Warning (2): file_get_contents(): https:// wrapper is disabled in the server configuration by allow_url_fopen=0 [ROOT/vendors/mathml_to_image.php, line 6]
file_get_contents - [internal], line ??
grabDataImage - ROOT/vendors/mathml_to_image.php, line 6
string_between - ROOT/vendors/mathml_to_image.php, line 30
math_to_image - ROOT/vendors/mathml_to_image.php, line 51
TopicsController::viewOnSearchTopic() - APP/Controller/TopicsController.php, line 98
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 490
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 191
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 165
[main] - APP/webroot/index.php, line 108
Warning (2): file_get_contents(https://www.wiris.net/demo/editor/render.png?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%26%238710%3B%3C%2Fmo%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfrac%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmfrac%3E%3Cmfenced+close%3D%22%7C%22+open%3D%22%7C%22+separators%3D%22%7C%22%3E%3Cmtable%3E%3Cmtr%3E%3Cmtd%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr%3E%3Cmtd%3E%3Cmn%3E6%3C%2Fmn%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr%3E%3Cmtd%3E%3Cmn%3E4%3C%2Fmn%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3C%2Fmtable%3E%3C%2Fmfenced%3E%3C%2Fmath%3E) [function.file-get-contents]: failed to open stream: no suitable wrapper could be found [ROOT/vendors/mathml_to_image.php, line 6]
file_get_contents - [internal], line ??
grabDataImage - ROOT/vendors/mathml_to_image.php, line 6
string_between - ROOT/vendors/mathml_to_image.php, line 30
math_to_image - ROOT/vendors/mathml_to_image.php, line 51
TopicsController::viewOnSearchTopic() - APP/Controller/TopicsController.php, line 98
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 490
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 191
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 165
[main] - APP/webroot/index.php, line 108
Warning (2): file_get_contents() [function.file-get-contents]: https:// wrapper is disabled in the server configuration by allow_url_fopen=0 [ROOT/vendors/mathml_to_image.php, line 6]
file_get_contents - [internal], line ??
grabDataImage - ROOT/vendors/mathml_to_image.php, line 6
string_between - ROOT/vendors/mathml_to_image.php, line 30
string_between - ROOT/vendors/mathml_to_image.php, line 34
math_to_image - ROOT/vendors/mathml_to_image.php, line 51
TopicsController::viewOnSearchTopic() - APP/Controller/TopicsController.php, line 98
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 490
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 191
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 165
[main] - APP/webroot/index.php, line 108
Warning (2): file_get_contents(https://www.wiris.net/demo/editor/render.png?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%26%238710%3B%3C%2Fmo%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfrac%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmfrac%3E%3Cmfenced+close%3D%22%7C%22+open%3D%22%7C%22+separators%3D%22%7C%22%3E%3Cmtable%3E%3Cmtr%3E%3Cmtd%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E7%3C%2Fmn%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr%3E%3Cmtd%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr%3E%3Cmtd%3E%3Cmn%3E10%3C%2Fmn%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E8%3C%2Fmn%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3C%2Fmtable%3E%3C%2Fmfenced%3E%3C%2Fmath%3E) [function.file-get-contents]: failed to open stream: no suitable wrapper could be found [ROOT/vendors/mathml_to_image.php, line 6]
file_get_contents - [internal], line ??
grabDataImage - ROOT/vendors/mathml_to_image.php, line 6
string_between - ROOT/vendors/mathml_to_image.php, line 30
string_between - ROOT/vendors/mathml_to_image.php, line 34
math_to_image - ROOT/vendors/mathml_to_image.php, line 51
TopicsController::viewOnSearchTopic() - APP/Controller/TopicsController.php, line 98
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 490
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 191
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 165
[main] - APP/webroot/index.php, line 108
Warning (2): file_get_contents() [function.file-get-contents]: https:// wrapper is disabled in the server configuration by allow_url_fopen=0 [ROOT/vendors/mathml_to_image.php, line 6]
file_get_contents - [internal], line ??
