A designer is creating various open-top boxes by cutting four equally-sized squares from the corners of a standard sheet of 8.5 inch by 11 inch paper, and then folding up and securing the resulting 'flaps' to be the sides of the box.

Let `x` represent the varying side length of the square cutouts in inches. Let `l,w,` and `h` represent the varying length, width and height of the box (in inches), respectively. Note that the width and length dimensions are such that `w < l` . Let `V` represent the varying volume of the box in cubic inches.

- Write formulas for length, width, and volume of the box, each in terms of `x` .

`l=`functoproc[1000] = 1; vlist[1000]="x"; flist[1000]=""; pts[1000]="-3.399,6.921,-9.519,5.481,-6.239,-0.679,-7.919,1.721,6.201,6.441,2.721,-2.639,6.561,3.681,7.121,6.121,6.081,-0.639,-7.679,8.361";

`w=`functoproc[1001] = 1; vlist[1001]="x"; flist[1001]=""; pts[1001]="-4.719,6.281,6.961,-5.479,-4.279,-3.839,-6.879,-5.519,-7.559,-5.679,-6.999,-1.759,0.521,2.601,-8.359,7.281,-1.479,3.041,1.161,5.161";

`h=`functoproc[1002] = 1; vlist[1002]="x"; flist[1002]=""; pts[1002]="-6.639,0.841,7.681,0.401,0.321,9.001,-2.039,8.361,-2.919,-5.879,2.161,4.241,-9.879,8.401,1.281,2.881,3.961,5.281,8.121,-5.679";

`V=`functoproc[1003] = 1; vlist[1003]="x"; flist[1003]=""; pts[1003]="-2.879,-6.119,-7.599,-5.879,-0.119,9.641,-6.719,-1.679,4.361,-2.239,5.041,-1.279,6.201,-7.199,-3.479,1.761,8.241,-7.759,-4.719,5.721"; - Given the following starting and ending values of `x` , find the change in `x` and the resulting change in `l` .

`x` changes from ... `Delta x` `Delta l` 0 to 0.5 in calctoproc[1004] = 1; calcformat[1004] = ''; calctoproc[1007] = 1; calcformat[1007] = ''; 0.5 to 1.5 in calctoproc[1005] = 1; calcformat[1005] = ''; calctoproc[1008] = 1; calcformat[1008] = ''; 1 to 4 in calctoproc[1006] = 1; calcformat[1006] = ''; calctoproc[1009] = 1; calcformat[1009] = '';

Does `l` change at a constant rate with respect to `x` ? If yes, enter the appropriate value to complete the statement. If no, enter "DNE".

`Delta l=`calctoproc[1010] = 1; calcformat[1010] = ''; `* Delta x` .