Answered: 2. (a) A dynamical written canonical form... |24HA

Messages Timeline Exceptions Events481 Views14 Route Queries20 Models68 Livewire0 Mails Gate Session Request

8.1.0620ms45MBGET college-homework-library/{category}/{subject}/{id}

Booting (404ms)time
Application (216ms)time
1 x Booting (65.18%)
404ms
1 x Application (34.82%)
216ms

Illuminate\Routing\Events\Routing (1.66ms)
Illuminate\Routing\Events\RouteMatched (544μs)
Illuminate\Foundation\Events\LocaleUpdated (4.67ms)
eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (234μs)
eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (234μs)
Illuminate\Database\Events\ConnectionEstablished (1.16ms)
Illuminate\Database\Events\StatementPrepared (12.85ms)
Illuminate\Database\Events\QueryExecuted (1.32ms)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (106μs)
eloquent.booting: App\Models\Subject (63μs)
eloquent.booted: App\Models\Subject (45μs)
Illuminate\Database\Events\StatementPrepared (1.85ms)
Illuminate\Database\Events\QueryExecuted (1.45ms)
eloquent.retrieved: App\Models\Subject (147μs)
eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (139μs)
eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (59μs)
Illuminate\Database\Events\StatementPrepared (749μs)
Illuminate\Database\Events\QueryExecuted (884μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (86μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (18μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (13μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (11μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (11μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (10μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (10μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (11μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (10μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (10μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (10μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (9μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (10μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (10μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (10μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (9μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (8μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (9μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (9μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (8μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (8μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (10μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (9μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (9μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (11μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (9μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (9μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (8μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (10μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (8μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (9μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (8μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (8μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (9μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (9μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (8μs)
eloquent.booting: App\Models\SubjectCat (582μs)
eloquent.booted: App\Models\SubjectCat (42μs)
Illuminate\Database\Events\StatementPrepared (991μs)
Illuminate\Database\Events\QueryExecuted (1.13ms)
eloquent.retrieved: App\Models\SubjectCat (101μs)
Illuminate\Cache\Events\CacheHit (17.21ms)
Illuminate\Cache\Events\CacheMissed (1.06ms)
Illuminate\Database\Events\StatementPrepared (1.08ms)
Illuminate\Database\Events\QueryExecuted (2.66ms)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (133μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (18μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (9μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (7μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (6μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (6μs)
Illuminate\Database\Events\StatementPrepared (929μs)
Illuminate\Database\Events\QueryExecuted (2.13ms)
eloquent.retrieved: App\Models\Subject (118μs)
Illuminate\Cache\Events\KeyWritten (996μs)
Illuminate\Database\Events\StatementPrepared (1.95ms)
Illuminate\Database\Events\QueryExecuted (1.13ms)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (51μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (15μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (7μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (6μs)
Illuminate\Database\Events\StatementPrepared (1.13ms)
Illuminate\Database\Events\QueryExecuted (864μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (45μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (18μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (12μs)
Illuminate\Database\Events\StatementPrepared (918μs)
Illuminate\Database\Events\QueryExecuted (5.79ms)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (47μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (19μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (11μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (10μs)
Illuminate\Cache\Events\CacheHit (668μs)
creating: homework.show (427μs)
composing: homework.show (161μs)
creating: components.breadcrumbs (474μs)
composing: components.breadcrumbs (172μs)
