1) The space is filled with background radiation, remnant of the e...

Question
1)
The space is filled with background radiation, remnant of the early age of the universe. Currently the distribution of this radiation is similar to the radiation of a blackbody at the temperature of 2.7 K. What is λmax corresponding to this radiation? What is its total intensity? Compare the intensity of the background radiation to the intensity of the Sun at the visual wavelengths.

2)
The temperature of a red giant is T = 2500 K and radius 100 times the solar radius. a) Find the total luminosity of the star, and the luminosity in the visual band 400 nm ≤ λ ≤ 700 nm. b) Compare the star with a 100 W lamp that radiates 5% of its energy in the visual band. What is the distance of the lamp if it looks as bright as the star?

The distance to the star is 10 pc.

3)
The effective temperature of Sirius is 10,000 K, apparent visual magnitude −1.5, distance 2.67 pc and bolometric correction 0.5. What is the radius of Sirius?

4)
a) The sun has a nominal surface temperature of 5778 K. Assuming the sun is a black-body emitter (which is mostly true), create a table with the [spectral] intensity as a function of wavelength across the near-visible range, 250–850 nm.
b) An ideal color filter is completely transparent for a range of wavelengths λ1 ≤ λ ≤ λ2 and completely opaque (no transmission) at all other wavelengths. An ideal camera is equally sensitive to all wavelengths. Suppose you have an ideal camera equipped with three ideal filters: a U filter that passes light between 320 and 400 nm, a B filter that passes 400–500 nm, and a V filter that passes 500–700 nm.
What are the color indices of the sun that you would measure with this camera (i.e., what are U − B and B − V )?
What would the color indices be for a red dwarf (T = 3500 K)? For a white dwarf (T = 17000 K)?
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
Solution.xlsx
Purchase Solution
$30.00
Google Pay
Amazon
Paypal
Mastercard
Visacard
Discover
Amex
View Available Physics 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)
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 Version670msRequest Duration45MBMemory UsageGET college-homework-library/{category}/{subject}/{id}Route
    • Booting (427ms)time
    • Application (244ms)time
    • 1 x Booting (63.65%)
      427ms
      1 x Application (36.35%)
      244ms
      • Illuminate\Routing\Events\Routing (1.8ms)
      • Illuminate\Routing\Events\RouteMatched (828μs)
      • Illuminate\Foundation\Events\LocaleUpdated (6.17ms)
      • eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (297μs)
      • eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (402μs)
      • Illuminate\Database\Events\ConnectionEstablished (1.72ms)
      • Illuminate\Database\Events\StatementPrepared (8.82ms)
      • Illuminate\Database\Events\QueryExecuted (1.68ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (143μs)
      • eloquent.booting: App\Models\Subject (142μs)
      • eloquent.booted: App\Models\Subject (61μs)
      • Illuminate\Database\Events\StatementPrepared (2.56ms)
      • Illuminate\Database\Events\QueryExecuted (2.66ms)
      • eloquent.retrieved: App\Models\Subject (158μs)
      • eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (164μs)
      • eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (62μs)
      • Illuminate\Database\Events\StatementPrepared (1.23ms)
      • Illuminate\Database\Events\QueryExecuted (1.07ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (88μs)
      • 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.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 (667μs)
      • eloquent.booted: App\Models\SubjectCat (46μs)
      • Illuminate\Database\Events\StatementPrepared (748μs)
      • Illuminate\Database\Events\QueryExecuted (1.26ms)
      • eloquent.retrieved: App\Models\SubjectCat (123μs)
      • Illuminate\Cache\Events\CacheHit (20.56ms)
      • Illuminate\Cache\Events\CacheMissed (1.08ms)
      • Illuminate\Database\Events\StatementPrepared (5.35ms)
      • Illuminate\Database\Events\QueryExecuted (3.07ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (208μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (26μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (41μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (14μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (232μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (29μs)
