1. Let Pn denote the set of all polynomials over R of degree at mos...

Question
Solution Preview

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references.
Students may use these solutions for personal skill-building and practice.
Unethical use is strictly forbidden.

This is only a preview of the solution.
Please use the purchase button to see the entire solution.
By purchasing this solution you'll be able to access the following files:
Solution.pdf
Purchase Solution
$35.00
Google Pay
Amazon
Paypal
Mastercard
Visacard
Discover
Amex
View Available Mathematics Tutors 529 tutors matched
ionut
Ionut
(ionut)
Hi! MSc Applied Informatics & Computer Science Engineer. Practical experience in many CS & IT branches.Research work & homework
5/5 (5,654+ sessions)
2 hours avg response
Leo
Leo
(Leo)
Hi! I have been a professor in New York and taught in a math department and in an applied math department.
4.9/5 (5,652+ sessions)
2 hours avg response
Pranay
(math1983)
Ph.D. in mathematics and working as an Assistant Professor in University. I can provide help in mathematics, statistics and allied areas.
4.6/5 (5,512+ sessions)
1 hour avg response

Similar Homework Solutions

8.1.0PHP Version301msRequest Duration45MBMemory UsageGET college-homework-library/{category}/{subject}/{id}Route
    • Booting (176ms)time
    • Application (125ms)time
    • 1 x Booting (58.53%)
      176ms
      1 x Application (41.47%)
      125ms
      • Illuminate\Routing\Events\Routing (1.02ms)
      • Illuminate\Routing\Events\RouteMatched (357μs)
      • Illuminate\Foundation\Events\LocaleUpdated (3.92ms)
      • eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (154μs)
      • eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (156μs)
      • Illuminate\Database\Events\ConnectionEstablished (779μs)
      • Illuminate\Database\Events\StatementPrepared (9.63ms)
      • Illuminate\Database\Events\QueryExecuted (1ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (94μs)
      • eloquent.booting: App\Models\Subject (93μs)
      • eloquent.booted: App\Models\Subject (42μs)
      • Illuminate\Database\Events\StatementPrepared (1.44ms)
      • Illuminate\Database\Events\QueryExecuted (779μs)
      • eloquent.retrieved: App\Models\Subject (90μs)
      • eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (99μs)
      • eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (39μs)
      • Illuminate\Database\Events\StatementPrepared (574μs)
      • Illuminate\Database\Events\QueryExecuted (656μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (58μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (14μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (7μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (6μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (5μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (5μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (5μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (5μs)
      • eloquent.booting: App\Models\SubjectCat (303μs)
      • eloquent.booted: App\Models\SubjectCat (38μs)
      • Illuminate\Database\Events\StatementPrepared (614μs)
      • Illuminate\Database\Events\QueryExecuted (735μs)
      • eloquent.retrieved: App\Models\SubjectCat (68μs)
      • Illuminate\Cache\Events\CacheHit (9.93ms)
      • Illuminate\Cache\Events\CacheMissed (194μs)
      • Illuminate\Database\Events\StatementPrepared (883μs)
      • Illuminate\Database\Events\QueryExecuted (9.11ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (86μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (16μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (8μs)
      • 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 (811μs)
      • Illuminate\Database\Events\QueryExecuted (796μs)
      • eloquent.retrieved: App\Models\Subject (79μs)
      • Illuminate\Cache\Events\KeyWritten (1.68ms)
      • Illuminate\Database\Events\StatementPrepared (1.53ms)
      • Illuminate\Database\Events\QueryExecuted (766μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (49μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (13μs)
      • Illuminate\Database\Events\StatementPrepared (912μs)
