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8.1.0429ms45MBGET college-homework-library/{category}/{subject}/{id}

Booting (277ms)time
Application (152ms)time
1 x Booting (64.64%)
277ms
1 x Application (35.36%)
152ms

Illuminate\Routing\Events\Routing (1.41ms)
Illuminate\Routing\Events\RouteMatched (531μs)
Illuminate\Foundation\Events\LocaleUpdated (4.3ms)
eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (162μs)
eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (168μs)
Illuminate\Database\Events\ConnectionEstablished (760μs)
Illuminate\Database\Events\StatementPrepared (16.08ms)
Illuminate\Database\Events\QueryExecuted (1.33ms)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (122μs)
eloquent.booting: App\Models\Subject (74μs)
eloquent.booted: App\Models\Subject (52μs)
Illuminate\Database\Events\StatementPrepared (1.49ms)
Illuminate\Database\Events\QueryExecuted (921μs)
eloquent.retrieved: App\Models\Subject (90μs)
eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (78μs)
eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (39μs)
Illuminate\Database\Events\StatementPrepared (1.17ms)
Illuminate\Database\Events\QueryExecuted (2.16ms)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (124μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (22μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (13μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (11μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (22μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (11μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (11μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (11μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (10μs)
eloquent.booting: App\Models\SubjectCat (453μs)
eloquent.booted: App\Models\SubjectCat (64μs)
Illuminate\Database\Events\StatementPrepared (1.04ms)
Illuminate\Database\Events\QueryExecuted (1.37ms)
eloquent.retrieved: App\Models\SubjectCat (92μs)
Illuminate\Cache\Events\CacheHit (10.55ms)
Illuminate\Cache\Events\CacheMissed (203μs)
Illuminate\Database\Events\StatementPrepared (1.08ms)
Illuminate\Database\Events\QueryExecuted (8.35ms)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (94μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (17μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (11μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (8μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (7μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (6μs)
Illuminate\Database\Events\StatementPrepared (907μs)
Illuminate\Database\Events\QueryExecuted (1.01ms)
eloquent.retrieved: App\Models\Subject (80μs)
Illuminate\Cache\Events\KeyWritten (905μs)
Illuminate\Database\Events\StatementPrepared (2.03ms)
Illuminate\Database\Events\QueryExecuted (1.21ms)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (72μs)
Illuminate\Database\Events\StatementPrepared (1.06ms)
Illuminate\Database\Events\QueryExecuted (1.08ms)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (53μs)
Illuminate\Database\Events\StatementPrepared (879μs)
Illuminate\Database\Events\QueryExecuted (1.06ms)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (49μs)
Illuminate\Cache\Events\CacheHit (415μs)
creating: homework.show (188μs)
composing: homework.show (70μs)
creating: components.breadcrumbs (254μs)
composing: components.breadcrumbs (130μs)
Illuminate\Database\Events\StatementPrepared (1.17ms)
Illuminate\Database\Events\QueryExecuted (940μs)
eloquent.retrieved: App\Models\SubjectCat (105μs)
Illuminate\Cache\Events\CacheMissed (3.95ms)
Illuminate\Database\Events\StatementPrepared (812μs)
Illuminate\Database\Events\QueryExecuted (1.11ms)
eloquent.retrieved: App\Models\SubjectCat (106μs)
Illuminate\Cache\Events\KeyWritten (413μs)
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Illuminate\Cache\Events\CacheHit (203μs)
Illuminate\Cache\Events\CacheHit (176μs)
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Illuminate\Cache\Events\CacheHit (146μs)
Illuminate\Cache\Events\CacheHit (269μs)
Illuminate\Cache\Events\CacheHit (175μs)
Illuminate\Cache\Events\CacheHit (189μs)
Illuminate\Cache\Events\CacheHit (169μs)
Illuminate\Cache\Events\CacheHit (285μs)
Illuminate\Cache\Events\CacheHit (186μs)
Illuminate\Cache\Events\CacheHit (206μs)
Illuminate\Cache\Events\CacheHit (210μs)
Illuminate\Cache\Events\CacheMissed (2.44ms)
Illuminate\Database\Events\StatementPrepared (627μs)
Illuminate\Database\Events\QueryExecuted (1.38ms)
eloquent.retrieved: App\Models\SubjectCat (103μs)
Illuminate\Cache\Events\KeyWritten (1.11ms)
Illuminate\Cache\Events\CacheHit (261μs)
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Illuminate\Cache\Events\CacheHit (151μs)
Illuminate\Cache\Events\CacheHit (136μs)
Illuminate\Cache\Events\CacheHit (146μs)
Illuminate\Cache\Events\CacheHit (143μs)
Illuminate\Cache\Events\CacheMissed (161μs)
Illuminate\Database\Events\StatementPrepared (779μs)
Illuminate\Database\Events\QueryExecuted (1.01ms)
eloquent.retrieved: App\Models\SubjectCat (86μs)
Illuminate\Cache\Events\KeyWritten (865μs)
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Illuminate\Cache\Events\CacheHit (198μs)
Illuminate\Cache\Events\CacheHit (121μs)
Illuminate\Cache\Events\CacheHit (129μs)
Illuminate\Cache\Events\CacheHit (109μs)
Illuminate\Cache\Events\CacheHit (148μs)
Illuminate\Cache\Events\CacheHit (173μs)
Illuminate\Cache\Events\CacheHit (144μs)
Illuminate\Cache\Events\CacheHit (126μs)
Illuminate\Cache\Events\CacheHit (174μs)
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Illuminate\Cache\Events\CacheHit (159μs)
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Illuminate\Cache\Events\CacheHit (122μs)
Illuminate\Cache\Events\CacheHit (227μs)
Illuminate\Cache\Events\CacheHit (140μs)