Illuminate\Database\Events\StatementPrepared (1.51ms)
Illuminate\Database\Events\QueryExecuted (929μs)
eloquent.retrieved: App\Models\SubjectCat (130μs)
Illuminate\Cache\Events\CacheMissed (4.11ms)
Illuminate\Database\Events\StatementPrepared (874μs)
Illuminate\Database\Events\QueryExecuted (1.04ms)
eloquent.retrieved: App\Models\SubjectCat (102μs)
Illuminate\Cache\Events\KeyWritten (491μs)
Illuminate\Cache\Events\CacheHit (254μs)
Illuminate\Cache\Events\CacheHit (304μs)
Illuminate\Cache\Events\CacheHit (252μs)
Illuminate\Cache\Events\CacheHit (202μs)
Illuminate\Cache\Events\CacheHit (202μs)
Illuminate\Cache\Events\CacheHit (383μs)
Illuminate\Cache\Events\CacheHit (186μs)
Illuminate\Cache\Events\CacheHit (194μs)
Illuminate\Cache\Events\CacheHit (325μs)
Illuminate\Cache\Events\CacheHit (229μs)
Illuminate\Cache\Events\CacheHit (181μs)
Illuminate\Cache\Events\CacheHit (185μs)
Illuminate\Cache\Events\CacheHit (171μs)
Illuminate\Cache\Events\CacheMissed (2.73ms)
Illuminate\Database\Events\StatementPrepared (760μs)
Illuminate\Database\Events\QueryExecuted (1.21ms)
eloquent.retrieved: App\Models\SubjectCat (83μs)
Illuminate\Cache\Events\KeyWritten (960μs)
Illuminate\Cache\Events\CacheHit (254μs)
Illuminate\Cache\Events\CacheHit (211μs)
Illuminate\Cache\Events\CacheHit (253μs)
Illuminate\Cache\Events\CacheHit (201μs)
Illuminate\Cache\Events\CacheHit (184μs)
Illuminate\Cache\Events\CacheHit (353μs)
Illuminate\Cache\Events\CacheHit (194μs)
Illuminate\Cache\Events\CacheMissed (237μs)
Illuminate\Database\Events\StatementPrepared (595μs)
Illuminate\Database\Events\QueryExecuted (902μs)
eloquent.retrieved: App\Models\SubjectCat (129μs)
Illuminate\Cache\Events\KeyWritten (1.2ms)
Illuminate\Cache\Events\CacheHit (321μs)
Illuminate\Cache\Events\CacheHit (231μs)
Illuminate\Cache\Events\CacheHit (174μs)
Illuminate\Cache\Events\CacheHit (315μs)
Illuminate\Cache\Events\CacheHit (178μs)
Illuminate\Cache\Events\CacheHit (349μs)
Illuminate\Cache\Events\CacheHit (192μs)
Illuminate\Cache\Events\CacheHit (199μs)
Illuminate\Cache\Events\CacheHit (284μs)
Illuminate\Cache\Events\CacheHit (188μs)
Illuminate\Cache\Events\CacheHit (165μs)
Illuminate\Cache\Events\CacheHit (302μs)
Illuminate\Cache\Events\CacheHit (247μs)
Illuminate\Cache\Events\CacheHit (191μs)
Illuminate\Cache\Events\CacheHit (165μs)
Illuminate\Cache\Events\CacheHit (180μs)
Illuminate\Cache\Events\CacheHit (192μs)
Illuminate\Cache\Events\CacheHit (189μs)
Illuminate\Cache\Events\CacheHit (167μs)
Illuminate\Cache\Events\CacheHit (185μs)
Illuminate\Cache\Events\CacheHit (161μs)
Illuminate\Cache\Events\CacheHit (211μs)
Illuminate\Cache\Events\CacheHit (199μs)
Illuminate\Cache\Events\CacheHit (188μs)
Illuminate\Cache\Events\CacheHit (162μs)
Illuminate\Cache\Events\CacheHit (201μs)
Illuminate\Cache\Events\CacheHit (180μs)
Illuminate\Cache\Events\CacheHit (193μs)
Illuminate\Cache\Events\CacheHit (177μs)
Illuminate\Cache\Events\CacheHit (193μs)
Illuminate\Cache\Events\CacheHit (173μs)
Illuminate\Cache\Events\CacheMissed (184μs)
Illuminate\Database\Events\StatementPrepared (806μs)
Illuminate\Database\Events\QueryExecuted (1.34ms)
eloquent.retrieved: App\Models\SubjectCat (132μs)
Illuminate\Cache\Events\KeyWritten (767μs)
Illuminate\Cache\Events\CacheHit (1.25ms)
Illuminate\Cache\Events\CacheHit (233μs)
Illuminate\Cache\Events\CacheHit (177μs)
Illuminate\Cache\Events\CacheHit (312μs)
Illuminate\Cache\Events\CacheHit (291μs)
Illuminate\Cache\Events\CacheHit (188μs)
Illuminate\Cache\Events\CacheHit (164μs)
Illuminate\Cache\Events\CacheHit (209μs)
Illuminate\Cache\Events\CacheHit (187μs)
Illuminate\Cache\Events\CacheHit (223μs)
Illuminate\Cache\Events\CacheHit (194μs)
Illuminate\Cache\Events\CacheHit (196μs)
Illuminate\Cache\Events\CacheHit (178μs)
Illuminate\Cache\Events\CacheHit (194μs)
Illuminate\Cache\Events\CacheHit (177μs)
Illuminate\Cache\Events\CacheHit (193μs)
Illuminate\Cache\Events\CacheHit (181μs)
Illuminate\Cache\Events\CacheHit (194μs)
Illuminate\Cache\Events\CacheHit (178μs)
Illuminate\Cache\Events\CacheHit (195μs)
Illuminate\Cache\Events\CacheHit (179μs)
Illuminate\Cache\Events\CacheHit (290μs)
Illuminate\Cache\Events\CacheHit (182μs)
Illuminate\Cache\Events\CacheHit (318μs)
Illuminate\Cache\Events\CacheHit (221μs)
Illuminate\Cache\Events\CacheHit (214μs)
Illuminate\Cache\Events\CacheHit (181μs)
Illuminate\Cache\Events\CacheHit (298μs)
Illuminate\Cache\Events\CacheHit (179μs)
Illuminate\Cache\Events\CacheHit (208μs)
Illuminate\Cache\Events\CacheHit (184μs)
Illuminate\Cache\Events\CacheHit (196μs)
Illuminate\Cache\Events\CacheHit (342μs)
Illuminate\Cache\Events\CacheHit (205μs)
Illuminate\Cache\Events\CacheHit (173μs)
Illuminate\Cache\Events\CacheHit (192μs)
Illuminate\Cache\Events\CacheHit (165μs)
Illuminate\Cache\Events\CacheHit (259μs)
Illuminate\Cache\Events\CacheHit (283μs)
Illuminate\Cache\Events\CacheMissed (381μs)
Illuminate\Database\Events\StatementPrepared (1.01ms)
Illuminate\Database\Events\QueryExecuted (1.21ms)
eloquent.retrieved: App\Models\SubjectCat (62μs)
Illuminate\Cache\Events\KeyWritten (337μs)
Illuminate\Cache\Events\CacheHit (1.02ms)
Illuminate\Cache\Events\CacheHit (209μs)
Illuminate\Cache\Events\CacheHit (164μs)
Illuminate\Cache\Events\CacheHit (182μs)
Illuminate\Cache\Events\CacheHit (206μs)
Illuminate\Cache\Events\CacheHit (300μs)
Illuminate\Cache\Events\CacheHit (324μs)
Illuminate\Cache\Events\CacheMissed (518μs)
Illuminate\Database\Events\StatementPrepared (1.19ms)
Illuminate\Database\Events\QueryExecuted (997μs)
