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For a certain type of rope, the equation $y=900a{x}^2$, where $a$ is a constant, gives the estimated breaking strength $y$, in pounds, of a rope with a circumference of $x$ inches. Based on this equation, if a rope of this type has a circumference of $1.75\text{ inches}$, it has an estimated breaking strength of $3,858.75\text{ pounds}$. What is the estimated breaking strength, in pounds, of a rope of this type that has a circumference of $3.50\text{ inches}$?

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