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]="-2.679,-9.199,4.281,8.921,-8.639,4.441,-1.759,6.961,4.001,2.081,-9.639,-1.079,9.481,2.401,7.281,8.281,2.681,-3.799,8.561,8.041";

`w=`functoproc[1001] = 1; vlist[1001]="x"; flist[1001]=""; pts[1001]="5.921,8.081,0.001,0.121,8.801,-8.839,7.001,-5.119,-5.359,-3.639,2.601,2.121,2.321,6.921,-7.679,-2.159,-9.959,-0.119,3.841,-0.399";

`h=`functoproc[1002] = 1; vlist[1002]="x"; flist[1002]=""; pts[1002]="0.921,-7.839,0.481,4.321,-0.479,-8.439,-2.399,-4.119,-8.559,6.441,6.601,-8.639,7.801,9.281,-2.319,1.441,9.361,-2.319,-3.959,-4.239";

`V=`functoproc[1003] = 1; vlist[1003]="x"; flist[1003]=""; pts[1003]="-6.759,5.881,-3.919,-8.399,5.481,1.721,-7.639,1.361,1.961,-5.919,7.601,-5.199,-9.439,1.441,4.241,-1.239,3.841,-8.319,-6.559,-5.039"; - 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` .