eloquent.retrieved: App\Models\SubjectCat (59μs)
Illuminate\Cache\Events\KeyWritten (359μs)
Illuminate\Cache\Events\CacheHit (1.17ms)
Illuminate\Cache\Events\CacheHit (256μs)
Illuminate\Cache\Events\CacheHit (173μs)
Illuminate\Cache\Events\CacheHit (508μs)
Illuminate\Cache\Events\CacheHit (207μs)
Illuminate\Cache\Events\CacheHit (492μs)
Illuminate\Cache\Events\CacheHit (214μs)
Illuminate\Cache\Events\CacheHit (208μs)
Illuminate\Cache\Events\CacheHit (162μs)
Illuminate\Cache\Events\CacheHit (202μs)
Illuminate\Cache\Events\CacheHit (178μs)
Illuminate\Cache\Events\CacheHit (1.05ms)
Illuminate\Cache\Events\CacheHit (161μs)
Illuminate\Cache\Events\CacheHit (180μs)
Illuminate\Cache\Events\CacheHit (163μs)
Illuminate\Cache\Events\CacheHit (177μs)
Illuminate\Cache\Events\CacheHit (164μs)
Illuminate\Cache\Events\CacheHit (266μs)
Illuminate\Cache\Events\CacheHit (180μs)
Illuminate\Cache\Events\CacheHit (178μs)
Illuminate\Cache\Events\CacheHit (159μs)
Illuminate\Cache\Events\CacheHit (287μs)
Illuminate\Cache\Events\CacheHit (255μs)
Illuminate\Cache\Events\CacheHit (179μs)
Illuminate\Cache\Events\CacheHit (297μs)
Illuminate\Cache\Events\CacheHit (386μs)
Illuminate\Cache\Events\CacheHit (258μs)
Illuminate\Cache\Events\CacheHit (373μs)
Illuminate\Cache\Events\CacheHit (214μs)
Illuminate\Cache\Events\CacheMissed (830μs)
Illuminate\Database\Events\StatementPrepared (1.21ms)
Illuminate\Database\Events\QueryExecuted (2.03ms)
eloquent.retrieved: App\Models\SubjectCat (71μs)
Illuminate\Cache\Events\KeyWritten (668μs)
Illuminate\Cache\Events\CacheHit (1.36ms)
Illuminate\Cache\Events\CacheHit (220μs)
Illuminate\Cache\Events\CacheHit (249μs)
Illuminate\Cache\Events\CacheHit (1.66ms)
Illuminate\Cache\Events\CacheHit (201μs)
Illuminate\Cache\Events\CacheHit (321μs)
Illuminate\Cache\Events\CacheHit (192μs)
Illuminate\Cache\Events\CacheHit (350μs)
Illuminate\Cache\Events\CacheHit (309μs)
Illuminate\Cache\Events\CacheHit (526μs)
Illuminate\Cache\Events\CacheHit (487μs)
Illuminate\Cache\Events\CacheHit (573μs)
Illuminate\Cache\Events\CacheHit (179μs)
Illuminate\Cache\Events\CacheHit (317μs)
Illuminate\Cache\Events\CacheHit (179μs)
Illuminate\Cache\Events\CacheHit (183μs)
Illuminate\Cache\Events\CacheHit (160μs)
Illuminate\Cache\Events\CacheHit (180μs)
Illuminate\Cache\Events\CacheHit (173μs)
Illuminate\Cache\Events\CacheHit (182μs)
Illuminate\Cache\Events\CacheHit (159μs)
Illuminate\Cache\Events\CacheHit (336μs)
Illuminate\Cache\Events\CacheHit (183μs)
Illuminate\Cache\Events\CacheHit (182μs)
Illuminate\Cache\Events\CacheHit (249μs)
Illuminate\Cache\Events\CacheHit (182μs)
Illuminate\Cache\Events\CacheHit (161μs)
Illuminate\Cache\Events\CacheHit (181μs)
Illuminate\Cache\Events\CacheHit (159μs)
Illuminate\Cache\Events\CacheHit (337μs)
Illuminate\Cache\Events\CacheHit (191μs)
Illuminate\Cache\Events\CacheHit (195μs)
Illuminate\Cache\Events\CacheHit (231μs)
Illuminate\Cache\Events\CacheHit (190μs)
Illuminate\Cache\Events\CacheHit (173μs)
Illuminate\Cache\Events\CacheHit (182μs)
Illuminate\Cache\Events\CacheHit (160μs)
Illuminate\Cache\Events\CacheHit (180μs)
Illuminate\Cache\Events\CacheHit (172μs)
Illuminate\Cache\Events\CacheHit (181μs)
Illuminate\Cache\Events\CacheHit (159μs)
Illuminate\Cache\Events\CacheHit (250μs)
Illuminate\Cache\Events\CacheHit (179μs)
Illuminate\Cache\Events\CacheHit (176μs)
Illuminate\Cache\Events\CacheHit (242μs)
Illuminate\Cache\Events\CacheHit (196μs)
Illuminate\Cache\Events\CacheHit (165μs)
Illuminate\Cache\Events\CacheHit (179μs)
Illuminate\Cache\Events\CacheHit (157μs)
Illuminate\Cache\Events\CacheHit (208μs)
Illuminate\Cache\Events\CacheHit (324μs)
Illuminate\Cache\Events\CacheHit (309μs)
Illuminate\Cache\Events\CacheHit (260μs)
Illuminate\Cache\Events\CacheHit (200μs)
Illuminate\Cache\Events\CacheHit (174μs)
Illuminate\Cache\Events\CacheHit (181μs)
Illuminate\Cache\Events\CacheHit (240μs)
Illuminate\Cache\Events\CacheHit (199μs)
Illuminate\Cache\Events\CacheHit (175μs)
Illuminate\Cache\Events\CacheHit (176μs)
Illuminate\Cache\Events\CacheHit (152μs)
Illuminate\Cache\Events\CacheHit (259μs)
Illuminate\Cache\Events\CacheHit (161μs)
Illuminate\Cache\Events\CacheMissed (392μs)
Illuminate\Database\Events\StatementPrepared (1.03ms)
Illuminate\Database\Events\QueryExecuted (1.16ms)
eloquent.retrieved: App\Models\SubjectCat (63μs)
Illuminate\Cache\Events\KeyWritten (354μs)
Illuminate\Cache\Events\CacheHit (1.43ms)
Illuminate\Cache\Events\CacheHit (247μs)
Illuminate\Cache\Events\CacheHit (179μs)
Illuminate\Cache\Events\CacheHit (230μs)
Illuminate\Cache\Events\CacheHit (363μs)
Illuminate\Cache\Events\CacheHit (213μs)
Illuminate\Cache\Events\CacheHit (174μs)
Illuminate\Cache\Events\CacheHit (272μs)
Illuminate\Cache\Events\CacheHit (228μs)
Illuminate\Cache\Events\CacheHit (186μs)
Illuminate\Cache\Events\CacheHit (162μs)
Illuminate\Cache\Events\CacheHit (177μs)
Illuminate\Cache\Events\CacheHit (158μs)
Illuminate\Cache\Events\CacheHit (214μs)
Illuminate\Cache\Events\CacheHit (169μs)
Illuminate\Cache\Events\CacheHit (199μs)
Illuminate\Cache\Events\CacheHit (168μs)
Illuminate\Cache\Events\CacheHit (1.05ms)
Illuminate\Cache\Events\CacheHit (158μs)
Illuminate\Cache\Events\CacheHit (182μs)
Illuminate\Cache\Events\CacheHit (375μs)
Illuminate\Cache\Events\CacheHit (190μs)
Illuminate\Cache\Events\CacheHit (166μs)
Illuminate\Cache\Events\CacheHit (304μs)
Illuminate\Cache\Events\CacheHit (523μs)
Illuminate\Cache\Events\CacheHit (448μs)