      • Illuminate\Database\Events\QueryExecuted (862μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (36μs)
      • Illuminate\Database\Events\StatementPrepared (694μs)
      • Illuminate\Database\Events\QueryExecuted (708μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (35μs)
      • Illuminate\Cache\Events\CacheHit (523μs)
      • creating: homework.show (399μs)
      • composing: homework.show (117μs)
      • creating: components.breadcrumbs (271μs)
      • composing: components.breadcrumbs (116μs)
      • Illuminate\Database\Events\StatementPrepared (1.02ms)
      • Illuminate\Database\Events\QueryExecuted (817μs)
      • eloquent.retrieved: App\Models\SubjectCat (106μs)
      • Illuminate\Cache\Events\CacheMissed (4.01ms)
      • Illuminate\Database\Events\StatementPrepared (666μs)
      • Illuminate\Database\Events\QueryExecuted (768μs)
      • eloquent.retrieved: App\Models\SubjectCat (52μs)
      • Illuminate\Cache\Events\KeyWritten (279μs)
      • Illuminate\Cache\Events\CacheHit (182μs)
      • Illuminate\Cache\Events\CacheHit (143μs)
      • Illuminate\Cache\Events\CacheHit (106μs)
      • Illuminate\Cache\Events\CacheHit (117μs)
      • Illuminate\Cache\Events\CacheHit (226μs)
      • Illuminate\Cache\Events\CacheHit (218μs)
      • Illuminate\Cache\Events\CacheHit (114μs)
      • Illuminate\Cache\Events\CacheHit (118μs)
      • Illuminate\Cache\Events\CacheHit (98μs)
      • Illuminate\Cache\Events\CacheHit (113μs)
      • Illuminate\Cache\Events\CacheHit (98μs)
      • Illuminate\Cache\Events\CacheHit (113μs)
      • Illuminate\Cache\Events\CacheHit (95μs)
      • Illuminate\Cache\Events\CacheMissed (184μs)
      • Illuminate\Database\Events\StatementPrepared (614μs)
      • Illuminate\Database\Events\QueryExecuted (764μs)
      • eloquent.retrieved: App\Models\SubjectCat (50μs)
      • Illuminate\Cache\Events\KeyWritten (258μs)
      • Illuminate\Cache\Events\CacheHit (170μs)
      • Illuminate\Cache\Events\CacheHit (144μs)
      • Illuminate\Cache\Events\CacheHit (114μs)
      • Illuminate\Cache\Events\CacheHit (128μs)
      • Illuminate\Cache\Events\CacheHit (106μs)
      • Illuminate\Cache\Events\CacheHit (122μs)
      • Illuminate\Cache\Events\CacheHit (103μs)
      • Illuminate\Cache\Events\CacheMissed (166μs)
      • Illuminate\Database\Events\StatementPrepared (549μs)
      • Illuminate\Database\Events\QueryExecuted (747μs)
      • eloquent.retrieved: App\Models\SubjectCat (50μs)
      • Illuminate\Cache\Events\KeyWritten (263μs)
      • Illuminate\Cache\Events\CacheHit (162μs)
      • Illuminate\Cache\Events\CacheHit (148μs)
      • Illuminate\Cache\Events\CacheHit (107μs)
      • Illuminate\Cache\Events\CacheHit (137μs)
      • Illuminate\Cache\Events\CacheHit (101μs)
      • Illuminate\Cache\Events\CacheHit (141μs)
      • Illuminate\Cache\Events\CacheHit (160μs)
      • Illuminate\Cache\Events\CacheHit (152μs)
      • Illuminate\Cache\Events\CacheHit (111μs)
      • Illuminate\Cache\Events\CacheHit (125μs)
      • Illuminate\Cache\Events\CacheHit (99μs)
      • Illuminate\Cache\Events\CacheHit (126μs)
      • Illuminate\Cache\Events\CacheHit (105μs)
      • Illuminate\Cache\Events\CacheHit (119μs)
      • Illuminate\Cache\Events\CacheHit (96μs)
      • Illuminate\Cache\Events\CacheHit (121μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • Illuminate\Cache\Events\CacheHit (252μs)
      • Illuminate\Cache\Events\CacheHit (121μs)
      • Illuminate\Cache\Events\CacheHit (134μs)
      • Illuminate\Cache\Events\CacheHit (102μs)
      • Illuminate\Cache\Events\CacheHit (195μs)
      • Illuminate\Cache\Events\CacheHit (132μs)
      • Illuminate\Cache\Events\CacheHit (123μs)
      • Illuminate\Cache\Events\CacheHit (97μs)
      • Illuminate\Cache\Events\CacheHit (122μs)
      • Illuminate\Cache\Events\CacheHit (104μs)
      • Illuminate\Cache\Events\CacheHit (119μs)
      • Illuminate\Cache\Events\CacheHit (102μs)
      • Illuminate\Cache\Events\CacheHit (117μs)
      • Illuminate\Cache\Events\CacheHit (161μs)
      • Illuminate\Cache\Events\CacheMissed (201μs)
      • Illuminate\Database\Events\StatementPrepared (579μs)
      • Illuminate\Database\Events\QueryExecuted (758μs)
      • eloquent.retrieved: App\Models\SubjectCat (50μs)
