Question

2010ÄêÉϺ£ÊÀ²©»á×éί»áΪ±£Ö¤ÓοͲι۵Ä˳Àû½øÐУ¬¶ÔÿÌìÔÚ¸÷ʱ¼ä¶Î½øÈëÔ°ÇøºÍÀ뿪԰ÇøµÄÈËÊý×÷ÁËÒ»¸öÄ£ÄâÔ¤²â£®ÎªÁË·½±ãÆð¼û£¬ÒÔ10·ÖÖÓΪһ¸ö¼ÆË㵥룬ÉÏÎç9µã10·Ö×÷ΪµÚÒ»¸ö¼ÆËãÈËÊýµÄʱ¼ä£¬¼´n=1£»9µã20·Ö×÷ΪµÚ¶þ¸ö¼ÆËãÈËÊýµÄʱ¼ä£¬¼´n=2£»ÒÀ´ËÀàÍÆ¡­£¬°ÑÒ»ÌìÄÚ´ÓÉÏÎç9µãµ½ÍíÉÏ24µã·Ö³ÉÁË90¸ö¼ÆË㵥λ£®
¶ÔµÚn¸öʱ¿Ì½øÈëÔ°ÇøµÄÈËÊýf£¨n£©ºÍʱ¼än£¨n¡ÊN^*£©Âú×ãÒÔϹØϵ£¨Èçͼ1£©£ºf£¨n£©=£¬n¡ÊN^*
¶ÔµÚn¸öʱ¿ÌÀ뿪԰ÇøµÄÈËÊýg£¨n£©ºÍʱ¼än£¨n¡ÊN^*£©Âú×ãÒÔϹØϵ£¨Èçͼ2£©£ºg£¨n£©=£¬n¡ÊN^*
£¨1£©ÊÔ¼ÆËãÔÚµ±ÌìÏÂÎç3µãÕû£¨¼´15µãÕû£©Ê±£¬ÊÀ²©Ô°ÇøÄÚ¹²ÓжàÉÙÓοͣ¿
£¨2£©ÇëÇó³öµ±ÌìÊÀ²©Ô°ÇøÄÚÓοÍ×ÜÈËÊý×î¶àµÄʱ¿Ì£®

Answer 1

¡¾´ð°¸¡¿·ÖÎö£º£¨1£©ÀûÓÃf£¨n£©ºÍg£¨n£©Çó³öÏÂÎç3µãÖÓ¼´n=36ʱ½øÔ°ÈËÊýºÍÀ뿪԰ÇøÈËÊý£¬È¡Æä²îÖµ¼´¿É
£¨2£©¶Ôn½øÐзÖÀ࣬ÀûÓÃf£¨n£©-g£¨n£©£¾0»¹ÊÇ£¼0ÅжÏÔ°ÖÐÈËÊýÊÇÔö¼Ó»¹ÊǼõÉÙ£¬ÇóµÃnµÄÖµ
½â´ð£º½â£º£¨1£©µ±0¡Ün¡Ü24ÇÒn¡ÊN^*ʱ£¬f£¨n£©=3600£¬
µ±25¡Ün¡Ü36ÇÒn¡ÊN^*ʱ£¬£¨2·Ö£©
ËùÒÔS₃₆=[f£¨1£©+f£¨2£©+f£¨3£©++f£¨24£©]++[f£¨25£©+f£¨26£©++f£¨36£©]
=3600×24+3600×
=86400+82299.59=168700£»£¨2·Ö£©
ÁíÒ»·½Ã棬ÒѾ­À뿪µÄÓοÍ×ÜÈËÊýÊÇ£º
T₁₂=g£¨25£©+g£¨26£©++g£¨36£©
=12×500=39000£»£¨2·Ö£©
ËùÒÔS=S₃₆-T₁₂=168700-39000=129700£¨ÈË£©
¹Êµ±ÌìÏÂÎç3µãÕû£¨¼´15µãÕû£©Ê±£¬ÊÀ²©Ô°ÇøÄÚ¹²ÓÐ129700λÓοͣ®£¨2·Ö£©
£¨2£©µ±f£¨n£©-g£¨n£©¡Ý0ʱ԰ÄÚÓοÍÈËÊýµÝÔö£»µ±f£¨n£©-g£¨n£©£¼0ʱ԰ÄÚÓοÍÈËÊýµÝ¼õ£®
£¨i£©µ±1¡Ün¡Ü24ʱ£¬Ô°ÇøÈËÊýÔ½À´Ô½¶à£¬ÈËÊý²»ÊÇ×î¶àµÄʱ¼ä£»£¨2·Ö£©
£¨ii£©µ±25¡Ün¡Ü36ʱ£¬Áî500n-12000¡Ü3600£¬µÃ³ön¡Ü31£¬
¼´µ±25¡Ün¡Ü31ʱ£¬½øÈëÔ°ÇøÈËÊý¶àÓÚÀ뿪ÈËÊý£¬×ÜÈËÊýÔ½À´Ô½¶à£»£¨2·Ö£©
µ±32¡Ün¡Ü36ʱ£¬£¬½øÈëÔ°ÇøÈËÊý¶àÓÚÀ뿪ÈËÊý£¬×ÜÈËÊýÔ½À´Ô½¶à£»£¨2·Ö£©
£¨iii£©µ±37¡Ün¡Ü72ʱ£¬Áî-300n+21600=500n-12000ʱ£¬n=42£¬
¼´ÔÚÏÂÎç4µãÕûʱ£¬Ô°ÇøÈËÊý´ïµ½×î¶à£®
´ËºóÀ뿪ÈËÊýÔ½À´Ô½¶à£¬¹ÊÔ°ÇøÄÚÈËÊý×î¶àµÄʱ¼äÊÇÏÂÎç4µãÕû£®£¨2·Ö£©
µãÆÀ£º´ËÌ⿼²éº¯ÊýµÄÓ¦Óã¬Ö÷Òª¿¼²é·ÖÀàÌÖÂÛ˼Ï룬ÓÐÒ»¶¨µÄÄѶȣ®