Illuminate\Cache\Events\CacheHit (142μs)
Illuminate\Cache\Events\CacheHit (186μs)
Illuminate\Cache\Events\CacheHit (180μs)
Illuminate\Cache\Events\CacheHit (119μs)
Illuminate\Cache\Events\CacheMissed (138μs)
Illuminate\Database\Events\StatementPrepared (688μs)
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eloquent.retrieved: App\Models\SubjectCat (84μs)
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Illuminate\Cache\Events\CacheHit (182μs)
Illuminate\Cache\Events\CacheHit (156μs)
Illuminate\Cache\Events\CacheHit (117μs)
Illuminate\Cache\Events\CacheHit (134μs)
Illuminate\Cache\Events\CacheHit (119μs)
Illuminate\Cache\Events\CacheHit (125μs)
Illuminate\Cache\Events\CacheHit (171μs)
Illuminate\Cache\Events\CacheHit (177μs)
Illuminate\Cache\Events\CacheHit (131μs)
Illuminate\Cache\Events\CacheHit (131μs)
Illuminate\Cache\Events\CacheHit (113μs)
Illuminate\Cache\Events\CacheHit (130μs)
Illuminate\Cache\Events\CacheHit (113μs)
Illuminate\Cache\Events\CacheHit (131μs)
Illuminate\Cache\Events\CacheHit (303μs)
Illuminate\Cache\Events\CacheHit (161μs)
Illuminate\Cache\Events\CacheHit (120μs)
Illuminate\Cache\Events\CacheHit (131μs)
Illuminate\Cache\Events\CacheHit (118μs)
Illuminate\Cache\Events\CacheHit (136μs)
Illuminate\Cache\Events\CacheHit (112μs)
Illuminate\Cache\Events\CacheHit (131μs)
Illuminate\Cache\Events\CacheHit (184μs)
Illuminate\Cache\Events\CacheHit (162μs)
Illuminate\Cache\Events\CacheHit (127μs)
Illuminate\Cache\Events\CacheHit (132μs)
Illuminate\Cache\Events\CacheHit (116μs)
Illuminate\Cache\Events\CacheHit (148μs)
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Illuminate\Cache\Events\CacheHit (135μs)
Illuminate\Cache\Events\CacheHit (112μs)
Illuminate\Cache\Events\CacheHit (147μs)
Illuminate\Cache\Events\CacheHit (120μs)
Illuminate\Cache\Events\CacheHit (180μs)
Illuminate\Cache\Events\CacheHit (176μs)
Illuminate\Cache\Events\CacheHit (156μs)
Illuminate\Cache\Events\CacheHit (105μs)
Illuminate\Cache\Events\CacheHit (214μs)
Illuminate\Cache\Events\CacheHit (148μs)
Illuminate\Cache\Events\CacheMissed (140μs)
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eloquent.retrieved: App\Models\SubjectCat (76μs)
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Illuminate\Cache\Events\CacheHit (154μs)
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Illuminate\Cache\Events\CacheMissed (118μs)
Illuminate\Database\Events\StatementPrepared (640μs)
Illuminate\Database\Events\QueryExecuted (957μs)
eloquent.retrieved: App\Models\SubjectCat (65μs)
Illuminate\Cache\Events\KeyWritten (245μs)
Illuminate\Cache\Events\CacheHit (173μs)
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Illuminate\Cache\Events\CacheHit (156μs)
Illuminate\Cache\Events\CacheHit (183μs)
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Illuminate\Cache\Events\CacheHit (131μs)
Illuminate\Cache\Events\CacheHit (156μs)
Illuminate\Cache\Events\CacheHit (133μs)
Illuminate\Cache\Events\CacheHit (102μs)
Illuminate\Cache\Events\CacheHit (128μs)
Illuminate\Cache\Events\CacheHit (114μs)
Illuminate\Cache\Events\CacheHit (636μs)
Illuminate\Cache\Events\CacheHit (114μs)
Illuminate\Cache\Events\CacheHit (137μs)
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Illuminate\Cache\Events\CacheHit (122μs)
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Illuminate\Cache\Events\CacheHit (111μs)
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Illuminate\Cache\Events\CacheHit (119μs)
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Illuminate\Database\Events\StatementPrepared (872μs)
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Illuminate\Cache\Events\KeyWritten (1.4ms)
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312 x Illuminate\Cache\Events\CacheHit (13.08%)	56.09ms
19 x Illuminate\Database\Events\StatementPrepared (7.9%)	33.90ms
19 x Illuminate\Database\Events\QueryExecuted (6.7%)	28.73ms
10 x Illuminate\Cache\Events\KeyWritten (1.9%)	8.16ms
10 x Illuminate\Cache\Events\CacheMissed (1.84%)	7.91ms
1 x Illuminate\Foundation\Events\LocaleUpdated (1%)	4.30ms
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1 x Illuminate\Database\Events\ConnectionEstablished (0.18%)	760μs
1 x Illuminate\Routing\Events\RouteMatched (0.12%)	531μs
1 x eloquent.booting: App\Models\SubjectCat (0.11%)	453μs
12 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.1%)	409μs
1 x creating: site.layouts.app (0.08%)	355μs
1 x creating: components.canonical (0.07%)	309μs
7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.06%)	265μs
1 x creating: components.breadcrumbs (0.06%)	254μs
1 x creating: site.headers.header (0.05%)	223μs
1 x creating: homework.show (0.04%)	188μs
2 x eloquent.retrieved: App\Models\Subject (0.04%)	170μs
1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.04%)	168μs
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1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.04%)	162μs
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1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.02%)	78μs
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1 x composing: components.footer (0.02%)	71μs
1 x composing: homework.show (0.02%)	70μs
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1x components.breadcrumbsbreadcrumbs.blade.phpblade
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1x components.open-graphopen-graph.blade.phpblade
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1x components.forms.contact-uscontact-us.blade.phpblade
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1x components.forms.tutor-subscription-waitlisttutor-subscription-waitlist.blade.phpblade
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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

