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]="-5.199,0.681,-1.559,8.401,-4.639,9.161,9.081,5.121,2.241,2.201,2.681,0.521,8.201,-8.559,-4.599,-7.599,-4.919,-0.599,-5.679,-5.079";

`w=`functoproc[1001] = 1; vlist[1001]="x"; flist[1001]=""; pts[1001]="8.321,4.721,-3.119,-0.439,-7.079,7.321,1.481,1.121,0.401,-2.519,4.721,2.321,-3.439,-0.759,4.361,-7.799,-8.639,-8.679,-0.879,-2.639";

`h=`functoproc[1002] = 1; vlist[1002]="x"; flist[1002]=""; pts[1002]="8.521,-2.519,8.641,7.121,-0.519,7.961,-6.959,-8.319,1.241,3.041,7.001,6.681,2.961,-3.719,8.681,-7.639,-8.839,-8.079,1.561,-6.879";

`V=`functoproc[1003] = 1; vlist[1003]="x"; flist[1003]=""; pts[1003]="-8.559,8.961,9.281,6.081,-6.119,7.481,-4.559,-6.999,-1.599,6.241,8.641,6.641,-0.879,2.641,-3.359,-1.679,-7.479,0.321,-2.639,-7.439"; - 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` .