Answered: 1. Show that if f R - R is continuous and... |24HA

Messages Timeline Exceptions Events444 Views14 Route Queries20 Models31 Livewire0 Mails Gate Session Request

8.1.0680ms45MBGET college-homework-library/{category}/{subject}/{id}

Booting (464ms)time
Application (216ms)time
1 x Booting (68.2%)
464ms
1 x Application (31.8%)
216ms

Illuminate\Routing\Events\Routing (1.83ms)
Illuminate\Routing\Events\RouteMatched (543μs)
Illuminate\Foundation\Events\LocaleUpdated (5.14ms)
eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (266μs)
eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (300μs)
Illuminate\Database\Events\ConnectionEstablished (2.77ms)
Illuminate\Database\Events\StatementPrepared (20.05ms)
Illuminate\Database\Events\QueryExecuted (1.53ms)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (269μs)
eloquent.booting: App\Models\Subject (292μs)
eloquent.booted: App\Models\Subject (96μs)
Illuminate\Database\Events\StatementPrepared (2.56ms)
Illuminate\Database\Events\QueryExecuted (1.18ms)
eloquent.retrieved: App\Models\Subject (147μs)
eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (153μs)
eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (139μs)
Illuminate\Database\Events\StatementPrepared (748μs)
Illuminate\Database\Events\QueryExecuted (3.46ms)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (273μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (27μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (14μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (13μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (10μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (10μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (9μs)
eloquent.booting: App\Models\SubjectCat (503μs)
eloquent.booted: App\Models\SubjectCat (68μs)
Illuminate\Database\Events\StatementPrepared (913μs)
Illuminate\Database\Events\QueryExecuted (2.79ms)
eloquent.retrieved: App\Models\SubjectCat (343μs)
Illuminate\Cache\Events\CacheHit (17.09ms)
Illuminate\Cache\Events\CacheMissed (1.32ms)
Illuminate\Database\Events\StatementPrepared (856μs)
Illuminate\Database\Events\QueryExecuted (3.36ms)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (77μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (19μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (11μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (12μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (9μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (11μs)
Illuminate\Database\Events\StatementPrepared (586μs)
Illuminate\Database\Events\QueryExecuted (969μs)
eloquent.retrieved: App\Models\Subject (72μs)
Illuminate\Cache\Events\KeyWritten (991μs)
Illuminate\Database\Events\StatementPrepared (2.39ms)
Illuminate\Database\Events\QueryExecuted (1.46ms)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (75μs)
Illuminate\Database\Events\StatementPrepared (1.07ms)
Illuminate\Database\Events\QueryExecuted (1.2ms)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (59μs)
Illuminate\Database\Events\StatementPrepared (714μs)
Illuminate\Database\Events\QueryExecuted (1ms)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (55μs)
Illuminate\Cache\Events\CacheHit (793μs)
creating: homework.show (369μs)
composing: homework.show (165μs)
creating: components.breadcrumbs (353μs)
composing: components.breadcrumbs (172μs)
Illuminate\Database\Events\StatementPrepared (1.32ms)
Illuminate\Database\Events\QueryExecuted (998μs)
eloquent.retrieved: App\Models\SubjectCat (92μs)
Illuminate\Cache\Events\CacheMissed (7.48ms)
Illuminate\Database\Events\StatementPrepared (795μs)
Illuminate\Database\Events\QueryExecuted (1.3ms)
eloquent.retrieved: App\Models\SubjectCat (162μs)
Illuminate\Cache\Events\KeyWritten (535μs)
Illuminate\Cache\Events\CacheHit (509μs)
Illuminate\Cache\Events\CacheHit (194μs)
Illuminate\Cache\Events\CacheHit (339μs)
Illuminate\Cache\Events\CacheHit (331μs)
Illuminate\Cache\Events\CacheHit (162μs)
