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O enunciado a seguir deve ser usado para a questão.
O Professor Euclideson estava estudando o seguinte problema, conforme a figura abaixo: No semicírculo Γ de raio r = 2024 u.c. (unidades de comprimento) e centro O, traçam-se duas cordas AD e BC, cada uma das quais divide o semicírculo em duas regiões de mesma área. Essas cordas intersectam-se no ponto P. O ângulo θ é medido em radianos.
Não satisfeito, o Professor Euclideson introduziu um sistema cartesiano de coordenadas no plano de tal modo que O = (0,0), a
semirreta 
coincidiu com o semieixo positivo dos x e a semirreta com início em O, perpendicular à reta 
e contida no mesmo
semiplano que o semicírculo Γ com relação à reta coincidiu com o semieixo positivo dos y.
Nesse sistema, o ponto P tem coordenadas:
O enunciado a seguir deve ser usado para a questão.
O Professor Euclideson estava estudando o seguinte problema, conforme a figura abaixo: No semicírculo Γ de raio r = 2024 u.c. (unidades de comprimento) e centro O, traçam-se duas cordas AD e BC, cada uma das quais divide o semicírculo em duas regiões de mesma área. Essas cordas intersectam-se no ponto P. O ângulo θ é medido em radianos.
é igual a: 
, opostos, nesta ordem, aos lados medindo a, b e c.
Se o gráfico da função
dada por f(x) = c(x2 − 1) + 2bx + a(x2 + 1), toca o eixo x em exatamente um ponto. Denotando por X a raiz de f, é CORRETO afirmar que X-1 é igual a: O enunciado a seguir deve ser usado para a questão.
Seja M o conjunto de todas as matrizes 3 × 3 cujas entradas são todas números inteiros satisfazendo as seguintes condições:
●Todas as entradas da primeira coluna são múltiplas de 2;
● Todas as entradas da segunda coluna são múltiplas de 3;
●Todas as entradas da terceira coluna são múltiplas de 5;
●Todas as entradas da primeira linha são múltiplas de 5;
●Todas as entradas da segunda linha são múltiplas de 3;
●Todas as entradas da terceira linha são múltiplos de 2.
O enunciado a seguir deve ser usado para a questão.
Seja M o conjunto de todas as matrizes 3 × 3 cujas entradas são todas números inteiros satisfazendo as seguintes condições:
●Todas as entradas da primeira coluna são múltiplas de 2;
● Todas as entradas da segunda coluna são múltiplas de 3;
●Todas as entradas da terceira coluna são múltiplas de 5;
●Todas as entradas da primeira linha são múltiplas de 5;
●Todas as entradas da segunda linha são múltiplas de 3;
●Todas as entradas da terceira linha são múltiplos de 2.
O valor de n é:
Seja T um conjunto de 2023 triângulos T1, T 2 ,..., T 2023 no plano euclidiano, com a seguinte propriedade: existe uma constante real α, com 0 < α < 1, tal que, para todo j = 1, ..., 2022, os triângulos Tj e Tj+1 são semelhantes e
em que, em cada fração acima, o numerador é a medida de um lado de Tj+1 e o denominador é medida do lado correspondente de j+1 Tj .Denotando Sj a área de Tj , para cada j = 1 ,..., 2023, a soma
é igual a:
Aritmetisvalda, mãe de Jurisvaldo, não tinha o dinheiro necessário para dar ao filho para que comprasse o item à vista, mas decidiu fazer-lhe uma surpresa. Ela investiu, a juros compostos, os R$ 100,00 de que dispunha, a fim de, ao final dos 12 meses das prestações, dar de presente a Jurisvaldo o valor total que o item lhe custou.
Ela não investiu nenhum outro valor nem fez nenhuma retirada, referente ao investimento feito, e conseguiu atingir seu objetivo.
A taxa de juros do investimento feito por Aritmetisvalda era de, aproximadamente:
(Se necessário, use 0,838 como aproximação de
1,286 como aproximação de e 
1,554 como aproximação de 
Logo, a área do triângulo ABC é igual à:
Sabe-se que, se n é um número inteiro da forma n = 2k+ 1 para algum inteiro k, então n³ − n é divisível por 24.
Assinale o único número abaixo que pode ser escrito na forma 2k³ + 3k² + k:
A respeito da equação
resolvida para 
é CORRETO afirmar que:
A respeito da função 
dada por
São feitas as seguintes afirmações:
I- O numerador e o denominador de f(k)são primos entre si, qualquer que seja o inteiro k > 0.
II- f(k)∉
, qualquer que seja o inteiro k < 0.
III- 0 ϵé o único inteiro k tal que f(k) = k.
É CORRETO o que se afirma, apenas, em:
READ THE FOLLOWING TEXTTO ANSWER QUESTION.
TEXT 4
According to the Brazilian National Education Guidelines and Framework Law enacted in 2017, English language teaching is mandatory from the sixth year of elementary school until the last years of high school. However, the curriculum does not guarantee that all Brazilian students will receive English teaching. In 2013, Data Popular, a Brazilian research institute, drafted a report for the British Council analyzing the problems concerning knowledge of English in Brazil. The report claims that the low level of English proficiency amongst Brazilians reflects the educational opportunities available in the country […].
