Answered: Below are given two circles (with centers... |24HA

Messages Timeline Exceptions Events400 Views14 Route Queries10 Models17 Livewire0 Mails Gate Session Request

8.1.0591ms45MBGET college-homework-library/{category}/{subject}/{id}

Booting (398ms)time
Application (192ms)time
1 x Booting (67.4%)
398ms
1 x Application (32.6%)
192ms

Illuminate\Routing\Events\Routing (1.56ms)
Illuminate\Routing\Events\RouteMatched (1.67ms)
Illuminate\Foundation\Events\LocaleUpdated (6.43ms)
eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (602μs)
eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (227μs)
Illuminate\Database\Events\ConnectionEstablished (1.41ms)
Illuminate\Database\Events\StatementPrepared (9.57ms)
Illuminate\Database\Events\QueryExecuted (1.4ms)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (133μs)
eloquent.booting: App\Models\Subject (162μs)
eloquent.booted: App\Models\Subject (64μs)
Illuminate\Database\Events\StatementPrepared (3.33ms)
Illuminate\Database\Events\QueryExecuted (1.94ms)
eloquent.retrieved: App\Models\Subject (93μs)
eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (199μs)
eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (49μs)
Illuminate\Database\Events\StatementPrepared (867μs)
Illuminate\Database\Events\QueryExecuted (3.17ms)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (167μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (458μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (20μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (11μs)
eloquent.booting: App\Models\SubjectCat (487μs)
eloquent.booted: App\Models\SubjectCat (64μs)
Illuminate\Database\Events\StatementPrepared (849μs)
Illuminate\Database\Events\QueryExecuted (1.22ms)
eloquent.retrieved: App\Models\SubjectCat (107μs)
Illuminate\Cache\Events\CacheHit (17.89ms)
Illuminate\Cache\Events\CacheMissed (470μs)
Illuminate\Database\Events\StatementPrepared (1.13ms)
Illuminate\Database\Events\QueryExecuted (4.86ms)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (152μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (24μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (48μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (17μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (12μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (12μs)
Illuminate\Database\Events\StatementPrepared (1.19ms)
Illuminate\Database\Events\QueryExecuted (1.07ms)
eloquent.retrieved: App\Models\Subject (117μs)
Illuminate\Cache\Events\KeyWritten (1.47ms)
Illuminate\Database\Events\StatementPrepared (1.93ms)
Illuminate\Database\Events\QueryExecuted (1.48ms)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (72μs)
Illuminate\Database\Events\StatementPrepared (866μs)
Illuminate\Database\Events\QueryExecuted (1.1ms)
Illuminate\Database\Events\StatementPrepared (1.1ms)
Illuminate\Database\Events\QueryExecuted (937μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (42μs)
Illuminate\Cache\Events\CacheHit (1.04ms)
creating: homework.show (763μs)
composing: homework.show (273μs)
creating: components.breadcrumbs (665μs)
composing: components.breadcrumbs (184μs)
Illuminate\Database\Events\StatementPrepared (1.34ms)
Illuminate\Database\Events\QueryExecuted (1.23ms)
eloquent.retrieved: App\Models\SubjectCat (91μs)
Illuminate\Cache\Events\CacheHit (5.29ms)
Illuminate\Cache\Events\CacheHit (306μs)
Illuminate\Cache\Events\CacheHit (331μs)
Illuminate\Cache\Events\CacheHit (187μs)
Illuminate\Cache\Events\CacheHit (180μs)
Illuminate\Cache\Events\CacheHit (155μs)
Illuminate\Cache\Events\CacheHit (259μs)
Illuminate\Cache\Events\CacheHit (413μs)
Illuminate\Cache\Events\CacheHit (256μs)
Illuminate\Cache\Events\CacheHit (177μs)
Illuminate\Cache\Events\CacheHit (303μs)
Illuminate\Cache\Events\CacheHit (158μs)
Illuminate\Cache\Events\CacheHit (166μs)
Illuminate\Cache\Events\CacheHit (238μs)
Illuminate\Cache\Events\CacheHit (1.65ms)
Illuminate\Cache\Events\CacheHit (203μs)
Illuminate\Cache\Events\CacheHit (188μs)
Illuminate\Cache\Events\CacheHit (153μs)
Illuminate\Cache\Events\CacheHit (174μs)
Illuminate\Cache\Events\CacheHit (149μs)
Illuminate\Cache\Events\CacheHit (171μs)
Illuminate\Cache\Events\CacheHit (146μs)
Illuminate\Cache\Events\CacheHit (184μs)
Illuminate\Cache\Events\CacheHit (168μs)
Illuminate\Cache\Events\CacheHit (193μs)
Illuminate\Cache\Events\CacheHit (274μs)
Illuminate\Cache\Events\CacheHit (194μs)
Illuminate\Cache\Events\CacheHit (173μs)
Illuminate\Cache\Events\CacheHit (301μs)
Illuminate\Cache\Events\CacheHit (208μs)
Illuminate\Cache\Events\CacheHit (392μs)
Illuminate\Cache\Events\CacheHit (275μs)
Illuminate\Cache\Events\CacheHit (222μs)
Illuminate\Cache\Events\CacheHit (174μs)
Illuminate\Cache\Events\CacheHit (295μs)
Illuminate\Cache\Events\CacheHit (181μs)
Illuminate\Cache\Events\CacheHit (189μs)
Illuminate\Cache\Events\CacheHit (155μs)
Illuminate\Cache\Events\CacheHit (188μs)
Illuminate\Cache\Events\CacheHit (169μs)
Illuminate\Cache\Events\CacheHit (185μs)
Illuminate\Cache\Events\CacheHit (457μs)
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Illuminate\Cache\Events\CacheHit (158μs)
Illuminate\Cache\Events\CacheHit (204μs)
Illuminate\Cache\Events\CacheHit (592μs)
Illuminate\Cache\Events\CacheHit (421μs)
Illuminate\Cache\Events\CacheHit (171μs)
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Illuminate\Cache\Events\CacheHit (501μs)