      • Illuminate\Database\Events\StatementPrepared (1.34ms)
      • Illuminate\Database\Events\QueryExecuted (2.33ms)
      • eloquent.retrieved: App\Models\Subject (249μs)
      • Illuminate\Cache\Events\KeyWritten (2.24ms)
      • Illuminate\Database\Events\StatementPrepared (2.94ms)
      • Illuminate\Database\Events\QueryExecuted (1.08ms)
      • Illuminate\Database\Events\StatementPrepared (741μs)
      • Illuminate\Database\Events\QueryExecuted (1.19ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (56μs)
      • Illuminate\Database\Events\StatementPrepared (973μs)
      • Illuminate\Database\Events\QueryExecuted (1.46ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (53μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (15μs)
      • Illuminate\Cache\Events\CacheHit (800μs)
      • creating: homework.show (278μs)
      • composing: homework.show (120μs)
      • creating: components.breadcrumbs (270μs)
      • composing: components.breadcrumbs (123μs)
      • Illuminate\Database\Events\StatementPrepared (2.22ms)
      • Illuminate\Database\Events\QueryExecuted (2.09ms)
      • eloquent.retrieved: App\Models\SubjectCat (98μs)
      • Illuminate\Cache\Events\CacheMissed (5.53ms)
      • Illuminate\Database\Events\StatementPrepared (779μs)
      • Illuminate\Database\Events\QueryExecuted (1.8ms)
      • eloquent.retrieved: App\Models\SubjectCat (87μs)
      • Illuminate\Cache\Events\KeyWritten (743μs)
      • Illuminate\Cache\Events\CacheHit (878μs)
      • Illuminate\Cache\Events\CacheHit (354μs)
      • Illuminate\Cache\Events\CacheHit (293μs)
      • Illuminate\Cache\Events\CacheHit (362μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (163μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (109μs)
      • Illuminate\Cache\Events\CacheHit (137μs)
      • Illuminate\Cache\Events\CacheHit (137μs)
      • Illuminate\Cache\Events\CacheHit (357μs)
      • Illuminate\Cache\Events\CacheHit (129μs)
      • Illuminate\Cache\Events\CacheMissed (209μs)
      • Illuminate\Database\Events\StatementPrepared (645μs)
      • Illuminate\Database\Events\QueryExecuted (1.01ms)
      • eloquent.retrieved: App\Models\SubjectCat (140μs)
      • Illuminate\Cache\Events\KeyWritten (432μs)
      • Illuminate\Cache\Events\CacheHit (201μs)
      • Illuminate\Cache\Events\CacheHit (223μs)
      • Illuminate\Cache\Events\CacheHit (139μs)
      • Illuminate\Cache\Events\CacheHit (141μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • Illuminate\Cache\Events\CacheHit (326μs)
      • Illuminate\Cache\Events\CacheHit (210μs)
      • Illuminate\Cache\Events\CacheMissed (422μs)
      • Illuminate\Database\Events\StatementPrepared (831μs)
      • Illuminate\Database\Events\QueryExecuted (1.01ms)
      • eloquent.retrieved: App\Models\SubjectCat (71μs)
      • Illuminate\Cache\Events\KeyWritten (693μs)
      • Illuminate\Cache\Events\CacheHit (308μs)
      • Illuminate\Cache\Events\CacheHit (272μs)
      • Illuminate\Cache\Events\CacheHit (276μs)
      • Illuminate\Cache\Events\CacheHit (397μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (238μs)
      • Illuminate\Cache\Events\CacheHit (355μs)
      • Illuminate\Cache\Events\CacheHit (232μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (221μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (198μs)
      • Illuminate\Cache\Events\CacheHit (3.45ms)
      • Illuminate\Cache\Events\CacheHit (1.26ms)
      • Illuminate\Cache\Events\CacheHit (747μs)
      • Illuminate\Cache\Events\CacheHit (355μs)
      • Illuminate\Cache\Events\CacheHit (1.88ms)
      • Illuminate\Cache\Events\CacheHit (227μs)
      • Illuminate\Cache\Events\CacheHit (219μs)
      • Illuminate\Cache\Events\CacheHit (408μs)
      • Illuminate\Cache\Events\CacheHit (321μs)
      • Illuminate\Cache\Events\CacheHit (254μs)
      • Illuminate\Cache\Events\CacheHit (328μs)
      • Illuminate\Cache\Events\CacheHit (216μs)
      • Illuminate\Cache\Events\CacheHit (480μs)
      • Illuminate\Cache\Events\CacheHit (298μs)
      • Illuminate\Cache\Events\CacheHit (266μs)
