ÐÂÎűêÌ⣺ÐĮ̈³õÖÐÕþÖ訵¼°à
ÐĮ̈³õÖÐÕþÖÎÊÇÐĮ̈³õÖÐÕþÖÎÅàѵ»ú¹¹µÄÖØµãרҵ£¬ÐĮ̈ÊÐÖªÃûµÄ³õÖÐÕþÖÎÅàѵ»ú¹¹£¬½ÌÓýÅàѵ֪ÃûÆ·ÅÆ£¬ÐĮ̈³õÖÐÕþÖÎÅàѵ»ú¹¹Ê¦×ÊÁ¦Á¿ÐÛºñ£¬È«¹ú¸÷´ó³ÇÊоùÉèÓзÖУ£¬Ñ§Ð£»¶ÓÄãµÄ¼ÓÈë¡£
1¡¢×¨ÒµµÄ½ÌʦÍŶӣ¬ÕÆÎÕÇ°ÑØµÄ½Ìѧ·½·¨ 2¡¢½Ìѧ¾Ñé·á¸»£¬ÉÆÓÚ¼¤·¢Ñ§ÉúµÄDZÄÜ 3¡¢ÉÆÓÚ´ø¶¯Ñ§Ô±ÈÚÈëÇé¾°ÌåÑéʽ¿ÎÌÃ
ÐĮ̈³õÖÐÕþÖÎÅàѵ»ú¹¹·Ö²¼ÐĮ̈ÊÐÇŶ«Çø,ÇÅÎ÷Çø,ÄϹ¬ÊÐ,ɳºÓÊÐ,ÐÏÌ¨ÏØ,ÁÙ³ÇÏØ,ÄÚÇðÏØ,°ØÏçÏØ,Â¡Ò¢ÏØ,ÈÎÏØ,ÄϺÍÏØ,Äþ½úÏØ,¾ÞÂ¹ÏØ,кÓÏØ,¹ã×ÚÏØ,ƽÏçÏØ,ÍþÏØ,ÇåºÓÏØ,ÁÙÎ÷ÏØµÈµØ,ÊÇÐĮ̈Êм«¾ßÓ°ÏìÁ¦µÄ³õÖÐÕþÖÎÅàѵ»ú¹¹¡£
Ç¿µ÷ѧÉúÊÇѧϰµÄÖ÷Ì壬½ÌʦµÄÖ÷µ¼×÷ÓñØÐëÓëѧÉúµÄÖ÷Ìå×÷ÓÃÏà½áºÏ¡£
ÈçÀÊËл¡¢±³Ëл¡¢ÓïÎÄ»ù´¡ÖªÊ¶¾ºÈü¡¢×÷ÎıÈÈüµÈ£¬²Î¼ÓÕâЩ»î¶¯µÄʱºòʱºò£¬ÄãÒ»¶¨ÒªÖ÷¶¯»ý¼«´óµ¨£¬²»ÒªÓÐʲô¹ËÂÇ£»ËÒ²»á·¸´íÎóµÄ£¬¶à²Î¼Ó¼¸´Î¾Íʲô¶¼½â¾öÁË£¬Ëµ²»¶¨Ä㻹Äܹ»×öÒ»¸ö³É¹¦µÄÖ÷³ÖÈËÄØ£¡Ò»¿ªÊ¼¾Í±»±ðÈËÕ¼ÁË»ú»á£¬ÒÔºó¾ÍûÓÐÄÇôÈÝÒ×ÁË¡£ÔÚѧϰÉϾÍÊÇÒªºÍ±ðµÄͬѧÕùÒ»»ØÏÈ£¬ÕâÑù×öÊÇÕýÈ·µÄ¡£
Èý¡¢ÒªÓкõÄѧϰ·½·¨
Êýѧ¡°Ô´ÓÚÏÖʵ£¬Ô¢ÓÚÏÖʵ£¬¸ßÓÚÏÖʵ¡±£¬Êýѧ֪ʶÀ´Ô´ÓÚÉú»îʵ¼Ê£¬Éú»î±¾Éí¾ÍÊÇÒ»¸ö¾Þ´óµÄÊýѧ¿ÎÌá£Èç¹ûÍÑÀëÉú»îÏÖʵ̸Êýѧ£¬Êýѧ¸øÈ˸оõÍùÍùÊÇ¿ÝÔïµÄ¡¢³éÏóµÄ¡£Òò´Ë£¬ÔÚпÎÒýÈËʱ£¬×¢