19 statements were executed, 5 of which were duplicates, 14 unique. Show only duplicated48.14ms

Connection Establishedtwenty4_siteHomeworkLibraryController.php#91

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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` = '57263' limit 1

16.56mstwenty4_siteHomeworkLibraryController.php#97

Bindings	0: published 1: 0 2: 57263
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 (15)

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 (57263)

2.68mstwenty4_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` = 3 limit 1

1.81mstwenty4_siteHomeworkLibrary.php#201

Bindings	0: 3
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` <> 57263 and `subject` = 15 and `status` = 'published' and `price` > 0 order by RAND() limit 6

8.68mstwenty4_siteHomeworkLibraryRepository.php#30

Bindings	0: 57263 1: 15 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 (15)

1.23mstwenty4_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` = 57263 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc

1.34mstwenty4_siteHomeworkLibrary.php#260

Bindings	0: 57263 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` = 57263 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'teaser' order by `order` asc, `id` asc

1.27mstwenty4_siteHomeworkLibrary.php#260

Bindings	0: 57263 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` = 57263 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'solution' order by `order` asc, `id` asc

1.24mstwenty4_siteHomeworkLibrary.php#260

Bindings	0: 57263 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` = 3 limit 1

1.13mstwenty4_siteHomeworkLibrary.php#201

Bindings	0: 3
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select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1

1.32mstwenty4_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

1.08mstwenty4_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

1.39mstwenty4_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

1.09mstwenty4_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

1.14mstwenty4_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

1.22mstwenty4_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` = 34 limit 1

1.28mstwenty4_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

1.24mstwenty4_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

1.39mstwenty4_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: 12HomeworkLibraryFile.php
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App\Models\HomeworkLibrary\HomeworkLibrary: 7HomeworkLibrary.php
App\Models\Subject: 2Subject.php

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1 Functions (15 P.) Prove or disprove the following statements. a...

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