      • Illuminate\Cache\Events\CacheHit (298μs)
      • Illuminate\Cache\Events\CacheHit (195μs)
      • Illuminate\Cache\Events\CacheHit (311μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheMissed (493μs)
      • Illuminate\Database\Events\StatementPrepared (1.1ms)
      • Illuminate\Database\Events\QueryExecuted (2.54ms)
      • eloquent.retrieved: App\Models\SubjectCat (211μs)
      • Illuminate\Cache\Events\KeyWritten (625μs)
      • Illuminate\Cache\Events\CacheHit (224μs)
      • Illuminate\Cache\Events\CacheHit (212μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (207μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (682μs)
      • Illuminate\Cache\Events\CacheHit (265μs)
      • Illuminate\Cache\Events\CacheHit (1.52ms)
      • Illuminate\Cache\Events\CacheHit (221μs)
      • Illuminate\Cache\Events\CacheHit (1.2ms)
      • Illuminate\Cache\Events\CacheHit (582μs)
      • Illuminate\Cache\Events\CacheHit (1.29ms)
      • Illuminate\Cache\Events\CacheHit (224μs)
      • Illuminate\Cache\Events\CacheHit (205μs)
      • Illuminate\Cache\Events\CacheHit (186μs)
      • Illuminate\Cache\Events\CacheHit (202μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheHit (488μs)
      • Illuminate\Cache\Events\CacheHit (198μs)
      • Illuminate\Cache\Events\CacheHit (1.08ms)
      • Illuminate\Cache\Events\CacheHit (322μs)
      • Illuminate\Cache\Events\CacheHit (346μs)
      • Illuminate\Cache\Events\CacheHit (957μs)
      • Illuminate\Cache\Events\CacheHit (221μs)
      • Illuminate\Cache\Events\CacheHit (263μs)
      • Illuminate\Cache\Events\CacheHit (282μs)
      • Illuminate\Cache\Events\CacheHit (565μs)
      • Illuminate\Cache\Events\CacheHit (288μs)
      • Illuminate\Cache\Events\CacheHit (462μs)
      • Illuminate\Cache\Events\CacheHit (256μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (200μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheHit (203μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (162μs)
      • Illuminate\Cache\Events\CacheHit (867μs)
      • Illuminate\Cache\Events\CacheHit (335μs)
      • Illuminate\Cache\Events\CacheMissed (832μs)
      • Illuminate\Database\Events\StatementPrepared (1.61ms)
      • Illuminate\Database\Events\QueryExecuted (2.13ms)
      • eloquent.retrieved: App\Models\SubjectCat (228μs)
      • Illuminate\Cache\Events\KeyWritten (610μs)
      • Illuminate\Cache\Events\CacheHit (1.97ms)
      • Illuminate\Cache\Events\CacheHit (296μs)
      • Illuminate\Cache\Events\CacheHit (244μs)
      • Illuminate\Cache\Events\CacheHit (254μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (196μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheMissed (357μs)
      • Illuminate\Database\Events\StatementPrepared (1.28ms)
      • Illuminate\Database\Events\QueryExecuted (1.5ms)
      • eloquent.retrieved: App\Models\SubjectCat (140μs)
      • Illuminate\Cache\Events\KeyWritten (772μs)
      • Illuminate\Cache\Events\CacheHit (391μs)
      • Illuminate\Cache\Events\CacheHit (514μs)
      • Illuminate\Cache\Events\CacheHit (358μs)
      • Illuminate\Cache\Events\CacheHit (263μs)
      • Illuminate\Cache\Events\CacheHit (257μs)
      • Illuminate\Cache\Events\CacheHit (274μs)
      • Illuminate\Cache\Events\CacheHit (199μs)
      • Illuminate\Cache\Events\CacheHit (215μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (628μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (1.12ms)
      • Illuminate\Cache\Events\CacheHit (270μs)
      • Illuminate\Cache\Events\CacheHit (211μs)
      • Illuminate\Cache\Events\CacheHit (165μs)
      • Illuminate\Cache\Events\CacheHit (612μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (306μs)
      • Illuminate\Cache\Events\CacheHit (311μs)
      • Illuminate\Cache\Events\CacheHit (367μs)
      • Illuminate\Cache\Events\CacheHit (200μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (264μs)
      • Illuminate\Cache\Events\CacheHit (186μs)
      • Illuminate\Cache\Events\CacheHit (453μs)
      • Illuminate\Cache\Events\CacheHit (460μs)
      • Illuminate\Cache\Events\CacheHit (268μs)
      • Illuminate\Cache\Events\CacheHit (981μs)
      • Illuminate\Cache\Events\CacheMissed (1.07ms)
      • Illuminate\Database\Events\StatementPrepared (887μs)
      • Illuminate\Database\Events\QueryExecuted (1.27ms)