Òâ°Ñ֪ʶÄÚÈÝÓëÉú»îʵ¼ù½áºÏÆðÀ´£¬¾«ÐÄÉèÎÊ£¬Ò»·½ÃæÊÇѧÉú¹ØÐĵϰÌ⣬Äܼ¤·¢ÆðѧÉúµÄѧϰ»ý¼«ÐÔ£¬ÁíÒ»·½ÃæÊ¹Ñ§ÉúÆÈÇÐÏëÖªµÀÈçºÎÔËÓÃËùѧ֪ʶ½â¾öÎÊÌ⣬ÄÜ»½ÆðѧÉúµÄÇóÖªÓû¡£¶øÈ¤Î¶ÐÔµÄ֪ʶ×ÜÄÜÎüÒýÈË£¬È¤Î¶ÐÔµÄÎÊÌâ×ÜÄÜÒý·¢Ñ§Éú¶ÔÎÊÌâµÄ̽¾¿ºÍÉî²ã´ÎµÄ˼¿¼¡£ÔÚпÎÒýÈËʱ£¬¶àΪѧÉúÌṩһЩÊýѧʷ»òÆäËûÓÐȤµÄ֪ʶ£¬¼ÈÄܼ¤·¢Ñ§ÉúµÄѧϰÐËȤ£¬ÓÖÄÜÀ©´óѧÉúµÄÖªÊ¶Ãæ¡£Èý¡¢×¢ÖØÖªÊ¶µÄÉú³É¹ý³Ì£¬Ìá¸ßѧϰÄÜÁ¦
³õÖÐ ÊýѧÈçºÎת»¯²îÉú
ѧÉúѧϰ°üÀ¨×Å¿Îǰ¡¢¿ÎÖкͿκóµÄѧϰ£¬Õë¶Ô¿Îºóѧϰ£¬½ÌʦÔòÓ¦¸Ã¶à¼ÓÒªÇóѧÉú×Ô¼º¸ù¾ÝÐËȤȥ̽Ë÷һЩ½Ì²ÄÒÔÍâµÄÊýѧ֪ʶ£¬ÅàÑø×Ô¼ºµÄ¶À×Ô´´ÔìÒâʶºÍ½â¾öÎÊÌâµÄÄÜÁ¦¡£¿Îºó×ÔÖ÷̽Ë÷µÄѧϰҲÊǶԽ̲Ä֪ʶµÄ½øÒ»²½¹®¹ÌºÍÉ£¬ÔÚÀí½âµÄ»ù´¡Éϲ»¶Ï´´ÔìµÄ¹ý³Ì¡£ÀýÈçËս̰æ³õÖÐÊýѧÆßÄê¼¶ÉϲáÖС°×ß½øÍ¼ÐεÄÊÀ½ç¡±£¬ÆäÖÐÓÐÉæ¼°µ½¶Ô¡°Ö÷ÊÓͼ¡¢×óÊÓͼ¡¢ÓÒÊÓͼ¡±µÄѧϰ£¬Ñ§ÉúÔڿκóÓгä×ãµÄ³¡µØºÍµÀ¾ßÀ´Ì½Ë÷Õâ¸öÎÊÌ⣬ËûÃÇ¿ÉÒÔ½èÖú¼ÒÀïµÄ¸÷ÖÖÎïÌåÀ´½øÐÐÖ÷¡¢×ó¡¢ÓÒÊÓͼµÄ¹Û²ì¡£³ý´ËÍ⣬ѧÉú»¹¿ÉÒÔ½øÒ»²½¹Û²ìÎïÌåµÄ¸©ÊÓͼ¡¢ÑöÊÓͼ¡¢²àÊÓͼµÈ²»Í¬½Ç¶ÈµÄÎïÌåÐÎ̬£¬²¢ÇÒ¿ÉÒÔÓûͼµÄ·½Ê½¼Ç¼Ï¸÷¸ö½Ç¶ÈµÄÎïÌåÐÎ̬£¬È»ºóÔÚ¿ÎÌÃÉϽ²½â¸øÆäËûѧÉú×Ô¼º¹Û²ìµÄ½á¹û¡£Í¨¹ýÕâÖÖ·½Ê½Ñ§ÉúÖ®¼äÒ²¿ÉÒÔ½øÒ»²½µØ½øÐÐÊýѧÎÊÌâ½»Á÷£¬¼«´óÍØ¿íÁËÊýѧѧϰµÄ¿Õ¼ä£¬°Ñ½Ì²ÄµÄ¾ÖÏÞÐÔËõС¡£
