In each of the following cases, the variable in question varies directly or inversely as specified. We will write the corresponding variation equation using $k$ as the constant of variation.

1. $W$ varies jointly as $c$ and the square of $a$ and inversely as $b$.

$W = k \frac{c \cdot a^2}{b}$

2. $P$ varies directly as the square of $x$ and inversely as $s$.

$P = k \frac{x^2}{s}$

3. The electrical resistance $R$ of a wire varies directly as its length $l$ and inversely as the square of its diameter $d$.

$R = k \frac{l}{d^2}$

4. The acceleration $A$ of a moving object varies directly as the distance $d$ it travels and inversely as the square of the time $r$ it travels.

$A = k \frac{d}{r^2}$

5. The pressure $P$ of a gas varies directly as its temperature $T$ and inversely as its volume $V$.

$P = k \frac{T}{V}$

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Related Questions:

1. What is the significance of the constant $k$ in each variation equation?
2. How does a joint variation differ from a direct or inverse variation?
3. Can you derive the formula for a situation where $W$ varies inversely as both $b$ and $d^2$?
4. How does changing the temperature affect the pressure in the gas variation equation?
5. In the second equation, if $s$ doubles, how does $P$ change?

Tip:

In joint variations, remember that variables can influence the outcome both directly and inversely. Organizing them correctly ensures you write the equation accurately.