      • eloquent.retrieved: App\Models\SubjectCat (218μs)
      • Illuminate\Cache\Events\KeyWritten (383μs)
      • Illuminate\Cache\Events\CacheHit (231μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (165μs)
      • Illuminate\Cache\Events\CacheHit (430μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (156μs)
      • Illuminate\Cache\Events\CacheHit (335μs)
      • Illuminate\Cache\Events\CacheHit (274μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (165μs)
      • Illuminate\Cache\Events\CacheHit (573μs)
      • Illuminate\Cache\Events\CacheHit (317μs)
      • Illuminate\Cache\Events\CacheHit (303μs)
      • Illuminate\Cache\Events\CacheHit (522μs)
      • Illuminate\Cache\Events\CacheHit (228μs)
      • Illuminate\Cache\Events\CacheHit (739μs)
      • Illuminate\Cache\Events\CacheHit (211μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (243μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (242μs)
      • Illuminate\Cache\Events\CacheHit (231μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (161μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (225μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (163μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (163μs)
      • Illuminate\Cache\Events\CacheHit (381μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (165μs)
      • Illuminate\Cache\Events\CacheHit (264μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (170μs)
      • Illuminate\Cache\Events\CacheHit (182μs)
      • Illuminate\Cache\Events\CacheHit (216μs)
      • Illuminate\Cache\Events\CacheHit (268μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (248μs)
      • Illuminate\Cache\Events\CacheHit (193μs)
      • Illuminate\Cache\Events\CacheHit (280μs)
      • Illuminate\Cache\Events\CacheHit (1.68ms)
      • Illuminate\Cache\Events\CacheHit (438μs)
      • Illuminate\Cache\Events\CacheHit (603μs)
      • Illuminate\Cache\Events\CacheHit (198μs)
      • Illuminate\Cache\Events\CacheHit (313μs)
      • Illuminate\Cache\Events\CacheHit (208μs)
      • Illuminate\Cache\Events\CacheHit (391μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (162μs)
      • Illuminate\Cache\Events\CacheHit (196μs)
      • Illuminate\Cache\Events\CacheHit (425μs)
      • Illuminate\Cache\Events\CacheHit (222μs)
      • Illuminate\Cache\Events\CacheHit (241μs)
      • Illuminate\Cache\Events\CacheMissed (298μs)
      • Illuminate\Database\Events\StatementPrepared (955μs)
      • Illuminate\Database\Events\QueryExecuted (2.26ms)
      • eloquent.retrieved: App\Models\SubjectCat (116μs)
      • Illuminate\Cache\Events\KeyWritten (577μs)
      • Illuminate\Cache\Events\CacheHit (186μs)
      • Illuminate\Cache\Events\CacheHit (486μs)
      • Illuminate\Cache\Events\CacheHit (200μs)
      • Illuminate\Cache\Events\CacheHit (273μs)
      • Illuminate\Cache\Events\CacheHit (246μs)
      • Illuminate\Cache\Events\CacheHit (238μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (266μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (207μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (159μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (163μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (312μs)
      • Illuminate\Cache\Events\CacheHit (972μs)
      • Illuminate\Cache\Events\CacheHit (328μs)
      • Illuminate\Cache\Events\CacheHit (285μs)
      • Illuminate\Cache\Events\CacheHit (161μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (298μs)
      • Illuminate\Cache\Events\CacheHit (277μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (162μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (381μs)
      • Illuminate\Cache\Events\CacheHit (410μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (348μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (285μs)
      • Illuminate\Cache\Events\CacheHit (383μs)
      • Illuminate\Cache\Events\CacheHit (256μs)
      • Illuminate\Cache\Events\CacheHit (214μs)
      • Illuminate\Cache\Events\CacheHit (274μs)
      • Illuminate\Cache\Events\CacheHit (210μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (195μs)
      • Illuminate\Cache\Events\CacheHit (168μs)
      • Illuminate\Cache\Events\CacheHit (262μs)
      • Illuminate\Cache\Events\CacheHit (231μs)
