anonymous
  • anonymous
work check? calculus An open rectangular bow is made from a square peice of metal (each side is 12 inches) by cutting out square corners and folding up the sides. what size corners should be cut to maximize the volume of the box... i got 4 but i don't think that right?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
Bow? If you can draw the picture, then I can try the problem.
anonymous
  • anonymous
|dw:1333416243960:dw|
inkyvoyd
  • inkyvoyd
area of box: 24^2-4x^2

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inkyvoyd
  • inkyvoyd
we seek to maximize (24-2x)(24-2x)(x)
anonymous
  • anonymous
That is the equation, but you have to take the derivative and set equal to zero
anonymous
  • anonymous
couldnt you graph it and find the vertex?
inkyvoyd
  • inkyvoyd
That's the same thing.
anonymous
  • anonymous
You could as long as you are doing so with the derivative.
inkyvoyd
  • inkyvoyd
Finding the vertex is only really possible by taking th derivative
inkyvoyd
  • inkyvoyd
sorry, I thought you were seeking to maximize the volume for the area. Apparently it's just volueme
inkyvoyd
  • inkyvoyd
then only the volume equation applies.
anonymous
  • anonymous
Wait, not the vertex, you find where y=0
inkyvoyd
  • inkyvoyd
(24-2x)(24-2x)(x)=V 4x(12-x)^2=V we set the derivative to 0 after we find it. dV/dx=4x*2(12-x)*-1+((12-x)^2)*4 0=-8x(12-x)+4(12-x)^2 0=(12-x)(48-4x-8x) 0=12(12-x)(4-x) x=12, or x=4.
anonymous
  • anonymous
... so im correct?
inkyvoyd
  • inkyvoyd
Yes. Note that x=/=12 because that would mean you would cut the whole sheet, which makes no sense.
anonymous
  • anonymous
ok thanks

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