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]="7.161,9.201,-9.439,6.801,-6.679,-1.719,-4.799,2.401,4.721,7.561,6.561,-9.279,2.281,-2.399,-5.719,-7.999,8.081,3.641,0.241,-4.439";

`w=`functoproc[1001] = 1; vlist[1001]="x"; flist[1001]=""; pts[1001]="3.401,-6.959,4.721,-4.439,-7.839,4.281,-7.959,-1.079,-5.479,9.601,-5.799,-8.759,-0.839,-3.399,-8.599,-1.839,-0.079,4.121,-6.599,3.201";

`h=`functoproc[1002] = 1; vlist[1002]="x"; flist[1002]=""; pts[1002]="-0.439,0.801,9.441,3.441,9.161,1.561,-8.999,-2.279,1.961,-4.799,4.681,-9.919,-1.639,-9.039,1.321,3.081,1.481,6.121,-3.879,4.641";

`V=`functoproc[1003] = 1; vlist[1003]="x"; flist[1003]=""; pts[1003]="-1.359,-4.039,-0.038999999999999,-8.479,4.281,2.161,-9.679,-2.679,9.961,-2.319,-6.199,-6.079,4.401,2.241,9.841,6.721,-7.119,-2.919,4.401,-5.359"; - 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` .