      • Illuminate\Cache\Events\CacheHit (321μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheHit (297μs)
      • Illuminate\Cache\Events\CacheHit (247μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (285μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (1.6ms)
      • Illuminate\Cache\Events\CacheHit (234μs)
      • Illuminate\Cache\Events\CacheHit (360μs)
      • Illuminate\Cache\Events\CacheHit (226μs)
      • Illuminate\Cache\Events\CacheHit (237μs)
      • Illuminate\Cache\Events\CacheHit (200μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (268μs)
      • Illuminate\Cache\Events\CacheHit (318μs)
      • Illuminate\Cache\Events\CacheHit (204μs)
      • Illuminate\Cache\Events\CacheHit (168μs)
      • Illuminate\Cache\Events\CacheHit (305μs)
      • Illuminate\Cache\Events\CacheHit (317μs)
      • Illuminate\Cache\Events\CacheHit (263μs)
      • Illuminate\Cache\Events\CacheHit (335μs)
      • Illuminate\Cache\Events\CacheHit (216μs)
      • Illuminate\Cache\Events\CacheHit (370μs)
      • Illuminate\Cache\Events\CacheHit (217μs)
      • Illuminate\Cache\Events\CacheHit (170μs)
      • Illuminate\Cache\Events\CacheHit (360μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (247μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (1.55ms)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (275μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (165μs)
      • Illuminate\Cache\Events\CacheHit (193μs)
      • Illuminate\Cache\Events\CacheHit (164μs)
      • Illuminate\Cache\Events\CacheHit (270μs)
      • Illuminate\Cache\Events\CacheHit (164μs)
      • Illuminate\Cache\Events\CacheHit (388μs)
      • Illuminate\Cache\Events\CacheHit (395μs)
      • Illuminate\Cache\Events\CacheMissed (614μs)
      • Illuminate\Database\Events\StatementPrepared (1.11ms)
      • Illuminate\Database\Events\QueryExecuted (937μs)
      • eloquent.retrieved: App\Models\SubjectCat (67μs)
      • Illuminate\Cache\Events\KeyWritten (418μs)
      • Illuminate\Cache\Events\CacheHit (280μs)
      • Illuminate\Cache\Events\CacheHit (287μs)
      • Illuminate\Cache\Events\CacheHit (266μs)
      • Illuminate\Cache\Events\CacheHit (443μs)
      • Illuminate\Cache\Events\CacheHit (336μs)
      • Illuminate\Cache\Events\CacheHit (243μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • Illuminate\Cache\Events\CacheHit (221μs)
      • Illuminate\Cache\Events\CacheHit (248μs)
      • Illuminate\Cache\Events\CacheHit (206μs)
      • Illuminate\Cache\Events\CacheHit (303μs)
      • Illuminate\Cache\Events\CacheHit (338μs)
      • Illuminate\Cache\Events\CacheHit (376μs)
      • Illuminate\Cache\Events\CacheHit (211μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (2.41ms)
      • Illuminate\Cache\Events\CacheHit (219μs)
      • creating: site.layouts.app (511μs)
      • composing: site.layouts.app (26μs)
      • creating: components.canonical (1.25ms)
      • composing: components.canonical (118μs)
      • creating: components.open-graph (240μs)
      • composing: components.open-graph (96μs)
      • creating: site.headers.header (1.62ms)
      • composing: site.headers.header (136μs)
      • Illuminate\Cache\Events\CacheHit (1.95ms)
      • creating: components.footer (86μs)
      • composing: components.footer (92μs)
      • Illuminate\Cache\Events\CacheHit (1ms)
      • Illuminate\Cache\Events\CacheMissed (386μs)
      • Illuminate\Database\Events\StatementPrepared (940μs)
      • Illuminate\Database\Events\QueryExecuted (1.37ms)
      • eloquent.retrieved: App\Models\SubjectCat (78μs)
      • Illuminate\Cache\Events\KeyWritten (1.46ms)
      • Illuminate\Cache\Events\CacheHit (510μs)
      • Illuminate\Cache\Events\CacheHit (208μs)
      • Illuminate\Cache\Events\CacheHit (351μs)
      • Illuminate\Cache\Events\CacheHit (212μs)
      • Illuminate\Cache\Events\CacheHit (186μs)
      • Illuminate\Cache\Events\CacheHit (303μs)
      • Illuminate\Cache\Events\CacheHit (321μs)
      • Illuminate\Cache\Events\CacheHit (204μs)
      • Illuminate\Cache\Events\CacheHit (255μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (209μs)
      • Illuminate\Cache\Events\CacheHit (206μs)
      • creating: components.forms.contact-us (263μs)
      • composing: components.forms.contact-us (148μs)
      • creating: components.forms.get-started (126μs)
