Mathematics, 11.11.2020 17:00 kaylaelaine18
Jae is constructing an open box from a piece of cardboard that is 9 in. Wide and 12 in. Long. Jae cuts squares of equal size from each corner of the cardboard, and then folds up the sides of the box. Write and simplify a polynomial function V for the volume of the box in terms of x.
Answers: 2
![V = 108\cdot x -42\cdot x^{2}+4\cdot x^{3}\,\,\,[in^{3}]](/tpl/images/0887/7651/f76ff.png)
.
), measured in cubic inches, is described by the volume of a right parellelepiped. That is:
(1)
, 
and 
are the width, length and height of the open box, respectively, measured in inches. Please notice that width of the open box is the width of the piece of cardboard (
), measured in inches, minus two times the side of the cut squares (
), measured in inches, length of the open box is the length of the piece of cardboard (
), measured in inches, minus two times the side of the cut squares and the height of the open box is the side of the cut squares. That is:
(2)
(3)
(4)
(5)
and 
, then the equation above is:![V = (9-2\cdot x)\cdot (12-2\cdot x)\cdot x\,\,\,[in^{3}]](/tpl/images/0887/7651/e9ff9.png)
![V = (108-24\cdot x-18\cdot x+4\cdot x^{2})\cdot x\,\,\,[in^{3}]](/tpl/images/0887/7651/08918.png)
![V = (108-42\cdot x +4\cdot x^{2})\cdot x \,\,\,[in^{3}]](/tpl/images/0887/7651/9b9b5.png)
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Jae is constructing an open box from a piece of cardboard that is 9 in. Wide and 12 in. Long. Jae cu...
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