MHB Inverse Variation: Solving Problem Formula

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Pressure (P) varies inversely with area (A), expressed by the formula P = k/A, where k is a constant of proportionality. To find k, substitute the given values of area and pressure, specifically (A, P) = (40, 4), into the equation. Solving for k yields a value that aligns with the relationship described. This approach illustrates how inverse variation can be applied to real-world problems involving pressure and area. Understanding this concept is crucial for solving similar mathematical problems effectively.
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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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