Illuminate\Cache\Events\CacheHit (181μs)
Illuminate\Cache\Events\CacheHit (277μs)
Illuminate\Cache\Events\CacheHit (216μs)
Illuminate\Cache\Events\CacheHit (147μs)
Illuminate\Cache\Events\CacheHit (161μs)
Illuminate\Cache\Events\CacheHit (141μs)
Illuminate\Cache\Events\CacheHit (179μs)
Illuminate\Cache\Events\CacheHit (294μs)
Illuminate\Cache\Events\CacheMissed (206μs)
Illuminate\Database\Events\StatementPrepared (920μs)
Illuminate\Database\Events\QueryExecuted (1.05ms)
eloquent.retrieved: App\Models\SubjectCat (97μs)
Illuminate\Cache\Events\KeyWritten (532μs)
Illuminate\Cache\Events\CacheHit (1.5ms)
Illuminate\Cache\Events\CacheHit (232μs)
Illuminate\Cache\Events\CacheHit (191μs)
Illuminate\Cache\Events\CacheHit (199μs)
Illuminate\Cache\Events\CacheHit (190μs)
Illuminate\Cache\Events\CacheHit (229μs)
Illuminate\Cache\Events\CacheHit (191μs)
Illuminate\Cache\Events\CacheMissed (278μs)
Illuminate\Database\Events\StatementPrepared (769μs)
Illuminate\Database\Events\QueryExecuted (989μs)
eloquent.retrieved: App\Models\SubjectCat (68μs)
Illuminate\Cache\Events\KeyWritten (333μs)
Illuminate\Cache\Events\CacheHit (232μs)
Illuminate\Cache\Events\CacheHit (167μs)
Illuminate\Cache\Events\CacheHit (111μs)
Illuminate\Cache\Events\CacheHit (123μs)
Illuminate\Cache\Events\CacheHit (180μs)
Illuminate\Cache\Events\CacheHit (329μs)
Illuminate\Cache\Events\CacheHit (264μs)
Illuminate\Cache\Events\CacheHit (219μs)
Illuminate\Cache\Events\CacheHit (179μs)
Illuminate\Cache\Events\CacheHit (209μs)
Illuminate\Cache\Events\CacheHit (176μs)
Illuminate\Cache\Events\CacheHit (201μs)
Illuminate\Cache\Events\CacheHit (235μs)
Illuminate\Cache\Events\CacheHit (300μs)
Illuminate\Cache\Events\CacheHit (248μs)
Illuminate\Cache\Events\CacheHit (303μs)
Illuminate\Cache\Events\CacheHit (201μs)
Illuminate\Cache\Events\CacheHit (199μs)
Illuminate\Cache\Events\CacheHit (172μs)
Illuminate\Cache\Events\CacheHit (273μs)
Illuminate\Cache\Events\CacheHit (175μs)
Illuminate\Cache\Events\CacheHit (204μs)
Illuminate\Cache\Events\CacheHit (177μs)
Illuminate\Cache\Events\CacheHit (290μs)
Illuminate\Cache\Events\CacheHit (229μs)
Illuminate\Cache\Events\CacheHit (201μs)
Illuminate\Cache\Events\CacheHit (383μs)
Illuminate\Cache\Events\CacheHit (682μs)
Illuminate\Cache\Events\CacheHit (591μs)
Illuminate\Cache\Events\CacheHit (1.97ms)
Illuminate\Cache\Events\CacheHit (304μs)
Illuminate\Cache\Events\CacheMissed (580μs)
Illuminate\Database\Events\StatementPrepared (1.08ms)
Illuminate\Database\Events\QueryExecuted (1.44ms)
eloquent.retrieved: App\Models\SubjectCat (77μs)
Illuminate\Cache\Events\KeyWritten (434μs)
Illuminate\Cache\Events\CacheHit (217μs)
Illuminate\Cache\Events\CacheHit (163μs)
Illuminate\Cache\Events\CacheHit (296μs)
Illuminate\Cache\Events\CacheHit (220μs)
Illuminate\Cache\Events\CacheHit (243μs)
Illuminate\Cache\Events\CacheHit (211μs)
Illuminate\Cache\Events\CacheHit (162μs)
Illuminate\Cache\Events\CacheHit (247μs)
Illuminate\Cache\Events\CacheHit (240μs)
Illuminate\Cache\Events\CacheHit (214μs)
Illuminate\Cache\Events\CacheHit (203μs)
Illuminate\Cache\Events\CacheHit (466μs)
Illuminate\Cache\Events\CacheHit (242μs)
Illuminate\Cache\Events\CacheHit (224μs)
Illuminate\Cache\Events\CacheHit (190μs)
Illuminate\Cache\Events\CacheHit (294μs)
Illuminate\Cache\Events\CacheHit (245μs)
Illuminate\Cache\Events\CacheHit (399μs)
Illuminate\Cache\Events\CacheHit (529μs)
Illuminate\Cache\Events\CacheHit (527μs)
Illuminate\Cache\Events\CacheHit (276μs)
Illuminate\Cache\Events\CacheHit (262μs)
Illuminate\Cache\Events\CacheHit (190μs)
Illuminate\Cache\Events\CacheHit (295μs)
Illuminate\Cache\Events\CacheHit (289μs)
Illuminate\Cache\Events\CacheHit (326μs)
Illuminate\Cache\Events\CacheHit (252μs)
Illuminate\Cache\Events\CacheHit (228μs)
Illuminate\Cache\Events\CacheHit (187μs)
Illuminate\Cache\Events\CacheHit (211μs)
Illuminate\Cache\Events\CacheHit (185μs)
Illuminate\Cache\Events\CacheHit (209μs)