grabDataImage - ROOT/vendors/mathml_to_image.php, line 6
string_between - ROOT/vendors/mathml_to_image.php, line 30
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
math_to_image - ROOT/vendors/mathml_to_image.php, line 51
TopicsController::viewOnSearchTopic() - APP/Controller/TopicsController.php, line 98
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 490
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 191
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 165
[main] - APP/webroot/index.php, line 108
Warning (2): file_get_contents(https://www.wiris.net/demo/editor/render.png?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%26%238710%3B%3C%2Fmo%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfrac%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmfrac%3E%3Cmfenced+open%3D%22%7C%22+close%3D%22%7C%22+separators%3D%22%7C%22%3E%3Cmtable%3E%3Cmtr%3E%3Cmtd%3E%3Cmi%3Ea%3C%2Fmi%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmi%3Eb%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3Ec%3C%2Fmi%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr%3E%3Cmtd%3E%3Cmi%3Eb%3C%2Fmi%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmi%3Ec%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3Ea%3C%2Fmi%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr%3E%3Cmtd%3E%3Cmi%3Ec%3C%2Fmi%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3Eb%3C%2Fmi%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3C%2Fmtable%3E%3C%2Fmfenced%3E%3C%2Fmath%3E) [function.file-get-contents]: failed to open stream: no suitable wrapper could be found [ROOT/vendors/mathml_to_image.php, line 6]
file_get_contents - [internal], line ??
grabDataImage - ROOT/vendors/mathml_to_image.php, line 6
string_between - ROOT/vendors/mathml_to_image.php, line 30
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
math_to_image - ROOT/vendors/mathml_to_image.php, line 51
TopicsController::viewOnSearchTopic() - APP/Controller/TopicsController.php, line 98
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 490
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 191
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 165
[main] - APP/webroot/index.php, line 108
Warning (2): file_get_contents() [function.file-get-contents]: https:// wrapper is disabled in the server configuration by allow_url_fopen=0 [ROOT/vendors/mathml_to_image.php, line 6]
file_get_contents - [internal], line ??
grabDataImage - ROOT/vendors/mathml_to_image.php, line 6
string_between - ROOT/vendors/mathml_to_image.php, line 30
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
math_to_image - ROOT/vendors/mathml_to_image.php, line 51
TopicsController::viewOnSearchTopic() - APP/Controller/TopicsController.php, line 98
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 490
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 191
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 165
[main] - APP/webroot/index.php, line 108
Warning (2): file_get_contents(https://www.wiris.net/demo/editor/render.png?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfrac%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmfrac%3E%3Cmfenced+close%3D%22%7C%22+open%3D%22%7C%22+separators%3D%22%7C%22%3E%3Cmtable%3E%3Cmtr%3E%3Cmtd%3E%3Cmi%3Ea%3C%2Fmi%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmi%3Eb%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3Ec%3C%2Fmi%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr%3E%3Cmtd%3E%3Cmi%3Eb%3C%2Fmi%3E%3Cmo%3E-%3C%2Fmo%3E%3Cmi%3Ea%3C%2Fmi%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmo%3E-%3C%2Fmo%3E%3Cmi%3Eb%3C%2Fmi%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr%3E%3Cmtd%3E%3Cmi%3Ec%3C%2Fmi%3E%3Cmo%3E-%3C%2Fmo%3E%3Cmi%3Ea%3C%2Fmi%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmi%3Ec%3C%2Fmi%3E%3Cmo%3E-%3C%2Fmo%3E%3Cmi%3Ec%3C%2Fmi%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3C%2Fmtable%3E%3C%2Fmfenced%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmi%3E%3C%2Fmi%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3Ep%3C%2Fmi%3E%3Cmi%3Ep%3C%2Fmi%3E%3Cmi%3El%3C%2Fmi%3E%3Cmi%3Ey%3C%2Fmi%3E%3Cmi%3Ei%3C%2Fmi%3E%3Cmi%3En%3C%2Fmi%3E%3Cmi%3Eg%3C%2Fmi%3E%