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]="5.601,3.961,9.201,-9.479,2.361,-3.559,-3.759,-3.159,4.561,9.201,-3.319,-5.359,6.041,-4.999,1.441,-6.719,-9.759,-3.159,3.281,-0.639";

`w=`functoproc[1001] = 1; vlist[1001]="x"; flist[1001]=""; pts[1001]="1.401,-6.439,-9.119,-5.799,-0.599,0.241,-8.639,-0.839,-7.399,4.121,-6.919,-6.519,8.041,7.201,-5.119,8.081,-9.399,-0.639,-0.799,-1.879";

`h=`functoproc[1002] = 1; vlist[1002]="x"; flist[1002]=""; pts[1002]="8.641,2.641,-8.679,-0.319,-5.039,-4.399,-3.639,8.561,-9.999,1.681,3.641,4.561,0.561,-5.199,4.961,4.401,9.681,-8.799,3.161,-4.519";

`V=`functoproc[1003] = 1; vlist[1003]="x"; flist[1003]=""; pts[1003]="5.281,-4.319,1.881,0.040999999999999,-2.399,9.881,-8.559,-5.279,0.241,-1.199,-7.599,-1.119,-5.119,-2.119,-6.759,-2.239,8.881,-3.039,0.121,-7.639"; - 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` .