Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 546

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 548

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 546

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 548

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 644

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 644

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 644

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 931

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 931

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 644

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 644

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 644

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 644

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 644

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 644

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 644

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 644

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 613

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 614

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 617

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 625

Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 629

Warning: Cannot modify header information - headers already sent by (output started at /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php:613) in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 1489

Warning: Cannot modify header information - headers already sent by (output started at /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php:613) in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 1489

Warning: Cannot modify header information - headers already sent by (output started at /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php:613) in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 1489

Warning: Cannot modify header information - headers already sent by (output started at /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php:613) in /home/timfahlberg/mathcasts.org/mtwiki/pmwiki.php on line 1489
(:title Speed of the Wind / Speed of the River Current :) [table border=1 cellpadding=3 width=825] [row] []This is analysis page - [[InterA/BoatCurrent|%red c11%Click here for Ready-to-Use InterActivity with Student & Teacher Guides%%]] [row] []Typical Problems for River Current (:div13 style="margin-left:10px":) >>&<<>>&<<(:showhide init=hide div=div111 lshow="+" lhide="-":) %pra%1. Level 1 - Well Stated%% (:div111 id=div111 :) (:div style="margin-left:10px":) >>&<>&<< (:div111end :) >>&<<(:showhide init=hide div=div112 lshow="+" lhide="-":) %exa%2. Level 1 - Poorly Stated%% (:div112 id=div112 :) (:div style="margin-left:10px":) >>&<>&<< (:div112end :) >>&<<(:showhide init=hide div=div113 lshow="+" lhide="-":) %mor%3. Level 2 - Well Stated%% (:div113 id=div113 :) (:div style="margin-left:10px":) >>&<< A boat went 15km downstream in 20 minutes and then upstream 50km in 2 hours. At what speed would a piece of driftwood move in this river? Assume that the speed of the boat in still water and speed of the current of the river are constant. (:divend:) >>&<< (:div113end :) (:div13end:) >>&<< [tableend] >>&<< [table border=1 cellspacing=3 width=825] [row] [] [table border=0 cellpadding=3 width=815] [row] [] (:showhide init=show div=div5 lshow="+" lhide="-":) %c14 b pra%InterActivity%% [tableend] >>-<< (:div5 id=div5 :) Click and drag the sliders to set: %red%speed of boat in still water%%, %yel%speed of current%% and %up%direction of boat%%. (:html:)
Then click on the animation buttons:   
Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)
(:htmlend:) (:div5end :) [tableend] >>-<< [table border=1 cellpadding=3 width=825] [row] []>>&<<(:showhide init=hide div=div7 lshow="+" lhide="-":) Problem Solving Techniques (:div7 id=div7 :) {$ \left\{ \matrix{ \color{red}{x + y = 60} \cr \color{blue}{x - y = 40} \cr} \right. \Leftrightarrow \left\{ \matrix{ x + y = 60 \cr \color{purple}{2x + 0y = 100} \cr} \right. \Leftrightarrow \left\{ \matrix{ x + y = 60 \cr \color{purple}{2x = 100} \cr} \right. $} (:showhide init=hide div=div81 lshow="+" lhide="-":) Mathcasts (:div71 id=div71 :) *... (:div71end :) >>&<< (:div7end :) [tableend] >>-<< [table border=1 cellpadding=3 width=825] [row] []>>&<<(:showhide init=hide div=div8 lshow="+" lhide="-":) Comments on this type of problem (:div8 id=div8 :) (:showhide init=hide div=div81 lshow="+" lhide="-":) Positive (:div81 id=div81 :) *The "weight" of the problem is in the setup of the equation/equations. *Once setup - the solution is straightforward. *It is a fairly realistic problem. (:div81end :) >>&<< (:showhide init=hide div=div82 lshow="+" lhide="-":) Negative (:div82 id=div82 :) *Usually this type of problem is so badly stated - if a student hasn't solved one like it in class, he won't even understand what is being asked! *It is more natural to setup with two equations in two unknowns, but frequently a student is required to solve it using only one unknown. (:div82end :) >>&<< (:div8end :) >>&<< [tableend] >>-<< [table border=1 cellpadding=3 width=825] [row] []>>&<<(:showhide init=hide div=div9 lshow="+" lhide="-":) '''Metadata''' (:div9 id=div9 :) [table class=column border=1 width=810 cellpadding=3] [row] [ width=110px] Global []Wind and River Current Problem Solving [row] []Brief []Examines the idea of wind and river current adding and subtracting from the speed of plane or boat. [row] []Grade []8    (good problem for beginning systems of equations 2x2) [row] []Strand []Algebra 1 [[http://math247.pbwiki.com/Algebra+with+GeoGebra| AF at Math247]] Matrix Algebra [[http://math247.pbwiki.com/Matrix+Algebra+with+GeoGebra| Algebra at Math247]] [row] []Standard []%popwin%[[Standards/Is1al3-4?action=popopen|Algebra 1 3.4]] %popwin%[[standards/ACTee28?action=popopen|ACT EE 28-32]] [row] []Keywords []linear, equation, system, 2 variables, algebra, dynamic, freeware, applet, offline, online [row] []Comments []Images are terrible - looking for new ones :) [row] []Download []coming soon [row] []Author []LFS - [[mailto:emath@emathforall.com?subject=ggb_problems|contact]] [row] []Type []Freeware - Available for Offline and Online Use - Translatable (html) [row] []Use []Requires [[http://www.java.com/en/download/index.jsp|sunJava player]] [tableend] (:div9end:) [tableend] >>-<< ---- >>&<< %rel b%Related Topics%% * [[GlossaryT/Systems2|Systems of 2 Linear Equations in 2 Variables]] >>&<< ---- [table width=825] [row] [][[ProblemsT/| Attach:main/tri_purple_up_a.gif ]] [[ProblemsT/| Up one level]] [r](:html:)
(:htmlend:) [tableend]