3Cmo+mathvariant%3D%22italic%22%3E%26nbsp%3B%3C%2Fmo%3E%3Cmsub%3E%3Cmi%3ER%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmo%3E%26rarr%3B%3C%2Fmo%3E%3Cmsub%3E%3Cmi%3ER%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmo%3E-%3C%2Fmo%3E%3Cmsub%3E%3Cmi%3ER%3C%2Fmi%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmi%3En%3C%2Fmi%3E%3Cmi%3Ed%3C%2Fmi%3E%3Cmo+mathvariant%3D%22italic%22%3E%26nbsp%3B%3C%2Fmo%3E%3Cmsub%3E%3Cmi%3ER%3C%2Fmi%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmo%3E%26rarr%3B%3C%2Fmo%3E%3Cmsub%3E%3Cmi%3ER%3C%2Fmi%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmo%3E-%3C%2Fmo%3E%3Cmsub%3E%3Cmi%3ER%3C%2Fmi%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmath%3E) [function.file-get-contents]: failed to open stream: no suitable wrapper could be found [ROOT/vendors/mathml_to_image.php, line 6]
file_get_contents - [internal], line ??
grabDataImage - ROOT/vendors/mathml_to_image.php, line 6
string_between - ROOT/vendors/mathml_to_image.php, line 30
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
math_to_image - ROOT/vendors/mathml_to_image.php, line 51
TopicsController::viewOnSearchTopic() - APP/Controller/TopicsController.php, line 98
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 490
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 191
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 165
[main] - APP/webroot/index.php, line 108
Warning (2): file_get_contents() [function.file-get-contents]: https:// wrapper is disabled in the server configuration by allow_url_fopen=0 [ROOT/vendors/mathml_to_image.php, line 6]
file_get_contents - [internal], line ??
grabDataImage - ROOT/vendors/mathml_to_image.php, line 6
string_between - ROOT/vendors/mathml_to_image.php, line 30
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
math_to_image - ROOT/vendors/mathml_to_image.php, line 51
TopicsController::viewOnSearchTopic() - APP/Controller/TopicsController.php, line 98
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 490
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 191
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 165
[main] - APP/webroot/index.php, line 108
Warning (2): file_get_contents(https://www.wiris.net/demo/editor/render.png?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfrac%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmfrac%3E%3Cmfenced+separators%3D%22%7C%22%3E%3Cmrow%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmo%3E-%3C%2Fmo%3E%3Cmi%3Eb%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmfenced%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmi%3Ec%3C%2Fmi%3E%3Cmo%3E-%3C%2Fmo%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmo%3E%29%3C%2Fmo%3E%3Cmfenced+close%3D%22%7C%22+open%3D%22%7C%22+separators%3D%22%7C%22%3E%3Cmtable%3E%3Cmtr%3E%3Cmtd%3E%3Cmi%3Ea%3C%2Fmi%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmi%3Eb%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3Ec%3C%2Fmi%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr%3E%3Cmtd%3E%3Cmo%3E-%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr%3E%3Cmtd%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmo%3E-%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3C%2Fmtable%3E%3C%2Fmfenced%3E%3C%2Fmath%3E) [function.file-get-contents]: failed to open stream: no suitable wrapper could be found [ROOT/vendors/mathml_to_image.php, line 6]
file_get_contents - [internal], line ??
grabDataImage - ROOT/vendors/mathml_to_image.php, line 6
string_between - ROOT/vendors/mathml_to_image.php, line 30
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
math_to_image - ROOT/vendors/mathml_to_image.php, line 51
TopicsController::viewOnSearchTopic() - APP/Controller/TopicsController.php, line 98
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 490
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 191
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 165
[main] - APP/webroot/index.php, line 108
Warning (2): file_get_contents() [function.file-get-contents]: https:// wrapper is disabled in the server configuration by allow_url_fopen=0 [ROOT/vendors/mathml_to_image.php, line 6]
file_get_contents - [internal], line ??
