An open box is to be made from a square piece of cardboard having dimensions 34 inches by 34 inches by cutting out squares of area from each corner as shown in the figure below.If the volume of the box is given by state the domain of V .
E) all real numbers

Question

An open box is to be made from a square piece of cardboard having dimensions 34 inches by 34 inches by cutting out squares of area  from each corner as shown in the figure below.If the volume of the box is given by  state the domain of V .   
E) all real numbers

Quizplus · Accepted Answer

The volume of the box is given by: V = (34-2x)(34-2x)x where x is the length of the side of the square cut out from each corner. To ensure that the box is open, we need to have: 34-2x > 0 which gives: x < 17 Also, the volume V must be positive. So we have: (34-2x)(34-2x)x > 0 which implies that: x > 0 and 17-x > 0 or 0 < x < 17 Therefore, the domain of V is: 0 < x < 17 and the best choice is B.

An Open Box Is to Be Made from a Square