Illuminate\Cache\Events\CacheHit (216μs)
Illuminate\Cache\Events\CacheHit (180μs)
Illuminate\Cache\Events\CacheHit (269μs)
Illuminate\Cache\Events\CacheHit (188μs)
Illuminate\Cache\Events\CacheHit (163μs)
Illuminate\Cache\Events\CacheHit (179μs)
Illuminate\Cache\Events\CacheHit (158μs)
Illuminate\Cache\Events\CacheHit (179μs)
Illuminate\Cache\Events\CacheHit (299μs)
Illuminate\Cache\Events\CacheHit (215μs)
Illuminate\Cache\Events\CacheHit (272μs)
Illuminate\Cache\Events\CacheHit (557μs)
Illuminate\Cache\Events\CacheHit (339μs)
Illuminate\Cache\Events\CacheHit (192μs)
Illuminate\Cache\Events\CacheHit (163μs)
Illuminate\Cache\Events\CacheHit (494μs)
Illuminate\Cache\Events\CacheHit (168μs)
Illuminate\Cache\Events\CacheHit (181μs)
Illuminate\Cache\Events\CacheHit (160μs)
Illuminate\Cache\Events\CacheHit (181μs)
Illuminate\Cache\Events\CacheHit (159μs)
Illuminate\Cache\Events\CacheHit (179μs)
Illuminate\Cache\Events\CacheHit (160μs)
Illuminate\Cache\Events\CacheHit (179μs)
Illuminate\Cache\Events\CacheHit (158μs)
Illuminate\Cache\Events\CacheHit (178μs)
Illuminate\Cache\Events\CacheHit (164μs)
Illuminate\Cache\Events\CacheHit (180μs)
Illuminate\Cache\Events\CacheHit (260μs)
Illuminate\Cache\Events\CacheHit (264μs)
Illuminate\Cache\Events\CacheHit (202μs)
Illuminate\Cache\Events\CacheHit (186μs)
Illuminate\Cache\Events\CacheHit (165μs)
Illuminate\Cache\Events\CacheHit (292μs)
Illuminate\Cache\Events\CacheHit (170μs)
Illuminate\Cache\Events\CacheHit (246μs)
Illuminate\Cache\Events\CacheHit (175μs)
Illuminate\Cache\Events\CacheHit (180μs)
Illuminate\Cache\Events\CacheHit (160μs)
Illuminate\Cache\Events\CacheHit (178μs)
Illuminate\Cache\Events\CacheHit (158μs)
Illuminate\Cache\Events\CacheHit (182μs)
Illuminate\Cache\Events\CacheHit (160μs)
Illuminate\Cache\Events\CacheHit (214μs)
Illuminate\Cache\Events\CacheHit (180μs)
Illuminate\Cache\Events\CacheHit (186μs)
Illuminate\Cache\Events\CacheHit (170μs)
Illuminate\Cache\Events\CacheHit (272μs)
Illuminate\Cache\Events\CacheHit (239μs)
Illuminate\Cache\Events\CacheHit (303μs)
Illuminate\Cache\Events\CacheHit (357μs)
Illuminate\Cache\Events\CacheHit (406μs)
Illuminate\Cache\Events\CacheHit (181μs)
Illuminate\Cache\Events\CacheHit (282μs)
Illuminate\Cache\Events\CacheHit (191μs)
Illuminate\Cache\Events\CacheHit (286μs)
Illuminate\Cache\Events\CacheHit (208μs)
Illuminate\Cache\Events\CacheHit (286μs)
Illuminate\Cache\Events\CacheHit (253μs)
Illuminate\Cache\Events\CacheHit (213μs)
Illuminate\Cache\Events\CacheHit (167μs)
Illuminate\Cache\Events\CacheHit (188μs)
Illuminate\Cache\Events\CacheHit (161μs)
Illuminate\Cache\Events\CacheMissed (543μs)
Illuminate\Database\Events\StatementPrepared (866μs)
Illuminate\Database\Events\QueryExecuted (956μs)
eloquent.retrieved: App\Models\SubjectCat (63μs)
Illuminate\Cache\Events\KeyWritten (441μs)
Illuminate\Cache\Events\CacheHit (986μs)
Illuminate\Cache\Events\CacheHit (228μs)
Illuminate\Cache\Events\CacheHit (170μs)
Illuminate\Cache\Events\CacheHit (360μs)
Illuminate\Cache\Events\CacheHit (299μs)
Illuminate\Cache\Events\CacheHit (375μs)
Illuminate\Cache\Events\CacheHit (4.32ms)
Illuminate\Cache\Events\CacheHit (1.23ms)
Illuminate\Cache\Events\CacheHit (250μs)
Illuminate\Cache\Events\CacheHit (205μs)
Illuminate\Cache\Events\CacheHit (411μs)
Illuminate\Cache\Events\CacheHit (247μs)
Illuminate\Cache\Events\CacheHit (190μs)
Illuminate\Cache\Events\CacheHit (265μs)
Illuminate\Cache\Events\CacheHit (171μs)
Illuminate\Cache\Events\CacheHit (178μs)
Illuminate\Cache\Events\CacheHit (453μs)
creating: site.layouts.app (540μs)
composing: site.layouts.app (28μs)
creating: components.canonical (935μs)
composing: components.canonical (110μs)
creating: components.open-graph (229μs)
composing: components.open-graph (80μs)
creating: site.headers.header (317μs)
composing: site.headers.header (80μs)
Illuminate\Cache\Events\CacheHit (2.88ms)
creating: components.footer (95μs)
composing: components.footer (107μs)
Illuminate\Cache\Events\CacheHit (2.63ms)
Illuminate\Cache\Events\CacheMissed (590μs)
Illuminate\Database\Events\StatementPrepared (910μs)
Illuminate\Database\Events\QueryExecuted (1.03ms)
eloquent.retrieved: App\Models\SubjectCat (94μs)
Illuminate\Cache\Events\KeyWritten (2.61ms)
Illuminate\Cache\Events\CacheHit (399μs)
Illuminate\Cache\Events\CacheHit (281μs)
Illuminate\Cache\Events\CacheHit (321μs)
Illuminate\Cache\Events\CacheHit (249μs)
Illuminate\Cache\Events\CacheHit (229μs)
Illuminate\Cache\Events\CacheHit (365μs)
Illuminate\Cache\Events\CacheHit (324μs)
Illuminate\Cache\Events\CacheHit (198μs)
Illuminate\Cache\Events\CacheHit (321μs)
Illuminate\Cache\Events\CacheHit (371μs)
Illuminate\Cache\Events\CacheHit (211μs)
Illuminate\Cache\Events\CacheHit (203μs)
creating: components.forms.contact-us (347μs)
composing: components.forms.contact-us (151μs)
creating: components.forms.get-started (115μs)
composing: components.forms.get-started (138μs)
creating: components.forms.free-tool-download (111μs)
composing: components.forms.free-tool-download (67μs)
creating: components.forms.claim-free-worksheet (95μs)
composing: components.forms.claim-free-worksheet (62μs)
creating: components.forms.tutor-subscription-waitlist (95μs)
composing: components.forms.tutor-subscription-waitlist (156μs)
creating: components.forms.tutor-subscription-join (122μs)
composing: components.forms.tutor-subscription-join (70μs)
creating: components.forms.tutor-support (215μs)
composing: components.forms.tutor-support (70μs)

