The root numbers in toothpaste (help)

  • Thread starter venger
  • Start date
  • #1
venger
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0
Pardon me for not using latex.

Homework Statement


A toothpaste box has square ends. The length is 12cm greater than the width. The volume of the box is 135cm^3. What are the dimensions of the box?


Homework Equations


Quadratic theory, Random pluggin for x, common factoring, Family of functions, graph


The Attempt at a Solution


Okay, i need 3 numbers when multiplied, will give me 135...
5 into 135 = 27 into 3 times 3 times 3 = 27
okay, good.
and now I'm stuck
 

Answers and Replies

  • #2
cristo
Staff Emeritus
Science Advisor
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The length is 12cm greater than the width.

Can you use this condition to set up an equation for, say, x; the sides of the square end?
 
  • #3
venger
58
0
Alright im not so stuck anymore, here we go:
V=LWH
135=L(L-12)H
Does this seem right?
 
Last edited:
  • #4
robb_
340
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Well, you have two variables and only one equation.
*edit* where is the 15 on the r.h.s. coming from?
 
  • #5
cristo
Staff Emeritus
Science Advisor
8,140
74
Alright im not so stuck anymore, here we go:
V=LWH
135=L(L-15)H
Does this seem right?
No, where does 15 come from?

The simplest way is to take w, say, as the width of the box(note, this is also the height, since the ends are square). Then, the length l, say, is 12 cm greater than w. So, can you express l in terms of w? Then, your formula v=lwh=135 is correct, so substitute into this (again, noting that w=h).
 
  • #6
venger
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0
Edited... width is 12 cm less than Length
 
  • #7
robb_
340
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okay, now how is the width related to the height?
 
  • #8
venger
58
0
A toothpaste box has square ends. The length is 12cm greater than the width. The volume of the box is 135cm^3. What are the dimensions of the box?
 
  • #9
robb_
340
0
The ends are square, which I think you are denoting each side of the square as height and width. Now the two sides of a square are____?
 
  • #10
venger
58
0
You Smart Little .... Ugh Why am i so Blind.... WOW!!
 
  • #11
robb_
340
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I am blind too, just spent more time in this darkness!
 
  • #12
robb_
340
0
You have the width listed as w. The length is listed as l = w + 12. The height is the other side of the square at the end of the box. What is the relationsip between the width and the height? this will give youone equation with one unknown- no trial and error.
 
  • #13
venger
58
0
humph....
W H are the same therefore W subs H as W^2
V=(W+12)W^2
135=W^3 +12W^2
0=W^3 +12W^2-135
Cannot go any further therefore must use remainder theorem? Cannot use Quadratic theory, since its not a perfect parabola...
 
  • #14
robb_
340
0
Now that looks like the right equation! : )
You have a cubic which in general has three roots.
 
  • #15
venger
58
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but how do i get 5 from that?
 
  • #16
robb_
340
0
To find the solution, now you can guess one of the roots by staring at the equation, then it will reduce to a simpler problem, essentially a quadratic (still a cubic though).
 
  • #17
venger
58
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In other words how do i solve for W?
 
  • #18
robb_
340
0
I dont think that 5 is a solution.
 
  • #19
robb_
340
0
Try a few small integers for w and see if any work.
 
  • #20
venger
58
0
So... Make the question into an equation then break it down until it is simple to guess the variable?
 
  • #21
robb_
340
0
I am not sure what you are asking here. For this cubic, guessing a root is probably the simplest method. Have you found it?
 
  • #22
venger
58
0
ya its three....
 
  • #23
robb_
340
0
good, bye now
 
  • #24
venger
58
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I know I know, I meant i need to use the pluggin theory
 
  • #25
robb_
340
0
Well, i havent heard of the so called plug in theory but that does work here
 
  • #26
venger
58
0
I don't know the real name of plug in theory.. but its a theory
 

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