Inverse Variation: Solving Problem Formula

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SUMMARY

The formula for inverse variation between pressure \( P \) and area \( A \) is defined as \( P = \frac{k}{A} \), where \( k \) is the constant of proportionality. Given the values \( (A, P) = (40, 4) \), substituting these into the equation allows for the calculation of \( k \). The resulting value of \( k \) confirms the relationship between pressure and area in this context.

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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:

$$P=\frac{k}{A}\tag{1}$$

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:

$$(A,P)=(40,4)$$

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. ;)
 

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