311 x Illuminate\Cache\Events\CacheHit (17.33%)	108ms
20 x Illuminate\Database\Events\StatementPrepared (5.36%)	33.23ms
20 x Illuminate\Database\Events\QueryExecuted (4.86%)	30.17ms
11 x Illuminate\Cache\Events\CacheMissed (1.87%)	11.58ms
11 x Illuminate\Cache\Events\KeyWritten (1.48%)	9.18ms
1 x Illuminate\Foundation\Events\LocaleUpdated (0.75%)	4.67ms
1 x Illuminate\Routing\Events\Routing (0.27%)	1.66ms
1 x Illuminate\Database\Events\ConnectionEstablished (0.19%)	1.16ms
12 x eloquent.retrieved: App\Models\SubjectCat (0.18%)	1.09ms
1 x creating: components.canonical (0.15%)	935μs
47 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.11%)	665μs
1 x eloquent.booting: App\Models\SubjectCat (0.09%)	582μs
1 x Illuminate\Routing\Events\RouteMatched (0.09%)	544μs
1 x creating: site.layouts.app (0.09%)	540μs
1 x creating: components.breadcrumbs (0.08%)	474μs
1 x creating: homework.show (0.07%)	427μs
1 x creating: components.forms.contact-us (0.06%)	347μs
1 x creating: site.headers.header (0.05%)	317μs
7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.05%)	285μs
2 x eloquent.retrieved: App\Models\Subject (0.04%)	265μs
1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.04%)	234μs
1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.04%)	234μs
1 x creating: components.open-graph (0.04%)	229μs
1 x creating: components.forms.tutor-support (0.03%)	215μs
1 x composing: components.breadcrumbs (0.03%)	172μs
1 x composing: homework.show (0.03%)	161μs
1 x composing: components.forms.tutor-subscription-waitlist (0.03%)	156μs
1 x composing: components.forms.contact-us (0.02%)	151μs
1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.02%)	139μs
1 x composing: components.forms.get-started (0.02%)	138μs
1 x creating: components.forms.tutor-subscription-join (0.02%)	122μs
1 x creating: components.forms.get-started (0.02%)	115μs
1 x creating: components.forms.free-tool-download (0.02%)	111μs
1 x composing: components.canonical (0.02%)	110μs
1 x composing: components.footer (0.02%)	107μs
1 x creating: components.forms.tutor-subscription-waitlist (0.02%)	95μs
1 x creating: components.footer (0.02%)	95μs
1 x creating: components.forms.claim-free-worksheet (0.02%)	95μs
1 x composing: components.open-graph (0.01%)	80μs
1 x composing: site.headers.header (0.01%)	80μs
1 x composing: components.forms.tutor-subscription-join (0.01%)	70μs
1 x composing: components.forms.tutor-support (0.01%)	70μs
1 x composing: components.forms.free-tool-download (0.01%)	67μs
1 x eloquent.booting: App\Models\Subject (0.01%)	63μs
1 x composing: components.forms.claim-free-worksheet (0.01%)	62μs
1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.01%)	59μs
1 x eloquent.booted: App\Models\Subject (0.01%)	45μs
1 x eloquent.booted: App\Models\SubjectCat (0.01%)	42μs
1 x composing: site.layouts.app (0%)	28μs

