Inverse Variation Math Example 4

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Example 4

hard
The pressure \(P\) and volume \(V\) of a gas at constant temperature satisfy \(PV = k\). If \(P = 4\) atm when \(V = 6\) L, find \(P\) when \(V = 8\) L.

Solution

  1. 1
    \(k = PV = 4 \times 6 = 24\).
  2. 2
    \(P = k/V = 24/8 = 3\) atm.
  3. 3
    As volume increases, pressure decreases (Boyle's Law).

Answer

\(P = 3\) atm
Boyle's Law is an inverse variation: \(PV = 24\). Increasing V from 6 to 8 L decreases P from 4 to 3 atm.

About Inverse Variation

A relationship where y=kxy = \frac{k}{x}: as one quantity doubles, the other halves—their product stays constant.

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More Inverse Variation Examples

Example 1 medium

(y) varies inversely with (x), and (y = 8) when (x = 3). Find (k) and the equation. Then find (y) wh

Example 2 hard

Speed and travel time are inversely proportional for a fixed distance. At 60 km/h the trip takes 4 h

Example 3 medium

If (y = k/x) and (y = 12) when (x = 5), find (y) when (x = 15).

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