Illuminate\Cache\Events\CacheHit (188μs)
Illuminate\Cache\Events\CacheHit (208μs)
Illuminate\Cache\Events\CacheHit (175μs)
Illuminate\Cache\Events\CacheHit (201μs)
Illuminate\Cache\Events\CacheHit (182μs)
Illuminate\Cache\Events\CacheHit (301μs)
Illuminate\Cache\Events\CacheHit (268μs)
Illuminate\Cache\Events\CacheMissed (287μs)
Illuminate\Database\Events\StatementPrepared (1.06ms)
Illuminate\Database\Events\QueryExecuted (1.19ms)
eloquent.retrieved: App\Models\SubjectCat (93μs)
Illuminate\Cache\Events\KeyWritten (384μs)
Illuminate\Cache\Events\CacheHit (1.03ms)
Illuminate\Cache\Events\CacheHit (204μs)
Illuminate\Cache\Events\CacheHit (163μs)
Illuminate\Cache\Events\CacheHit (319μs)
Illuminate\Cache\Events\CacheHit (264μs)
Illuminate\Cache\Events\CacheHit (576μs)
Illuminate\Cache\Events\CacheHit (327μs)
Illuminate\Cache\Events\CacheMissed (327μs)
Illuminate\Database\Events\StatementPrepared (864μs)
Illuminate\Database\Events\QueryExecuted (2.04ms)
eloquent.retrieved: App\Models\SubjectCat (126μs)
Illuminate\Cache\Events\KeyWritten (553μs)
Illuminate\Cache\Events\CacheHit (377μs)
Illuminate\Cache\Events\CacheHit (1.08ms)
Illuminate\Cache\Events\CacheHit (290μs)
Illuminate\Cache\Events\CacheHit (427μs)
Illuminate\Cache\Events\CacheHit (297μs)
Illuminate\Cache\Events\CacheHit (643μs)
Illuminate\Cache\Events\CacheHit (293μs)
Illuminate\Cache\Events\CacheHit (236μs)
Illuminate\Cache\Events\CacheHit (173μs)
Illuminate\Cache\Events\CacheHit (367μs)
Illuminate\Cache\Events\CacheHit (197μs)
Illuminate\Cache\Events\CacheHit (1.14ms)
Illuminate\Cache\Events\CacheHit (379μs)
Illuminate\Cache\Events\CacheHit (609μs)
Illuminate\Cache\Events\CacheHit (667μs)
Illuminate\Cache\Events\CacheHit (467μs)
Illuminate\Cache\Events\CacheHit (708μs)
Illuminate\Cache\Events\CacheHit (220μs)
Illuminate\Cache\Events\CacheHit (172μs)
Illuminate\Cache\Events\CacheHit (181μs)
Illuminate\Cache\Events\CacheHit (977μs)
Illuminate\Cache\Events\CacheHit (476μs)
Illuminate\Cache\Events\CacheHit (314μs)
Illuminate\Cache\Events\CacheHit (296μs)
Illuminate\Cache\Events\CacheHit (645μs)
Illuminate\Cache\Events\CacheHit (213μs)
Illuminate\Cache\Events\CacheHit (169μs)
Illuminate\Cache\Events\CacheHit (219μs)
Illuminate\Cache\Events\CacheHit (170μs)
Illuminate\Cache\Events\CacheMissed (372μs)
Illuminate\Database\Events\StatementPrepared (929μs)
Illuminate\Database\Events\QueryExecuted (1.07ms)
eloquent.retrieved: App\Models\SubjectCat (89μs)
Illuminate\Cache\Events\KeyWritten (303μs)
Illuminate\Cache\Events\CacheHit (239μs)
Illuminate\Cache\Events\CacheHit (219μs)
Illuminate\Cache\Events\CacheHit (453μs)
Illuminate\Cache\Events\CacheHit (406μs)
Illuminate\Cache\Events\CacheHit (172μs)
Illuminate\Cache\Events\CacheHit (297μs)
Illuminate\Cache\Events\CacheHit (232μs)
Illuminate\Cache\Events\CacheHit (230μs)
Illuminate\Cache\Events\CacheHit (171μs)
Illuminate\Cache\Events\CacheHit (342μs)
Illuminate\Cache\Events\CacheHit (212μs)
Illuminate\Cache\Events\CacheHit (207μs)
Illuminate\Cache\Events\CacheHit (171μs)
Illuminate\Cache\Events\CacheHit (191μs)
Illuminate\Cache\Events\CacheHit (168μs)
Illuminate\Cache\Events\CacheHit (190μs)
Illuminate\Cache\Events\CacheHit (165μs)
Illuminate\Cache\Events\CacheHit (212μs)
Illuminate\Cache\Events\CacheHit (164μs)
Illuminate\Cache\Events\CacheHit (188μs)
Illuminate\Cache\Events\CacheHit (164μs)
Illuminate\Cache\Events\CacheHit (187μs)
Illuminate\Cache\Events\CacheHit (164μs)
Illuminate\Cache\Events\CacheHit (187μs)
Illuminate\Cache\Events\CacheHit (163μs)
Illuminate\Cache\Events\CacheHit (190μs)
Illuminate\Cache\Events\CacheHit (163μs)
Illuminate\Cache\Events\CacheHit (190μs)
Illuminate\Cache\Events\CacheHit (163μs)
Illuminate\Cache\Events\CacheHit (343μs)
Illuminate\Cache\Events\CacheHit (265μs)
Illuminate\Cache\Events\CacheHit (237μs)
Illuminate\Cache\Events\CacheHit (174μs)
Illuminate\Cache\Events\CacheHit (202μs)
Illuminate\Cache\Events\CacheHit (176μs)
Illuminate\Cache\Events\CacheHit (200μs)
