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]="3.761,6.481,7.681,-6.119,-3.719,-8.319,-9.359,-0.559,9.161,-8.719,-6.839,9.241,3.521,-6.799,8.041,5.641,-1.759,-2.479,-0.079,2.841";

`w=`functoproc[1001] = 1; vlist[1001]="x"; flist[1001]=""; pts[1001]="4.601,5.241,-9.479,-5.639,2.841,5.001,-7.639,-6.999,9.001,8.721,1.001,-4.079,7.841,-2.239,8.801,7.001,4.801,-5.079,-2.479,-9.719";

`h=`functoproc[1002] = 1; vlist[1002]="x"; flist[1002]=""; pts[1002]="-8.599,7.401,-3.359,9.881,2.481,-4.199,-9.199,-4.999,-3.759,7.321,-1.279,5.241,-0.038999999999999,-2.559,5.641,1.281,1.201,4.321,3.281,2.001";

`V=`functoproc[1003] = 1; vlist[1003]="x"; flist[1003]=""; pts[1003]="-9.959,0.001,-4.079,-1.959,-6.559,-2.959,7.321,-0.559,-7.839,-2.279,-2.359,4.881,-6.559,0.281,-7.239,9.241,-7.679,0.401,-9.719,-9.359"; - 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` .