Inverse Variation: Solving Problem Formula

In summary, inverse variation is a mathematical relationship where one variable increases while the other decreases in a constant and proportional manner. To solve problems involving inverse variation, the formula y = k/x can be used. It can be represented graphically by a hyperbola and the constant of variation (k) represents the proportionality constant. Inverse variation can also be applied in real-life situations, such as speed and time, and Boyle's Law.
  • #1
Coder74
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What is the formula to solving a problem like this?
Thanks in advance!

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The statement that pressure $P$ varies inversely with area $A$ may be written mathematically as:

\(\displaystyle P=\frac{k}{A}\tag{1}\)

Where $k$ is called the constant of proportionality. We may determine $k$ from the information provided, namely that we know the pressure for a given area. We are given:

\(\displaystyle (A,P)=(40,4)\)

Substitute that ordered pair into equation (1), and then solve for $k$...what do you get? You should in fact find that the value of $k$ makes perfect sense here. ;)
 

FAQ: Inverse Variation: Solving Problem Formula

What is inverse variation?

Inverse variation is a mathematical relationship between two variables in which one variable increases while the other decreases, or vice versa, in a constant and proportional manner.

How do you solve problems involving inverse variation?

To solve problems involving inverse variation, you can use the formula y = k/x, where y and x are the two variables and k is the constant of variation. Simply plug in the given values and solve for the missing variable.

Can inverse variation be represented graphically?

Yes, inverse variation can be represented graphically by a hyperbola. As one variable increases, the other decreases, resulting in a curved line that approaches but never touches the axes.

What is the significance of the constant of variation in inverse variation?

The constant of variation (k) in inverse variation represents the proportionality constant. It remains the same for all values and is used to find the missing variable in the inverse variation formula.

Can inverse variation be applied in real-life situations?

Yes, inverse variation can be applied in various real-life situations, such as the relationship between speed and time, where speed increases as time decreases, and the relationship between pressure and volume in Boyle's Law.

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