14 templates were rendered

1x homework.showshow.blade.phpblade
1x components.breadcrumbsbreadcrumbs.blade.phpblade
1x site.layouts.appapp.blade.phpblade
1x components.canonicalcanonical.blade.phpblade
1x components.open-graphopen-graph.blade.phpblade
1x site.headers.headerheader.blade.phpblade
1x components.footerfooter.blade.phpblade
1x components.forms.contact-uscontact-us.blade.phpblade
1x components.forms.get-startedget-started.blade.phpblade
1x components.forms.free-tool-downloadfree-tool-download.blade.phpblade
1x components.forms.claim-free-worksheetclaim-free-worksheet.blade.phpblade
1x components.forms.tutor-subscription-waitlisttutor-subscription-waitlist.blade.phpblade
1x components.forms.tutor-subscription-jointutor-subscription-join.blade.phpblade
1x components.forms.tutor-supporttutor-support.blade.phpblade

uri: GET college-homework-library/{category}/{subject}/{id}
middleware: web, utm.parameters
controller: App\Http\Controllers\HomeworkLibraryController@show
namespace
where
as: homework.show
file: app/Http/Controllers/HomeworkLibraryController.php:79-176

20 statements were executed, 5 of which were duplicates, 15 unique. Show only duplicated43.28ms

Connection Establishedtwenty4_siteHomeworkLibraryController.php#91

Backtrace

13. app/Http/Controllers/HomeworkLibraryController.php:91
14. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
15. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
16. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205

select * from `solutionslibrary` where `status` = 'published' and `price` > 0 and `solutionslibrary`.`id` = '61749' limit 1

13.19mstwenty4_siteHomeworkLibraryController.php#97

Bindings	0: published 1: 0 2: 61749
Backtrace	16. app/Http/Controllers/HomeworkLibraryController.php:97 17. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54 18. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43 19. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260 20. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205

select * from `subjects` where `subjects`.`id` in (220)

1.53mstwenty4_siteHomeworkLibraryController.php#97

Backtrace

21. app/Http/Controllers/HomeworkLibraryController.php:97
22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205

select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` in (61749)

1.02mstwenty4_siteHomeworkLibraryController.php#97

Backtrace

21. app/Http/Controllers/HomeworkLibraryController.php:97
22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205

select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1

1.4mstwenty4_siteHomeworkLibrary.php#201

Bindings	0: 1
Backtrace	20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201 26. app/Http/Controllers/HomeworkLibraryController.php:105 27. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54 28. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43 29. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260

select * from `solutionslibrary` where `id` <> 61749 and `subject` = 220 and `status` = 'published' and `price` > 0 order by RAND() limit 6

2.63mstwenty4_siteHomeworkLibraryRepository.php#30

Bindings	0: 61749 1: 220 2: published 3: 0
Backtrace	14. app/Repositories/HomeworkLibraryRepository.php:30 15. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397 16. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419 18. app/Repositories/HomeworkLibraryRepository.php:39 19. app/Http/Controllers/HomeworkLibraryController.php:139

select * from `subjects` where `subjects`.`id` in (220)

2.22mstwenty4_siteHomeworkLibraryRepository.php#30

Backtrace

19. app/Repositories/HomeworkLibraryRepository.php:30
20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
21. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
23. app/Repositories/HomeworkLibraryRepository.php:39
24. app/Http/Controllers/HomeworkLibraryController.php:139

select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 61749 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc

1.01mstwenty4_siteHomeworkLibrary.php#260

Bindings	0: 61749 1: question
Backtrace	15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:58 19. vendor/league/fractal/src/TransformerAbstract.php:128 20. vendor/league/fractal/src/TransformerAbstract.php:107 21. vendor/league/fractal/src/Scope.php:383

select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 61749 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'teaser' order by `order` asc, `id` asc

920μstwenty4_siteHomeworkLibrary.php#260

Bindings	0: 61749 1: teaser
Backtrace	15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:69 19. vendor/league/fractal/src/TransformerAbstract.php:128 20. vendor/league/fractal/src/TransformerAbstract.php:107 21. vendor/league/fractal/src/Scope.php:383

select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 61749 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'solution' order by `order` asc, `id` asc

5.53mstwenty4_siteHomeworkLibrary.php#260

Bindings	0: 61749 1: solution
Backtrace	15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:80 19. vendor/league/fractal/src/TransformerAbstract.php:128 20. vendor/league/fractal/src/TransformerAbstract.php:107 21. vendor/league/fractal/src/Scope.php:383

select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1

1.19mstwenty4_siteHomeworkLibrary.php#201

Bindings	0: 1
Backtrace	20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201 32. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110 33. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58 34. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69 35. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70

select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1

1.23mstwenty4_siteSubject.php#100

Bindings	0: 1
Backtrace	18. app/Models/Subject.php:100 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419 22. app/Models/Subject.php:101 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110

select * from `subject_cats` where `subject_cats`.`id` = 3 limit 1

1.23mstwenty4_siteSubject.php#100

Bindings	0: 3
Backtrace	18. app/Models/Subject.php:100 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419 22. app/Models/Subject.php:101 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110

