Question

use the inverse variation equation to fill in the table.

\\p = \frac{8.31}{v}\\

volume (liters)	pressure (kilopascals)
b	0.4
415.5	c

\\(a = \\) , \\(b = \\) , \\(c = \\)

Explanation:

🆕 New Concept Discovered: Inverse Variation
When one value goes up, the other goes down.

Step 1: Solve for \( a \)

Substitute \( V = 83.1 \) into the equation:

$$ p = \frac{8.31}{V} $$

$$ a = \frac{8.31}{83.1} $$

$$ a = 0.1 $$

Step 2: Solve for \( b \)

Substitute \( p = 0.4 \) into the equation:

$$ 0.4 = \frac{8.31}{b} $$

Multiply both sides by \( b \):

$$ 0.4b = 8.31 $$

Divide by \( 0.4 \):

$$ b = \frac{8.31}{0.4} $$

$$ b = 20.775 $$

Step 3: Solve for \( c \)

Substitute \( V = 415.5 \) into the equation:

$$ c = \frac{8.31}{415.5} $$

$$ c = 0.02 $$

Answer:

\( a = 0.1 \), \( b = 20.775 \), \( c = 0.02 \)