anonymous
  • anonymous
An open box is to be made from a square piece of material with a side length of 10 inches by cutting equal squares from the corners and turning up the sides. What size of a square would you cut off if the volume of the box must be 48 cubic inches.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
|dw:1332561462328:dw|
AccessDenied
  • AccessDenied
well, all four sides would be the same since its a square piece of material with side lengths 10 in. |dw:1332561497073:dw| The box we make will look something like... |dw:1332561638263:dw|
anonymous
  • anonymous
thanks for the drawing :)

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anonymous
  • anonymous
I started with v = s^3 so v = 48 my side is 10-2x (10-2x)^3 =48 is that right so far?
anonymous
  • anonymous
then factoring out I got 1000 - 600x + 120x^2 - 8x^3 = 48 952 - 600x +120xx^2 -8x^3 = 0
AccessDenied
  • AccessDenied
well, the box we make is not necessarily a cube, so we can't use the volume of a cube instead, we should use the area of the base, which is the square with sides 10-2x and then the height of the box, x, which is created when we fold those edges up after cutting off the squares with sides x
AccessDenied
  • AccessDenied
|dw:1332562007280:dw| if my drawing can at all help visualize as cluttered as I am making it. :P
anonymous
  • anonymous
im following...can you help me with answer again we are looking for the area CUT out
AccessDenied
  • AccessDenied
the volume of the box would be (10-2x)^2 * x since the base is a square of side-lengths 10-2x and the height is that x we cut out So, because we want the volume to be 48, we set that volume equal to 48 as you did previously (10-2x)^2 * x = 48 (10-2x)(10-2x)(x) = 48 (100 - 40x + 4x^2)(x) = 48 100x - 40x^2 + 4x^3 = 48 4x^3 - 40x^2 + 100x = 48 4x^3 - 40x^2 + 100x - 48 = 0
anonymous
  • anonymous
I got 3 by 3. Thanks much access
AccessDenied
  • AccessDenied
Yeah, that's what I find as well. not sure about this other x-intercept x~0.6277 tho the third x-intercept is cut off from a restriction that x<5
AccessDenied
  • AccessDenied
i guess since its too difficult to measure that value to significant accuracy to get a volume of 48 exactly, that's why you wouldn't use it. lol
anonymous
  • anonymous
So\[x^3-10x+25-12=0 \implies x=3 or x=\frac {7-\sqrt{33}}{2} \] Y'all are correct that it's a solution, but it wouldn't make a very practical size for a box.
AccessDenied
  • AccessDenied
just curious, how did you get that x-value exactly? i just used a graph to get an approximate answer. :P btw, you can use tilde in the eq editor to make spaces, just a helpful thing i saw previously
anonymous
  • anonymous
I used synthetic division to find the factor of (x-3), and the quotient was x^2-7x +4. I set it equal to zero, and used the quadratic formula.
anonymous
  • anonymous
Thanks for the note about the spaces. I obviously need to know that, LOL.
AccessDenied
  • AccessDenied
ohh, okay. I didn't even think about that!

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