Illuminate\Cache\Events\CacheHit (173μs)
Illuminate\Cache\Events\CacheHit (289μs)
Illuminate\Cache\Events\CacheHit (175μs)
Illuminate\Cache\Events\CacheHit (193μs)
Illuminate\Cache\Events\CacheHit (165μs)
Illuminate\Cache\Events\CacheHit (311μs)
Illuminate\Cache\Events\CacheHit (171μs)
Illuminate\Cache\Events\CacheHit (189μs)
Illuminate\Cache\Events\CacheHit (166μs)
Illuminate\Cache\Events\CacheHit (187μs)
Illuminate\Cache\Events\CacheHit (163μs)
Illuminate\Cache\Events\CacheHit (186μs)
Illuminate\Cache\Events\CacheHit (165μs)
Illuminate\Cache\Events\CacheHit (214μs)
Illuminate\Cache\Events\CacheHit (274μs)
Illuminate\Cache\Events\CacheHit (366μs)
Illuminate\Cache\Events\CacheHit (192μs)
Illuminate\Cache\Events\CacheHit (203μs)
Illuminate\Cache\Events\CacheHit (177μs)
Illuminate\Cache\Events\CacheHit (341μs)
Illuminate\Cache\Events\CacheHit (180μs)
Illuminate\Cache\Events\CacheHit (206μs)
Illuminate\Cache\Events\CacheHit (163μs)
Illuminate\Cache\Events\CacheHit (264μs)
Illuminate\Cache\Events\CacheHit (239μs)
Illuminate\Cache\Events\CacheHit (205μs)
Illuminate\Cache\Events\CacheHit (164μs)
Illuminate\Cache\Events\CacheMissed (295μs)
Illuminate\Database\Events\StatementPrepared (1.03ms)
Illuminate\Database\Events\QueryExecuted (925μs)
eloquent.retrieved: App\Models\SubjectCat (89μs)
Illuminate\Cache\Events\KeyWritten (411μs)
Illuminate\Cache\Events\CacheHit (255μs)
Illuminate\Cache\Events\CacheHit (214μs)
Illuminate\Cache\Events\CacheHit (121μs)
Illuminate\Cache\Events\CacheHit (226μs)
Illuminate\Cache\Events\CacheHit (146μs)
Illuminate\Cache\Events\CacheHit (220μs)
Illuminate\Cache\Events\CacheHit (184μs)
Illuminate\Cache\Events\CacheHit (307μs)
Illuminate\Cache\Events\CacheHit (174μs)
Illuminate\Cache\Events\CacheHit (192μs)
Illuminate\Cache\Events\CacheHit (173μs)
Illuminate\Cache\Events\CacheHit (219μs)
Illuminate\Cache\Events\CacheHit (554μs)
Illuminate\Cache\Events\CacheHit (321μs)
Illuminate\Cache\Events\CacheHit (173μs)
Illuminate\Cache\Events\CacheHit (259μs)
Illuminate\Cache\Events\CacheHit (306μs)
Illuminate\Cache\Events\CacheHit (1.38ms)
Illuminate\Cache\Events\CacheHit (166μs)
Illuminate\Cache\Events\CacheHit (294μs)
Illuminate\Cache\Events\CacheHit (154μs)
Illuminate\Cache\Events\CacheHit (187μs)
Illuminate\Cache\Events\CacheHit (167μs)
Illuminate\Cache\Events\CacheHit (305μs)
Illuminate\Cache\Events\CacheHit (234μs)
Illuminate\Cache\Events\CacheHit (189μs)
Illuminate\Cache\Events\CacheHit (165μs)
Illuminate\Cache\Events\CacheHit (184μs)
Illuminate\Cache\Events\CacheHit (162μs)
Illuminate\Cache\Events\CacheHit (180μs)
Illuminate\Cache\Events\CacheHit (162μs)
Illuminate\Cache\Events\CacheHit (180μs)
Illuminate\Cache\Events\CacheHit (158μs)
Illuminate\Cache\Events\CacheHit (179μs)
Illuminate\Cache\Events\CacheHit (165μs)
Illuminate\Cache\Events\CacheHit (217μs)
Illuminate\Cache\Events\CacheHit (171μs)
Illuminate\Cache\Events\CacheHit (198μs)
Illuminate\Cache\Events\CacheHit (160μs)
Illuminate\Cache\Events\CacheHit (179μs)
Illuminate\Cache\Events\CacheHit (161μs)
Illuminate\Cache\Events\CacheHit (175μs)
Illuminate\Cache\Events\CacheHit (163μs)
Illuminate\Cache\Events\CacheHit (205μs)
Illuminate\Cache\Events\CacheHit (257μs)
Illuminate\Cache\Events\CacheHit (257μs)
Illuminate\Cache\Events\CacheHit (171μs)
Illuminate\Cache\Events\CacheHit (181μs)
Illuminate\Cache\Events\CacheHit (161μs)
Illuminate\Cache\Events\CacheHit (178μs)
Illuminate\Cache\Events\CacheHit (160μs)
Illuminate\Cache\Events\CacheHit (177μs)
Illuminate\Cache\Events\CacheHit (217μs)
Illuminate\Cache\Events\CacheHit (208μs)
Illuminate\Cache\Events\CacheHit (166μs)
Illuminate\Cache\Events\CacheHit (203μs)
Illuminate\Cache\Events\CacheHit (161μs)
Illuminate\Cache\Events\CacheHit (181μs)
Illuminate\Cache\Events\CacheHit (160μs)
Illuminate\Cache\Events\CacheHit (174μs)
Illuminate\Cache\Events\CacheHit (157μs)
Illuminate\Cache\Events\CacheHit (179μs)
Illuminate\Cache\Events\CacheHit (159μs)
