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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 :)
 one year ago
 one year ago
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 :)
 one year ago
 one year ago

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zaphodBest ResponseYou've already chosen the best response.0
@satellite73 @Callisto @Omniscience @amistre64
 one year ago

amistre64Best ResponseYou've already chosen the best response.1
dw:1349789270142:dw \[b*b*h=4000\]
 one year ago

amistre64Best ResponseYou've already chosen the best response.1
and theres some calculus involved to find minimum stuff eh
 one year ago

amistre64Best 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 :)
 one year ago

amistre64Best 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
 one year ago

amistre64Best ResponseYou've already chosen the best response.1
another equation we need to consider it "amount of material"
 one year ago

ZekariasBest 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.
 one year ago

ZekariasBest ResponseYou've already chosen the best response.2
dw:1349789802165:dw
 one year ago

amistre64Best 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
 one year ago

ZekariasBest 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?
 one year ago

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

ZekariasBest ResponseYou've already chosen the best response.2
That is what I am saying. Thanks
 one year ago

zaphodBest ResponseYou've already chosen the best response.0
b = 20 thanks everyone:)
 one year ago

amistre64Best 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 \[A'=4\frac{4000}{b^2}2\frac{b^2\frac{8000^2}{b^6}}{\frac{4000}{b^2}}\frac{b^2\frac{8000}{b^3}}{\frac{4000}{b^2}}\] \[A'=\frac{16000}{b^2}\frac{32000}{b^2}+2b\] \[A'=2b\frac{16000}{b^2}\] \[A'=\frac{2b^316000}{b^2}=0\] \[b=2(1000)^{1/3}=20\]
 one year ago

amistre64Best ResponseYou've already chosen the best response.1
im sure that was not the simplest route to take lol
 one year ago
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