      • Illuminate\Cache\Events\KeyWritten (239μs)
      • Illuminate\Cache\Events\CacheHit (155μs)
      • Illuminate\Cache\Events\CacheHit (146μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (140μs)
      • Illuminate\Cache\Events\CacheHit (100μs)
      • Illuminate\Cache\Events\CacheHit (153μs)
      • Illuminate\Cache\Events\CacheHit (136μs)
      • Illuminate\Cache\Events\CacheHit (162μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • Illuminate\Cache\Events\CacheHit (124μs)
      • Illuminate\Cache\Events\CacheHit (105μs)
      • Illuminate\Cache\Events\CacheHit (121μs)
      • Illuminate\Cache\Events\CacheHit (104μs)
      • Illuminate\Cache\Events\CacheHit (119μs)
      • Illuminate\Cache\Events\CacheHit (101μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (126μs)
      • Illuminate\Cache\Events\CacheHit (122μs)
      • Illuminate\Cache\Events\CacheHit (102μs)
      • Illuminate\Cache\Events\CacheHit (115μs)
      • Illuminate\Cache\Events\CacheHit (98μs)
      • Illuminate\Cache\Events\CacheHit (114μs)
      • Illuminate\Cache\Events\CacheHit (99μs)
      • Illuminate\Cache\Events\CacheHit (115μs)
      • Illuminate\Cache\Events\CacheHit (98μs)
      • Illuminate\Cache\Events\CacheHit (133μs)
      • Illuminate\Cache\Events\CacheHit (100μs)
      • Illuminate\Cache\Events\CacheHit (120μs)
      • Illuminate\Cache\Events\CacheHit (101μs)
      • Illuminate\Cache\Events\CacheHit (116μs)
      • Illuminate\Cache\Events\CacheHit (101μs)
      • Illuminate\Cache\Events\CacheHit (115μs)
      • Illuminate\Cache\Events\CacheHit (102μs)
      • Illuminate\Cache\Events\CacheHit (117μs)
      • Illuminate\Cache\Events\CacheHit (96μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • Illuminate\Cache\Events\CacheHit (94μs)
      • Illuminate\Cache\Events\CacheHit (124μs)
      • Illuminate\Cache\Events\CacheHit (103μs)
      • Illuminate\Cache\Events\CacheMissed (182μs)
      • Illuminate\Database\Events\StatementPrepared (629μs)
      • Illuminate\Database\Events\QueryExecuted (781μs)
      • eloquent.retrieved: App\Models\SubjectCat (53μs)
      • Illuminate\Cache\Events\KeyWritten (227μs)
      • Illuminate\Cache\Events\CacheHit (155μs)
      • Illuminate\Cache\Events\CacheHit (137μs)
      • Illuminate\Cache\Events\CacheHit (106μs)
      • Illuminate\Cache\Events\CacheHit (119μs)
      • Illuminate\Cache\Events\CacheHit (99μs)
      • Illuminate\Cache\Events\CacheHit (114μs)
      • Illuminate\Cache\Events\CacheHit (96μs)
      • Illuminate\Cache\Events\CacheMissed (225μs)
      • Illuminate\Database\Events\StatementPrepared (583μs)
      • Illuminate\Database\Events\QueryExecuted (765μs)
      • eloquent.retrieved: App\Models\SubjectCat (51μs)
      • Illuminate\Cache\Events\KeyWritten (222μs)
      • Illuminate\Cache\Events\CacheHit (159μs)
      • Illuminate\Cache\Events\CacheHit (148μs)
      • Illuminate\Cache\Events\CacheHit (106μs)
      • Illuminate\Cache\Events\CacheHit (144μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • Illuminate\Cache\Events\CacheHit (124μs)
      • Illuminate\Cache\Events\CacheHit (206μs)
      • Illuminate\Cache\Events\CacheHit (156μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • Illuminate\Cache\Events\CacheHit (123μs)
      • Illuminate\Cache\Events\CacheHit (105μs)
      • Illuminate\Cache\Events\CacheHit (553μs)
      • Illuminate\Cache\Events\CacheHit (105μs)
      • Illuminate\Cache\Events\CacheHit (114μs)
      • Illuminate\Cache\Events\CacheHit (95μs)
      • Illuminate\Cache\Events\CacheHit (109μs)
      • Illuminate\Cache\Events\CacheHit (94μs)
      • Illuminate\Cache\Events\CacheHit (107μs)
      • Illuminate\Cache\Events\CacheHit (92μs)
      • Illuminate\Cache\Events\CacheHit (105μs)
      • Illuminate\Cache\Events\CacheHit (92μs)
      • Illuminate\Cache\Events\CacheHit (106μs)
      • Illuminate\Cache\Events\CacheHit (91μs)
      • Illuminate\Cache\Events\CacheHit (103μs)
      • Illuminate\Cache\Events\CacheHit (91μs)
      • Illuminate\Cache\Events\CacheHit (123μs)
      • Illuminate\Cache\Events\CacheHit (109μs)
      • Illuminate\Cache\Events\CacheHit (137μs)
      • Illuminate\Cache\Events\CacheHit (106μs)