Illuminate\Cache\Events\CacheHit (191μs)
Illuminate\Cache\Events\CacheHit (166μs)
Illuminate\Cache\Events\CacheHit (180μs)
Illuminate\Cache\Events\CacheHit (284μs)
Illuminate\Cache\Events\CacheHit (231μs)
Illuminate\Cache\Events\CacheHit (164μs)
Illuminate\Cache\Events\CacheHit (208μs)
Illuminate\Cache\Events\CacheHit (168μs)
Illuminate\Cache\Events\CacheHit (265μs)
Illuminate\Cache\Events\CacheHit (278μs)
Illuminate\Cache\Events\CacheHit (186μs)
Illuminate\Cache\Events\CacheHit (170μs)
Illuminate\Cache\Events\CacheHit (182μs)
Illuminate\Cache\Events\CacheHit (157μs)
Illuminate\Cache\Events\CacheHit (277μs)
Illuminate\Cache\Events\CacheHit (177μs)
Illuminate\Cache\Events\CacheHit (199μs)
Illuminate\Cache\Events\CacheHit (153μs)
Illuminate\Cache\Events\CacheHit (169μs)
Illuminate\Cache\Events\CacheHit (154μs)
Illuminate\Cache\Events\CacheHit (182μs)
Illuminate\Cache\Events\CacheHit (159μs)
Illuminate\Cache\Events\CacheHit (190μs)
Illuminate\Cache\Events\CacheHit (247μs)
Illuminate\Cache\Events\CacheHit (348μs)
Illuminate\Cache\Events\CacheHit (242μs)
Illuminate\Cache\Events\CacheMissed (289μs)
Illuminate\Database\Events\StatementPrepared (916μs)
Illuminate\Database\Events\QueryExecuted (1.2ms)
eloquent.retrieved: App\Models\SubjectCat (70μs)
Illuminate\Cache\Events\KeyWritten (358μs)
Illuminate\Cache\Events\CacheHit (187μs)
Illuminate\Cache\Events\CacheHit (213μs)
Illuminate\Cache\Events\CacheHit (286μs)
Illuminate\Cache\Events\CacheHit (274μs)
Illuminate\Cache\Events\CacheHit (179μs)
Illuminate\Cache\Events\CacheHit (209μs)
Illuminate\Cache\Events\CacheHit (169μs)
Illuminate\Cache\Events\CacheHit (309μs)
Illuminate\Cache\Events\CacheHit (366μs)
Illuminate\Cache\Events\CacheHit (351μs)
Illuminate\Cache\Events\CacheHit (405μs)
Illuminate\Cache\Events\CacheHit (191μs)
Illuminate\Cache\Events\CacheHit (165μs)
Illuminate\Cache\Events\CacheHit (187μs)
Illuminate\Cache\Events\CacheHit (328μs)
Illuminate\Cache\Events\CacheHit (274μs)
Illuminate\Cache\Events\CacheHit (182μs)
creating: site.layouts.app (735μs)
composing: site.layouts.app (26μs)
creating: components.canonical (539μs)
composing: components.canonical (112μs)
creating: components.open-graph (229μs)
composing: components.open-graph (86μs)
creating: site.headers.header (299μs)
composing: site.headers.header (77μs)
Illuminate\Cache\Events\CacheHit (2.03ms)
creating: components.footer (224μs)
composing: components.footer (151μs)
Illuminate\Cache\Events\CacheHit (974μs)
Illuminate\Cache\Events\CacheMissed (407μs)
Illuminate\Database\Events\StatementPrepared (821μs)
Illuminate\Database\Events\QueryExecuted (931μs)
eloquent.retrieved: App\Models\SubjectCat (75μs)
Illuminate\Cache\Events\KeyWritten (478μs)
Illuminate\Cache\Events\CacheHit (536μs)
Illuminate\Cache\Events\CacheHit (297μs)
Illuminate\Cache\Events\CacheHit (143μs)
Illuminate\Cache\Events\CacheHit (376μs)
Illuminate\Cache\Events\CacheHit (196μs)
Illuminate\Cache\Events\CacheHit (396μs)
Illuminate\Cache\Events\CacheHit (331μs)
Illuminate\Cache\Events\CacheHit (194μs)
Illuminate\Cache\Events\CacheHit (201μs)
Illuminate\Cache\Events\CacheHit (179μs)
Illuminate\Cache\Events\CacheHit (196μs)
Illuminate\Cache\Events\CacheHit (287μs)
creating: components.forms.contact-us (289μs)
composing: components.forms.contact-us (255μs)
creating: components.forms.get-started (223μs)
composing: components.forms.get-started (243μs)
creating: components.forms.free-tool-download (167μs)
composing: components.forms.free-tool-download (84μs)
creating: components.forms.claim-free-worksheet (132μs)
composing: components.forms.claim-free-worksheet (60μs)
creating: components.forms.tutor-subscription-waitlist (128μs)
composing: components.forms.tutor-subscription-waitlist (67μs)
creating: components.forms.tutor-subscription-join (121μs)
composing: components.forms.tutor-subscription-join (64μs)
creating: components.forms.tutor-support (118μs)
composing: components.forms.tutor-support (66μs)