ÂÌÉ«µÄ·îÏ×´ÓÂÌÉ«µÄ·îÏ×¾«ÉñÈëÊÖ£¬Ð´Ò»ÆªÊãÇéÉ¢ÎÄ¡£
ÂÌÉ«£¬ÊÇ·îÏ׵ϝÉí¡£Ëü¸øÖ²ÎïËÍÈ¥ÉúÃü£¬ÈÃ´óµØ³äÂúÉú»ú¡£ÂÌÊÇÄÇÒ»ÉíÉíéÏéÉ«µÄ¾ü·þ£¬ÒÙÁ¢ÔÚ׿¹úµÄ±ß½®¡¢º£·À£¬ÂÌÊÇÀÏʦ°ì¹«ÊÒµÄÄÇÅèÏÉÈËÕÆ£¬Ä¿¶Ã×ÅÀÏʦÓɺڷ¢µ½°×Í·¡¡
×÷Ϊ½ÌʦҪת±ä½Ìѧ¹ÛÄ¸Ä±äÖ»¿´ÑÝÒï¹ý³ÌµÄÑÏÃÜÐÔ¶øºöÊÓÖ±¾õ²ÂÏëµÄ¼ÛÖµ£¬×¢ÒâÀûÓÃÎÊÌâµÄÍØ¹ãÀ´ÎüÒýѧÉú¶à½Ç¶ÈÉèÏ룬¶à·½Î»Ë¼Î¬£¬Òýµ¼Ñ§Éú´ÓÕûÌåÉϰÑÎÕÎÊÌ⣬¹ÄÀøÑ§Éú´óµ¨µØ²ÂÏ룬²»Ð¸µØÒªÇóѧÉú¹éÄÉÓëÑÝÒï½»»¥Ê¹Óã¬ÐÎÏó˼άÓë³éÏó˼άÐͬ£¬Ê¹Ñ§ÉúÒâʶµ½Ã¿Ò»¸öÎÊÌâ¶¼¿ÉÄÜÓв»Í¬µÄ½âÊÍ»ò½â¾ö·½·¨¡£
¸ÅÄîµÄÆÊÎöÊǼÇÒäµÄ»ù´¡£¬¼ÇÒäÊǽ¨Á¢ÔÚÀí½âµÄ»ù´¡Éϵģ¬Àí½âÉî¿Ì²ÅÄܼÇÒä׼ȷ¡£µ±È»£¬¼ÇÒäʱ¿É²ÉȡһЩ¸¨Öú·½Ê½£¬È缸ºÎ¸ÅÄîµÄ¼ÇÒäʱ¿ÉÒÔͨ¹ý»Í¼µÄ·½Ê½½øÐжà¸Ð¹Ù´Ì¼¤£¬ÓɸÅÄîÄÚº¬µÄ³éÏ󻯹ý¶Éµ½¸ÅÄîÍâÑÓµÄÐÎÏ󻯡£
ËÄ¡¢¸ÅÄîµÄÓ¦ÓÃ
µÚÒ»²½£º¿ìËÙɨÃ裬ÕûÌå¸Ð֪ȫÎÄ¡£
Ìå»á¾ä×ӵĸÐÇéÉ«²Ê
ͨ¹ý·ÖÎö¹éÄÉ£¬ÅàÑøÑ§Éú´´ÐÂ˼ά
ÓÖÈçÔÚ½ÌÑ§Æ½ÃæÍ¼ÐεÄÃæ»ý¼ÆË㹫ʽºó£¬ÎÒÒªÇóѧÉú¹éÄɳöÒ»¸öÄܸÅÀ¨¸÷¸öÆ½ÃæÍ¼ÐÎÃæ»ý¼ÆËãµÄ¹«Ê½£¬ÎÒÈÃѧÉú½øÐÐÌÖÂÛ£¬¾¹ýÌÖÂÛ£¬Ñ§ÉúÃǹéÄɳö£¬ÔÚСѧ½×¶Îѧ¹ýµÄÃæ»ý¹«Ê½¶¼¿ÉÒÔÓÃÌÝÐεÄÃæ»ý¼ÆË㹫ʽÀ´½øÐиÅÀ¨£¬ÒòΪÌÝÐεÄÃæ»ý¼ÆË㹫ʽÊÇ£º(ÉÏµ× +ϵ×)¡Á¸ß¡Â2 ¡£¶ø³¤·½ÐΡ¢Õý·½ÐΡ¢Æ½ÐÐËıßÐεÄÉϵ׺Íϵ×ÏàµÈ£¬¼´¿É½«Õ⹫ʽ±ä³É£ºµ×(³¤¡¢±ß³¤)¡Á¸ß(¿í¡¢±ß³¤)¡Á2¡Â2 = µ×(³¤¡¢±ß³¤)¡Á¸ß(¿í¡¢±ß³¤);
