# Connexions

You are here: Home » Content » Ejercicios de Optimizacion4

### Recently Viewed

This feature requires Javascript to be enabled.

# Ejercicios de Optimizacion4

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

Summary: Ejercicios de Optimizacion

OPTIMIZACION4

1. Se desea construir un recipiente cilindrico de metal con tapa que tenga una superficie total de 80 cm cuadrados. determine sus dimensiones de modo que tenga el mayor volumen posible.

v = π r 2 h v = π r 2 h
(1)
A = 2 π r 2 + 2 π rh = 80 cm 2 A = 2 π r 2 + 2 π rh = 80 cm 2
(2)

una funcion

v = π r 2 h v = π r 2 h
(3)

una ecuacion

2 π r 2 + 2 π rh = 80 2 π r 2 + 2 π rh = 80
(4)
2 π r 2 + 2 π rh = 80 π r 2 + π rh = 40 π rh = 40 - π r 2 h = 40 - π r 2 π r 2 π r 2 + 2 π rh = 80 π r 2 + π rh = 40 π rh = 40 - π r 2 h = 40 - π r 2 π r
(5)
v = π r 2 h π r 2 ( 40 - π r 2 π r ) r ( 40 - π r 2 ) v = 40 r - π r 3 v = π r 2 h π r 2 ( 40 - π r 2 π r ) r ( 40 - π r 2 ) v = 40 r - π r 3
(6)
v ' = 40 - 3 π r 2 v ' = 40 - 3 π r 2
(7)
v ' = 0 40 - 3 π r 2 = 0 r 2 = 40 3 π 4 . 2441 v ' = 0 40 - 3 π r 2 = 0 r 2 = 40 3 π 4 . 2441
(8)
r = 4 . 2441 ± 2 . 0601 r = 4 . 2441 ± 2 . 0601
(9)

se toma el valor positivo de la raiz.

v ' = 40 - 3 π r 2 v ' ' = - 6 π r v ' = 40 - 3 π r 2 v ' ' = - 6 π r
(10)
v ' ' = - 6 π r - 6 π ( 2 . 0601 ) < 0 v ' ' = - 6 π r - 6 π ( 2 . 0601 ) < 0
(11)
h = 40 - π r 2 π r 40 - π ( 2 . 0601 ) 2 π ( 2 . 0601 ) 4 . 1203 h = 40 - π r 2 π r 40 - π ( 2 . 0601 ) 2 π ( 2 . 0601 ) 4 . 1203
(12)

las dimensiones del cilindro son:

r 2 . 0601 & h 4 . 1203 r 2 . 0601 & h 4 . 1203
(13)

## Content actions

PDF | EPUB (?)

### What is an EPUB file?

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

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?

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