The volume of a chemical solution in a tank is described by the formula \(\dfrac{kT^2c}{p},\) where k is a constant, T

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The volume of a chemical solution in a tank is described by the formula \(\dfrac{kT^2c}{p},\) where k is a constant, T is the temperature, c is the concentration of the chemical solution, and p is the atmospheric pressure. The solution in the tank can be either hot or cold. When hot, c if half of what it is when cold, p is double what it is when cold, and T is triple what it is when cold.

If the tank can be no more than 3/4 full when hot for safety reasons, what is the maximum fraction of capacity of which the tank can be filled when the solution is cold?

A. 1/9
B. 1/6
C. 1/5
D. 1/3
E. 2/3

OA D