Question
1. SC Structure:
(a)Crystallographic Direction: Your SC model has 8 unique atoms. If you look down the [100] direction, how many atoms do you see that are not hidden behind other atoms?
(b) Crystallographic Plane: How many of these atoms are completely bisected by the (100) plane (i.e. their center lies exactly on the (100) plane)? What are the coordinates of these atoms? Please use proper crystallographic notation
(c) Angles: Identify and calculate the angles between
1. The [100] and [110] directions
2. The [100] and [111] directions

2. BCC Structure:
(a) Crystallographic Direction: If you arrange your model so that you are looking down the [110] direction, how many atoms do you see that are not hidden behind other atoms?
(b) Crystallographic Plane: How many of these atoms are completely bisected by the (110) plane (i.e. their center lies exactly on the (110) plane)? What are the coordinates of these atoms? Please use proper crystallographic notation.
(c) Linear Packing Density: Look down (010],[101] and [111] directions
1. Intuitively, which direction seems to have the higher atom density?
2. How many atoms lie along each direction?
3. For each direction, are they touching (yes or no)?
4. Deduce the atomic radius R as a function of the lattice parameter a
5. For each direction, determine the linear packing fraction (% of the distance occupied by atoms) and the linear packing density (# atoms per nm) in the case of an atom of Lithium
(c) Planar Packing Density: Consider the (101) plane
1. How many atoms lie on this plane?
2. Sketch this plane. Represent the atoms by circles and indicate the significant lengths used as a function of R and a (exact values for atomic radius or lattice parameter are not necessary, but relative atom positions are important).
3. Calculate the planar packing fraction and planar packing density of the (101)BCC plane in the case of an atom of Barium
(a) Crystallographic Direction: If you arrange your model so that you are looking down the [110] direction, how many atoms do you see that are not hidden behind other atoms?
(b) Crystallographic Plane: How many of these atoms are completely bisected by the (111) plane (i.e. their center lies exactly on the (111) plane)? What are the coordinates of these atoms? Please use proper crystallographic notation
(c) Linear Packing Density: Look down [010], [101]. and [111] directions
1. Intuitively, which direction seems to have the higher atom density?
2. How many atoms lie along each direction?
3. For each direction, are they touching (yes or no)?
4. Deduce the atomic radius r as function of the lattice parameter a
5. For each direction, determine the linear packing fraction (% of the distance occupied by atoms) and the linear packing density (# atoms per nm) in the case of an atom of Aluminum
(d) Planar Packing Density: Consider the (111) plane
1. How many atoms lie on this plane?
2. Sketch this plane. Represent the atoms by circles and indicate the significant lengths used as a function of and A (exact values for atomic radius or lattice parameter are not necessary, but relative atom positions are important).
3. Calculate the planar packing fraction and planar packing density of the (111)FCC plane in the case of an atom of Copper
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
$88.00
Google Pay
Amazon
Paypal
Mastercard
Visacard
Discover
Amex
View Available Engineering Tutors 529 tutors matched
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 Version584msRequest Duration45MBMemory UsageGET college-homework-library/{category}/{subject}/{id}Route
    • Booting (384ms)time
    • Application (200ms)time
    • 1 x Booting (65.8%)
      384ms
      1 x Application (34.2%)
      200ms
      • Illuminate\Routing\Events\Routing (882μs)
      • Illuminate\Routing\Events\RouteMatched (352μs)
      • Illuminate\Foundation\Events\LocaleUpdated (1.57ms)
      • eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (123μs)
      • eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (107μs)
      • Illuminate\Database\Events\ConnectionEstablished (616μs)
      • Illuminate\Database\Events\StatementPrepared (6.13ms)
      • Illuminate\Database\Events\QueryExecuted (1.56ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (126μs)
      • eloquent.booting: App\Models\Subject (134μs)
      • eloquent.booted: App\Models\Subject (63μs)
      • Illuminate\Database\Events\StatementPrepared (2.33ms)
      • Illuminate\Database\Events\QueryExecuted (944μs)
      • eloquent.retrieved: App\Models\Subject (134μs)
      • eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (156μs)
      • eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (59μs)
      • Illuminate\Database\Events\StatementPrepared (652μs)