311 x Illuminate\Cache\Events\CacheHit (14.96%)	102ms
20 x Illuminate\Database\Events\StatementPrepared (5.94%)	40.38ms
20 x Illuminate\Database\Events\QueryExecuted (4.42%)	30.10ms
11 x Illuminate\Cache\Events\CacheMissed (1.74%)	11.84ms
11 x Illuminate\Cache\Events\KeyWritten (0.78%)	5.31ms
1 x Illuminate\Foundation\Events\LocaleUpdated (0.76%)	5.14ms
1 x Illuminate\Database\Events\ConnectionEstablished (0.41%)	2.77ms
1 x Illuminate\Routing\Events\Routing (0.27%)	1.83ms
12 x eloquent.retrieved: App\Models\SubjectCat (0.2%)	1.38ms
1 x creating: site.layouts.app (0.11%)	735μs
10 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.08%)	546μs
1 x Illuminate\Routing\Events\RouteMatched (0.08%)	543μs
1 x creating: components.canonical (0.08%)	539μs
1 x eloquent.booting: App\Models\SubjectCat (0.07%)	503μs
7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.06%)	408μs
1 x creating: homework.show (0.05%)	369μs
1 x creating: components.breadcrumbs (0.05%)	353μs
1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.04%)	300μs
1 x creating: site.headers.header (0.04%)	299μs
1 x eloquent.booting: App\Models\Subject (0.04%)	292μs
1 x creating: components.forms.contact-us (0.04%)	289μs
1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.04%)	266μs
1 x composing: components.forms.contact-us (0.04%)	255μs
1 x composing: components.forms.get-started (0.04%)	243μs
1 x creating: components.open-graph (0.03%)	229μs
1 x creating: components.footer (0.03%)	224μs
1 x creating: components.forms.get-started (0.03%)	223μs
2 x eloquent.retrieved: App\Models\Subject (0.03%)	219μs
1 x composing: components.breadcrumbs (0.03%)	172μs
1 x creating: components.forms.free-tool-download (0.02%)	167μs
1 x composing: homework.show (0.02%)	165μs
1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.02%)	153μs
1 x composing: components.footer (0.02%)	151μs
1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.02%)	139μs
1 x creating: components.forms.claim-free-worksheet (0.02%)	132μs
1 x creating: components.forms.tutor-subscription-waitlist (0.02%)	128μs
1 x creating: components.forms.tutor-subscription-join (0.02%)	121μs
1 x creating: components.forms.tutor-support (0.02%)	118μs
1 x composing: components.canonical (0.02%)	112μs
1 x eloquent.booted: App\Models\Subject (0.01%)	96μs
1 x composing: components.open-graph (0.01%)	86μs
1 x composing: components.forms.free-tool-download (0.01%)	84μs
1 x composing: site.headers.header (0.01%)	77μs
1 x eloquent.booted: App\Models\SubjectCat (0.01%)	68μs
1 x composing: components.forms.tutor-subscription-waitlist (0.01%)	67μs
1 x composing: components.forms.tutor-support (0.01%)	66μs
1 x composing: components.forms.tutor-subscription-join (0.01%)	64μs
1 x composing: components.forms.claim-free-worksheet (0.01%)	60μs
1 x composing: site.layouts.app (0%)	26μs