      • Illuminate\Cache\Events\CacheMissed (163μs)
      • Illuminate\Database\Events\StatementPrepared (616μs)
      • Illuminate\Database\Events\QueryExecuted (720μs)
      • eloquent.retrieved: App\Models\SubjectCat (50μs)
      • Illuminate\Cache\Events\KeyWritten (214μs)
      • Illuminate\Cache\Events\CacheHit (152μs)
      • Illuminate\Cache\Events\CacheHit (135μs)
      • Illuminate\Cache\Events\CacheHit (104μs)
      • Illuminate\Cache\Events\CacheHit (117μs)
      • Illuminate\Cache\Events\CacheHit (98μs)
      • Illuminate\Cache\Events\CacheHit (111μs)
      • Illuminate\Cache\Events\CacheHit (95μs)
      • Illuminate\Cache\Events\CacheHit (170μs)
      • Illuminate\Cache\Events\CacheHit (122μs)
      • Illuminate\Cache\Events\CacheHit (120μs)
      • Illuminate\Cache\Events\CacheHit (98μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • Illuminate\Cache\Events\CacheHit (96μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • Illuminate\Cache\Events\CacheHit (95μs)
      • Illuminate\Cache\Events\CacheHit (110μs)
      • Illuminate\Cache\Events\CacheHit (96μs)
      • Illuminate\Cache\Events\CacheHit (139μs)
      • Illuminate\Cache\Events\CacheHit (97μs)
      • Illuminate\Cache\Events\CacheHit (111μs)
      • Illuminate\Cache\Events\CacheHit (94μs)
      • Illuminate\Cache\Events\CacheHit (109μs)
      • Illuminate\Cache\Events\CacheHit (94μs)
      • Illuminate\Cache\Events\CacheHit (108μs)
      • Illuminate\Cache\Events\CacheHit (93μs)
      • Illuminate\Cache\Events\CacheHit (109μs)
      • Illuminate\Cache\Events\CacheHit (93μs)
      • Illuminate\Cache\Events\CacheHit (107μs)
      • Illuminate\Cache\Events\CacheHit (95μs)
      • Illuminate\Cache\Events\CacheHit (234μs)
      • Illuminate\Cache\Events\CacheHit (132μs)
      • Illuminate\Cache\Events\CacheHit (129μs)
      • Illuminate\Cache\Events\CacheHit (106μs)
      • Illuminate\Cache\Events\CacheHit (123μs)
      • Illuminate\Cache\Events\CacheHit (97μs)
      • Illuminate\Cache\Events\CacheHit (113μs)
      • Illuminate\Cache\Events\CacheHit (94μs)
      • Illuminate\Cache\Events\CacheHit (110μs)
      • Illuminate\Cache\Events\CacheHit (95μs)
      • Illuminate\Cache\Events\CacheHit (109μs)
      • Illuminate\Cache\Events\CacheHit (94μs)
      • Illuminate\Cache\Events\CacheHit (111μs)
      • Illuminate\Cache\Events\CacheHit (94μs)
      • Illuminate\Cache\Events\CacheHit (110μs)
      • Illuminate\Cache\Events\CacheHit (93μs)
      • Illuminate\Cache\Events\CacheHit (109μs)
      • Illuminate\Cache\Events\CacheHit (95μs)
      • Illuminate\Cache\Events\CacheHit (120μs)
      • Illuminate\Cache\Events\CacheHit (92μs)
      • Illuminate\Cache\Events\CacheHit (120μs)
      • Illuminate\Cache\Events\CacheHit (101μs)
      • Illuminate\Cache\Events\CacheHit (356μs)
      • Illuminate\Cache\Events\CacheHit (136μs)
      • Illuminate\Cache\Events\CacheHit (123μs)
      • Illuminate\Cache\Events\CacheHit (98μs)
      • Illuminate\Cache\Events\CacheHit (111μs)
      • Illuminate\Cache\Events\CacheHit (94μs)
      • Illuminate\Cache\Events\CacheHit (118μs)
      • Illuminate\Cache\Events\CacheHit (95μs)
      • Illuminate\Cache\Events\CacheHit (109μs)
      • Illuminate\Cache\Events\CacheHit (91μs)
      • Illuminate\Cache\Events\CacheHit (114μs)
      • Illuminate\Cache\Events\CacheHit (107μs)
      • Illuminate\Cache\Events\CacheMissed (278μs)
      • Illuminate\Database\Events\StatementPrepared (654μs)
      • Illuminate\Database\Events\QueryExecuted (794μs)
      • eloquent.retrieved: App\Models\SubjectCat (53μs)
      • Illuminate\Cache\Events\KeyWritten (235μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (232μs)
      • Illuminate\Cache\Events\CacheHit (133μs)
      • Illuminate\Cache\Events\CacheHit (144μs)
      • Illuminate\Cache\Events\CacheHit (158μs)
      • Illuminate\Cache\Events\CacheHit (140μs)
      • Illuminate\Cache\Events\CacheHit (162μs)
      • Illuminate\Cache\Events\CacheHit (126μs)
      • Illuminate\Cache\Events\CacheHit (99μs)
      • Illuminate\Cache\Events\CacheHit (114μs)
      • Illuminate\Cache\Events\CacheHit (98μs)
      • Illuminate\Cache\Events\CacheHit (111μs)
      • Illuminate\Cache\Events\CacheHit (96μs)