      • Illuminate\Database\Events\QueryExecuted (5.4ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (104μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (20μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (12μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (10μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (9μs)
      • eloquent.booting: App\Models\SubjectCat (445μs)
      • eloquent.booted: App\Models\SubjectCat (116μs)
      • Illuminate\Database\Events\StatementPrepared (662μs)
      • Illuminate\Database\Events\QueryExecuted (1.01ms)
      • eloquent.retrieved: App\Models\SubjectCat (97μs)
      • Illuminate\Cache\Events\CacheHit (15.91ms)
      • Illuminate\Cache\Events\CacheMissed (252μs)
      • Illuminate\Database\Events\StatementPrepared (1.13ms)
      • Illuminate\Database\Events\QueryExecuted (2.52ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (70μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (14μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (9μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (6μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (6μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (6μs)
      • Illuminate\Database\Events\StatementPrepared (626μs)
      • Illuminate\Database\Events\QueryExecuted (1.8ms)
      • eloquent.retrieved: App\Models\Subject (107μs)
      • Illuminate\Cache\Events\KeyWritten (1.16ms)
      • Illuminate\Database\Events\StatementPrepared (5.39ms)
      • Illuminate\Database\Events\QueryExecuted (1.23ms)
      • Illuminate\Database\Events\StatementPrepared (951μs)
      • Illuminate\Database\Events\QueryExecuted (860μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (71μs)
      • Illuminate\Database\Events\StatementPrepared (1.02ms)
      • Illuminate\Database\Events\QueryExecuted (747μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (130μs)
      • Illuminate\Cache\Events\CacheHit (731μs)
      • creating: homework.show (369μs)
      • composing: homework.show (160μs)
      • creating: components.breadcrumbs (340μs)
      • composing: components.breadcrumbs (169μs)
      • Illuminate\Database\Events\StatementPrepared (1.91ms)
      • Illuminate\Database\Events\QueryExecuted (953μs)
      • eloquent.retrieved: App\Models\SubjectCat (94μs)
      • Illuminate\Cache\Events\CacheMissed (4.11ms)
      • Illuminate\Database\Events\StatementPrepared (792μs)
      • Illuminate\Database\Events\QueryExecuted (918μs)
      • eloquent.retrieved: App\Models\SubjectCat (86μs)
      • Illuminate\Cache\Events\KeyWritten (356μs)
      • Illuminate\Cache\Events\CacheHit (279μs)
      • Illuminate\Cache\Events\CacheHit (232μs)
      • Illuminate\Cache\Events\CacheHit (182μs)
      • Illuminate\Cache\Events\CacheHit (315μs)
      • Illuminate\Cache\Events\CacheHit (202μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (170μs)
      • Illuminate\Cache\Events\CacheHit (264μs)
      • Illuminate\Cache\Events\CacheHit (295μs)
      • Illuminate\Cache\Events\CacheHit (541μs)
      • Illuminate\Cache\Events\CacheHit (466μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (260μs)
      • Illuminate\Cache\Events\CacheMissed (2.47ms)
      • Illuminate\Database\Events\StatementPrepared (637μs)
      • Illuminate\Database\Events\QueryExecuted (1.56ms)
      • eloquent.retrieved: App\Models\SubjectCat (93μs)
      • Illuminate\Cache\Events\KeyWritten (442μs)
      • Illuminate\Cache\Events\CacheHit (307μs)
      • Illuminate\Cache\Events\CacheHit (296μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (290μs)
      • Illuminate\Cache\Events\CacheHit (195μs)
      • Illuminate\Cache\Events\CacheHit (138μs)
      • Illuminate\Cache\Events\CacheHit (278μs)
      • Illuminate\Cache\Events\CacheMissed (170μs)
      • Illuminate\Database\Events\StatementPrepared (574μs)
      • Illuminate\Database\Events\QueryExecuted (999μs)
      • eloquent.retrieved: App\Models\SubjectCat (75μs)
      • Illuminate\Cache\Events\KeyWritten (792μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (215μs)
      • Illuminate\Cache\Events\CacheHit (182μs)
      • Illuminate\Cache\Events\CacheHit (201μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheHit (259μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (287μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
      • Illuminate\Cache\Events\CacheHit (285μs)
      • Illuminate\Cache\Events\CacheHit (209μs)
      • Illuminate\Cache\Events\CacheHit (204μs)
      • Illuminate\Cache\Events\CacheHit (168μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (246μs)
      • Illuminate\Cache\Events\CacheHit (269μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (270μs)
      • Illuminate\Cache\Events\CacheHit (280μs)
      • Illuminate\Cache\Events\CacheHit (218μs)
      • Illuminate\Cache\Events\CacheHit (344μs)
      • Illuminate\Cache\Events\CacheHit (228μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (206μs)