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 duplicated48.23ms

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` = '11770' limit 1

20.26mstwenty4_siteHomeworkLibraryController.php#97

Bindings	0: published 1: 0 2: 11770
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 (3)

1.05mstwenty4_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 (11770)

3.47mstwenty4_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

1.27mstwenty4_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` <> 11770 and `subject` = 3 and `status` = 'published' and `price` > 0 order by RAND() limit 6

3.21mstwenty4_siteHomeworkLibraryRepository.php#30

Bindings	0: 11770 1: 3 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 (3)

900μstwenty4_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` = 11770 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc

1.41mstwenty4_siteHomeworkLibrary.php#260

Bindings	0: 11770 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` = 11770 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'teaser' order by `order` asc, `id` asc

1.15mstwenty4_siteHomeworkLibrary.php#260

Bindings	0: 11770 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` = 11770 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'solution' order by `order` asc, `id` asc

970μstwenty4_siteHomeworkLibrary.php#260

Bindings	0: 11770 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

1.1mstwenty4_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

1.25mstwenty4_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

1.21mstwenty4_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

1.1mstwenty4_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

1.55mstwenty4_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

1.5mstwenty4_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

1.99mstwenty4_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

1.35mstwenty4_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

1.23mstwenty4_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

1.14mstwenty4_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

1.12mstwenty4_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\SubjectCat: 12SubjectCat.php
App\Models\HomeworkLibrary\HomeworkLibraryFile: 10HomeworkLibraryFile.php
App\Models\HomeworkLibrary\HomeworkLibrary: 7HomeworkLibrary.php
App\Models\Subject: 2Subject.php

_token: 38ckhTR1SS8UGuZpRJBfsz74ELUE87GKPAmm3eC3
utm_source: direct
redirectUrl: /college-homework-library/Mathematics/Geometry/11770
_previous: array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/Mathematics/Geo...
_flash: array:2 [ "old" => [] "new" => [] ]
PHPDEBUGBAR_STACK_DATA: []

