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]="-1.999,8.601,1.961,-2.159,3.521,-7.599,-7.279,-2.759,1.001,-3.719,5.161,2.241,0.561,-7.319,-7.839,-2.279,-1.039,1.041,-9.559,5.361";

`w=`functoproc[1001] = 1; vlist[1001]="x"; flist[1001]=""; pts[1001]="5.721,-1.799,4.321,7.401,7.761,1.841,6.721,6.041,7.201,4.801,0.841,-2.359,-5.959,7.921,-8.479,-0.159,-8.639,0.361,-5.039,-9.679";

`h=`functoproc[1002] = 1; vlist[1002]="x"; flist[1002]=""; pts[1002]="1.401,-7.279,2.681,1.641,3.961,9.641,2.201,-2.919,1.081,8.601,4.361,-6.679,4.321,6.761,3.601,-1.879,-9.559,-8.239,-9.279,2.961";

`V=`functoproc[1003] = 1; vlist[1003]="x"; flist[1003]=""; pts[1003]="-9.159,4.161,4.281,9.001,0.481,-7.559,-0.679,-8.919,8.521,-3.399,3.241,-3.479,2.241,5.761,-0.599,-8.599,8.561,0.961,-9.719,-5.599"; - 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` .