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]="3.761,8.001,8.961,-5.719,-1.239,-2.279,-7.799,-4.919,3.201,-6.639,3.161,-7.999,-0.599,3.961,4.561,4.521,-6.119,8.321,1.241,3.481";

`w=`functoproc[1001] = 1; vlist[1001]="x"; flist[1001]=""; pts[1001]="7.601,3.321,-8.959,-0.079,4.721,0.081,2.401,5.121,5.361,-1.959,-3.439,7.401,7.321,-7.079,-6.919,9.041,-2.559,-1.599,-8.559,0.441";

`h=`functoproc[1002] = 1; vlist[1002]="x"; flist[1002]=""; pts[1002]="-3.079,-7.239,1.961,-1.279,7.481,-7.719,-3.359,9.641,6.161,-7.639,-8.279,4.321,-3.759,5.921,4.201,2.961,-7.159,8.361,2.681,-7.599";

`V=`functoproc[1003] = 1; vlist[1003]="x"; flist[1003]=""; pts[1003]="-9.439,-6.599,2.601,-6.999,0.881,7.921,-0.359,-9.079,2.081,-5.239,8.801,4.881,-2.839,-5.119,5.281,-6.359,-2.999,2.961,-7.719,2.401"; - 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` .