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razon de cambio

Module by: diego diaz torres. E-mail the author

Summary: razon de cambio

Razon de Cambio

  • La altura de un triangulo equilatero aumenta a razon de 3 cm/seg. ?`cual es la velocidad de aumento del area?

DESARROLLO:

A = a · h 2 A = a · h 2
(1)
⇒ a 2 = a 2 4 + h 2 ⇒ a 2 = a 2 4 + h 2
(2)
3 4 a 2 = h 2 3 4 a 2 = h 2
(3)
⇒ a = 2 3 h ⇒ a = 2 3 h
(4)
⇒ A = h 2 3 ⇒ dA dt = 2 3 h dh dt ⇒ A = h 2 3 ⇒ dA dt = 2 3 h dh dt
(5)
⇒ dA dt = 2 3 h · 3 cm / seg ⇒ dA dt = 2 3 h · 3 cm / seg
(6)
⇒ dA dt = 2 3 h cm / seg ⇒ dA dt = 2 3 h cm / seg
(7)

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