HMMT 二月 2000 · 团队赛 · 第 2 题
HMMT February 2000 — Team Round — Problem 2
题目详情
英文原题
- The pri e of a gold ring in a ertain univ erse is prop ortional to the square of its purit yand the ub e of its diameter. The purit y is in v ersely prop ortional to the square of thedepth of the gold mine and dire tly prop ortional to the square of the pri e, while thediameter is determined so that it is prop ortional to the ub e ro ot of the pri e and alsodire tly prop ortional to the depth of the mine. Ho w do es the pri e v ary solely in termsof the depth of the gold mine?
解析
英文解析
- Let =pri e, p =purit y , d =diameter, h =depth of gold mine, k = onstan t. W e are giv eni
2 4 p
2 3 2 3 3 5 1 4 = k p d , p = k , and d = k h . So, = k k k h = k . Th us, k = h ,3
1 2 2 3 1 4 4 4
2 3
h h h
1 1
4 4
and = k h . Th us, p v aries as h .
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