Question

question 23 - of 24 step 2 of 2 an open - top box is to be constructed from a sheet of tin that measures 22 inches by 14 inches by cutting out squares from each corner as shown and then folding up the sides. let v(x) denote the volume of the resulting box. step 2 of 2: among the values of x for which v(x) = 0, which are physically possible? l = 22 inches w = 14 inches answerhow to enter your answer (opens in new window) 2 points if necessary, separate multiple answers with a comma.

Explanation:

Step 1: Recall Volume Formula

The volume \( V(x) \) of the box is \( V(x) = x(22 - 2x)(14 - 2x) \). Set \( V(x) = 0 \):
\( x(22 - 2x)(14 - 2x) = 0 \).

Step 2: Solve for \( x \)

Solve each factor:

• \( x = 0 \) (physical: cutting no squares, possible).
• \( 22 - 2x = 0 \Rightarrow x = 11 \) (physical: \( 14 - 2(11) = -8 \), invalid length).
• \( 14 - 2x = 0 \Rightarrow x = 7 \) (physical: \( 22 - 2(7) = 8 \), valid length).

Answer:

0, 7