Illuminate\Cache\Events\CacheHit (201μs)
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Illuminate\Cache\Events\CacheHit (195μs)
Illuminate\Cache\Events\CacheHit (210μs)
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Illuminate\Cache\Events\CacheHit (377μs)
Illuminate\Cache\Events\CacheHit (196μs)
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Illuminate\Cache\Events\CacheHit (421μs)
Illuminate\Cache\Events\CacheHit (371μs)
Illuminate\Cache\Events\CacheHit (718μs)
Illuminate\Cache\Events\CacheHit (1.22ms)
Illuminate\Cache\Events\CacheHit (1.12ms)
Illuminate\Cache\Events\CacheHit (415μs)
Illuminate\Cache\Events\CacheHit (333μs)
Illuminate\Cache\Events\CacheHit (465μs)
Illuminate\Cache\Events\CacheHit (235μs)
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Illuminate\Cache\Events\CacheHit (185μs)
Illuminate\Cache\Events\CacheHit (214μs)
Illuminate\Cache\Events\CacheHit (202μs)
Illuminate\Cache\Events\CacheHit (283μs)
Illuminate\Cache\Events\CacheHit (181μs)
Illuminate\Cache\Events\CacheHit (252μs)
Illuminate\Cache\Events\CacheHit (289μs)
Illuminate\Cache\Events\CacheHit (319μs)
Illuminate\Cache\Events\CacheHit (344μs)
Illuminate\Cache\Events\CacheHit (655μs)
Illuminate\Cache\Events\CacheHit (342μs)
Illuminate\Cache\Events\CacheHit (525μs)
Illuminate\Cache\Events\CacheHit (374μs)
Illuminate\Cache\Events\CacheHit (316μs)
Illuminate\Cache\Events\CacheHit (557μs)
Illuminate\Cache\Events\CacheHit (265μs)
Illuminate\Cache\Events\CacheHit (185μs)
Illuminate\Cache\Events\CacheHit (199μs)
Illuminate\Cache\Events\CacheHit (169μs)
Illuminate\Cache\Events\CacheHit (192μs)
Illuminate\Cache\Events\CacheHit (167μs)
Illuminate\Cache\Events\CacheHit (309μs)
Illuminate\Cache\Events\CacheHit (204μs)
Illuminate\Cache\Events\CacheHit (213μs)
Illuminate\Cache\Events\CacheHit (164μs)
Illuminate\Cache\Events\CacheHit (357μs)
Illuminate\Cache\Events\CacheHit (186μs)
Illuminate\Cache\Events\CacheHit (198μs)
Illuminate\Cache\Events\CacheHit (176μs)
Illuminate\Cache\Events\CacheHit (195μs)
Illuminate\Cache\Events\CacheHit (171μs)
Illuminate\Cache\Events\CacheHit (319μs)
Illuminate\Cache\Events\CacheHit (188μs)
Illuminate\Cache\Events\CacheHit (236μs)
Illuminate\Cache\Events\CacheHit (185μs)
Illuminate\Cache\Events\CacheHit (283μs)
Illuminate\Cache\Events\CacheHit (306μs)
Illuminate\Cache\Events\CacheHit (212μs)
Illuminate\Cache\Events\CacheHit (179μs)
Illuminate\Cache\Events\CacheHit (283μs)
Illuminate\Cache\Events\CacheHit (178μs)
Illuminate\Cache\Events\CacheHit (316μs)
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Illuminate\Cache\Events\CacheHit (164μs)
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Illuminate\Cache\Events\CacheHit (386μs)
Illuminate\Cache\Events\CacheHit (221μs)
Illuminate\Cache\Events\CacheHit (259μs)
Illuminate\Cache\Events\CacheHit (194μs)
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Illuminate\Cache\Events\CacheHit (182μs)
Illuminate\Cache\Events\CacheHit (162μs)
Illuminate\Cache\Events\CacheHit (244μs)
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Illuminate\Cache\Events\CacheHit (427μs)
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Illuminate\Cache\Events\CacheHit (270μs)
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Illuminate\Cache\Events\CacheHit (323μs)
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Illuminate\Cache\Events\CacheHit (180μs)
Illuminate\Cache\Events\CacheHit (167μs)
Illuminate\Cache\Events\CacheHit (538μs)
Illuminate\Cache\Events\CacheHit (235μs)
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Illuminate\Cache\Events\CacheHit (182μs)
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Illuminate\Cache\Events\CacheHit (569μs)
Illuminate\Cache\Events\CacheHit (281μs)
Illuminate\Cache\Events\CacheHit (347μs)
creating: site.layouts.app (704μs)
composing: site.layouts.app (26μs)
creating: components.canonical (515μs)
composing: components.canonical (115μs)
creating: components.open-graph (309μs)
composing: components.open-graph (91μs)
creating: site.headers.header (423μs)
composing: site.headers.header (89μs)
Illuminate\Cache\Events\CacheHit (2.23ms)
creating: components.footer (82μs)
composing: components.footer (99μs)
Illuminate\Cache\Events\CacheHit (1.03ms)
Illuminate\Cache\Events\CacheHit (291μs)
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Illuminate\Cache\Events\CacheHit (175μs)
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Illuminate\Cache\Events\CacheHit (196μs)
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creating: components.forms.contact-us (266μs)
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creating: components.forms.get-started (192μs)
composing: components.forms.get-started (181μs)
creating: components.forms.free-tool-download (159μs)
composing: components.forms.free-tool-download (81μs)
creating: components.forms.claim-free-worksheet (205μs)
composing: components.forms.claim-free-worksheet (85μs)
creating: components.forms.tutor-subscription-waitlist (152μs)
composing: components.forms.tutor-subscription-waitlist (88μs)
creating: components.forms.tutor-subscription-join (430μs)
composing: components.forms.tutor-subscription-join (123μs)
creating: components.forms.tutor-support (533μs)
composing: components.forms.tutor-support (81μs)