      • composing: components.forms.get-started (63μs)
      • creating: components.forms.free-tool-download (96μs)
      • composing: components.forms.free-tool-download (62μs)
      • creating: components.forms.claim-free-worksheet (96μs)
      • composing: components.forms.claim-free-worksheet (61μs)
      • creating: components.forms.tutor-subscription-waitlist (260μs)
      • composing: components.forms.tutor-subscription-waitlist (76μs)
      • creating: components.forms.tutor-subscription-join (106μs)
      • composing: components.forms.tutor-subscription-join (65μs)
      • creating: components.forms.tutor-support (97μs)
      • composing: components.forms.tutor-support (63μs)
      • 311 x Illuminate\Cache\Events\CacheHit (18.66%)
        125ms
        20 x Illuminate\Database\Events\StatementPrepared (5.53%)
        37.05ms
        20 x Illuminate\Database\Events\QueryExecuted (5.03%)
        33.70ms
        11 x Illuminate\Cache\Events\CacheMissed (1.68%)
        11.29ms
        11 x Illuminate\Cache\Events\KeyWritten (1.33%)
        8.95ms
        1 x Illuminate\Foundation\Events\LocaleUpdated (0.92%)
        6.17ms
        1 x Illuminate\Routing\Events\Routing (0.27%)
        1.80ms
        1 x Illuminate\Database\Events\ConnectionEstablished (0.26%)
        1.72ms
        1 x creating: site.headers.header (0.24%)
        1.62ms
        12 x eloquent.retrieved: App\Models\SubjectCat (0.24%)
        1.58ms
        1 x creating: components.canonical (0.19%)
        1.25ms
        1 x Illuminate\Routing\Events\RouteMatched (0.12%)
        828μs
        7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.1%)
        693μs
        1 x eloquent.booting: App\Models\SubjectCat (0.1%)
        667μs
        1 x creating: site.layouts.app (0.08%)
        511μs
        2 x eloquent.retrieved: App\Models\Subject (0.06%)
        407μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.06%)
        402μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.04%)
        297μs
        1 x creating: homework.show (0.04%)
        278μs
        1 x creating: components.breadcrumbs (0.04%)
        270μs
        11 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.04%)
        263μs
        1 x creating: components.forms.contact-us (0.04%)
        263μs
        1 x creating: components.forms.tutor-subscription-waitlist (0.04%)
        260μs
        1 x creating: components.open-graph (0.04%)
        240μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.02%)
        164μs
        1 x composing: components.forms.contact-us (0.02%)
        148μs
        1 x eloquent.booting: App\Models\Subject (0.02%)
        142μs
        1 x composing: site.headers.header (0.02%)
        136μs
        1 x creating: components.forms.get-started (0.02%)
        126μs
        1 x composing: components.breadcrumbs (0.02%)
        123μs
        1 x composing: homework.show (0.02%)
        120μs
        1 x composing: components.canonical (0.02%)
        118μs
        1 x creating: components.forms.tutor-subscription-join (0.02%)
        106μs
        1 x creating: components.forms.tutor-support (0.01%)
        97μs
        1 x composing: components.open-graph (0.01%)
        96μs
        1 x creating: components.forms.free-tool-download (0.01%)
        96μs
        1 x creating: components.forms.claim-free-worksheet (0.01%)
        96μs
        1 x composing: components.footer (0.01%)
        92μs
        1 x creating: components.footer (0.01%)
        86μs
        1 x composing: components.forms.tutor-subscription-waitlist (0.01%)
        76μs
        1 x composing: components.forms.tutor-subscription-join (0.01%)
        65μs
        1 x composing: components.forms.get-started (0.01%)
        63μs
        1 x composing: components.forms.tutor-support (0.01%)
        63μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.01%)
        62μs
        1 x composing: components.forms.free-tool-download (0.01%)
        62μs
        1 x eloquent.booted: App\Models\Subject (0.01%)
        61μs
        1 x composing: components.forms.claim-free-worksheet (0.01%)
        61μs
        1 x eloquent.booted: App\Models\SubjectCat (0.01%)
        46μs
        1 x composing: site.layouts.app (0%)
