anonymous
  • anonymous
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 :)
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
@satellite73 @Callisto @Omniscience @amistre64
amistre64
  • amistre64
is this roll call?
anonymous
  • anonymous
here!

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
yes?
amistre64
  • amistre64
|dw:1349789270142:dw| \[b*b*h=4000\]
amistre64
  • amistre64
and theres some calculus involved to find minimum stuff eh
amistre64
  • amistre64
\[b^2h=4000\] \[D[b^2h=4000]\] \[D[b^2h]=D[4000]\] \[D[b^2]h+b^2D[h]=D[4000]\] \[2bb'h+b^2h'=0\] its been awhile since i tried figuring this one out, but hheres my first idea :)
anonymous
  • anonymous
what does D mean?
amistre64
  • amistre64
D is just notation for "take the derivative of" with respect to some arbitrary independant variable; at the moment
amistre64
  • amistre64
another equation we need to consider it "amount of material"
anonymous
  • anonymous
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.
anonymous
  • anonymous
i dont understand ><
anonymous
  • anonymous
|dw:1349789802165:dw|
anonymous
  • anonymous
now i get it
anonymous
  • anonymous
what did u get?
amistre64
  • amistre64
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
anonymous
  • anonymous
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?
anonymous
  • anonymous
yes dA/db = 0 \[1600b^{-1} + b^{2}\] \[0 = -1600b^{-2} + 2b\] solve for b
anonymous
  • anonymous
That is what I am saying. Thanks
anonymous
  • anonymous
b = 20 thanks everyone:)
amistre64
  • amistre64
we can prolly assume we can work this by adjusting the base with respect to itself so b'=1 \[A'=4h+4bh'+2b\]\[0=2bh+b^2h'\] \[2b=\frac{-b^2h'}{h}\] \[A'=4h-2\frac{b^2h'}{h}h'-\frac{b^2h'}{h}\]using h=4000b^-2, h'=-8000b^-3 \[A'=4\frac{4000}{b^2}-2\frac{b^2\frac{-8000^2}{b^6}}{\frac{4000}{b^2}}-\frac{b^2\frac{-8000}{b^3}}{\frac{4000}{b^2}}\] \[A'=\frac{16000}{b^2}-\frac{32000}{b^2}+2b\] \[A'=2b-\frac{16000}{b^2}\] \[A'=\frac{2b^3-16000}{b^2}=0\] \[b=2(1000)^{1/3}=20\]
amistre64
  • amistre64
im sure that was not the simplest route to take lol
anonymous
  • anonymous
hehe anyways thanks:)

Looking for something else?

Not the answer you are looking for? Search for more explanations.