CÁLCULO II
Uma escada de 13 m está apoiada em uma parede vertical. A base da escada está sendo empurrada no sentido contrário ao da parede, a uma taxa constante de 6 m/min. Qual a velocidade com a qual o topo da escada se move para baixo, encostada à parede, quando a base da escada está a 5 m da parede?
No instante em que a base da escada está a 5 m da parede, seu topo desce a velocidade de 5,2 m/min.
No instante em que a base da escada está a 5 m da parede, seu topo desce a velocidade de 2,5 m/min.
No instante em que a base da escada está a 5 m da parede, seu topo desce a velocidade de 0,9 m/min.
No instante em que a base da escada está a 5 m da parede, seu topo desce a velocidade de 3,6 m/min.
No instante em que a base da escada está a 5 m da parede, seu topo desce a velocidade de 4,5 m/min.
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Uma área retangular em uma fazenda será cercada por um lado com uma cerca de três fios e nos outros lados, por uma cerca elétrica com um fio. Com 800 m de fio à disposição, determine quais as dimensões da maior área que poderá ser cercada e calcule o valor dessa área.
As dimensões do retângulo são 50 m no lado paralelo à cerca de três fios por 300 m no lado perpendicular a essa cerca, resultando numa área total de 15.000 m2.
As dimensões do retângulo são 300 m no lado paralelo à cerca de três fios por 200 m no lado perpendicular a essa cerca, resultando numa área total de 20.000 m2.
As dimensões do retângulo são 120 m no lado paralelo à cerca de três fios por 160 m no lado perpendicular a essa cerca, resultando numa área total de 19.200 m2.
As dimensões do retângulo são 100 m no lado paralelo à cerca de três fios por 200 m no lado perpendicular a essa cerca, resultando numa área total de 20.000 m2.
As dimensões do retângulo são 150 m no lado paralelo à cerca de três fios por 100 m no lado perpendicular a essa cerca, resultando numa área total de 15.000 m2.
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No instante em que a base da escada está a 5 m da parede, seu topo desce a velocidade de 5,2 m/min.
No instante em que a base da escada está a 5 m da parede, seu topo desce a velocidade de 2,5 m/min.
No instante em que a base da escada está a 5 m da parede, seu topo desce a velocidade de 0,9 m/min.
No instante em que a base da escada está a 5 m da parede, seu topo desce a velocidade de 3,6 m/min.
No instante em que a base da escada está a 5 m da parede, seu topo desce a velocidade de 4,5 m/min.
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)
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![](data:image/png;base64,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)
Uma área retangular em uma fazenda será cercada por um lado com uma cerca de três fios e nos outros lados, por uma cerca elétrica com um fio. Com 800 m de fio à disposição, determine quais as dimensões da maior área que poderá ser cercada e calcule o valor dessa área.
As dimensões do retângulo são 50 m no lado paralelo à cerca de três fios por 300 m no lado perpendicular a essa cerca, resultando numa área total de 15.000 m2.
As dimensões do retângulo são 300 m no lado paralelo à cerca de três fios por 200 m no lado perpendicular a essa cerca, resultando numa área total de 20.000 m2.
As dimensões do retângulo são 120 m no lado paralelo à cerca de três fios por 160 m no lado perpendicular a essa cerca, resultando numa área total de 19.200 m2.
As dimensões do retângulo são 100 m no lado paralelo à cerca de três fios por 200 m no lado perpendicular a essa cerca, resultando numa área total de 20.000 m2.
As dimensões do retângulo são 150 m no lado paralelo à cerca de três fios por 100 m no lado perpendicular a essa cerca, resultando numa área total de 15.000 m2.
![](data:image/png;base64,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)
Uma área retangular em uma fazenda será cercada por um lado com uma cerca de três fios e nos outros lados, por uma cerca elétrica com um fio. Com 800 m de fio à disposição, determine quais as dimensões da maior área que poderá ser cercada e calcule o valor dessa área.
As dimensões do retângulo são 50 m no lado paralelo à cerca de três fios por 300 m no lado perpendicular a essa cerca, resultando numa área total de 15.000 m2.
As dimensões do retângulo são 300 m no lado paralelo à cerca de três fios por 200 m no lado perpendicular a essa cerca, resultando numa área total de 20.000 m2.
As dimensões do retângulo são 120 m no lado paralelo à cerca de três fios por 160 m no lado perpendicular a essa cerca, resultando numa área total de 19.200 m2.
As dimensões do retângulo são 100 m no lado paralelo à cerca de três fios por 200 m no lado perpendicular a essa cerca, resultando numa área total de 20.000 m2.
As dimensões do retângulo são 150 m no lado paralelo à cerca de três fios por 100 m no lado perpendicular a essa cerca, resultando numa área total de 15.000 m2.
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As dimensões do retângulo são 50 m no lado paralelo à cerca de três fios por 300 m no lado perpendicular a essa cerca, resultando numa área total de 15.000 m2.
As dimensões do retângulo são 300 m no lado paralelo à cerca de três fios por 200 m no lado perpendicular a essa cerca, resultando numa área total de 20.000 m2.
As dimensões do retângulo são 120 m no lado paralelo à cerca de três fios por 160 m no lado perpendicular a essa cerca, resultando numa área total de 19.200 m2.
As dimensões do retângulo são 100 m no lado paralelo à cerca de três fios por 200 m no lado perpendicular a essa cerca, resultando numa área total de 20.000 m2.
As dimensões do retângulo são 150 m no lado paralelo à cerca de três fios por 100 m no lado perpendicular a essa cerca, resultando numa área total de 15.000 m2.