      • Illuminate\Cache\Events\CacheHit (239μs)
      • Illuminate\Cache\Events\CacheHit (217μs)
      • Illuminate\Cache\Events\CacheHit (280μs)
      • Illuminate\Cache\Events\CacheMissed (155μs)
      • Illuminate\Database\Events\StatementPrepared (592μs)
      • Illuminate\Database\Events\QueryExecuted (934μs)
      • eloquent.retrieved: App\Models\SubjectCat (90μs)
      • Illuminate\Cache\Events\KeyWritten (380μs)
      • Illuminate\Cache\Events\CacheHit (1.64ms)
      • Illuminate\Cache\Events\CacheHit (494μs)
      • Illuminate\Cache\Events\CacheHit (195μs)
      • Illuminate\Cache\Events\CacheHit (203μs)
      • Illuminate\Cache\Events\CacheHit (207μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • Illuminate\Cache\Events\CacheHit (218μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (182μs)
      • Illuminate\Cache\Events\CacheHit (1.19ms)
      • Illuminate\Cache\Events\CacheHit (308μs)
      • Illuminate\Cache\Events\CacheHit (262μs)
      • Illuminate\Cache\Events\CacheHit (296μs)
      • Illuminate\Cache\Events\CacheHit (201μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (182μs)
      • Illuminate\Cache\Events\CacheHit (196μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (196μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (338μs)
      • Illuminate\Cache\Events\CacheHit (331μs)
      • Illuminate\Cache\Events\CacheHit (353μs)
      • Illuminate\Cache\Events\CacheHit (525μs)
      • Illuminate\Cache\Events\CacheHit (443μs)
      • Illuminate\Cache\Events\CacheHit (332μs)
      • Illuminate\Cache\Events\CacheHit (450μs)
      • Illuminate\Cache\Events\CacheHit (598μs)
      • Illuminate\Cache\Events\CacheHit (214μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (163μs)
      • Illuminate\Cache\Events\CacheHit (198μs)
      • Illuminate\Cache\Events\CacheHit (182μs)
      • Illuminate\Cache\Events\CacheMissed (295μs)
      • Illuminate\Database\Events\StatementPrepared (948μs)
      • Illuminate\Database\Events\QueryExecuted (976μs)
      • eloquent.retrieved: App\Models\SubjectCat (65μs)
      • Illuminate\Cache\Events\KeyWritten (1.35ms)
      • Illuminate\Cache\Events\CacheHit (226μs)
      • Illuminate\Cache\Events\CacheHit (195μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • Illuminate\Cache\Events\CacheHit (182μs)
      • Illuminate\Cache\Events\CacheHit (158μs)
      • Illuminate\Cache\Events\CacheHit (288μs)
      • Illuminate\Cache\Events\CacheHit (243μs)
      • Illuminate\Cache\Events\CacheMissed (196μs)
      • Illuminate\Database\Events\StatementPrepared (724μs)
      • Illuminate\Database\Events\QueryExecuted (1.05ms)
      • eloquent.retrieved: App\Models\SubjectCat (89μs)
      • Illuminate\Cache\Events\KeyWritten (1.69ms)
      • Illuminate\Cache\Events\CacheHit (376μs)
      • Illuminate\Cache\Events\CacheHit (278μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (265μs)
      • Illuminate\Cache\Events\CacheHit (272μs)
      • Illuminate\Cache\Events\CacheHit (310μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (159μs)
      • Illuminate\Cache\Events\CacheHit (211μs)
      • Illuminate\Cache\Events\CacheHit (173μs)
      • Illuminate\Cache\Events\CacheHit (844μs)
      • Illuminate\Cache\Events\CacheHit (164μs)
      • Illuminate\Cache\Events\CacheHit (279μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (298μs)
      • Illuminate\Cache\Events\CacheHit (317μs)
      • Illuminate\Cache\Events\CacheHit (276μs)
      • Illuminate\Cache\Events\CacheHit (335μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (160μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (159μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (159μs)
      • Illuminate\Cache\Events\CacheHit (223μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheMissed (185μs)
      • Illuminate\Database\Events\StatementPrepared (731μs)
      • Illuminate\Database\Events\QueryExecuted (1.11ms)
      • eloquent.retrieved: App\Models\SubjectCat (254μs)
      • Illuminate\Cache\Events\KeyWritten (2.17ms)
      • Illuminate\Cache\Events\CacheHit (540μs)
      • Illuminate\Cache\Events\CacheHit (492μs)
      • Illuminate\Cache\Events\CacheHit (253μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (158μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (158μs)
      • Illuminate\Cache\Events\CacheHit (201μs)
      • Illuminate\Cache\Events\CacheHit (170μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (161μs)
      • Illuminate\Cache\Events\CacheHit (276μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (159μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (160μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (160μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (163μs)
      • Illuminate\Cache\Events\CacheHit (251μs)
      • Illuminate\Cache\Events\CacheHit (162μs)
      • Illuminate\Cache\Events\CacheHit (220μs)
