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]="-8.319,-7.559,-8.279,-9.079,5.841,-7.919,9.241,-4.039,-3.359,9.441,-0.999,-4.479,8.081,-9.879,4.321,-7.079,5.481,5.361,5.281,-3.559";

`w=`functoproc[1001] = 1; vlist[1001]="x"; flist[1001]=""; pts[1001]="4.441,1.121,-7.999,-3.079,-7.519,8.441,-3.479,-1.279,5.561,3.601,3.521,3.361,4.321,-0.959,-9.999,-9.039,-5.879,5.121,9.601,4.401";

`h=`functoproc[1002] = 1; vlist[1002]="x"; flist[1002]=""; pts[1002]="3.201,7.521,-1.919,-0.038999999999999,1.761,-3.359,2.641,-7.599,9.401,-7.679,-0.479,2.161,-4.039,2.881,3.321,0.721,1.761,-1.279,-3.199,1.161";

`V=`functoproc[1003] = 1; vlist[1003]="x"; flist[1003]=""; pts[1003]="3.841,5.241,-9.359,-4.799,3.641,9.201,-9.439,-1.999,1.121,6.001,-2.999,-8.079,3.281,-2.919,-1.119,-3.199,6.921,-2.879,8.001,3.401"; - 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` .