Question

for the inverse variation equation \\(p = \frac{8}{v}\\), what is the value of \\(v\\) when \\(p = \frac{1}{2}\\)?

\\(\bigcirc\\) \\(\frac{1}{16}\\)

\\(\bigcirc\\) \\(\frac{1}{4}\\)

\\(\bigcirc\\) 4

\\(\bigcirc\\) 16

Explanation:

🆕 New Concept Discovered: Inverse Variation Equations
One variable goes up as the other goes down.

Step 1: Substitute the given value

Substitute \( p = \frac{1}{2} \) into the given equation \( p = \frac{8}{V} \):

$$ \frac{1}{2} = \frac{8}{V} $$

Step 2: Solve for V

Cross-multiply to solve the proportion:

$$ 1 \cdot V = 8 \cdot 2 $$

$$ V = 16 $$

Answer:

16