      • Illuminate\Cache\Events\CacheHit (250μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheHit (215μs)
      • Illuminate\Cache\Events\CacheHit (186μs)
      • Illuminate\Cache\Events\CacheHit (165μs)
      • Illuminate\Cache\Events\CacheHit (432μs)
      • Illuminate\Cache\Events\CacheHit (208μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (161μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (159μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (165μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (452μs)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (218μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (158μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (242μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (330μs)
      • Illuminate\Cache\Events\CacheHit (288μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (271μs)
      • Illuminate\Cache\Events\CacheHit (299μs)
      • Illuminate\Cache\Events\CacheHit (195μs)
      • Illuminate\Cache\Events\CacheHit (163μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (777μs)
      • Illuminate\Cache\Events\CacheHit (285μs)
      • Illuminate\Cache\Events\CacheHit (866μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (222μs)
      • Illuminate\Cache\Events\CacheHit (195μs)
      • Illuminate\Cache\Events\CacheHit (163μs)
      • Illuminate\Cache\Events\CacheMissed (182μs)
      • Illuminate\Database\Events\StatementPrepared (772μs)
      • Illuminate\Database\Events\QueryExecuted (1.07ms)
      • eloquent.retrieved: App\Models\SubjectCat (97μs)
      • Illuminate\Cache\Events\KeyWritten (420μs)
      • Illuminate\Cache\Events\CacheHit (1.44ms)
      • Illuminate\Cache\Events\CacheHit (240μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (215μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (235μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (165μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (316μs)
      • Illuminate\Cache\Events\CacheHit (271μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (160μs)
      • Illuminate\Cache\Events\CacheHit (200μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (1.05ms)
      • Illuminate\Cache\Events\CacheHit (242μs)
      • Illuminate\Cache\Events\CacheHit (337μs)
      • Illuminate\Cache\Events\CacheHit (256μs)
      • Illuminate\Cache\Events\CacheHit (526μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (353μs)
      • Illuminate\Cache\Events\CacheHit (298μs)
      • Illuminate\Cache\Events\CacheHit (683μs)
      • Illuminate\Cache\Events\CacheHit (241μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (374μs)
      • Illuminate\Cache\Events\CacheHit (216μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (165μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (234μs)
      • Illuminate\Cache\Events\CacheHit (217μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (206μs)
      • Illuminate\Cache\Events\CacheHit (412μs)
      • Illuminate\Cache\Events\CacheHit (269μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (158μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (156μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (156μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (157μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (159μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (156μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (155μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (270μs)
      • Illuminate\Cache\Events\CacheHit (202μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (207μs)
      • Illuminate\Cache\Events\CacheHit (170μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (159μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (160μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (158μs)
      • Illuminate\Cache\Events\CacheHit (208μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (287μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (168μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (249μs)
      • Illuminate\Cache\Events\CacheHit (293μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (223μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (216μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheHit (164μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • Illuminate\Cache\Events\CacheHit (273μs)
      • Illuminate\Cache\Events\CacheHit (164μs)
      • Illuminate\Cache\Events\CacheMissed (283μs)
      • Illuminate\Database\Events\StatementPrepared (1.03ms)
      • Illuminate\Database\Events\QueryExecuted (969μs)
      • eloquent.retrieved: App\Models\SubjectCat (82μs)
      • Illuminate\Cache\Events\KeyWritten (1.19ms)
      • Illuminate\Cache\Events\CacheHit (220μs)
      • Illuminate\Cache\Events\CacheHit (222μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheHit (162μs)
