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高中数学平面向量5类解题技巧（“爪子定理”、系数和（等和线）、极化恒等式、奔驰定理与三角形四心问题、范围与最值问题）原卷+解析12页.zip

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本文标题：高中数学平面向量5类解题技巧（“爪子定理”、系数和（等和线）、极化恒等式、奔驰定理与三角形四心问题、范围与最值问题）原卷+解析12页.zip

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/www/wwwroot/www.gwzjk.com/application/base/model/Reward.php ( 6.34 KB )
/www/wwwroot/www.gwzjk.com/application/base/model/RewardType.php ( 2.52 KB )
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[ DB ] CONNECT:[ UseTime:0.000136s ] mysql:host=localhost;dbname=www.gwzjk.com;charset=utf8
[ SQL ] SHOW COLUMNS FROM `ye_spiders` [ RunTime:0.000263s ]
[ SQL ] INSERT INTO `ye_spiders` (`name` , `url` , `create_time` , `update_time`) VALUES ('其它蜘蛛' , 'http://www.gwzjk.com//index/article/detail/detail_id/40227.html' , '2025-04-05 05:58:19.466071' , '2025-04-05 05:58:19.466078') [ RunTime:0.000136s ]
[ SQL ] SHOW COLUMNS FROM `ye_hotkey` [ RunTime:0.000275s ]
[ SQL ] SELECT * FROM `ye_hotkey` WHERE `status` > -1 ORDER BY `sort` DESC LIMIT 0,8 [ RunTime:0.000109s ]
[ EXPLAIN : array ( 'id' => 1, 'select_type' => 'SIMPLE', 'table' => 'ye_hotkey', 'partitions' => NULL, 'type' => 'ALL', 'possible_keys' => NULL, 'key' => NULL, 'key_len' => NULL, 'ref' => NULL, 'rows' => 30, 'filtered' => 33.32999801635742, 'extra' => 'Using where; Using filesort', ) ]
[ SQL ] SHOW COLUMNS FROM `ye_article` [ RunTime:0.000379s ]
[ SQL ] SELECT *,type as article_type FROM `ye_article` WHERE `status` = 1 AND `id` = 40227 LIMIT 1 [ RunTime:0.000267s ]
[ EXPLAIN : array ( 'id' => 1, 'select_type' => 'SIMPLE', 'table' => 'ye_article', 'partitions' => NULL, 'type' => 'const', 'possible_keys' => 'PRIMARY', 'key' => 'PRIMARY', 'key_len' => '4', 'ref' => 'const', 'rows' => 1, 'filtered' => 100.0, 'extra' => NULL, ) ]
[ DB ] CONNECT:[ UseTime:0.000139s ] mysql:host=localhost;dbname=www.gwzjk.com;charset=utf8
[ SQL ] SHOW COLUMNS FROM `ye_article_content` [ RunTime:0.000258s ]
[ SQL ] SELECT * FROM `ye_article_content` WHERE `id` = 40227 LIMIT 1 [ RunTime:0.000158s ]
[ EXPLAIN : array ( 'id' => 1, 'select_type' => 'SIMPLE', 'table' => 'ye_article_content', 'partitions' => NULL, 'type' => 'const', 'possible_keys' => 'PRIMARY,idx_id', 'key' => 'PRIMARY', 'key_len' => '4', 'ref' => 'const', 'rows' => 1, 'filtered' => 100.0, 'extra' => NULL, ) ]
[ SQL ] SHOW COLUMNS FROM `ye_reward` [ RunTime:0.000245s ]
[ SQL ] SELECT COUNT(*) AS tp_count FROM `ye_reward` WHERE `detail_id` = 40227 AND `status` = 1 [ RunTime:0.000183s ]
[ EXPLAIN : array ( 'id' => 1, 'select_type' => 'SIMPLE', 'table' => 'ye_reward', 'partitions' => NULL, 'type' => 'ref', 'possible_keys' => 'index_detail_id', 'key' => 'index_detail_id', 'key_len' => '7', 'ref' => 'const,const', 'rows' => 1, 'filtered' => 100.0, 'extra' => 'Using index', ) ]
[ SQL ] SHOW COLUMNS FROM `ye_reward_type` [ RunTime:0.000228s ]
[ SQL ] SELECT * FROM `ye_reward_type` WHERE `status` > -1 ORDER BY `sort` DESC LIMIT 0,9 [ RunTime:0.000092s ]
[ EXPLAIN : array ( 'id' => 1, 'select_type' => 'SIMPLE', 'table' => 'ye_reward_type', 'partitions' => NULL, 'type' => 'ALL', 'possible_keys' => 'index_status', 'key' => NULL, 'key_len' => NULL, 'ref' => NULL, 'rows' => 9, 'filtered' => 100.0, 'extra' => 'Using where; Using filesort', ) ]
[ SQL ] SELECT * FROM `ye_article` WHERE `status` = 1 AND `display` = 1 AND `id` < 40227 AND `category_id` = 291 LIMIT 1 [ RunTime:0.003754s ]
[ EXPLAIN : array ( 'id' => 1, 'select_type' => 'SIMPLE', 'table' => 'ye_article', 'partitions' => NULL, 'type' => 'index_merge', 'possible_keys' => 'PRIMARY,idx_category,idx_status', 'key' => 'idx_status,idx_category', 'key_len' => '8,9', 'ref' => NULL, 'rows' => 1126, 'filtered' => 100.0, 'extra' => 'Using intersect(idx_status,idx_category); Using where', ) ]
[ SQL ] SELECT * FROM `ye_article` WHERE `status` = 1 AND `display` = 1 AND `id` > 40227 AND `category_id` = 291 LIMIT 1 [ RunTime:0.000295s ]
[ EXPLAIN : array ( 'id' => 1, 'select_type' => 'SIMPLE', 'table' => 'ye_article', 'partitions' => NULL, 'type' => 'index_merge', 'possible_keys' => 'PRIMARY,idx_category,idx_status', 'key' => 'idx_status,idx_category', 'key_len' => '8,9', 'ref' => NULL, 'rows' => 3588, 'filtered' => 100.0, 'extra' => 'Using intersect(idx_status,idx_category); Using where', ) ]

0.039233s

高中数学平面向量5类解题技巧（“爪子定理”、系数和（等和线）、极化恒等式、奔驰定理与三角形四心问题、范围与最值问题）原卷+解析12页.zip

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