Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
zaphod
Group Title
An open rectangular box is to be made wit a square base, and its capacity is to be 4000cm^3. find the length of the side of the base when the amount of material used to make the box is as small as possible...
PLEASE HELP :)
 2 years ago
 2 years ago
zaphod Group Title
An open rectangular box is to be made wit a square base, and its capacity is to be 4000cm^3. find the length of the side of the base when the amount of material used to make the box is as small as possible... PLEASE HELP :)
 2 years ago
 2 years ago

This Question is Closed

zaphod Group TitleBest ResponseYou've already chosen the best response.0
@satellite73 @Callisto @Omniscience @amistre64
 2 years ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.1
is this roll call?
 2 years ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.1
dw:1349789270142:dw \[b*b*h=4000\]
 2 years ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.1
and theres some calculus involved to find minimum stuff eh
 2 years ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.1
\[b^2h=4000\] \[D[b^2h=4000]\] \[D[b^2h]=D[4000]\] \[D[b^2]h+b^2D[h]=D[4000]\] \[2bb'h+b^2h'=0\] its been awhile since i tried figuring this one out, but hheres my first idea :)
 2 years ago

zaphod Group TitleBest ResponseYou've already chosen the best response.0
what does D mean?
 2 years ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.1
D is just notation for "take the derivative of" with respect to some arbitrary independant variable; at the moment
 2 years ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.1
another equation we need to consider it "amount of material"
 2 years ago

Zekarias Group TitleBest ResponseYou've already chosen the best response.2
The amount of the material can be expressed through total surface area. Thus \[A_{t}=4bh+b^{2}\]But \[h=\frac{ 4000 }{ b^{2} }\] Now insert the expression of h in At, the take derivative.
 2 years ago

zaphod Group TitleBest ResponseYou've already chosen the best response.0
i dont understand ><
 2 years ago

Zekarias Group TitleBest ResponseYou've already chosen the best response.2
dw:1349789802165:dw
 2 years ago

zaphod Group TitleBest ResponseYou've already chosen the best response.0
now i get it
 2 years ago

Zekarias Group TitleBest ResponseYou've already chosen the best response.2
what did u get?
 2 years ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.1
using the surface area formula pforvided by Zek \[A=4bh+b^2\] \[D[A=4bh+b^2]\] \[D[A]=D[4bh]+D[b^2]\] \[A'=4(D[bh])+2bb'\] \[A'=4(D[b]h+bD[h])+2bb'\] \[A'=4(b'h+bh')+2bb'\] \[A'=4b'h+4bh'+2bb'\] this gives us 2 equations that work together \[A'=4b'h+4bh'+2bb'\]\[0=2bb'h+b^2h'\] just trying to recall if i needed to go thru all that ... if not just for the practice
 2 years ago

Zekarias Group TitleBest ResponseYou've already chosen the best response.2
It is not what I am saying. What I am trying too explain is we have the volume 4000 = hbb and At = 4hb+bb. Now combining this two equations we get\[A_{t}=\frac{ 1600 }{ b }+b^{2}\]Therfore take the derivative at this stage. Will u do that?
 2 years ago

zaphod Group TitleBest ResponseYou've already chosen the best response.0
yes dA/db = 0 \[1600b^{1} + b^{2}\] \[0 = 1600b^{2} + 2b\] solve for b
 2 years ago

Zekarias Group TitleBest ResponseYou've already chosen the best response.2
That is what I am saying. Thanks
 2 years ago

zaphod Group TitleBest ResponseYou've already chosen the best response.0
b = 20 thanks everyone:)
 2 years ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.1
we can prolly assume we can work this by adjusting the base with respect to itself so b'=1 \[A'=4h+4bh'+2b\]\[0=2bh+b^2h'\] \[2b=\frac{b^2h'}{h}\] \[A'=4h2\frac{b^2h'}{h}h'\frac{b^2h'}{h}\]using h=4000b^2, h'=8000b^3 \[A'=4\frac{4000}{b^2}2\frac{b^2\frac{8000^2}{b^6}}{\frac{4000}{b^2}}\frac{b^2\frac{8000}{b^3}}{\frac{4000}{b^2}}\] \[A'=\frac{16000}{b^2}\frac{32000}{b^2}+2b\] \[A'=2b\frac{16000}{b^2}\] \[A'=\frac{2b^316000}{b^2}=0\] \[b=2(1000)^{1/3}=20\]
 2 years ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.1
im sure that was not the simplest route to take lol
 2 years ago

zaphod Group TitleBest ResponseYou've already chosen the best response.0
hehe anyways thanks:)
 2 years ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.