      • Illuminate\Cache\Events\CacheHit (312μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (203μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (164μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (161μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (198μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (199μs)
      • creating: site.layouts.app (1.52ms)
      • composing: site.layouts.app (23μs)
      • creating: components.canonical (459μs)
      • composing: components.canonical (108μs)
      • creating: components.open-graph (210μs)
      • composing: components.open-graph (79μs)
      • creating: site.headers.header (318μs)
      • composing: site.headers.header (80μs)
      • Illuminate\Cache\Events\CacheHit (3.06ms)
      • creating: components.footer (99μs)
      • composing: components.footer (107μs)
      • Illuminate\Cache\Events\CacheHit (1.02ms)
      • Illuminate\Cache\Events\CacheMissed (369μs)
      • Illuminate\Database\Events\StatementPrepared (906μs)
      • Illuminate\Database\Events\QueryExecuted (1.13ms)
      • eloquent.retrieved: App\Models\SubjectCat (96μs)
      • Illuminate\Cache\Events\KeyWritten (1.61ms)
      • Illuminate\Cache\Events\CacheHit (548μs)
      • Illuminate\Cache\Events\CacheHit (235μs)
      • Illuminate\Cache\Events\CacheHit (3.88ms)
      • Illuminate\Cache\Events\CacheHit (1.99ms)
      • Illuminate\Cache\Events\CacheHit (972μs)
      • Illuminate\Cache\Events\CacheHit (2.1ms)
      • Illuminate\Cache\Events\CacheHit (597μs)
      • Illuminate\Cache\Events\CacheHit (244μs)
      • Illuminate\Cache\Events\CacheHit (222μs)
      • Illuminate\Cache\Events\CacheHit (214μs)
      • Illuminate\Cache\Events\CacheHit (556μs)
      • Illuminate\Cache\Events\CacheHit (213μs)
      • creating: components.forms.contact-us (292μs)
      • composing: components.forms.contact-us (156μs)
      • creating: components.forms.get-started (211μs)
      • composing: components.forms.get-started (99μs)
      • creating: components.forms.free-tool-download (114μs)
      • composing: components.forms.free-tool-download (107μs)
      • creating: components.forms.claim-free-worksheet (106μs)
      • composing: components.forms.claim-free-worksheet (68μs)
      • creating: components.forms.tutor-subscription-waitlist (124μs)
      • composing: components.forms.tutor-subscription-waitlist (66μs)
      • creating: components.forms.tutor-subscription-join (101μs)
      • composing: components.forms.tutor-subscription-join (65μs)
      • creating: components.forms.tutor-support (104μs)
      • composing: components.forms.tutor-support (65μs)
      • 311 x Illuminate\Cache\Events\CacheHit (17.89%)
        104ms
        20 x Illuminate\Database\Events\StatementPrepared (4.88%)
        28.50ms
        20 x Illuminate\Database\Events\QueryExecuted (4.75%)
        27.73ms
        11 x Illuminate\Cache\Events\KeyWritten (1.98%)
        11.57ms
        11 x Illuminate\Cache\Events\CacheMissed (1.48%)
        8.67ms
        1 x Illuminate\Foundation\Events\LocaleUpdated (0.27%)
        1.57ms
        1 x creating: site.layouts.app (0.26%)
        1.52ms
        12 x eloquent.retrieved: App\Models\SubjectCat (0.21%)
        1.22ms
        1 x Illuminate\Routing\Events\Routing (0.15%)
        882μs
        1 x Illuminate\Database\Events\ConnectionEstablished (0.11%)
        616μs
        1 x creating: components.canonical (0.08%)
        459μs
        1 x eloquent.booting: App\Models\SubjectCat (0.08%)
        445μs
        1 x creating: homework.show (0.06%)
        369μs
        7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.06%)
        356μs
        1 x Illuminate\Routing\Events\RouteMatched (0.06%)
        352μs
        1 x creating: components.breadcrumbs (0.06%)
        340μs
        1 x creating: site.headers.header (0.05%)
        318μs
        1 x creating: components.forms.contact-us (0.05%)
        292μs
        2 x eloquent.retrieved: App\Models\Subject (0.04%)
        241μs
        7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.04%)
        237μs
        1 x creating: components.forms.get-started (0.04%)
        211μs
        1 x creating: components.open-graph (0.04%)
        210μs
        1 x composing: components.breadcrumbs (0.03%)
        169μs
        1 x composing: homework.show (0.03%)
        160μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.03%)
        156μs
        1 x composing: components.forms.contact-us (0.03%)
        156μs
        1 x eloquent.booting: App\Models\Subject (0.02%)
        134μs
        1 x creating: components.forms.tutor-subscription-waitlist (0.02%)
        124μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.02%)
        123μs
        1 x eloquent.booted: App\Models\SubjectCat (0.02%)
        116μs
        1 x creating: components.forms.free-tool-download (0.02%)
        114μs
        1 x composing: components.canonical (0.02%)
        108μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.02%)
        107μs
        1 x composing: components.forms.free-tool-download (0.02%)
        107μs
        1 x composing: components.footer (0.02%)
        107μs
        1 x creating: components.forms.claim-free-worksheet (0.02%)
        106μs
        1 x creating: components.forms.tutor-support (0.02%)
        104μs
        1 x creating: components.forms.tutor-subscription-join (0.02%)
        101μs
        1 x creating: components.footer (0.02%)
        99μs
        1 x composing: components.forms.get-started (0.02%)
        99μs
        1 x composing: site.headers.header (0.01%)
        80μs
        1 x composing: components.open-graph (0.01%)
        79μs
        1 x composing: components.forms.claim-free-worksheet (0.01%)
        68μs
        1 x composing: components.forms.tutor-subscription-waitlist (0.01%)
        66μs
        1 x composing: components.forms.tutor-subscription-join (0.01%)
        65μs
        1 x composing: components.forms.tutor-support (0.01%)
        65μs
        1 x eloquent.booted: App\Models\Subject (0.01%)
        63μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.01%)
        59μs
        1 x composing: site.layouts.app (0%)
        23μs
      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 duplicated33.48ms
      • 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` = '61779' limit 1
        6.73mstwenty4_siteHomeworkLibraryController.php#97
        Bindings
        • 0: published
        • 1: 0
        • 2: 61779
        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 (406)
        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 (61779)
        4.81mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subject_cats` where `subject_cats`.`id` = 10 limit 1
        1.08mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 10
        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` <> 61779 and `subject` = 406 and `status` = 'published' and `price` > 0 order by RAND() limit 6
        2.83mstwenty4_siteHomeworkLibraryRepository.php#30
        Bindings
        • 0: 61779
        • 1: 406
        • 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 (406)
        1.15mstwenty4_siteHomeworkLibraryRepository.php#30
        Backtrace
        • 19. app/Repositories/HomeworkLibraryRepository.php:30
        • 20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 21. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 23. app/Repositories/HomeworkLibraryRepository.php:39
        • 24. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 61779 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        1.04mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 61779
        • 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` = 61779 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'teaser' order by `order` asc, `id` asc
        1.04mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 61779
        • 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` = 61779 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'solution' order by `order` asc, `id` asc
        840μstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 61779
        • 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` = 10 limit 1
        1.11mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 10
        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
        1.14mstwenty4_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
        1.04mstwenty4_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
        1.12mstwenty4_siteSubject.php#100
        Bindings
        • 0: 4
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 10 limit 1
        1.04mstwenty4_siteSubject.php#100
        Bindings
        • 0: 10
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 33 limit 1
        1.16mstwenty4_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
        1.25mstwenty4_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
        1.1mstwenty4_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
        1.23mstwenty4_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
        1.33mstwenty4_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
        1.31mstwenty4_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\HomeworkLibrary
      7HomeworkLibrary.php
      App\Models\HomeworkLibrary\HomeworkLibraryFile
      7HomeworkLibraryFile.php
      App\Models\Subject
      2Subject.php
          _token
          VtWfe1sI1HJLirFI21HRBETIxoVbkSvrrUnt3HMx
          utm_source
          direct
          redirectUrl
          /college-homework-library/Engineering/Materials-Science/61779
          _previous
          array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/Engineering/Mat...