ÀýÈ磬½Ìѧ¡°Ô²ÖùÌåµÄÌå»ý¡±Ê±£¬ÔÚѧÉúÒÑ¾ÕÆÎÕÔ²ÖùµÄÌå»ý¼ÆËã·½·¨ºó£¬ÀûÓÃÔÀýÌ⣬±äÔÓÐÌõ¼þΪ¡°°ÑÒ»¸öÖ±¾¶20ÀåÃ×µÄÔ²Öù£¬Ñص×ÃæÖ±¾¶´ÓÉϵ½Ï·ֳÉÈô¸ÉµÈ·Ý£¬È»ºóÆ´½Ó³ÉÒ»¸öºÍËüÌå»ýÏàµÈµÄ³¤·½Ì壬Õâ¸ö³¤·½ÌåµÄ±íÃæ»ý±ÈÔÀ´µÄÔ²Öù±íÃæ»ýÔö¼Ó7ƽ·½ÀåÃ×£¬³¤·½ÌåµÄÌå»ýÊǶàÉÙ?¡±½ÌʦÏÈΪѧÉúÌṩÁËÒ»¸öÕæÊµµÄ¾ÑéÇé¾³¡£Ñ§Éúͨ¹ý¹Û²ì»á·¢ÏÖ£¬Ô²Öù±äÐκó£¬ÐÂÐÎÌåºÍÔÐÎÌåµÈ»ý;ÐÂÐÎÌåµÄ³¤Ç¡ºÃÊÇÔ²Öùµ×ÃæÖܳ¤µÄ1/2£¬ÐÂÔö±íÃæ»ý7ƽ·½ÀåÃ×ÕýºÃÊÇÔ²ÖùÌå±äÐκóËùµÃ³¤·½Ìå×óÓÒ̾̾»ýÖ®ºÍ¡£Èç´Ë·ÖÎö̽¾¿Ö®ºó£¬Ñ§ÉúºÜ¿ì»áµÃ³öÕâ¸ö³¤·½Ìå(¼´±äÐÎǰԲÖùÌå)Ìå»ýΪ¡°³¤·½Ìå×ó(ÓÒ)Ãæ»ý¡Á³¤·½ÌåµÄ³¤¡±¡£´ËʱѧÉúµÄ˼ά·½ÏòºÜÃ÷È·£¬ÇÒÓÐ×ã¹»µÄ˼ά¿Õ¼ä¡£ÒòΪ³¤·½Ìå×ó(ÓÒ)Ãæ»ý=Ô²ÖùµÄµ×Ãæ°ë¾¶(r)¡ÁÔ²ÖùµÄ¸ß(h)=hr;³¤·½ÌåµÄ³¤=1/2Ô²Öܳ¤=¦Ðr¡£ËùÒÔ£¬Ô²ÖùÌå±äÐκóµÃµ½µÄеij¤·½ÌåµÄÌå»ýΪ¡°³¤·½Ìå×ó(ÓÒ)Ãæ»ý¡Á1/2Ô²Öܳ¤¡±£¬¼´¡°hr¡¤¦Ðr¡±£¬ÕûÀíºóµÃV=¦Ðr2¡¤h¡£ÉÏÊö˼ά»î¶¯¼ÓÉîÁËѧÉú¶ÔÔ²ÖùÌ弯Ëã¹«Ê½ÍÆµ¼¹ý³ÌµÄÀí½â£¬¶ÍÁ¶ÁËѧÉú˼άµÄ¶ÀÁ¢ÐÔÓëÃô½ÝÐÔ£¬´´ÔìÐÔµØÓ¦ÓÃÒÑÓÐ֪ʶ½â¾öÁËÐÂÎÊÌâ¡£
