Calcule !$ \oint_C - y^2 dx + 4xy \ dy !$ onde C é a curva formada pelos segmentos de reta de (1,0) a (0,1), de (0,1) a (0,2), de (0,2) a (2,0) e de (2,0) a (1,0).

O senhor Paolo José Alcides precisou fazer um empréstimo bancário após vários anos de afastamento do mercado de trabalho. Paolo José Alcides precisava de uma quantia equivalente a R$ 10.800,00. O gerente do Banco XRET, seu afilhado, lhe fez duas propostas:

I. Paolo poderia sacar a quantia, com uma proposta de juros compostos com taxa de 1,6 % ao mês por um período de 24 meses.

II. Paolo poderia sacar a quantia, com uma proposta de juros simples com uma taxa 1,8 % ao mês por um período de 24 meses.

Pergunta-se: Qual o valor total a ser pago por Paolo José Alcides pelo empréstimo, segundo a proposta de juros compostos e juros simples, respectivamente: