Difference between revisions of "2013 AIME II Problems"
| Line 2: | Line 2: | ||
==Problem 1== | ==Problem 1== | ||
| + | |||
| + | ==Problem 2== | ||
| + | |||
| + | ==Problem 3== | ||
| + | A large candle is <math>119</math> 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 <math>10</math> seconds to burn down the first centimeter from the top, <math>20</math> seconds to burn down the second centimeter, and <math>10k</math> seconds to burn down the <math>k</math>-th centimeter. Suppose it takes <math>T</math> seconds for the candle to burn down completely. Then <math>\tfrac{T}{2}</math> seconds after it is lit, the candle's height in centimeters will be <math>h</math>. Find <math>10h</math>. | ||
| + | |||
| + | [[2013 AIME II Problems/Problem 3|Solution]] | ||
Revision as of 14:54, 4 April 2013
| 2013 AIME II (Answer Key) | AoPS Contest Collections • PDF | ||
|
Instructions
| ||
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
to 
, inclusive. Your score will be the number of correct answers; i.e., there is neither partial credit nor a penalty for wrong answers.Problem 1
Problem 2
Problem 3
A large candle is 
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 
seconds to burn down the first centimeter from the top, 
seconds to burn down the second centimeter, and 
seconds to burn down the 
-th centimeter. Suppose it takes 
seconds for the candle to burn down completely. Then 
seconds after it is lit, the candle's height in centimeters will be 
. Find 
.
