Question

use the values in the table to find the value of \\(r\\).

\

$$\begin{tabular}{|c|c|} \\hline volume (liters) & pressure (kilopascals) \\\\ \\hline 4.155 & 2 \\\\ \\hline 16.62 & 0.5 \\\\ \\hline 33.24 & 0.25 \\\\ \\hline \\end{tabular}$$

\\(r = \\)

Explanation:

🆕 New Concept Discovered: Inverse Variation and Constant of Proportionality
Two quantities vary inversely when their product is constant.

Step 1: Identify the relationship

Looking at the table, as Volume (\(V\)) increases, Pressure (\(P\)) decreases. We test if their product is constant:

$$ R = P \times V $$

Step 2: Calculate the constant \(R\)

Using the first row:

$$ R = 4.155 \times 2 = 8.31 $$

Using the second row to verify:

$$ R = 16.62 \times 0.5 = 8.31 $$

Using the third row to verify:

$$ R = 33.24 \times 0.25 = 8.31 $$

Answer:

8.31