grabDataImage - ROOT/vendors/mathml_to_image.php, line 6
string_between - ROOT/vendors/mathml_to_image.php, line 30
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
math_to_image - ROOT/vendors/mathml_to_image.php, line 51
TopicsController::viewOnSearchTopic() - APP/Controller/TopicsController.php, line 98
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 490
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 191
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 165
[main] - APP/webroot/index.php, line 108
Warning (2): file_get_contents(https://www.wiris.net/demo/editor/render.png?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfrac%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmfrac%3E%3Cmfenced+separators%3D%22%7C%22%3E%3Cmrow%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmo%3E-%3C%2Fmo%3E%3Cmi%3Eb%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmfenced%3E%3Cmfenced+separators%3D%22%7C%22%3E%3Cmrow%3E%3Cmi%3Ec%3C%2Fmi%3E%3Cmo%3E-%3C%2Fmo%3E%3Cmi%3Ea%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmfenced%3E%3Cmfenced+close%3D%22%7C%22+open%3D%22%7C%22+separators%3D%22%7C%22%3E%3Cmtable%3E%3Cmtr%3E%3Cmtd%3E%3Cmi%3Ea%3C%2Fmi%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmi%3Eb%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3Ec%3C%2Fmi%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr%3E%3Cmtd%3E%3Cmo%3E-%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr%3E%3Cmtd%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3C%2Fmtable%3E%3C%2Fmfenced%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmo%3E%26nbsp%3B%3C%2Fmo%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3Ep%3C%2Fmi%3E%3Cmi%3Ep%3C%2Fmi%3E%3Cmi%3El%3C%2Fmi%3E%3Cmi%3Ey%3C%2Fmi%3E%3Cmi%3Ei%3C%2Fmi%3E%3Cmi%3En%3C%2Fmi%3E%3Cmi%3Eg%3C%2Fmi%3E%3Cmo+mathvariant%3D%22italic%22%3E%26nbsp%3B%3C%2Fmo%3E%3Cmsub%3E%3Cmi%3ER%3C%2Fmi%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmo%3E%26rarr%3B%3C%2Fmo%3E%3Cmsub%3E%3Cmi%3ER%3C%2Fmi%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmsub%3E%3Cmi%3ER%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmath%3E) [function.file-get-contents]: failed to open stream: no suitable wrapper could be found [ROOT/vendors/mathml_to_image.php, line 6]
file_get_contents - [internal], line ??
grabDataImage - ROOT/vendors/mathml_to_image.php, line 6
string_between - ROOT/vendors/mathml_to_image.php, line 30
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
math_to_image - ROOT/vendors/mathml_to_image.php, line 51
TopicsController::viewOnSearchTopic() - APP/Controller/TopicsController.php, line 98
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 490
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 191
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 165
[main] - APP/webroot/index.php, line 108
Warning (2): file_get_contents() [function.file-get-contents]: https:// wrapper is disabled in the server configuration by allow_url_fopen=0 [ROOT/vendors/mathml_to_image.php, line 6]
file_get_contents - [internal], line ??
grabDataImage - ROOT/vendors/mathml_to_image.php, line 6
string_between - ROOT/vendors/mathml_to_image.php, line 30
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
math_to_image - ROOT/vendors/mathml_to_image.php, line 51
TopicsController::viewOnSearchTopic() - APP/Controller/TopicsController.php, line 98
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 490
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 191
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 165
[main] - APP/webroot/index.php, line 108
Warning (2): file_get_contents(https://www.wiris.net/demo/editor/render.png?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%26%238710%3B%3C%2Fmo%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfrac%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmfrac%3E%3Cmfenced+close%3D%22%7C%22+open%3D%22%7C%22+separators%3D%22%7C%22%3E%3Cmtable%3E%3Cmtr%3E%3Cmtd%3E%3Cmsub%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmsub%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmsub%3E%3Cmi%3Ey%3C%2Fmi%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmsub%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr%3E%3Cmtd%3E%3Cmsub%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsub%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmsub%3E%3Cmi%3Ey%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsub%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr%3E%3Cmtd%3E%3Cmsub%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmsub%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmsub%3E%3Cmi%3Ey%3C%2Fmi%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmsub%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3C%2Fmtable%3E%3C%2Fmfenced%3E%3C%2Fmath%3E) [function.file-get-contents]: failed to open stream: no suitable wrapper could be found [ROOT/vendors/mathml_to_image.php, line 6]
file_get_contents - [internal], line ??
