Question
An open box is made by removing squares of length x in each corner of 8 unit by 6 unit rectangular piece ofcardboard. HOw long is × so that the volume of the resulting box is 192unit.
Answers
Reiny
base will be 8-2x by 6-2x
height = x
volume = x(8-2x)(6-2x) = 192 , where x<3
x(48 - 28x + 4x^2 = 192
4x^3 - 28x^2 + 48x - 192 = 0
x^3 - 7x^2 + 12x - 48 = 0
tried all the "nice" factors of 48, and found no solution.
So I let Wolfram graph it and solve it to ge
x = appr 6.3
but that would make the length and width turn out to be negative numbers,
your problem has no solution.
height = x
volume = x(8-2x)(6-2x) = 192 , where x<3
x(48 - 28x + 4x^2 = 192
4x^3 - 28x^2 + 48x - 192 = 0
x^3 - 7x^2 + 12x - 48 = 0
tried all the "nice" factors of 48, and found no solution.
So I let Wolfram graph it and solve it to ge
x = appr 6.3
but that would make the length and width turn out to be negative numbers,
your problem has no solution.