      • Illuminate\Cache\Events\CacheHit (110μs)
      • Illuminate\Cache\Events\CacheHit (96μs)
      • Illuminate\Cache\Events\CacheHit (203μs)
      • Illuminate\Cache\Events\CacheHit (113μs)
      • Illuminate\Cache\Events\CacheHit (604μs)
      • Illuminate\Cache\Events\CacheHit (209μs)
      • Illuminate\Cache\Events\CacheHit (146μs)
      • Illuminate\Cache\Events\CacheHit (101μs)
      • Illuminate\Cache\Events\CacheHit (113μs)
      • Illuminate\Cache\Events\CacheHit (97μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • Illuminate\Cache\Events\CacheHit (95μs)
      • Illuminate\Cache\Events\CacheHit (111μs)
      • Illuminate\Cache\Events\CacheHit (95μs)
      • Illuminate\Cache\Events\CacheHit (111μs)
      • Illuminate\Cache\Events\CacheHit (95μs)
      • Illuminate\Cache\Events\CacheHit (108μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (117μs)
      • Illuminate\Cache\Events\CacheHit (92μs)
      • Illuminate\Cache\Events\CacheHit (141μs)
      • Illuminate\Cache\Events\CacheHit (97μs)
      • Illuminate\Cache\Events\CacheHit (136μs)
      • Illuminate\Cache\Events\CacheHit (106μs)
      • Illuminate\Cache\Events\CacheHit (126μs)
      • Illuminate\Cache\Events\CacheHit (97μs)
      • Illuminate\Cache\Events\CacheHit (115μs)
      • Illuminate\Cache\Events\CacheHit (95μs)
      • Illuminate\Cache\Events\CacheHit (108μs)
      • Illuminate\Cache\Events\CacheHit (93μs)
      • Illuminate\Cache\Events\CacheHit (109μs)
      • Illuminate\Cache\Events\CacheHit (93μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (102μs)
      • Illuminate\Cache\Events\CacheHit (108μs)
      • Illuminate\Cache\Events\CacheHit (94μs)
      • Illuminate\Cache\Events\CacheHit (107μs)
      • Illuminate\Cache\Events\CacheHit (91μs)
      • Illuminate\Cache\Events\CacheHit (107μs)
      • Illuminate\Cache\Events\CacheHit (91μs)
      • Illuminate\Cache\Events\CacheHit (106μs)
      • Illuminate\Cache\Events\CacheHit (91μs)
      • Illuminate\Cache\Events\CacheHit (117μs)
      • Illuminate\Cache\Events\CacheHit (96μs)
      • Illuminate\Cache\Events\CacheHit (110μs)
      • Illuminate\Cache\Events\CacheHit (93μs)
      • Illuminate\Cache\Events\CacheHit (105μs)
      • Illuminate\Cache\Events\CacheHit (90μs)
      • Illuminate\Cache\Events\CacheHit (104μs)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (136μs)
      • Illuminate\Cache\Events\CacheHit (94μs)
      • Illuminate\Cache\Events\CacheHit (155μs)
      • Illuminate\Cache\Events\CacheHit (117μs)
      • Illuminate\Cache\Events\CacheHit (111μs)
      • Illuminate\Cache\Events\CacheHit (94μs)
      • Illuminate\Cache\Events\CacheHit (164μs)
      • Illuminate\Cache\Events\CacheHit (108μs)
      • Illuminate\Cache\Events\CacheHit (116μs)
      • Illuminate\Cache\Events\CacheHit (95μs)
      • Illuminate\Cache\Events\CacheHit (110μs)
      • Illuminate\Cache\Events\CacheHit (94μs)
      • Illuminate\Cache\Events\CacheHit (107μs)
      • Illuminate\Cache\Events\CacheHit (94μs)
      • Illuminate\Cache\Events\CacheHit (114μs)
      • Illuminate\Cache\Events\CacheHit (95μs)
      • Illuminate\Cache\Events\CacheHit (118μs)
      • Illuminate\Cache\Events\CacheHit (92μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (97μs)
      • Illuminate\Cache\Events\CacheHit (114μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • Illuminate\Cache\Events\CacheHit (119μs)
      • Illuminate\Cache\Events\CacheHit (98μs)
      • Illuminate\Cache\Events\CacheHit (121μs)
      • Illuminate\Cache\Events\CacheHit (92μs)
      • Illuminate\Cache\Events\CacheMissed (165μs)
      • Illuminate\Database\Events\StatementPrepared (678μs)
      • Illuminate\Database\Events\QueryExecuted (797μs)
      • eloquent.retrieved: App\Models\SubjectCat (57μs)
      • Illuminate\Cache\Events\KeyWritten (246μs)
      • Illuminate\Cache\Events\CacheHit (152μs)
      • Illuminate\Cache\Events\CacheHit (148μs)
      • Illuminate\Cache\Events\CacheHit (108μs)
      • Illuminate\Cache\Events\CacheHit (120μs)
      • Illuminate\Cache\Events\CacheHit (102μs)
      • Illuminate\Cache\Events\CacheHit (146μs)
      • Illuminate\Cache\Events\CacheHit (128μs)
      • Illuminate\Cache\Events\CacheHit (132μs)
      • Illuminate\Cache\Events\CacheHit (152μs)
      • Illuminate\Cache\Events\CacheHit (137μs)
      • Illuminate\Cache\Events\CacheHit (99μs)
      • Illuminate\Cache\Events\CacheHit (110μs)
      • Illuminate\Cache\Events\CacheHit (94μs)
      • Illuminate\Cache\Events\CacheHit (200μs)
      • Illuminate\Cache\Events\CacheHit (105μs)
      • Illuminate\Cache\Events\CacheHit (129μs)
      • Illuminate\Cache\Events\CacheHit (97μs)
      • creating: site.layouts.app (351μs)
      • composing: site.layouts.app (16μs)
      • creating: components.canonical (354μs)
      • composing: components.canonical (71μs)
      • creating: components.open-graph (131μs)
      • composing: components.open-graph (45μs)
      • creating: site.headers.header (203μs)
      • composing: site.headers.header (45μs)
      • Illuminate\Cache\Events\CacheHit (1.29ms)
      • creating: components.footer (66μs)
      • composing: components.footer (64μs)
      • Illuminate\Cache\Events\CacheHit (634μs)
      • Illuminate\Cache\Events\CacheMissed (231μs)
      • Illuminate\Database\Events\StatementPrepared (687μs)
      • Illuminate\Database\Events\QueryExecuted (926μs)
      • eloquent.retrieved: App\Models\SubjectCat (53μs)
      • Illuminate\Cache\Events\KeyWritten (237μs)
      • Illuminate\Cache\Events\CacheHit (219μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (122μs)
      • Illuminate\Cache\Events\CacheHit (110μs)
      • Illuminate\Cache\Events\CacheHit (113μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (243μs)
      • Illuminate\Cache\Events\CacheHit (143μs)
      • Illuminate\Cache\Events\CacheHit (121μs)
      • Illuminate\Cache\Events\CacheHit (113μs)
      • Illuminate\Cache\Events\CacheHit (277μs)
      • Illuminate\Cache\Events\CacheHit (135μs)
      • creating: components.forms.contact-us (178μs)
      • composing: components.forms.contact-us (165μs)
      • creating: components.forms.get-started (129μs)
      • composing: components.forms.get-started (50μs)
      • creating: components.forms.free-tool-download (85μs)
      • composing: components.forms.free-tool-download (40μs)
      • creating: components.forms.claim-free-worksheet (78μs)
      • composing: components.forms.claim-free-worksheet (40μs)
      • creating: components.forms.tutor-subscription-waitlist (77μs)
      • composing: components.forms.tutor-subscription-waitlist (38μs)
      • creating: components.forms.tutor-subscription-join (76μs)
      • composing: components.forms.tutor-subscription-join (36μs)
      • creating: components.forms.tutor-support (75μs)
      • composing: components.forms.tutor-support (37μs)
      • 311 x Illuminate\Cache\Events\CacheHit (16.83%)
        50.60ms
        20 x Illuminate\Database\Events\StatementPrepared (8.11%)
        24.37ms
        20 x Illuminate\Database\Events\QueryExecuted (8%)
        24.05ms
        11 x Illuminate\Cache\Events\CacheMissed (2%)
        6.00ms
        11 x Illuminate\Cache\Events\KeyWritten (1.36%)
        4.10ms
        1 x Illuminate\Foundation\Events\LocaleUpdated (1.3%)
        3.92ms
        1 x Illuminate\Routing\Events\Routing (0.34%)
        1.02ms
        1 x Illuminate\Database\Events\ConnectionEstablished (0.26%)
        779μs
        12 x eloquent.retrieved: App\Models\SubjectCat (0.23%)
        693μs
        1 x creating: homework.show (0.13%)
        399μs
        1 x Illuminate\Routing\Events\RouteMatched (0.12%)
        357μs
        1 x creating: components.canonical (0.12%)
        354μs
        1 x creating: site.layouts.app (0.12%)
        351μs
        1 x eloquent.booting: App\Models\SubjectCat (0.1%)
        303μs
        1 x creating: components.breadcrumbs (0.09%)
        271μs
        12 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.08%)
        238μs
        7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.07%)
        223μs
        1 x creating: site.headers.header (0.07%)
        203μs
        1 x creating: components.forms.contact-us (0.06%)
        178μs
        2 x eloquent.retrieved: App\Models\Subject (0.06%)
        169μs
        1 x composing: components.forms.contact-us (0.05%)
        165μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.05%)
        156μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.05%)
        154μs
        1 x creating: components.open-graph (0.04%)
        131μs
        1 x creating: components.forms.get-started (0.04%)
        129μs
        1 x composing: homework.show (0.04%)
        117μs
        1 x composing: components.breadcrumbs (0.04%)
        116μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.03%)
        99μs
        1 x eloquent.booting: App\Models\Subject (0.03%)
        93μs
        1 x creating: components.forms.free-tool-download (0.03%)
        85μs
        1 x creating: components.forms.claim-free-worksheet (0.03%)
        78μs
        1 x creating: components.forms.tutor-subscription-waitlist (0.03%)
        77μs
        1 x creating: components.forms.tutor-subscription-join (0.03%)
        76μs
        1 x creating: components.forms.tutor-support (0.02%)
        75μs
        1 x composing: components.canonical (0.02%)
        71μs
        1 x creating: components.footer (0.02%)
        66μs
        1 x composing: components.footer (0.02%)
        64μs
        1 x composing: components.forms.get-started (0.02%)
        50μs
        1 x composing: components.open-graph (0.01%)
        45μs
        1 x composing: site.headers.header (0.01%)
        45μs
        1 x eloquent.booted: App\Models\Subject (0.01%)
        42μs
        1 x composing: components.forms.free-tool-download (0.01%)
        40μs
        1 x composing: components.forms.claim-free-worksheet (0.01%)
        40μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.01%)
        39μs
        1 x eloquent.booted: App\Models\SubjectCat (0.01%)
        38μs
        1 x composing: components.forms.tutor-subscription-waitlist (0.01%)
        38μs
        1 x composing: components.forms.tutor-support (0.01%)
        37μs
        1 x composing: components.forms.tutor-subscription-join (0.01%)
        36μs
        1 x composing: site.layouts.app (0.01%)
        16μs
      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 duplicated36.64ms
      • 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` = '26548' limit 1
        9.93mstwenty4_siteHomeworkLibraryController.php#97
        Bindings
        • 0: published
        • 1: 0
        • 2: 26548
        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 (34)
        910μstwenty4_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 (26548)
        810μstwenty4_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
        940μstwenty4_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` <> 26548 and `subject` = 34 and `status` = 'published' and `price` > 0 order by RAND() limit 6
        9.32mstwenty4_siteHomeworkLibraryRepository.php#30
        Bindings
        • 0: 26548
        • 1: 34
        • 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 (34)
        1.12mstwenty4_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` = 26548 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        920μstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 26548
        • 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` = 26548 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'teaser' order by `order` asc, `id` asc
        1.05mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 26548
        • 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` = 26548 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'solution' order by `order` asc, `id` asc
        880μstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 26548
        • 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
        950μstwenty4_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
        990μstwenty4_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
        980μstwenty4_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
        910μstwenty4_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
        930μstwenty4_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
        960μstwenty4_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
        940μstwenty4_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
        940μstwenty4_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
        1.02mstwenty4_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
        980μstwenty4_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
        1.16mstwenty4_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
      App\Models\SubjectCat
      12SubjectCat.php
      App\Models\HomeworkLibrary\HomeworkLibrary
      7HomeworkLibrary.php
      App\Models\Subject
      2Subject.php
          _token
          BQDlzrtkp1sTuMTS1P43t58KeqGm8NQFqp2oHSP9
          utm_source
          direct
          redirectUrl
          /college-homework-library/Mathematics/Advanced-Math/26548
          _previous
          array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/Mathematics/Adv...
          _flash
          array:2 [ "old" => [] "new" => [] ]
          PHPDEBUGBAR_STACK_DATA
          []
          path_info
          /college-homework-library/Mathematics/Advanced-Math/26548
          status_code
          200
          
          status_text
          OK
          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=1-67f77630-1c118f26599252ed0c77a83f" ] "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 => "3.144.23.154" ] "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 => "Thu, 10 Apr 2025 07:41:36 GMT" ] "set-cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6IlRxT1ZadFRkN1FVQ3hFVEJKbkFhVFE9PSIsInZhbHVlIjoieUo5WGVWcnNaNHNxRzFQLzhKVjJFRWFJV0dBT3o2UDdqOTZxODdic3pXNjZWcE5DUFFWYjEvalNkenRPNCs2MDhpakdNc2UvMkxPeHN4V1JjZ25ReUVwdW1Gakt3TDg1UFdVN0VHSEwvbllFbEdUVG90Sjg1MkJNZ1JGeDlSNVIiLCJtYWMiOiJhNjJhZTE5YTEwZWI5YmM5MDgzMWE1NjJiZmY2ZjYzYTcxOTNmN2NmMjY1OWMzYTQ0OTI0NGIxNjNjYmQxMzQ0IiwidGFnIjoiIn0%3D; expires=Thu, 10 Apr 2025 09:41:36 GMT; Max-Age=7200; path=/; domain=.24houranswers.com; samesite=laxXSRF-TOKEN=eyJpdiI6IlRxT1ZadFRkN1FVQ3hFVEJKbkFhVFE9PSIsInZhbHVlIjoieUo5WGVWcnNaNHNxRzFQLzhKVjJFRWFJV0dBT3o2UDdqOTZxODdic3pXNjZWcE5DUFFWYjEvalNkenRPNCs2MDhpakdNc" 1 => "24houranswers_session=eyJpdiI6InI2ZWgxYUZyRXpqRTNzTW93TmZIL2c9PSIsInZhbHVlIjoiZHNCcVB5eFpCODJNemJ2RlFLMmFKYVZzN1Q3ZW9IMFBBcm93TVl4cGgyT2NqbkszZ281UjBac1Y4RkdaajljejlqYmZzbkQ1R2VJRU5hNktYRFFyZFVBUHR5bGJrcG9LZ1RncmxJckxKVVhnTGVTODhqTDdXUFhYN1dlb3pKT0giLCJtYWMiOiJjZDU5MjM2M2NjZGE5ZDgxNzkxNTljNDMzN2Y2NWJjMWIzYmExOWVjMGZhYzkyMDIxZmFlYmZmOTNmYzg4OWU3IiwidGFnIjoiIn0%3D; expires=Thu, 10 Apr 2025 09:41:36 GMT; Max-Age=7200; path=/; domain=.24houranswers.com; httponly; samesite=lax24houranswers_session=eyJpdiI6InI2ZWgxYUZyRXpqRTNzTW93TmZIL2c9PSIsInZhbHVlIjoiZHNCcVB5eFpCODJNemJ2RlFLMmFKYVZzN1Q3ZW9IMFBBcm93TVl4cGgyT2NqbkszZ281UjBac1Y4Rkdaaj" ] "Set-Cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6IlRxT1ZadFRkN1FVQ3hFVEJKbkFhVFE9PSIsInZhbHVlIjoieUo5WGVWcnNaNHNxRzFQLzhKVjJFRWFJV0dBT3o2UDdqOTZxODdic3pXNjZWcE5DUFFWYjEvalNkenRPNCs2MDhpakdNc2UvMkxPeHN4V1JjZ25ReUVwdW1Gakt3TDg1UFdVN0VHSEwvbllFbEdUVG90Sjg1MkJNZ1JGeDlSNVIiLCJtYWMiOiJhNjJhZTE5YTEwZWI5YmM5MDgzMWE1NjJiZmY2ZjYzYTcxOTNmN2NmMjY1OWMzYTQ0OTI0NGIxNjNjYmQxMzQ0IiwidGFnIjoiIn0%3D; expires=Thu, 10-Apr-2025 09:41:36 GMT; domain=.24houranswers.com; path=/XSRF-TOKEN=eyJpdiI6IlRxT1ZadFRkN1FVQ3hFVEJKbkFhVFE9PSIsInZhbHVlIjoieUo5WGVWcnNaNHNxRzFQLzhKVjJFRWFJV0dBT3o2UDdqOTZxODdic3pXNjZWcE5DUFFWYjEvalNkenRPNCs2MDhpakdNc" 1 => "24houranswers_session=eyJpdiI6InI2ZWgxYUZyRXpqRTNzTW93TmZIL2c9PSIsInZhbHVlIjoiZHNCcVB5eFpCODJNemJ2RlFLMmFKYVZzN1Q3ZW9IMFBBcm93TVl4cGgyT2NqbkszZ281UjBac1Y4RkdaajljejlqYmZzbkQ1R2VJRU5hNktYRFFyZFVBUHR5bGJrcG9LZ1RncmxJckxKVVhnTGVTODhqTDdXUFhYN1dlb3pKT0giLCJtYWMiOiJjZDU5MjM2M2NjZGE5ZDgxNzkxNTljNDMzN2Y2NWJjMWIzYmExOWVjMGZhYzkyMDIxZmFlYmZmOTNmYzg4OWU3IiwidGFnIjoiIn0%3D; expires=Thu, 10-Apr-2025 09:41:36 GMT; domain=.24houranswers.com; path=/; httponly24houranswers_session=eyJpdiI6InI2ZWgxYUZyRXpqRTNzTW93TmZIL2c9PSIsInZhbHVlIjoiZHNCcVB5eFpCODJNemJ2RlFLMmFKYVZzN1Q3ZW9IMFBBcm93TVl4cGgyT2NqbkszZ281UjBac1Y4Rkdaaj" ] ]
          session_attributes
          0 of 0
          array:6 [ "_token" => "BQDlzrtkp1sTuMTS1P43t58KeqGm8NQFqp2oHSP9" "utm_source" => "direct" "redirectUrl" => "/college-homework-library/Mathematics/Advanced-Math/26548" "_previous" => array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/Mathematics/Advanced-Math/26548" ] "_flash" => array:2 [ "old" => [] "new" => [] ] "PHPDEBUGBAR_STACK_DATA" => [] ]