path_info

/college-homework-library/Mathematics/Geometry/11770

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=1-6806a17d-51cd475716ab744154e8b05d"
  ]
  "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 => "18.224.54.247"
  ]
  "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 => "Mon, 21 Apr 2025 19:50:21 GMT"
  ]
  "set-cookie" => array:2 [▶
    0 => "XSRF-TOKEN=eyJpdiI6Ik5pTy8vZjU5cnE2Y0VxNXY2RVp5eEE9PSIsInZhbHVlIjoiSnY4Q3FxaXZydjY0RFF6NnBuYU9kTnBjdUZhNVlOYTNhR3RERW1NWXZVSndWdWduNmVNRTN2SnNEampkckdsM0RMcHZxV3UwQWdTNk1IU0ppSFF4S1ExQ3ZVUUsrOEIwMVcvVUhGdzJFeHRZRVJ0aWZTSmJyWU5FV3V2Z3JGOTQiLCJtYWMiOiJiZmE5MTU2YjNjZGY3MDlmZTNlNzMwN2Y2YzMwMjU0NDIzNTUwMTk4ODhlYWViNzM5ZTg5M2I2N2Q3N2NjYzBiIiwidGFnIjoiIn0%3D; expires=Mon, 21 Apr 2025 21:50:21 GMT; Max-Age=7200; path=/; domain=.24houranswers.com; samesite=lax ◀XSRF-TOKEN=eyJpdiI6Ik5pTy8vZjU5cnE2Y0VxNXY2RVp5eEE9PSIsInZhbHVlIjoiSnY4Q3FxaXZydjY0RFF6NnBuYU9kTnBjdUZhNVlOYTNhR3RERW1NWXZVSndWdWduNmVNRTN2SnNEampkckdsM0RMcHZxV ▶"
    1 => "24houranswers_session=eyJpdiI6IlVwaDE4UHRDQ1FpdVk1cXcveGlFQUE9PSIsInZhbHVlIjoiK3pRTDhPM1hjZ3Z4VUlwWkpyRTQxR3VoY1U4dys0SFcyRWV4WnFEQlJ6V2ZQMDZ0NU9HMFo1ZDNSbkFnRUFJcFRxUXZya01uNUE1dnZXeFQ0MThmb1ZkM05KQjVDNDdFYTJFQWNlbXFwL0ZvdWVJZDMxcGhwSU8vT0ZsQXIxZTAiLCJtYWMiOiI1MTEwNmEyNWVlZjY5YWVhODg0MzcxMmRlYTc0OWRmYTk5NjY5ODJmZmMwN2UwNGI1Yzg4ZWY5ZjdmMWRjYjY5IiwidGFnIjoiIn0%3D; expires=Mon, 21 Apr 2025 21:50:21 GMT; Max-Age=7200; path=/; domain=.24houranswers.com; httponly; samesite=lax ◀24houranswers_session=eyJpdiI6IlVwaDE4UHRDQ1FpdVk1cXcveGlFQUE9PSIsInZhbHVlIjoiK3pRTDhPM1hjZ3Z4VUlwWkpyRTQxR3VoY1U4dys0SFcyRWV4WnFEQlJ6V2ZQMDZ0NU9HMFo1ZDNSbkFnRU ▶"
  ]
  "Set-Cookie" => array:2 [▶
    0 => "XSRF-TOKEN=eyJpdiI6Ik5pTy8vZjU5cnE2Y0VxNXY2RVp5eEE9PSIsInZhbHVlIjoiSnY4Q3FxaXZydjY0RFF6NnBuYU9kTnBjdUZhNVlOYTNhR3RERW1NWXZVSndWdWduNmVNRTN2SnNEampkckdsM0RMcHZxV3UwQWdTNk1IU0ppSFF4S1ExQ3ZVUUsrOEIwMVcvVUhGdzJFeHRZRVJ0aWZTSmJyWU5FV3V2Z3JGOTQiLCJtYWMiOiJiZmE5MTU2YjNjZGY3MDlmZTNlNzMwN2Y2YzMwMjU0NDIzNTUwMTk4ODhlYWViNzM5ZTg5M2I2N2Q3N2NjYzBiIiwidGFnIjoiIn0%3D; expires=Mon, 21-Apr-2025 21:50:21 GMT; domain=.24houranswers.com; path=/ ◀XSRF-TOKEN=eyJpdiI6Ik5pTy8vZjU5cnE2Y0VxNXY2RVp5eEE9PSIsInZhbHVlIjoiSnY4Q3FxaXZydjY0RFF6NnBuYU9kTnBjdUZhNVlOYTNhR3RERW1NWXZVSndWdWduNmVNRTN2SnNEampkckdsM0RMcHZxV ▶"
    1 => "24houranswers_session=eyJpdiI6IlVwaDE4UHRDQ1FpdVk1cXcveGlFQUE9PSIsInZhbHVlIjoiK3pRTDhPM1hjZ3Z4VUlwWkpyRTQxR3VoY1U4dys0SFcyRWV4WnFEQlJ6V2ZQMDZ0NU9HMFo1ZDNSbkFnRUFJcFRxUXZya01uNUE1dnZXeFQ0MThmb1ZkM05KQjVDNDdFYTJFQWNlbXFwL0ZvdWVJZDMxcGhwSU8vT0ZsQXIxZTAiLCJtYWMiOiI1MTEwNmEyNWVlZjY5YWVhODg0MzcxMmRlYTc0OWRmYTk5NjY5ODJmZmMwN2UwNGI1Yzg4ZWY5ZjdmMWRjYjY5IiwidGFnIjoiIn0%3D; expires=Mon, 21-Apr-2025 21:50:21 GMT; domain=.24houranswers.com; path=/; httponly ◀24houranswers_session=eyJpdiI6IlVwaDE4UHRDQ1FpdVk1cXcveGlFQUE9PSIsInZhbHVlIjoiK3pRTDhPM1hjZ3Z4VUlwWkpyRTQxR3VoY1U4dys0SFcyRWV4WnFEQlJ6V2ZQMDZ0NU9HMFo1ZDNSbkFnRU ▶"
  ]
]

session_attributes

  0 of 0   
array:6 [▼
  "_token" => "38ckhTR1SS8UGuZpRJBfsz74ELUE87GKPAmm3eC3"
  "utm_source" => "direct"
  "redirectUrl" => "/college-homework-library/Mathematics/Geometry/11770"
  "_previous" => array:1 [▶
    "url" => "https://staging.dev.24houranswers.com/college-homework-library/Mathematics/Geometry/11770"
  ]
  "_flash" => array:2 [▶
    "old" => []
    "new" => []
  ]
  "PHPDEBUGBAR_STACK_DATA" => []
]

1. Show that if f R - R is continuous and has a 2-cycle (a,b}, then...

Similar Homework Solutions

1 x Booting (68.2%)	464ms
1 x Application (31.8%)	216ms