anonymous
  • anonymous
A box with an open top is to be constructed by cutting a-inch squares form the corners of a rectangular sheet of tin whose length is twice its width. What size sheet will produce a box having a volume of 480 in3, when a=4?
Algebra
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
A diagram would look like this . . .
1 Attachment
jdoe0001
  • jdoe0001
well, you have a box, that is a rectangular prism what would be the volume of say .... this => |dw:1378490690320:dw| in l, w, h terms
anonymous
  • anonymous
v=lwh

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jdoe0001
  • jdoe0001
yeap, so look at your box :), is the same thing, you want the volume for that, what will it be in terms of the "l w h" given there?
anonymous
  • anonymous
480 = lwh, right?
anonymous
  • anonymous
So, it looks to me like I have to calculate the area of the bottom, since there is no top, and solve for w. Then, multiply by 2 for length. But I don't see where a fits in
jdoe0001
  • jdoe0001
yes, thus we could say that \(\bf a = 4\\ volume = length \times width \times height\\ -------------------------\\\qquad \\ height = a = 4\qquad length = 2x-2a \implies 2x-2(4) \implies 2x-8\\ width = x-2a \implies x-2(4) \implies x-8\\ \textit{desired volume} = 480\\\qquad \\ -------------------------\\ 480 = (4) \times (2x-8) \times (x-8)\)
jdoe0001
  • jdoe0001
it will end up as a quadratic equation btw, so you'd need to equate it to 0, and solve for "x" a quadratic will give you 2 values, one will fit the context
anonymous
  • anonymous
Ok, cool. Thanks a lot!

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