        26μs
      14 templates were rendered
      • 1x homework.showshow.blade.phpblade
      • 1x components.breadcrumbsbreadcrumbs.blade.phpblade
      • 1x site.layouts.appapp.blade.phpblade
      • 1x components.canonicalcanonical.blade.phpblade
      • 1x components.open-graphopen-graph.blade.phpblade
      • 1x site.headers.headerheader.blade.phpblade
      • 1x components.footerfooter.blade.phpblade
      • 1x components.forms.contact-uscontact-us.blade.phpblade
      • 1x components.forms.get-startedget-started.blade.phpblade
      • 1x components.forms.free-tool-downloadfree-tool-download.blade.phpblade
      • 1x components.forms.claim-free-worksheetclaim-free-worksheet.blade.phpblade
      • 1x components.forms.tutor-subscription-waitlisttutor-subscription-waitlist.blade.phpblade
      • 1x components.forms.tutor-subscription-jointutor-subscription-join.blade.phpblade
      • 1x components.forms.tutor-supporttutor-support.blade.phpblade
      uri
      GET college-homework-library/{category}/{subject}/{id}
      middleware
      web, utm.parameters
      controller
      App\Http\Controllers\HomeworkLibraryController@show
      namespace
      where
      as
      homework.show
      file
      app/Http/Controllers/HomeworkLibraryController.php:79-176
      20 statements were executed, 5 of which were duplicates, 15 unique. Show only duplicated39.41ms
      • 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` = '29387' limit 1
        9.11mstwenty4_siteHomeworkLibraryController.php#97
        Bindings
        • 0: published
        • 1: 0
        • 2: 29387
        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 (223)
        2.75mstwenty4_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 (29387)
        1.25mstwenty4_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` = 34 limit 1
        1.22mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 34
        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` <> 29387 and `subject` = 223 and `status` = 'published' and `price` > 0 order by RAND() limit 6
        2.85mstwenty4_siteHomeworkLibraryRepository.php#30
        Bindings
        • 0: 29387
        • 1: 223
        • 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 (223)
        1.28mstwenty4_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` = 29387 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        1.38mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 29387
        • 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` = 29387 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'teaser' order by `order` asc, `id` asc
        1.23mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 29387
        • 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` = 29387 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'solution' order by `order` asc, `id` asc
        1.19mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 29387
        • 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` = 34 limit 1
        1.19mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 34
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 32. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 33. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 34. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
        • 35. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1
        1.34mstwenty4_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
        1.03mstwenty4_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
        1.14mstwenty4_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
        2.76mstwenty4_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
        2.58mstwenty4_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
        1.64mstwenty4_siteSubject.php#100
        Bindings
        • 0: 11
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 5 limit 1
        1.35mstwenty4_siteSubject.php#100
        Bindings
        • 0: 5
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 34 limit 1
        1.31mstwenty4_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
        1.57mstwenty4_siteSubject.php#100
        Bindings
        • 0: 36
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 28. view::components.footer:170