321 x Illuminate\Cache\Events\CacheHit (20.42%)	121ms
10 x Illuminate\Database\Events\StatementPrepared (3.75%)	22.17ms
10 x Illuminate\Database\Events\QueryExecuted (3.12%)	18.41ms
1 x Illuminate\Foundation\Events\LocaleUpdated (1.09%)	6.43ms
1 x Illuminate\Routing\Events\RouteMatched (0.28%)	1.67ms
1 x Illuminate\Routing\Events\Routing (0.26%)	1.56ms
1 x Illuminate\Cache\Events\KeyWritten (0.25%)	1.47ms
1 x Illuminate\Database\Events\ConnectionEstablished (0.24%)	1.41ms
6 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.13%)	770μs
1 x creating: homework.show (0.13%)	763μs
1 x creating: site.layouts.app (0.12%)	704μs
1 x creating: components.breadcrumbs (0.11%)	665μs
1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.1%)	602μs
1 x creating: components.forms.tutor-support (0.09%)	533μs
1 x creating: components.canonical (0.09%)	515μs
1 x eloquent.booting: App\Models\SubjectCat (0.08%)	487μs
1 x Illuminate\Cache\Events\CacheMissed (0.08%)	470μs
1 x creating: components.forms.tutor-subscription-join (0.07%)	430μs
1 x creating: site.headers.header (0.07%)	423μs
7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.07%)	398μs
1 x creating: components.open-graph (0.05%)	309μs
1 x composing: homework.show (0.05%)	273μs
1 x creating: components.forms.contact-us (0.05%)	266μs
1 x composing: components.forms.contact-us (0.04%)	260μs
1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.04%)	227μs
2 x eloquent.retrieved: App\Models\Subject (0.04%)	210μs
1 x creating: components.forms.claim-free-worksheet (0.03%)	205μs
1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.03%)	199μs
2 x eloquent.retrieved: App\Models\SubjectCat (0.03%)	198μs
1 x creating: components.forms.get-started (0.03%)	192μs
1 x composing: components.breadcrumbs (0.03%)	184μs
1 x composing: components.forms.get-started (0.03%)	181μs
1 x eloquent.booting: App\Models\Subject (0.03%)	162μs
1 x creating: components.forms.free-tool-download (0.03%)	159μs
1 x creating: components.forms.tutor-subscription-waitlist (0.03%)	152μs
1 x composing: components.forms.tutor-subscription-join (0.02%)	123μs
1 x composing: components.canonical (0.02%)	115μs
1 x composing: components.footer (0.02%)	99μs
1 x composing: components.open-graph (0.02%)	91μs
1 x composing: site.headers.header (0.02%)	89μs
1 x composing: components.forms.tutor-subscription-waitlist (0.01%)	88μs
1 x composing: components.forms.claim-free-worksheet (0.01%)	85μs
1 x creating: components.footer (0.01%)	82μs
1 x composing: components.forms.free-tool-download (0.01%)	81μs
1 x composing: components.forms.tutor-support (0.01%)	81μs
1 x eloquent.booted: App\Models\SubjectCat (0.01%)	64μs
1 x eloquent.booted: App\Models\Subject (0.01%)	64μs
1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.01%)	49μs
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