To understand the reasons why English teaching does not seem efficient for all students, it is important to highlight the English language teaching provision in Brazil. Formal English teaching in Brazil takes place in four different contexts: English schools, bilingual schools, regular private schools, and public schools. In general, people who wish to learn English believe that effective learning occurs only in private English schools or bilingual schools because the structure (the teaching methods and the quality of support materials) is more likely to provide successful learning. The focus in those institutions is on oral expression. Learners have more exposure to the target language because classes are taught entirely in English, and teachers are usually well trained to comply with that requirement. In addition, groups are smaller, so students can receive personal support and enjoy a comfortable learning environment, not to mention access to multimedia resources.
(Adapted from: https://academic.oup.com/eltj/75/1/103/6169556)
READ THE FOLLOWING TEXTTO ANSWER QUESTION.
TEXT 4
According to the Brazilian National Education Guidelines and Framework Law enacted in 2017, English language teaching is mandatory from the sixth year of elementary school until the last years of high school. However, the curriculum does not guarantee that all Brazilian students will receive English teaching. In 2013, Data Popular, a Brazilian research institute, drafted a report for the British Council analyzing the problems concerning knowledge of English in Brazil. The report claims that the low level of English proficiency amongst Brazilians reflects the educational opportunities available in the country […].
To understand the reasons why English teaching does not seem efficient for all students, it is important to highlight the English language teaching provision in Brazil. Formal English teaching in Brazil takes place in four different contexts: English schools, bilingual schools, regular private schools, and public schools. In general, people who wish to learn English believe that effective learning occurs only in private English schools or bilingual schools because the structure (the teaching methods and the quality of support materials) is more likely to provide successful learning. The focus in those institutions is on oral expression. Learners have more exposure to the target language because classes are taught entirely in English, and teachers are usually well trained to comply with that requirement. In addition, groups are smaller, so students can receive personal support and enjoy a comfortable learning environment, not to mention access to multimedia resources.
(Adapted from: https://academic.oup.com/eltj/75/1/103/6169556)
READ THE FOLLOWING TEXTTO ANSWER QUESTION.
TEXT 4
According to the Brazilian National Education Guidelines and Framework Law enacted in 2017, English language teaching is mandatory from the sixth year of elementary school until the last years of high school. However, the curriculum does not guarantee that all Brazilian students will receive English teaching. In 2013, Data Popular, a Brazilian research institute, drafted a report for the British Council analyzing the problems concerning knowledge of English in Brazil. The report claims that the low level of English proficiency amongst Brazilians reflects the educational opportunities available in the country […].
To understand the reasons why English teaching does not seem efficient for all students, it is important to highlight the English language teaching provision in Brazil. Formal English teaching in Brazil takes place in four different contexts: English schools, bilingual schools, regular private schools, and public schools. In general, people who wish to learn English believe that effective learning occurs only in private English schools or bilingual schools because the structure (the teaching methods and the quality of support materials) is more likely to provide successful learning. The focus in those institutions is on oral expression. Learners have more exposure to the target language because classes are taught entirely in English, and teachers are usually well trained to comply with that requirement. In addition, groups are smaller, so students can receive personal support and enjoy a comfortable learning environment, not to mention access to multimedia resources.
(Adapted from: https://academic.oup.com/eltj/75/1/103/6169556)
Read the following sentences:
I- The library was supposed to open early today; however, due to unforeseen circumstances, it will remain closed.
II- She has been working hard to improve her fitness levels, yet she feels more exhausted than ever.
III- The project deadline was fast approaching; nevertheless, the team decided to start from scratch.
The use of connectors is CORRECT in:
READ THE FOLLOWING TEXTTO ANSWER QUESTION.
TEXT 3
“The sudden spike of artificial intelligence (AI) technologies has had and continues to have a transformative impact on various domains, including education. The advent of AI-powered large language models [LLM], such as OpenAI's ChatGPT, will significantly enhance the way English as a foreign language (EFL) is taught and learned. This article explores the versatile applications of ChatGPT as a valuable tool in any EFLteacher's toolkit, specifically focusing on material development and assessment. The demand for effective EFLteaching and learning strategies has been steadily on the rise for years due to globalization and the widespread adoption of English as the lingua franca for international communication. Consequently, the integration of technology in language education has become crucial in addressing the diverse needs of EFL learners and teachers. ChatGPT, a cutting-edge LLM, holds considerable promise in revolutionizing EFLeducation, as it combines advanced natural language processing capabilities with a realistic instantaneous humanlike interaction. This article aims to provide some potential benefits of utilizing ChatGPT in EFL education. First, we examine how ChatGPTcan be employed in material development, streamlining the process of creating engaging and contextually relevant resources tailored to the needs of individual learners, as well as other more general uses. Second, we explore the role of ChatGPT in text assessment, highlighting the fact that, unlike humans, it has the potential of offering real-time, personalized feedback on learners' performance, thereby enhancing the overall learning experience. It is worth noting that this article as well as the applications suggested in it are based on the latest ChatGPT4 and not the older ChatGPT3.5.”
(Adapted from: https://langedutech.com/letjournal/index.php/let/article/view/48 )
Considering this period, the word steadily can be substituted, without change in meaning, by which one of the following?
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