What are the dimensions of the boxes? - what are the dimensions of a of a dvd
A company wants to take advantage of 48IN ^ 3 volume of sheets of cardboard 8 inches by 10 inches by cutting squares from each corner. How big are the squares of Nice? What are the dimensions of the boxes?
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I continue to come near the answer, but not quite. Can someone tell me in the right direction or show me how you could do that?
What Are The Dimensions Of A Of A Dvd What Are The Dimensions Of The Boxes?
3 comments:
Factor 48: 2 ^ 4 * 3
If they cut the field, they fold.
The length of one side of the square = s
This means that
(s) (8-2s) (10-2) = 48
You can solve, but you take two long. The side of the square should be a factor of 48. If we are by a factor (eg, sharing 2) of 48, you get 24th Now you have two factors of 24, which are from 8 a.m. to 10 p.m. the same distance. Let's see ... 4 a.m. to 6 p.m. to work (8-4 = 10-6, right?). Therefore, the answer is 4x6x2.
x = one side of the square are cut from the corners
The basic dimensions (8-2x) by (10-2x)
The height is x.
Equal volumes (8-2x) (10-2x) (x) = 48
80x-36x ² ³ = 4 x 48
4x-36x ² ³ 80 x 48 = 0
x-9x ² ³ 20 x 12 = 0, must be rational roots sentence can factor or a graphing calculator to find the zeros
(x-1) (x ²-8x +12) = 0
(x-1) (x-6) (x-2) = 0
x = 1 inch squares 1 by "1", the image is 6 "8" by 1 "
x = 2 cm square is 2 "by 2", the picture is 4 inches by 6 inches by 2 "
x = 6 cm, not because the board is not big enough
Take him to see:
Dimensions of the box is 8 x - 2 x 10 - 2x
(2x, because the city cut off from each side)
same volume = x (8 - 2x) (10 - 2x) = 48
So:
x (80-36x + 4x ^ 2) = 48
4x ^ 3 - 36x ^ 2 + 80x = 48
4x ^ 3 - 36x ^ 2 + 80x - 48 = 0
must be within the range (0, 4), so that the dimensions, the positive
4 (x ^ 3 - 9x ^ 2 + 20x - 12) = 0
by inspection of the coefficients, x = 1 is a root of
x ^ 3 - 9x ^ 2 + 20x - = (x - 1) (x ^ 2 - 8x 12 + 12)
Factoring more information:
x ^ 2 - 8x + 12 = (x - 6) (x - 2)
Thus, the roots are x = 1, x = 2 and x = 6
but only 1 and 2 are in the desired domain
if x = 1, size 1 x 6 x 8 = 48
When x = 2, size 2 x 4 x 6 = 48
for 1 or 2 inches to work on a volume of 48IN give ^ 3
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Edit: Blake nice approach ... very intuitive
Should, however, for completeness, verify the factor of 1, as follows:
48 = 1 * 2 * 2 * 2 * 2 * 3
Analysis, it would also includeUde 1 6 / 8
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