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]="-7.799,9.561,-1.399,-4.959,-8.279,-7.239,9.761,-6.319,-0.359,7.321,-2.039,5.041,-1.239,1.201,-8.959,-7.759,7.081,-6.719,7.801,-5.159";

`w=`functoproc[1001] = 1; vlist[1001]="x"; flist[1001]=""; pts[1001]="5.841,7.401,-9.959,-5.159,6.521,9.761,7.721,-5.839,-7.519,-1.999,-8.359,-2.919,-5.719,-9.359,-0.999,-0.199,8.001,-5.319,1.681,5.881";

`h=`functoproc[1002] = 1; vlist[1002]="x"; flist[1002]=""; pts[1002]="-1.999,-1.199,6.601,-2.159,-6.199,5.561,-2.279,-2.719,-4.679,-2.079,-7.879,1.321,4.441,-3.199,1.401,-6.159,-4.079,-6.639,8.841,-0.479";

`V=`functoproc[1003] = 1; vlist[1003]="x"; flist[1003]=""; pts[1003]="5.001,9.041,9.041,-2.879,-7.559,9.361,3.961,1.841,-6.559,1.361,7.001,9.401,-7.279,-9.759,-2.759,8.961,1.841,6.721,-7.999,-9.719"; - 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` .