      App\Models\SubjectCat
      12SubjectCat.php
      App\Models\HomeworkLibrary\HomeworkLibraryFile
      11HomeworkLibraryFile.php
      App\Models\HomeworkLibrary\HomeworkLibrary
      7HomeworkLibrary.php
      App\Models\Subject
      2Subject.php
          _token
          KrXkJtEY27U7D2lDBwX9RUe4hDA3gAXnNlpGfti5
          utm_source
          direct
          redirectUrl
          /college-homework-library/Physics/Astrophysics/29387
          _previous
          array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/Physics/Astroph...
          _flash
          array:2 [ "old" => [] "new" => [] ]
          PHPDEBUGBAR_STACK_DATA
          []
          path_info
          /college-homework-library/Physics/Astrophysics/29387
          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=1-68066a11-03bd968a75dee77b6806d145" ] "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 => "18.219.87.235" ] "content-length" => array:1 [ 0 => "" ] "content-type" => array:1 [ 0 => "" ] ]
          request_cookies
          []
          
          response_headers
          0 of 0
          array:5 [ "content-type" => array:1 [ 0 => "text/html; charset=UTF-8" ] "cache-control" => array:1 [ 0 => "no-cache, private" ] "date" => array:1 [ 0 => "Mon, 21 Apr 2025 15:53:53 GMT" ] "set-cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6ImxCUE1hajR1akwvOWhOdm93QStVeVE9PSIsInZhbHVlIjoiRnd6KzhjUE1ESWkwRVBiWWJaV0VpRTVpVGl2Vm5vYTQzK3dxY3ozcEZpYXZzQWR2VzJTK0RkdkwweU1uRnRhbTFOcE1jbFVuKzNRbHpNeWFuU0JZbnpZQzVtQm1xYjlmam9seTgydHYxM2xHMmFZN3BjcVRZNDhEWTB0TjNCaW4iLCJtYWMiOiIxYmU1YzhkMTlkNTJiODNhMmY1MjY0ZTA1OTQ4ZDBiYTZmYzRlMGQ3MjlhNDhkMmM2MjUwZTE5MWIzY2VkMjhlIiwidGFnIjoiIn0%3D; expires=Mon, 21 Apr 2025 17:53:53 GMT; Max-Age=7200; path=/; domain=.24houranswers.com; samesite=laxXSRF-TOKEN=eyJpdiI6ImxCUE1hajR1akwvOWhOdm93QStVeVE9PSIsInZhbHVlIjoiRnd6KzhjUE1ESWkwRVBiWWJaV0VpRTVpVGl2Vm5vYTQzK3dxY3ozcEZpYXZzQWR2VzJTK0RkdkwweU1uRnRhbTFOcE1jb" 1 => "24houranswers_session=eyJpdiI6Inh0bGRIU3p1YkJ1U2cySm1VQjVRd1E9PSIsInZhbHVlIjoiNktIeFMybks5ZHhXckswRnRGTGJKeWtvRHpyV3BsZFpielp5dGx4cFNpVm5ZTFhwcGtERHFXbUtPQ1VaQXdDMU9rUmZSQ2RyVnFsUE83YkRmbEozQk5UdzkzVkVnWWxQRk1LUEcrcEdpOWNPbFFkd3FYd2pOZ1lCdGdSWTAvRjQiLCJtYWMiOiI3MjU1MjQzNDcyZjU1OTk5NzEwNWRhMzkzNTM1NmVkYjMzZTc5MjU1NDRjMjc3NTJmMGQzMWIwMDc5NjU4ZWQxIiwidGFnIjoiIn0%3D; expires=Mon, 21 Apr 2025 17:53:53 GMT; Max-Age=7200; path=/; domain=.24houranswers.com; httponly; samesite=lax24houranswers_session=eyJpdiI6Inh0bGRIU3p1YkJ1U2cySm1VQjVRd1E9PSIsInZhbHVlIjoiNktIeFMybks5ZHhXckswRnRGTGJKeWtvRHpyV3BsZFpielp5dGx4cFNpVm5ZTFhwcGtERHFXbUtPQ1VaQX" ] "Set-Cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6ImxCUE1hajR1akwvOWhOdm93QStVeVE9PSIsInZhbHVlIjoiRnd6KzhjUE1ESWkwRVBiWWJaV0VpRTVpVGl2Vm5vYTQzK3dxY3ozcEZpYXZzQWR2VzJTK0RkdkwweU1uRnRhbTFOcE1jbFVuKzNRbHpNeWFuU0JZbnpZQzVtQm1xYjlmam9seTgydHYxM2xHMmFZN3BjcVRZNDhEWTB0TjNCaW4iLCJtYWMiOiIxYmU1YzhkMTlkNTJiODNhMmY1MjY0ZTA1OTQ4ZDBiYTZmYzRlMGQ3MjlhNDhkMmM2MjUwZTE5MWIzY2VkMjhlIiwidGFnIjoiIn0%3D; expires=Mon, 21-Apr-2025 17:53:53 GMT; domain=.24houranswers.com; path=/XSRF-TOKEN=eyJpdiI6ImxCUE1hajR1akwvOWhOdm93QStVeVE9PSIsInZhbHVlIjoiRnd6KzhjUE1ESWkwRVBiWWJaV0VpRTVpVGl2Vm5vYTQzK3dxY3ozcEZpYXZzQWR2VzJTK0RkdkwweU1uRnRhbTFOcE1jb" 1 => "24houranswers_session=eyJpdiI6Inh0bGRIU3p1YkJ1U2cySm1VQjVRd1E9PSIsInZhbHVlIjoiNktIeFMybks5ZHhXckswRnRGTGJKeWtvRHpyV3BsZFpielp5dGx4cFNpVm5ZTFhwcGtERHFXbUtPQ1VaQXdDMU9rUmZSQ2RyVnFsUE83YkRmbEozQk5UdzkzVkVnWWxQRk1LUEcrcEdpOWNPbFFkd3FYd2pOZ1lCdGdSWTAvRjQiLCJtYWMiOiI3MjU1MjQzNDcyZjU1OTk5NzEwNWRhMzkzNTM1NmVkYjMzZTc5MjU1NDRjMjc3NTJmMGQzMWIwMDc5NjU4ZWQxIiwidGFnIjoiIn0%3D; expires=Mon, 21-Apr-2025 17:53:53 GMT; domain=.24houranswers.com; path=/; httponly24houranswers_session=eyJpdiI6Inh0bGRIU3p1YkJ1U2cySm1VQjVRd1E9PSIsInZhbHVlIjoiNktIeFMybks5ZHhXckswRnRGTGJKeWtvRHpyV3BsZFpielp5dGx4cFNpVm5ZTFhwcGtERHFXbUtPQ1VaQX" ] ]
          session_attributes
          0 of 0
          array:6 [ "_token" => "KrXkJtEY27U7D2lDBwX9RUe4hDA3gAXnNlpGfti5" "utm_source" => "direct" "redirectUrl" => "/college-homework-library/Physics/Astrophysics/29387" "_previous" => array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/Physics/Astrophysics/29387" ] "_flash" => array:2 [ "old" => [] "new" => [] ] "PHPDEBUGBAR_STACK_DATA" => [] ]