1.In a rectangle ABCD, AB=100 and BC=70. A beam of light leaves a and travels through P which has perpendicular distance 3 and 4 from AB and AD respectively. The beam is reflected every time it reaches a side of ABCD. How much distance would it travel before hitting a vertex?
2.S is a set of some integers and includes 1 and 2002. For every integer contained in S, the average of the remaining integers in S is also integer. What is the maximum possible number of integers in S.
2006-10-14 06:48:38 · 2 answers · asked by Amit K 2 in Science & Mathematics ➔ Mathematics
For the first one, the horizontal distance travelled will be a multiple of 100, since that's where the vertices occur. This is the same as AP 25 times. So each time the horizontal part of the beam goes 100 units, the vertical goes 75. Now we just need to find the LCM of 70 and 75, which is 14*15*5=1050, or 14*75, so the beam will need 14 vertical reflections before it gets back to a vertex. The horizontal distance is then 1400, and vertical 1050. Thise equate to 350*4 and 350*3, so the total distance travelled (via Pythagorean triple, since it's all linear) is 350*5=1750 units.
For the second one, I have no idea how to start it, aside from noting that 3 integers in such a set is impossible.
2006-10-14 16:10:06 · answer #1 · answered by zex20913 5 · 1⤊ 0⤋
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2006-10-14 07:35:58 · answer #2 · answered by Anonymous · 0⤊ 0⤋