10 statements were executed, 4 of which were duplicates, 6 unique. Show only duplicated25.67ms

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` = '11322' limit 1

9.92mstwenty4_siteHomeworkLibraryController.php#97

Bindings	0: published 1: 0 2: 11322
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)

1.18mstwenty4_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 (11322)

2.81mstwenty4_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

1.13mstwenty4_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` <> 11322 and `subject` = 3 and `status` = 'published' and `price` > 0 order by RAND() limit 6

4.84mstwenty4_siteHomeworkLibraryRepository.php#30

Bindings	0: 11322 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)

1.15mstwenty4_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` = 11322 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc

1.27mstwenty4_siteHomeworkLibrary.php#260

Bindings	0: 11322 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` = 11322 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'teaser' order by `order` asc, `id` asc

1.02mstwenty4_siteHomeworkLibrary.php#260

Bindings	0: 11322 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` = 11322 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'solution' order by `order` asc, `id` asc

1.07mstwenty4_siteHomeworkLibrary.php#260

Bindings	0: 11322 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

1.28mstwenty4_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

App\Models\HomeworkLibrary\HomeworkLibrary: 7HomeworkLibrary.php
App\Models\HomeworkLibrary\HomeworkLibraryFile: 6HomeworkLibraryFile.php
App\Models\Subject: 2Subject.php
App\Models\SubjectCat: 2SubjectCat.php

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Below are given two circles (with centers O and P) tangent to each...

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