To find the value that fits the inequality \( 99 < 9^2 < x < 10^2 \), let's first calculate the values of \( 9^2 \) and \( 10^2 \):
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Calculate \( 9^2 \): \[ 9^2 = 81 \]
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Calculate \( 10^2 \): \[ 10^2 = 100 \]
Now the inequality can be rewritten with these values:
\[ 99 < 81 < x < 100 \]
However, since \( 81 < 99 \), this inequality does not hold as stated. It appears there may have been a misunderstanding in the formulation of the inequality. The correct setup should be looking for a value between \( 81 \) and \( 100 \) because the left portion states \( 99 < 81 \), which is false.
Assuming you might be looking for a number \( x \) such that:
\[ 81 < x < 100 \]
Then any number between \( 81 \) and \( 100 \) (like \( 90 \), for instance) would satisfy this modified condition. Please clarify if there's a mistake or if you're looking for a specific type of number!