×ÜÊÇÈÏΪ¼ÆË㹫ʽÎÊÌâ±È·ÖÎöÓ¦ÓÃÎÊÌâÈÝÒ׵ö࣬¶ÔһЩ¹æÂÉ¡¢¹æÂɵÈ֪ʶѧϰÀι̣¬¼ÆËãÊÇÒ»ÏîÈÝÒ׵Ť×÷£¬ÒòΪ±»¼ÆË㣬»ò¹ýÓÚ×ÔÐÅ£¬»ò×¢ÒâÁ¦²»Äܼ¯ÖУ¬½á¹ûÊÇ100¸ö´íÎó¡£
ÈÃѧÉúÒ»Ìâ¶à½â£¬ÅàÑøË¼Î¬µÄÁé»îÐÔ
´´ÐÂÄÜÁ¦ÔÚÊýѧ½ÌѧÖÐÖ÷Òª±íÏÖ¶ÔÒѽâ¾öÎÊÌâѰÇóеĽⷨ¡£¡°Ñ§ÆðÓÚ˼£¬Ë¼Ô´ÓÚÒÉ¡±£¬Ñ§Éú̽Ë÷֪ʶµÄ˼ά¹ý³Ì×ÜÊÇ´ÓÎÊÌ⿪ʼ£¬ÓÖÔÚ½â¾öÎÊÌâÖеõ½·¢Õ¹ºÍ´´Ð¡£½Ìѧ¹ý³ÌÖÐѧÉúÔÚ½Ìʦ´´ÉèµÄÇ龳ϣ¬×Ô¼º¶¯ÊÖ²Ù×÷¡¢¶¯ÄÔ˼¿¼¡¢¶¯¿Ú±í´ï£¬Ì½Ë÷δ֪ÁìÓò£¬Ñ°Õҿ͹ÛÕæÀí£¬³ÉΪ·¢ÏÖÕߣ¬ÒªÈÃѧÉú×ÔʼÖÁÖյزÎÓëÕâһ̽Ë÷¹ý³Ì£¬·¢Õ¹Ñ§Éú´´ÐÂÄÜÁ¦¡£ÈçÔÚÇòµÄÌå»ý½ÌѧÖУ¬ÎÒÀûÓÿÎÓàʱ¼ä½«Ñ§Éú·ÖΪÈý×飬ҪÇóµÚÒ»×éÿÈË×ö°ë¾¶Îª10ÀåÃ׵İëÇò;
Ç×°®µÄÀÏʦ£¬Ä㻹ÔÚÎÒ¹ÊÏçÄdz¤×ÅÐí¶àÀóÖ¦Ê÷µÄɽ´åСѧÈνÌÂð£¿Ä㻹ÔÚ±³£¨b¨¥i b¨¨i£©×ÅÎÒ¹ÊÏçµÄСѧÉúÉæ¹ýÄÇÌõÍļ±µÄСºÓÂð£¿ÄãµÄÒôÈÝЦòʱʱ¸¡ÏÖÔÚÎÒµÄÄÔº£ÀÒýÆðÎÒÐí¶àÃÀºÃµÄ»ØÒä¡£
×÷ÎÄÊÇÖп¼µÄ°ë±Ú½É½£¬ËüµÄ³É°ÜÖ±½Ó¹ØÏµ×ÅÖп¼³É¼¨µÄ¸ßµÍ£¬È»¶øÔÚ¸´Ï°ÖУ¬Ñ§ÉúÊÜËØ²ÄØÑ·¦¡¢Éú»îÔÄÀúÉÙ¡¢Ë¼Â·²»¿ªÀ«µÄ¾ÖÏÞ£¬¸´Ï°Ð§¹û²»ÊÇÌ«Ã÷ÏÔ£¬³ÉΪѧÉúÖп¼×÷Îijö²ÊµÄÆ¿¾±¡£¶Ô´Ë£¬½¨Òé²ÉÈ¡ÈýÏß²¢Ðеķ½·¨¡£
ͨ¹ýµäÐÍÊÂÀý±íÏÖÈËÎïÆ·ÖÊ
ÐĮ̈³õÖÐÕþÖÎÅàѵ»ú¹¹³É¾ÍÄãµÄÃÎÏëÖ®Âá£Ñ§³õÖÐÕþÖξÍÀ´ÐĮ̈³õÖÐÕþÖÎÅàѵ»ú¹¹
Åàѵ×Éѯµç»°£ºµã»÷×ó²àÀëÏß±¦Ãâ·Ñ×Éѯ