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Cookies are packaged in boxes that measure 18cm by 20cm by 6cm. A larger box is being...

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Cookies are packaged in boxes that measure 18cm by 20cm by 6cm. A larger box is being designed by increasing the length, width, and height of ...

the smaller box by the same length so that the volume is at least 5280 cm^3. What are the minimum dimensions of the larger box?

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The volume of a box is calculated by V = length times width times height.  The volume of the box is V=(18)(20)(6). The volume of the larger box is V=(18+x)(20+x)(6+x) where x represents the increase for each edge. The inequality needed to be solved to find x is:

`(x+18)(x+20)(x+6)>=5280`

`(x^2+38x+360)(x+6)>=5280`

`x^3+44x^2+588x+2160>=5280`

`x^3+44x^2+588x-3120>=0`

Graphing the polynomial, the only x-intercept is at x=4.

The dimensions of the larger box are: 18+4=22, 20+4=24, and 6+4=10.

22 cm, 24 cm, and 10 cm.

 

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