grabDataImage - ROOT/vendors/mathml_to_image.php, line 6
string_between - ROOT/vendors/mathml_to_image.php, line 30
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
math_to_image - ROOT/vendors/mathml_to_image.php, line 51
TopicsController::viewOnSearchTopic() - APP/Controller/TopicsController.php, line 98
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 490
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 191
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 165
[main] - APP/webroot/index.php, line 108
Warning (2): file_get_contents() [function.file-get-contents]: https:// wrapper is disabled in the server configuration by allow_url_fopen=0 [ROOT/vendors/mathml_to_image.php, line 6]
file_get_contents - [internal], line ??
grabDataImage - ROOT/vendors/mathml_to_image.php, line 6
string_between - ROOT/vendors/mathml_to_image.php, line 30
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
math_to_image - ROOT/vendors/mathml_to_image.php, line 51
TopicsController::viewOnSearchTopic() - APP/Controller/TopicsController.php, line 98
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 490
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 191
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 165
[main] - APP/webroot/index.php, line 108
Warning (2): file_get_contents(https://www.wiris.net/demo/editor/render.png?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%26%238710%3B%3C%2Fmo%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfrac%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmfrac%3E%3Cmfenced+close%3D%22%7C%22+open%3D%22%7C%22+separators%3D%22%7C%22%3E%3Cmtable%3E%3Cmtr%3E%3Cmtd%3E%3Cmi%3Ek%3C%2Fmi%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr%3E%3Cmtd%3E%3Cmn%3E4%3C%2Fmn%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr%3E%3Cmtd%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3C%2Fmtable%3E%3C%2Fmfenced%3E%3C%2Fmath%3E) [function.file-get-contents]: failed to open stream: no suitable wrapper could be found [ROOT/vendors/mathml_to_image.php, line 6]
file_get_contents - [internal], line ??
grabDataImage - ROOT/vendors/mathml_to_image.php, line 6
string_between - ROOT/vendors/mathml_to_image.php, line 30
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
math_to_image - ROOT/vendors/mathml_to_image.php, line 51
TopicsController::viewOnSearchTopic() - APP/Controller/TopicsController.php, line 98
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 490
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 191
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 165
[main] - APP/webroot/index.php, line 108
Warning (2): file_get_contents() [function.file-get-contents]: https:// wrapper is disabled in the server configuration by allow_url_fopen=0 [ROOT/vendors/mathml_to_image.php, line 6]
file_get_contents - [internal], line ??
grabDataImage - ROOT/vendors/mathml_to_image.php, line 6
string_between - ROOT/vendors/mathml_to_image.php, line 30
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
math_to_image - ROOT/vendors/mathml_to_image.php, line 51
TopicsController::viewOnSearchTopic() - APP/Controller/TopicsController.php, line 98
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 490
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 191
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 165
[main] - APP/webroot/index.php, line 108
Warning (2): file_get_contents(https://www.wiris.net/demo/editor/render.png?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%26%238710%3B%3C%2Fmo%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfrac%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmfrac%3E%3Cmfenced+close%3D%22%7C%22+open%3D%22%7C%22+separators%3D%22%7C%22%3E%3Cmtable%3E%3Cmtr%3E%3Cmtd%3E%3Cmo%3E-%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr%3E%3Cmtd%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E4%3C%2Fmn%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr%3E%3Cmtd%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmi%3Ek%3C%2Fmi%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3C%2Fmtable%3E%3C%2Fmfenced%3E%3C%2Fmath%3E) [function.file-get-contents]: failed to open stream: no suitable wrapper could be found [ROOT/vendors/mathml_to_image.php, line 6]
file_get_contents - [internal], line ??
