Skip to content Skip to navigation

Connexions

You are here: Home » Content » Ejercicio de razon de cambio3

Navigation

Recently Viewed

This feature requires Javascript to be enabled.
 

Ejercicio de razon de cambio3

Module by: DIEGO DIAZ LEON. E-mail the author

Summary: Ejercicio de razon de cambio

RAZON DE CAMBIO

2. Un recipiente tiene la forma de un cono circular recto invertido y la longitud de su altura es el doble de la de su diametro. Al recipiente le esta entrando agua a una rapidez constante, por lo que la profundidad del agua va en aumento. cuando la profundidad es de 1m, la superficie sube a razon de 1 cm po minuto.?`a que rapidez la esta entrando agua al recipiente?

v = π 3 r 2 h v = π 3 r 2 h
(1)
r h = R H ⇒ r h = R 4 R ⇒ r = h 4 r h = R H ⇒ r h = R 4 R ⇒ r = h 4
(2)
v = π 3 ( h 4 ) 2 h ⇒ π 48 h 3 v = π 3 ( h 4 ) 2 h ⇒ π 48 h 3
(3)
dv dt = π 48 3 h 2 ( dh dt ) ⇒ π 16 h 2 ( dh dt ) dv dt = π 48 3 h 2 ( dh dt ) ⇒ π 16 h 2 ( dh dt )
(4)

en el instante en que h=100cm=10dm y dh/dt=0.1dm/min:

dv dt = π 16 h 2 ( dh dt ) ⇒ π 16 ( 10 dm ) 2 ( 0 . 1 dm / min ) ⇒ 10 π 16 dm 3 / min dv dt = π 16 h 2 ( dh dt ) ⇒ π 16 ( 10 dm ) 2 ( 0 . 1 dm / min ) ⇒ 10 π 16 dm 3 / min
(5)
dv dt = 5 π 8 l / m ≈ 1 . 963 l / min dv dt = 5 π 8 l / m ≈ 1 . 963 l / min
(6)

DIEGO DIAZ LEON

CALCULO DIFERENCIAL

Content actions

Download module as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Add module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks