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
$6.00 $3
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 Version428msRequest Duration45MBMemory UsageGET college-homework-library/{category}/{subject}/{id}Route
    • Booting (284ms)time
    • Application (144ms)time
    • 1 x Booting (66.37%)
      284ms
      1 x Application (33.63%)
      144ms
      • Illuminate\Routing\Events\Routing (1.38ms)
      • Illuminate\Routing\Events\RouteMatched (578μs)
      • Illuminate\Foundation\Events\LocaleUpdated (6.39ms)
      • eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (190μs)
      • eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (168μs)
      • Illuminate\Database\Events\ConnectionEstablished (885μs)
      • Illuminate\Database\Events\StatementPrepared (8.58ms)
      • Illuminate\Database\Events\QueryExecuted (1.25ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (101μs)
      • eloquent.booting: App\Models\Subject (120μs)
      • eloquent.booted: App\Models\Subject (40μs)
      • Illuminate\Database\Events\StatementPrepared (1.64ms)
      • Illuminate\Database\Events\QueryExecuted (1.07ms)
      • eloquent.retrieved: App\Models\Subject (254μs)
      • eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (186μs)
      • eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (60μs)
      • Illuminate\Database\Events\StatementPrepared (712μs)
      • Illuminate\Database\Events\QueryExecuted (2.03ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (127μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (16μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (8μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (6μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (6μs)
      • eloquent.booting: App\Models\SubjectCat (321μs)
      • eloquent.booted: App\Models\SubjectCat (44μs)
      • Illuminate\Database\Events\StatementPrepared (890μs)
      • Illuminate\Database\Events\QueryExecuted (1ms)
      • eloquent.retrieved: App\Models\SubjectCat (101μs)
      • Illuminate\Cache\Events\CacheHit (15.14ms)
      • Illuminate\Cache\Events\CacheMissed (312μs)
      • Illuminate\Database\Events\StatementPrepared (1.07ms)
      • Illuminate\Database\Events\QueryExecuted (8.52ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (100μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (18μs)
      • 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 (761μs)
      • Illuminate\Database\Events\QueryExecuted (1.18ms)
      • eloquent.retrieved: App\Models\Subject (108μs)
      • Illuminate\Cache\Events\KeyWritten (1.09ms)
      • Illuminate\Database\Events\StatementPrepared (1.86ms)
      • Illuminate\Database\Events\QueryExecuted (1.27ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (65μs)
      • Illuminate\Database\Events\StatementPrepared (1.03ms)
      • Illuminate\Database\Events\QueryExecuted (1.17ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (58μs)
      • Illuminate\Database\Events\StatementPrepared (994μs)
      • Illuminate\Database\Events\QueryExecuted (1.03ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (44μs)
      • Illuminate\Cache\Events\CacheHit (572μs)
      • creating: homework.show (264μs)
      • composing: homework.show (122μs)
      • creating: components.breadcrumbs (280μs)
      • composing: components.breadcrumbs (131μs)
      • Illuminate\Database\Events\StatementPrepared (1.08ms)
      • Illuminate\Database\Events\QueryExecuted (963μs)
      • eloquent.retrieved: App\Models\SubjectCat (107μs)
      • Illuminate\Cache\Events\CacheHit (4.73ms)
      • Illuminate\Cache\Events\CacheHit (222μs)
      • Illuminate\Cache\Events\CacheHit (214μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (203μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (161μs)
      • Illuminate\Cache\Events\CacheHit (245μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (159μs)
      • Illuminate\Cache\Events\CacheHit (205μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (246μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (196μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (204μs)
      • Illuminate\Cache\Events\CacheHit (158μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (164μs)
      • Illuminate\Cache\Events\CacheHit (198μs)
      • Illuminate\Cache\Events\CacheHit (163μs)
      • Illuminate\Cache\Events\CacheHit (226μs)
      • Illuminate\Cache\Events\CacheHit (232μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (198μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (204μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (163μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (163μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (159μs)
      • Illuminate\Cache\Events\CacheHit (195μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (206μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (159μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (227μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheHit (168μs)
      • Illuminate\Cache\Events\CacheHit (199μs)
      • Illuminate\Cache\Events\CacheHit (168μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (158μs)
      • Illuminate\Cache\Events\CacheHit (204μs)
      • Illuminate\Cache\Events\CacheHit (198μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheHit (198μs)
      • Illuminate\Cache\Events\CacheHit (202μs)
      • Illuminate\Cache\Events\CacheHit (173μs)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
      • Illuminate\Cache\Events\CacheHit (229μs)
      • Illuminate\Cache\Events\CacheHit (170μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (211μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (195μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (193μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
      • Illuminate\Cache\Events\CacheHit (196μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (198μs)
      • Illuminate\Cache\Events\CacheHit (216μs)
      • Illuminate\Cache\Events\CacheHit (219μs)
      • Illuminate\Cache\Events\CacheHit (165μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (164μs)
      • Illuminate\Cache\Events\CacheHit (204μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (164μs)
      • Illuminate\Cache\Events\CacheHit (207μs)
      • Illuminate\Cache\Events\CacheHit (162μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (159μs)
      • Illuminate\Cache\Events\CacheHit (221μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (165μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (154μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (168μs)
      • Illuminate\Cache\Events\CacheHit (955μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (209μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (158μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (160μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
      • Illuminate\Cache\Events\CacheHit (155μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheHit (153μs)
      • Illuminate\Cache\Events\CacheHit (182μs)
      • Illuminate\Cache\Events\CacheHit (158μs)
      • Illuminate\Cache\Events\CacheHit (205μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (203μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
      • Illuminate\Cache\Events\CacheHit (213μs)
      • Illuminate\Cache\Events\CacheHit (156μs)
      • Illuminate\Cache\Events\CacheHit (173μs)
      • Illuminate\Cache\Events\CacheHit (157μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (159μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheHit (159μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (168μs)
      • Illuminate\Cache\Events\CacheHit (182μs)
      • Illuminate\Cache\Events\CacheHit (161μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (156μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (156μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (158μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (222μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (157μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (158μs)
      • Illuminate\Cache\Events\CacheHit (221μs)
      • Illuminate\Cache\Events\CacheHit (168μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (157μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (155μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (156μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (238μs)
      • Illuminate\Cache\Events\CacheHit (182μs)
      • Illuminate\Cache\Events\CacheHit (198μs)
      • Illuminate\Cache\Events\CacheHit (206μs)
      • Illuminate\Cache\Events\CacheHit (201μs)
      • Illuminate\Cache\Events\CacheHit (173μs)
      • Illuminate\Cache\Events\CacheHit (227μs)
      • Illuminate\Cache\Events\CacheHit (199μs)
      • Illuminate\Cache\Events\CacheHit (199μs)
      • Illuminate\Cache\Events\CacheHit (173μs)
      • Illuminate\Cache\Events\CacheHit (204μs)
      • Illuminate\Cache\Events\CacheHit (158μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (160μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheHit (155μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • Illuminate\Cache\Events\CacheHit (152μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (164μs)
      • Illuminate\Cache\Events\CacheHit (216μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheHit (199μs)
      • Illuminate\Cache\Events\CacheHit (170μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (222μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (157μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (159μs)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (158μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (159μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (163μs)
      • Illuminate\Cache\Events\CacheHit (200μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (968μs)
      • Illuminate\Cache\Events\CacheHit (162μs)
      • Illuminate\Cache\Events\CacheHit (182μs)
      • Illuminate\Cache\Events\CacheHit (156μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (222μs)
      • Illuminate\Cache\Events\CacheHit (186μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (142μs)
      • Illuminate\Cache\Events\CacheHit (198μs)
      • Illuminate\Cache\Events\CacheHit (156μs)
      • Illuminate\Cache\Events\CacheHit (173μs)
      • Illuminate\Cache\Events\CacheHit (152μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (156μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheHit (156μs)
      • Illuminate\Cache\Events\CacheHit (213μs)
      • Illuminate\Cache\Events\CacheHit (170μs)
      • Illuminate\Cache\Events\CacheHit (186μs)
      • Illuminate\Cache\Events\CacheHit (156μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (162μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (160μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (161μs)
      • Illuminate\Cache\Events\CacheHit (228μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (186μs)
      • Illuminate\Cache\Events\CacheHit (162μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (186μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (158μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (165μs)
      • Illuminate\Cache\Events\CacheHit (195μs)
      • Illuminate\Cache\Events\CacheHit (163μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (155μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (163μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (158μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (158μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (158μs)
      • Illuminate\Cache\Events\CacheHit (173μs)
      • Illuminate\Cache\Events\CacheHit (245μs)
      • Illuminate\Cache\Events\CacheHit (208μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (158μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (158μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (157μs)
      • Illuminate\Cache\Events\CacheHit (182μs)
      • Illuminate\Cache\Events\CacheHit (157μs)
      • Illuminate\Cache\Events\CacheHit (170μs)
      • Illuminate\Cache\Events\CacheHit (152μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (163μs)
      • Illuminate\Cache\Events\CacheHit (208μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (157μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (146μs)
      • Illuminate\Cache\Events\CacheHit (231μs)
      • Illuminate\Cache\Events\CacheHit (160μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (162μs)
      • Illuminate\Cache\Events\CacheHit (290μs)
      • Illuminate\Cache\Events\CacheHit (163μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (162μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (158μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (155μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheHit (156μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (160μs)
      • creating: site.layouts.app (495μs)
      • composing: site.layouts.app (25μs)
      • creating: components.canonical (550μs)
      • composing: components.canonical (172μs)
      • creating: components.open-graph (255μs)
      • composing: components.open-graph (92μs)
      • creating: site.headers.header (369μs)
      • composing: site.headers.header (104μs)
      • Illuminate\Cache\Events\CacheHit (1.69ms)
      • creating: components.footer (64μs)
      • composing: components.footer (87μs)
      • Illuminate\Cache\Events\CacheHit (927μs)
      • Illuminate\Cache\Events\CacheHit (357μs)
      • Illuminate\Cache\Events\CacheHit (319μs)
      • Illuminate\Cache\Events\CacheHit (271μs)
      • Illuminate\Cache\Events\CacheHit (241μs)
      • Illuminate\Cache\Events\CacheHit (206μs)
      • Illuminate\Cache\Events\CacheHit (207μs)
      • Illuminate\Cache\Events\CacheHit (305μs)
      • Illuminate\Cache\Events\CacheHit (326μs)
      • Illuminate\Cache\Events\CacheHit (204μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (203μs)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • creating: components.forms.contact-us (263μs)
      • composing: components.forms.contact-us (173μs)
      • creating: components.forms.get-started (178μs)
      • composing: components.forms.get-started (85μs)
      • creating: components.forms.free-tool-download (183μs)
      • composing: components.forms.free-tool-download (79μs)
      • creating: components.forms.claim-free-worksheet (193μs)
      • composing: components.forms.claim-free-worksheet (80μs)
      • creating: components.forms.tutor-subscription-waitlist (149μs)
      • composing: components.forms.tutor-subscription-waitlist (77μs)
      • creating: components.forms.tutor-subscription-join (145μs)
      • composing: components.forms.tutor-subscription-join (75μs)
      • creating: components.forms.tutor-support (142μs)
      • composing: components.forms.tutor-support (79μs)
      • 321 x Illuminate\Cache\Events\CacheHit (19.26%)
        82.54ms
        10 x Illuminate\Database\Events\QueryExecuted (4.54%)
        19.47ms
        10 x Illuminate\Database\Events\StatementPrepared (4.35%)
        18.62ms
        1 x Illuminate\Foundation\Events\LocaleUpdated (1.49%)
        6.39ms
        1 x Illuminate\Routing\Events\Routing (0.32%)
        1.38ms
        1 x Illuminate\Cache\Events\KeyWritten (0.25%)
        1.09ms
        1 x Illuminate\Database\Events\ConnectionEstablished (0.21%)
        885μs
        1 x Illuminate\Routing\Events\RouteMatched (0.13%)
        578μs
        1 x creating: components.canonical (0.13%)
        550μs
        1 x creating: site.layouts.app (0.12%)
        495μs
        1 x creating: site.headers.header (0.09%)
        369μs
        2 x eloquent.retrieved: App\Models\Subject (0.08%)
        362μs
        8 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.08%)
        330μs
        1 x eloquent.booting: App\Models\SubjectCat (0.07%)
        321μs
        1 x Illuminate\Cache\Events\CacheMissed (0.07%)
        312μs
        1 x creating: components.breadcrumbs (0.07%)
        280μs
        1 x creating: homework.show (0.06%)
        264μs
        1 x creating: components.forms.contact-us (0.06%)
        263μs
        1 x creating: components.open-graph (0.06%)
        255μs
        7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.06%)
        246μs
        2 x eloquent.retrieved: App\Models\SubjectCat (0.05%)
        208μs
        1 x creating: components.forms.claim-free-worksheet (0.05%)
        193μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.04%)
        190μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.04%)
        186μs
        1 x creating: components.forms.free-tool-download (0.04%)
        183μs
        1 x creating: components.forms.get-started (0.04%)
        178μs
        1 x composing: components.forms.contact-us (0.04%)
        173μs
        1 x composing: components.canonical (0.04%)
        172μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.04%)
        168μs
        1 x creating: components.forms.tutor-subscription-waitlist (0.03%)
        149μs
        1 x creating: components.forms.tutor-subscription-join (0.03%)
        145μs
        1 x creating: components.forms.tutor-support (0.03%)
        142μs
        1 x composing: components.breadcrumbs (0.03%)
        131μs
        1 x composing: homework.show (0.03%)
        122μs
        1 x eloquent.booting: App\Models\Subject (0.03%)
        120μs
        1 x composing: site.headers.header (0.02%)
        104μs
        1 x composing: components.open-graph (0.02%)
        92μs
        1 x composing: components.footer (0.02%)
        87μs
        1 x composing: components.forms.get-started (0.02%)
        85μs
        1 x composing: components.forms.claim-free-worksheet (0.02%)
        80μs
        1 x composing: components.forms.free-tool-download (0.02%)
        79μs
        1 x composing: components.forms.tutor-support (0.02%)
        79μs
        1 x composing: components.forms.tutor-subscription-waitlist (0.02%)
        77μs
        1 x composing: components.forms.tutor-subscription-join (0.02%)
        75μs
        1 x creating: components.footer (0.01%)
        64μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.01%)
        60μs
        1 x eloquent.booted: App\Models\SubjectCat (0.01%)
        44μs
        1 x eloquent.booted: App\Models\Subject (0.01%)
        40μs
        1 x composing: site.layouts.app (0.01%)
        25μs
      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 duplicated27.72ms
      • 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` = '30119' limit 1
        9.02mstwenty4_siteHomeworkLibraryController.php#97
        Bindings
        • 0: published
        • 1: 0
        • 2: 30119
        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 (10)
        1.13mstwenty4_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 (30119)
        2.12mstwenty4_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
        1.07mstwenty4_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` <> 30119 and `subject` = 10 and `status` = 'published' and `price` > 0 order by RAND() limit 6
        8.43mstwenty4_siteHomeworkLibraryRepository.php#30
        Bindings
        • 0: 30119
        • 1: 10
        • 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 (10)
        1.29mstwenty4_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` = 30119 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        1.17mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 30119
        • 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` = 30119 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'teaser' order by `order` asc, `id` asc
        1.18mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 30119
        • 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` = 30119 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'solution' order by `order` asc, `id` asc
        1.29mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 30119
        • 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
        1.02mstwenty4_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\HomeworkLibraryFile
      8HomeworkLibraryFile.php
      App\Models\HomeworkLibrary\HomeworkLibrary
      7HomeworkLibrary.php
      App\Models\Subject
      2Subject.php
      App\Models\SubjectCat
      2SubjectCat.php
          _token
          pF5Zzqd2Q32D2qHIhRcgSWEqUqDfklVH0zw31IaO
          utm_source
          direct
          redirectUrl
          /college-homework-library/Mathematics/Differential-Equations/30119
          _previous
          array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/Mathematics/Dif...
          _flash
          array:2 [ "old" => [] "new" => [] ]
          PHPDEBUGBAR_STACK_DATA
          []
          path_info
          /college-homework-library/Mathematics/Differential-Equations/30119
          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=1-680c84f0-2c67b5852e17eb3e77a90811" ] "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 => "18.188.146.223" ] "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 => "Sat, 26 Apr 2025 07:02:08 GMT" ] "set-cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6ImdadmVZRW10WDFqVjg2VjU4bENYZ0E9PSIsInZhbHVlIjoicHhkWVFWeENjS3NCRHR2c1d0bVFjbTRIbE5KL3hLV2R1dm4yZmlYcldjQ05wS01nTkQxelA1Qmp3cFllQXRjc085VXk0MTk5WDFnTHJpQ2RyR1J0Y3UvbWxqT00wTXNuakNCa2R3ZXlMcVVoNUQwek04Wml3N2JmMTRtWlkyWlQiLCJtYWMiOiIyOWM0YjI4MjM1M2Y3ZDk5Y2Q3N2FlMDgyMjA4ZTlkMTlkZmMwYWM3OWRiODYwNzYyZjA2ZTM3YzZmMDhlYjM5IiwidGFnIjoiIn0%3D; expires=Sat, 26 Apr 2025 09:02:08 GMT; Max-Age=7200; path=/; domain=.24houranswers.com; samesite=laxXSRF-TOKEN=eyJpdiI6ImdadmVZRW10WDFqVjg2VjU4bENYZ0E9PSIsInZhbHVlIjoicHhkWVFWeENjS3NCRHR2c1d0bVFjbTRIbE5KL3hLV2R1dm4yZmlYcldjQ05wS01nTkQxelA1Qmp3cFllQXRjc085VXk0M" 1 => "24houranswers_session=eyJpdiI6Ill2TXhGRkYyN3dML3MrSzdBWDZLV0E9PSIsInZhbHVlIjoicmFFV2kxREc0SlN6YXFJODJzUUpkYzhuTCswUFJDMndjVnVuMWdpeGIrek5SbkJMUURXYXRYRlhvWHY0OXNhS2VLTGtIcFk4c1JUYkFJak94SFNlTm5iS1JjUG9mTDJYU3dscjJRYmVxamVmWmRIVHIyZTlBOGJYR1p2dE1JOTciLCJtYWMiOiI0NGY4YzNmN2MxNDMzYjYwZmQyZGIxNzRjNDVhYmExNmNmMDRkN2EzZDZhMjUwZGZjNzdkYjlmMTgxMzFiMGExIiwidGFnIjoiIn0%3D; expires=Sat, 26 Apr 2025 09:02:08 GMT; Max-Age=7200; path=/; domain=.24houranswers.com; httponly; samesite=lax24houranswers_session=eyJpdiI6Ill2TXhGRkYyN3dML3MrSzdBWDZLV0E9PSIsInZhbHVlIjoicmFFV2kxREc0SlN6YXFJODJzUUpkYzhuTCswUFJDMndjVnVuMWdpeGIrek5SbkJMUURXYXRYRlhvWHY0OX" ] "Set-Cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6ImdadmVZRW10WDFqVjg2VjU4bENYZ0E9PSIsInZhbHVlIjoicHhkWVFWeENjS3NCRHR2c1d0bVFjbTRIbE5KL3hLV2R1dm4yZmlYcldjQ05wS01nTkQxelA1Qmp3cFllQXRjc085VXk0MTk5WDFnTHJpQ2RyR1J0Y3UvbWxqT00wTXNuakNCa2R3ZXlMcVVoNUQwek04Wml3N2JmMTRtWlkyWlQiLCJtYWMiOiIyOWM0YjI4MjM1M2Y3ZDk5Y2Q3N2FlMDgyMjA4ZTlkMTlkZmMwYWM3OWRiODYwNzYyZjA2ZTM3YzZmMDhlYjM5IiwidGFnIjoiIn0%3D; expires=Sat, 26-Apr-2025 09:02:08 GMT; domain=.24houranswers.com; path=/XSRF-TOKEN=eyJpdiI6ImdadmVZRW10WDFqVjg2VjU4bENYZ0E9PSIsInZhbHVlIjoicHhkWVFWeENjS3NCRHR2c1d0bVFjbTRIbE5KL3hLV2R1dm4yZmlYcldjQ05wS01nTkQxelA1Qmp3cFllQXRjc085VXk0M" 1 => "24houranswers_session=eyJpdiI6Ill2TXhGRkYyN3dML3MrSzdBWDZLV0E9PSIsInZhbHVlIjoicmFFV2kxREc0SlN6YXFJODJzUUpkYzhuTCswUFJDMndjVnVuMWdpeGIrek5SbkJMUURXYXRYRlhvWHY0OXNhS2VLTGtIcFk4c1JUYkFJak94SFNlTm5iS1JjUG9mTDJYU3dscjJRYmVxamVmWmRIVHIyZTlBOGJYR1p2dE1JOTciLCJtYWMiOiI0NGY4YzNmN2MxNDMzYjYwZmQyZGIxNzRjNDVhYmExNmNmMDRkN2EzZDZhMjUwZGZjNzdkYjlmMTgxMzFiMGExIiwidGFnIjoiIn0%3D; expires=Sat, 26-Apr-2025 09:02:08 GMT; domain=.24houranswers.com; path=/; httponly24houranswers_session=eyJpdiI6Ill2TXhGRkYyN3dML3MrSzdBWDZLV0E9PSIsInZhbHVlIjoicmFFV2kxREc0SlN6YXFJODJzUUpkYzhuTCswUFJDMndjVnVuMWdpeGIrek5SbkJMUURXYXRYRlhvWHY0OX" ] ]
          session_attributes
          0 of 0
          array:6 [ "_token" => "pF5Zzqd2Q32D2qHIhRcgSWEqUqDfklVH0zw31IaO" "utm_source" => "direct" "redirectUrl" => "/college-homework-library/Mathematics/Differential-Equations/30119" "_previous" => array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/Mathematics/Differential-Equations/30119" ] "_flash" => array:2 [ "old" => [] "new" => [] ] "PHPDEBUGBAR_STACK_DATA" => [] ]