select * from `subject_cats` where `subject_cats`.`id` = 4 limit 1

1.04mstwenty4_siteSubject.php#100

Bindings	0: 4
Backtrace	18. app/Models/Subject.php:100 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419 22. app/Models/Subject.php:101 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110

select * from `subject_cats` where `subject_cats`.`id` = 10 limit 1

1.26mstwenty4_siteSubject.php#100

Bindings	0: 10
Backtrace	18. app/Models/Subject.php:100 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419 22. app/Models/Subject.php:101 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110

select * from `subject_cats` where `subject_cats`.`id` = 33 limit 1

1.33mstwenty4_siteSubject.php#100

Bindings	0: 33
Backtrace	18. app/Models/Subject.php:100 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419 22. app/Models/Subject.php:101 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110

select * from `subject_cats` where `subject_cats`.`id` = 11 limit 1

1.09mstwenty4_siteSubject.php#100

Bindings	0: 11
Backtrace	18. app/Models/Subject.php:100 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419 22. app/Models/Subject.php:101 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110

select * from `subject_cats` where `subject_cats`.`id` = 5 limit 1

1.53mstwenty4_siteSubject.php#100

Bindings	0: 5
Backtrace	18. app/Models/Subject.php:100 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419 22. app/Models/Subject.php:101 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110

select * from `subject_cats` where `subject_cats`.`id` = 34 limit 1

1.53mstwenty4_siteSubject.php#100

Bindings	0: 34
Backtrace	18. app/Models/Subject.php:100 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419 22. app/Models/Subject.php:101 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110

select * from `subject_cats` where `subject_cats`.`id` = 31 limit 1

1.1mstwenty4_siteSubject.php#100

Bindings	0: 31
Backtrace	18. app/Models/Subject.php:100 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419 22. app/Models/Subject.php:101 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110

select * from `subject_cats` where `subject_cats`.`id` = 36 limit 1

1.3mstwenty4_siteSubject.php#100

Bindings	0: 36
Backtrace	18. app/Models/Subject.php:100 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419 22. app/Models/Subject.php:101 28. view::components.footer:170

App\Models\HomeworkLibrary\HomeworkLibraryFile: 47HomeworkLibraryFile.php
App\Models\SubjectCat: 12SubjectCat.php
App\Models\HomeworkLibrary\HomeworkLibrary: 7HomeworkLibrary.php
App\Models\Subject: 2Subject.php

_token: JOLTSG3HcfhabHLdyYCTAYE1BLvcwbY6CP4ro4zX
utm_source: direct
redirectUrl: /college-homework-library/Mathematics/Dynamical-Systems/61749
_previous: array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/Mathematics/Dyn...
_flash: array:2 [ "old" => [] "new" => [] ]
PHPDEBUGBAR_STACK_DATA: []

path_info

/college-homework-library/Mathematics/Dynamical-Systems/61749

status_code

status_text

format

html

content_type

text/html; charset=UTF-8

request_query

[]

request_request

[]

request_headers

  0 of 0   
array:21 [▼
  "priority" => array:1 [▶
    0 => "u=0, i"
  ]
  "accept-encoding" => array:1 [▶
    0 => "gzip, deflate, br, zstd"
  ]
  "sec-fetch-dest" => array:1 [▶
    0 => "document"
  ]
  "sec-fetch-user" => array:1 [▶
    0 => "?1"
  ]
  "sec-fetch-mode" => array:1 [▶
    0 => "navigate"
  ]
  "sec-fetch-site" => array:1 [▶
    0 => "none"
  ]
  "accept" => array:1 [▶
    0 => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7"
  ]
  "user-agent" => array:1 [▶
    0 => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)"
  ]
  "upgrade-insecure-requests" => array:1 [▶
    0 => "1"
  ]
  "sec-ch-ua-platform" => array:1 [▶
    0 => ""Windows""
  ]
  "sec-ch-ua-mobile" => array:1 [▶
    0 => "?0"
  ]
  "sec-ch-ua" => array:1 [▶
    0 => ""HeadlessChrome";v="129", "Not=A?Brand";v="8", "Chromium";v="129""
  ]
  "cache-control" => array:1 [▶
    0 => "no-cache"
  ]
  "pragma" => array:1 [▶
    0 => "no-cache"
  ]
  "x-amzn-trace-id" => array:1 [▶
    0 => "Root=1-67ffe264-624c85d4573a0cd1008428fe"
  ]
  "host" => array:1 [▶
    0 => "staging.dev.24houranswers.com"
  ]
  "x-forwarded-port" => array:1 [▶
    0 => "443"
  ]
  "x-forwarded-proto" => array:1 [▶
    0 => "https"
  ]
  "x-forwarded-for" => array:1 [▶
    0 => "3.144.8.165"
  ]
  "content-length" => array:1 [▶
    0 => ""
  ]
  "content-type" => array:1 [▶
    0 => ""
  ]
]

request_cookies

[]

