R proportional to [A]^2
R proportional to 1/[B]
R proportional to [A]^2/[B]
B increased by 100%, therefore B becomes 2B
R is now proportional to [A]^2/2[B]
to keep it proportional to [A]^2/[B] Numerator should become twice too. Or, A should become sqrt(2)A
sqrt(2)A ~ 1.4A
Or A should approx increase by 40%
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