Final answer:
The constant of proportionality for the height of the DVD cases stack is determined by dividing the height by the number of cases. To find the constant, use the given information for the stack with 8 cases. Once found, apply the constant to determine the height of a stack with 14 cases.
Step-by-step explanation:
The constant of proportionality (k) is found by dividing the height (h) by the number of cases (n) in the stack. Mathematically, this is expressed as k = h / n.
Given the stack with 8 cases, let's say the height is 32 units. Therefore, k = 32 / 8 = 4. Now, with the constant established, you can use it to find the height of a stack with 14 cases: h₍₁₄₎ = k × n₍₁₄₎ = 4 × 14 = 56.
In summary, the constant of proportionality is determined by the initial stack with 8 cases. The height of this stack is divided by the number of cases to find the constant. Once the constant is known, it can be applied to find the height of any stack in this proportional relationship. Therefore, the height of a stack with 14 cases is 56 units.