response_headers

  0 of 0   
array:5 [▼
  "content-type" => array:1 [▶
    0 => "text/html; charset=UTF-8"
  ]
  "cache-control" => array:1 [▶
    0 => "no-cache, private"
  ]
  "date" => array:1 [▶
    0 => "Wed, 16 Apr 2025 17:01:24 GMT"
  ]
  "set-cookie" => array:2 [▶
    0 => "XSRF-TOKEN=eyJpdiI6IjRSNTZ6VkN3ZnNQeUlBaXVpMndVYlE9PSIsInZhbHVlIjoiSVRzVXU4b2NYekFXTjNSMTBWR3I3T3BQZW9XdnVaUEs2NmpkNi92YTBSQXp0alIzb1c0TkJoWmJHdXpyNUplRW9OZ1lWQUtzL2xWZ2dxVWpmU2Yvak8xNUMzQkxuMnVNR05jWXlESzdCbGh5d3Y0QnIyOEJJK2RUN0FQVHM4cHkiLCJtYWMiOiI1NWI0MzEzOWZlNzdkMzZmN2M2ZDAyNTJmMzRjYzcwMmU5YzFjN2VkZDVlYWJmM2QxOWQ2M2RmNzExOWFkNTM4IiwidGFnIjoiIn0%3D; expires=Wed, 16 Apr 2025 19:01:24 GMT; Max-Age=7200; path=/; domain=.24houranswers.com; samesite=lax ◀XSRF-TOKEN=eyJpdiI6IjRSNTZ6VkN3ZnNQeUlBaXVpMndVYlE9PSIsInZhbHVlIjoiSVRzVXU4b2NYekFXTjNSMTBWR3I3T3BQZW9XdnVaUEs2NmpkNi92YTBSQXp0alIzb1c0TkJoWmJHdXpyNUplRW9OZ1lWQ ▶"
    1 => "24houranswers_session=eyJpdiI6InBpU2dqQ0NMUEhONlpNU1VhL0tnbUE9PSIsInZhbHVlIjoiWmpiUDA3ejNscThNdHhrOEIvKzU5RXBMRWJWWkFSMHowTjhvVC9tU25EZGxZbmw4S0VyVjJOa1V4NHNPMTA1ZGNrN2dlUDJLSHBiRkh6ajZjOGloTkxrNEQrMlB0Q3BVLzlURnRseC9yWURjZUVCSGw5dFJveExrNTkrbU03TnciLCJtYWMiOiIyYTQ3ODNkNGRkYjMyOTc5MTU2MWY2ZjUxNDE1ZTZjMmFkNmUxMmY3OTA3ZTgwN2Y3ZDBkNjI4MjY1YTM3MmYzIiwidGFnIjoiIn0%3D; expires=Wed, 16 Apr 2025 19:01:24 GMT; Max-Age=7200; path=/; domain=.24houranswers.com; httponly; samesite=lax ◀24houranswers_session=eyJpdiI6InBpU2dqQ0NMUEhONlpNU1VhL0tnbUE9PSIsInZhbHVlIjoiWmpiUDA3ejNscThNdHhrOEIvKzU5RXBMRWJWWkFSMHowTjhvVC9tU25EZGxZbmw4S0VyVjJOa1V4NHNPMT ▶"
  ]
  "Set-Cookie" => array:2 [▶
    0 => "XSRF-TOKEN=eyJpdiI6IjRSNTZ6VkN3ZnNQeUlBaXVpMndVYlE9PSIsInZhbHVlIjoiSVRzVXU4b2NYekFXTjNSMTBWR3I3T3BQZW9XdnVaUEs2NmpkNi92YTBSQXp0alIzb1c0TkJoWmJHdXpyNUplRW9OZ1lWQUtzL2xWZ2dxVWpmU2Yvak8xNUMzQkxuMnVNR05jWXlESzdCbGh5d3Y0QnIyOEJJK2RUN0FQVHM4cHkiLCJtYWMiOiI1NWI0MzEzOWZlNzdkMzZmN2M2ZDAyNTJmMzRjYzcwMmU5YzFjN2VkZDVlYWJmM2QxOWQ2M2RmNzExOWFkNTM4IiwidGFnIjoiIn0%3D; expires=Wed, 16-Apr-2025 19:01:24 GMT; domain=.24houranswers.com; path=/ ◀XSRF-TOKEN=eyJpdiI6IjRSNTZ6VkN3ZnNQeUlBaXVpMndVYlE9PSIsInZhbHVlIjoiSVRzVXU4b2NYekFXTjNSMTBWR3I3T3BQZW9XdnVaUEs2NmpkNi92YTBSQXp0alIzb1c0TkJoWmJHdXpyNUplRW9OZ1lWQ ▶"
    1 => "24houranswers_session=eyJpdiI6InBpU2dqQ0NMUEhONlpNU1VhL0tnbUE9PSIsInZhbHVlIjoiWmpiUDA3ejNscThNdHhrOEIvKzU5RXBMRWJWWkFSMHowTjhvVC9tU25EZGxZbmw4S0VyVjJOa1V4NHNPMTA1ZGNrN2dlUDJLSHBiRkh6ajZjOGloTkxrNEQrMlB0Q3BVLzlURnRseC9yWURjZUVCSGw5dFJveExrNTkrbU03TnciLCJtYWMiOiIyYTQ3ODNkNGRkYjMyOTc5MTU2MWY2ZjUxNDE1ZTZjMmFkNmUxMmY3OTA3ZTgwN2Y3ZDBkNjI4MjY1YTM3MmYzIiwidGFnIjoiIn0%3D; expires=Wed, 16-Apr-2025 19:01:24 GMT; domain=.24houranswers.com; path=/; httponly ◀24houranswers_session=eyJpdiI6InBpU2dqQ0NMUEhONlpNU1VhL0tnbUE9PSIsInZhbHVlIjoiWmpiUDA3ejNscThNdHhrOEIvKzU5RXBMRWJWWkFSMHowTjhvVC9tU25EZGxZbmw4S0VyVjJOa1V4NHNPMT ▶"
  ]
]

session_attributes

  0 of 0   
array:6 [▼
  "_token" => "JOLTSG3HcfhabHLdyYCTAYE1BLvcwbY6CP4ro4zX"
  "utm_source" => "direct"
  "redirectUrl" => "/college-homework-library/Mathematics/Dynamical-Systems/61749"
  "_previous" => array:1 [▶
    "url" => "https://staging.dev.24houranswers.com/college-homework-library/Mathematics/Dynamical-Systems/61749"
  ]
  "_flash" => array:2 [▶
    "old" => []
    "new" => []
  ]
  "PHPDEBUGBAR_STACK_DATA" => []
]

2. (a) A dynamical written canonical form gives as SY/ with (:) a...

Similar Homework Solutions

1 x Booting (65.18%)	404ms
1 x Application (34.82%)	216ms