Advanced functions problem - XP Math - Forums

 XP Math - Forums Advanced functions problem

 03-21-2010 #1 magmagod Last Achievements   Join Date: Mar 2010 Posts: 9 Advanced functions problem A box will be made of 2 identical pieces each with 3 sides. They will fit together to make a 6 sided box. Each piece will be cut from one piece of metal that is 20 cm by 20 cm by cutting out a square corner and folding up the two resulting flaps. What dimensions of the square cut-out will produce a box with a volume of 1125 cm^3? I tried solving it, and i came up with: 1125=(20-2x)(20-2x)(x) 1125=(400-40x-40x+4x^2)(x) 1125=(400-80x+4x^2)(x) 1125=(4x^2-80x+400)(x) At this point i was clueless.. anybody? i mean if you factored it youd get 4(x-10)^2(x) then im just clueless as to how this relates to the answer...please help me here math people.
 03-23-2010 #2 jmw106462 Last Achievements     Join Date: Feb 2010 Posts: 388 Me, I'm really not good at this stuff so maybe you should email Mr.hui He might know. __________________ Please refrain from sending me frivolous PM's
03-23-2010   #3

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problem

Quote:
 Originally Posted by jmw106462 Me, I'm really not good at this stuff so maybe you should email Mr.hui He might know.
I like jmw 106462 am not a complete expert
So what i do have is a site called
http://www.artofproblemsolving.org
This place it is completely about math and people their are very good
Either
Middle School Classroom Math (10-13)
OR
High School Basics (12-16)

03-24-2010   #4
MAS1

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Quote:
 Originally Posted by magmagod A box will be made of 2 identical pieces each with 3 sides. They will fit together to make a 6 sided box. Each piece will be cut from one piece of metal that is 20 cm by 20 cm by cutting out a square corner and folding up the two resulting flaps. What dimensions of the square cut-out will produce a box with a volume of 1125 cm^3? I tried solving it, and i came up with: 1125=(20-2x)(20-2x)(x) 1125=(400-40x-40x+4x^2)(x) 1125=(400-80x+4x^2)(x) 1125=(4x^2-80x+400)(x) At this point i was clueless.. anybody? i mean if you factored it youd get 4(x-10)^2(x) then im just clueless as to how this relates to the answer...please help me here math people.
I think you are close, but your equation is not quite correct. As I understand the problem you will be taking two 20x20 cm sheets of metal, cut a single square out of the corner of each sheet (NOT 4 square corners for each sheet), and fold each sheet so it has 3 surfaces. The two 3-surfaced pieces now can be fitted together into one box with a volume of 1125 cm^3. Therefore the dimensions of the box will be:

1125 = (20 - x)(20 - x)(x)
1125 = 400x - 40x^2 + x^3
0 = x^3 - 40x^2 + 400x - 1125

Solving the cubic equation gives x = 26.518, 5, and 8.486122

You can throw out the 26.518 number because 20 - 26.518 = -6.518 which is not possible. However, the other two values are the dimension of the square cutout, either 5 x 5, or 8.486122 x 8.486122 cm.

 03-25-2010 #5 jmw106462 Last Achievements     Join Date: Feb 2010 Posts: 388 What he said ^^ __________________ Please refrain from sending me frivolous PM's
 03-25-2010 #6 magmagod Last Achievements   Join Date: Mar 2010 Posts: 9 Wow thanks alot...now i get it.
 04-01-2010 #7 jmw106462 Last Achievements     Join Date: Feb 2010 Posts: 388 Yeah Mas1 is very smart! __________________ Please refrain from sending me frivolous PM's

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