x varies directly as the product of u and v and inversely as their sum. If x = 3 when u = 3 and v = 1, what is the value of x if u = 3 and v = 3?
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Correct Answer: Option C
Explanation:
\(x\propto \frac{uv}{u+v}\\x = \frac{kuv}{u+v}\\K = \frac{x(u+v)}{uv}\\\frac{3(3+1)}{3\times1}\\\frac{3\times4}{3}\\k = 4\\x=\frac{4uv}{u+v}\\x=\frac{4\times 3\times3}{3+3}\\x=\frac{36}{6}\\x=6\)
\(x\propto \frac{uv}{u+v}\\x = \frac{kuv}{u+v}\\K = \frac{x(u+v)}{uv}\\\frac{3(3+1)}{3\times1}\\\frac{3\times4}{3}\\k = 4\\x=\frac{4uv}{u+v}\\x=\frac{4\times 3\times3}{3+3}\\x=\frac{36}{6}\\x=6\)