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1. Candle height at half burn time ●●○○○ 20 ptsA large candle is $119$ centimeters tall. It is designed to burn down more quickly when it is first lit and more slowly as it approaches its bottom. Specifically, the candle takes $10$ seconds to burn down the first centimeter from the top, $20$ seconds to burn down the second centimeter, and $10k$ seconds to burn down the $k$-th centimeter. (The candle burns down each individual centimeter at a fixed rate.) Suppose it takes $T$ seconds for the candle to burn down completely. Compute the candle's height in centimeters $\tfrac{T}{2}$ seconds after it is lit.