Inverse Variation Calculator
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Inverse Variation Formula
The inverse variation formula is:
y = k/x
where:
- y is the dependent variable
- x is the independent variable
- k is the constant of variation
Properties of Inverse Variation
| Property | Description |
|---|---|
| Product | xy = k (constant) |
| Graph | Hyperbola with asymptotes at x = 0 and y = 0 |
| Domain | All real numbers except x = 0 |
| Range | All real numbers except y = 0 |
Common Applications
- Boyle's Law (pressure and volume)
- Electrical resistance and current
- Time and speed relationships
- Work and time relationships
Example Problems
Example 1: Pressure and Volume
If the pressure of a gas is 2 atm when the volume is 4 L, what is the pressure when the volume is 8 L?
P₁V₁ = P₂V₂
2 × 4 = P₂ × 8
P₂ = 1 atm
Example 2: Time and Speed
If it takes 2 hours to travel 60 miles, how long will it take to travel 90 miles at the same speed?
t₁d₁ = t₂d₂
2 × 60 = t₂ × 90
t₂ = 1.33 hours
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