grabDataImage - ROOT/vendors/mathml_to_image.php, line 6
string_between - ROOT/vendors/mathml_to_image.php, line 30
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
math_to_image - ROOT/vendors/mathml_to_image.php, line 51
TopicsController::viewOnSearchTopic() - APP/Controller/TopicsController.php, line 98
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 490
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 191
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 165
[main] - APP/webroot/index.php, line 108
Warning (2): file_get_contents() [function.file-get-contents]: https:// wrapper is disabled in the server configuration by allow_url_fopen=0 [ROOT/vendors/mathml_to_image.php, line 6]
file_get_contents - [internal], line ??
grabDataImage - ROOT/vendors/mathml_to_image.php, line 6
string_between - ROOT/vendors/mathml_to_image.php, line 30
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
math_to_image - ROOT/vendors/mathml_to_image.php, line 51
TopicsController::viewOnSearchTopic() - APP/Controller/TopicsController.php, line 98
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 490
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 191
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 165
Warning (2): file_get_contents(https://www.wiris.net/demo/editor/render.png?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%26there4%3B%3C%2Fmo%3E%3Cmi%3E%3C%2Fmi%3E%3Cmfrac%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmfrac%3E%3Cmfenced+close%3D%22%7C%22+open%3D%22%7C%22+separators%3D%22%7C%22%3E%3Cmtable%3E%3Cmtr%3E%3Cmtd%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr%3E%3Cmtd%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E6%3C%2Fmn%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr%3E%3Cmtd%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmi%3Ey%3C%2Fmi%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3C%2Fmtable%3E%3C%2Fmfenced%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmath%3E) [function.file-get-contents]: failed to open stream: no suitable wrapper could be found [ROOT/vendors/mathml_to_image.php, line 6]
file_get_contents - [internal], line ??
grabDataImage - ROOT/vendors/mathml_to_image.php, line 6
string_between - ROOT/vendors/mathml_to_image.php, line 30
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
math_to_image - ROOT/vendors/mathml_to_image.php, line 51
TopicsController::viewOnSearchTopic() - APP/Controller/TopicsController.php, line 98
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 490
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 191
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 165
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file_get_contents - [internal], line ??
grabDataImage - ROOT/vendors/mathml_to_image.php, line 6
string_between - ROOT/vendors/mathml_to_image.php, line 30
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
math_to_image - ROOT/vendors/mathml_to_image.php, line 51
TopicsController::viewOnSearchTopic() - APP/Controller/TopicsController.php, line 98
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 490
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 191
Warning (2): file_get_contents(https://www.wiris.net/demo/editor/render.png?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%26there4%3B%3C%2Fmo%3E%3Cmi%3E%3C%2Fmi%3E%3Cmfrac%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmfrac%3E%3Cmfenced+close%3D%22%7C%22+open%3D%22%7C%22+separators%3D%22%7C%22%3E%3Cmtable%3E%3Cmtr%3E%3Cmtd%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr%3E%3Cmtd%3E%3Cmn%3E9%3C%2Fmn%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr%3E%3Cmtd%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmi%3Ey%3C%2Fmi%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3C%2Fmtable%3E%3C%2Fmfenced%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmath%3E) [function.file-get-contents]: failed to open stream: no suitable wrapper could be found [ROOT/vendors/mathml_to_image.php, line 6]
file_get_contents - [internal], line ??
grabDataImage - ROOT/vendors/mathml_to_image.php, line 6
string_between - ROOT/vendors/mathml_to_image.php, line 30
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
math_to_image - ROOT/vendors/mathml_to_image.php, line 51
TopicsController::viewOnSearchTopic() - APP/Controller/TopicsController.php, line 98
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 490
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 191
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file_get_contents - [internal], line ??
