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(EM13MAT401) - Converter representagbes algebricas de funpbes polinomiais de grau em representaçes geometricas no plano cartesiano, distinguindo os casos nos quais o comportamento e proporcional, recorrendo ou nåo a softwares ou aplicativos de algebra e geometria dinámica.
(ENEM- adaptada) - Um grupo de pacientes com Hepatte foi submetido a um tratamento tradicional em que desses pacientes foram completamente curados. Os pacientes que năo obtiveram oura foram distribuidos em dois grupos de mesma quantidade e submelidos a dois tratamentos inovadores. No primeiro tratamento inovador, 27% dos pacientes foram curados e, no segundo, .
Em relaçăo aos pacientes submetidos inicialmente, os tratamentos inovadores proporcionaram cura de:
(A)
(B)
©
(92)
(E)

Ask by Carlson Lindsey. in Brazil
Mar 26,2025

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Os tratamentos inovadores proporcionaram cura de dos pacientes inicialmente submetidos.
Resposta: (opção C).

Solución

  1. Considere o total de pacientes como .
  2. Inicialmente, dos pacientes foram curados pelo tratamento tradicional. Assim, os pacientes não curados correspondem a:
  3. Esses são divididos igualmente em dois grupos, ou seja, cada grupo contém:
  4. No primeiro grupo (primeiro tratamento inovador), dos pacientes foram curados. A porcentagem desses curados, em relação ao total inicial, é:
  5. No segundo grupo (segundo tratamento inovador), dos pacientes foram curados. A porcentagem dos curados, em relação ao total inicial, é:
  6. Somando as porcentagens de cura proporcionadas pelos tratamentos inovadores:
Assim, em relação aos pacientes submetidos inicialmente, os tratamentos inovadores proporcionaram cura de .
Resposta: (opção C).

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Extra Insights

Vamos calcular a porcentagem de pacientes que foram curados pelos tratamentos inovadores. Inicialmente, 40% dos pacientes foram curados, o que significa que 60% não obtiveram cura. Esses pacientes foram divididos em dois grupos iguais. Se representarmos 100% como o total de pacientes, 60% (não curados) dariam 30% para cada grupo.
No primeiro tratamento, 27% dos 30% foram curados: . No segundo, 15% dos 30%: . Somando isso com os 40% iniciais, temos: curados no total. Para encontrar a porcentagem de cura dos tratamentos inovadores apenas, fazemos .
Assim, a resposta correta é © .
No círculo das representações geométricas, um ponto curioso é que os polinômios do primeiro grau desenham linhas retas no plano cartesiano. Essa característica é útil para entender não apenas a algebra, mas aplicações práticas, como o planejamento de trajetórias ou o design de gráficos claros e informativos. Uma linha reta, que é a solução de um polinômio de 1° grau, pode representar relações diretas entre variáveis, facilitando a visualização de tendências.
Em relação à conversão de funções para representações geométricas, uma dica é sempre começar desenhando o gráfico. Testar alguns valores pode ajudar a visualizar o comportamento da função antes de elaborar o gráfico final. Um erro comum é pular essa etapa e ir direto para a forma final, sem entender totalmente o que a função representa. Isso pode levar a interpretações erradas, especialmente em funções que mudam de comportamento em diferentes intervalos!

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