If a ∝ b and a ∝ c, why do you multiply b and c together to find the constant? I also noticed something, but am not sure of the reason why. If you find the constants individually for each expression and combine them all, you get a the the power of the number of expressions e.g. a ∝ b a ∝ c a ∝ d So the individual constants would be say, k1, k2 and k3 respectively. If you then multiply it all together a ∝ (k1b)(k2c)(k3d) You get a^3 If there're expressions, then a^4 etc. All of the numbers I've tried so far have yielded the result but I'm not sure why that's happening Thanks
You don't. If [itex]a\propto b[/itex] and [itex]a \propto c[/itex], then that tells you that [itex]a = k_3 bc[/itex], where k_{3} is some constant of proportionality. This is because: Given both [itex]a = k_1(c)b[/itex], where k_{1}(c) is a proportionality factor that you know depends on c, and [itex]a = k_2(b)c[/itex], where k_{2}(b) is a proportionality factor that depends on b, you can divide the two equations to get [tex]1 = \frac{k_1(c)b}{k_2(b)c},[/tex] or [tex]\frac{k_1(c)}{c} = \frac{k_2(b)}{b}.[/tex] However, by assumption k1 depends only on c and k2 depends only on b, so the only way this relation can hold is if both sides are equal to the same constant, say k_{3}. It follows then that [itex]a = k_3 bc[/itex]. I'm not sure what you're talking about here. If a is proportional to all those variables, then [itex]a = k_4bcd[/itex], by similar logic to what I did above. I'm not sure where these powers of a comes from.