grabDataImage - ROOT/vendors/mathml_to_image.php, line 6
string_between - ROOT/vendors/mathml_to_image.php, line 30
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
math_to_image - ROOT/vendors/mathml_to_image.php, line 51
TopicsController::viewOnSearchTopic() - APP/Controller/TopicsController.php, line 98
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 490
Warning (2): file_get_contents(https://www.wiris.net/demo/editor/render.png?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%26%238710%3B%3C%2Fmo%3E%3Cmi%3E%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfrac%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmfrac%3E%3Cmfenced+close%3D%22%7C%22+open%3D%22%7C%22+separators%3D%22%7C%22%3E%3Cmtable%3E%3Cmtr%3E%3Cmtd%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmo%3E-%3C%2Fmo%3E%3Cmn%3E6%3C%2Fmn%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr%3E%3Cmtd%3E%3Cmn%3E5%3C%2Fmn%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E4%3C%2Fmn%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr%3E%3Cmtd%3E%3Cmi%3Ek%3C%2Fmi%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E4%3C%2Fmn%3E%3C%2Fmtd%3E%3Cmtd%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3C%2Fmtable%3E%3C%2Fmfenced%3E%3C%2Fmath%3E) [function.file-get-contents]: failed to open stream: no suitable wrapper could be found [ROOT/vendors/mathml_to_image.php, line 6]
file_get_contents - [internal], line ??
grabDataImage - ROOT/vendors/mathml_to_image.php, line 6
string_between - ROOT/vendors/mathml_to_image.php, line 30
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
math_to_image - ROOT/vendors/mathml_to_image.php, line 51
TopicsController::viewOnSearchTopic() - APP/Controller/TopicsController.php, line 98
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 490
We know that the area of a triangle whose vertices are (x1, y1), (x2, y2), and (x3, y3) is the absolute value of the determinant (∆), where
It is given that the area of triangle is 4 square units.
∴ Δ = ± 4.
(i) The area of the triangle with vertices (k, 0), (4, 0), (0, 2) is given by the relation,
= ½ [k (0 - 2) – 0 (4 - 0) + 1(8 - 0)]
= ½ [-2k + 8] = -k + 4
∴ −k + 4 = ± 4
When −k + 4 = − 4, k = 8.
When −k + 4 = 4, k = 0.
Hence, k = 0, 8.
(ii) The area of the triangle with vertices (−2, 0), (0, 4), (0, k) is given by the relation,
= ½ [-2(4 - k)]
= k – 4
∴ k − 4 = ± 4
When k − 4 = − 4, k = 0.
When k − 4 = 4, k = 8.
Hence, k = 0, 8.
Question 4:
(i) Find equation of line joining (1, 2) and (3, 6) using determinants
(ii) Find equation of line joining (3, 1) and (9, 3) using determinants
Answer
(i) Let P (x, y) be any point on the line joining points A (1, 2) and B (3, 6). Then, the points A, B, and P are collinear. Therefore, the area of triangle ABP will be zero.
⇒ ½ [1 (6 - y) – 2 (3 - x) + 1(3y – 6x)] = 0
⇒ 6 – y – 6 + 2x + 3y – 6x = 0
⇒ 2y – 4x = 0
⇒ y = 2x
Hence, the equation of the line joining the given points is y = 2x.
(ii) Let P (x, y) be any point on the line joining points A (3, 1) and B (9, 3). Then, the points A, B, and P are collinear. Therefore, the area of triangle ABP will be zero.
⇒ ½ [3 (3 - y) – 1 (9 - x) + 1(9y – 3x)] = 0
⇒ 9 – 3y – 9 + x + 9y – 3x = 0
⇒ 6y – 2x = 0
⇒ x – 3y = 0
Hence, the equation of the line joining the given points is x − 3y = 0.
Question 5: If area of triangle is 35 square units with vertices (2, −6), (5, 4), and (k, 4). Then k is
A. 12 B. −2 C. −12, −2 D. 12, −2
Answer: D
The area of the triangle with vertices (2, −6), (5, 4), and (k, 4) is given by the relation,