          _flash
          array:2 [ "old" => [] "new" => [] ]
          PHPDEBUGBAR_STACK_DATA
          []
          path_info
          /college-homework-library/Engineering/Materials-Science/61779
          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=1-68001fc3-1c61d8c9559bd26e2357fce1" ] "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 => "3.22.234.133" ] "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 => "Wed, 16 Apr 2025 21:23:15 GMT" ] "set-cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6ImpsS2pqNlY0ZGVJSSt2Q0lOTm5JbGc9PSIsInZhbHVlIjoiVHNsUlRsK3czRVpEQnFUZ01sVENXSkptZVBPYVdHN0xDdnpDUnJuWEZESmo3WnpQSU85M1o0bjRJK3hmbHcrR2k2T2pFSXd6THo5T0lOeUZsaDFuS3RPMWQ3NDVVS3V1WFkxaXQrTTN5RG1VZldhbWM3emxScE5PM3VENGZPT1UiLCJtYWMiOiJmOTI4MjNiZDdhYmIyYzQ5YzkxOGVlZmU3ZjdiNzE3NDU5YWFhYTBhZmQ5NTZiMGMwZjQwYjg2OWY3NDQzMjVmIiwidGFnIjoiIn0%3D; expires=Wed, 16 Apr 2025 23:23:16 GMT; Max-Age=7200; path=/; domain=.24houranswers.com; samesite=laxXSRF-TOKEN=eyJpdiI6ImpsS2pqNlY0ZGVJSSt2Q0lOTm5JbGc9PSIsInZhbHVlIjoiVHNsUlRsK3czRVpEQnFUZ01sVENXSkptZVBPYVdHN0xDdnpDUnJuWEZESmo3WnpQSU85M1o0bjRJK3hmbHcrR2k2T2pFS" 1 => "24houranswers_session=eyJpdiI6IklEOW5xWjBBY2ZHWVhLcGM0anlHNmc9PSIsInZhbHVlIjoiS3ZKTTJONGx2OWs4cGtjeEdPVUxoQWxqWmdNOUJTUjliTU5DeTJ4dHlSTmxNSm5IM3JwbmxXb3ljbk12M2VDdnVyNkxpYzQ0SkZTNzN0VGVJNi91OFpKZHl5aURRSE9UMDB3Z2twN3pXbVg1SzU0bURBdTFYZFZabHBCa2JkOWEiLCJtYWMiOiI3NDhjMjJkODlkYzJmOWQ2ZjJhN2ViMjU2NWFlYmQ3ZjQ5ZWQ1Njk4NTBkNDQxM2UwYjE2NDFlOGQ5MjYzZGVkIiwidGFnIjoiIn0%3D; expires=Wed, 16 Apr 2025 23:23:16 GMT; Max-Age=7200; path=/; domain=.24houranswers.com; httponly; samesite=lax24houranswers_session=eyJpdiI6IklEOW5xWjBBY2ZHWVhLcGM0anlHNmc9PSIsInZhbHVlIjoiS3ZKTTJONGx2OWs4cGtjeEdPVUxoQWxqWmdNOUJTUjliTU5DeTJ4dHlSTmxNSm5IM3JwbmxXb3ljbk12M2" ] "Set-Cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6ImpsS2pqNlY0ZGVJSSt2Q0lOTm5JbGc9PSIsInZhbHVlIjoiVHNsUlRsK3czRVpEQnFUZ01sVENXSkptZVBPYVdHN0xDdnpDUnJuWEZESmo3WnpQSU85M1o0bjRJK3hmbHcrR2k2T2pFSXd6THo5T0lOeUZsaDFuS3RPMWQ3NDVVS3V1WFkxaXQrTTN5RG1VZldhbWM3emxScE5PM3VENGZPT1UiLCJtYWMiOiJmOTI4MjNiZDdhYmIyYzQ5YzkxOGVlZmU3ZjdiNzE3NDU5YWFhYTBhZmQ5NTZiMGMwZjQwYjg2OWY3NDQzMjVmIiwidGFnIjoiIn0%3D; expires=Wed, 16-Apr-2025 23:23:16 GMT; domain=.24houranswers.com; path=/XSRF-TOKEN=eyJpdiI6ImpsS2pqNlY0ZGVJSSt2Q0lOTm5JbGc9PSIsInZhbHVlIjoiVHNsUlRsK3czRVpEQnFUZ01sVENXSkptZVBPYVdHN0xDdnpDUnJuWEZESmo3WnpQSU85M1o0bjRJK3hmbHcrR2k2T2pFS" 1 => "24houranswers_session=eyJpdiI6IklEOW5xWjBBY2ZHWVhLcGM0anlHNmc9PSIsInZhbHVlIjoiS3ZKTTJONGx2OWs4cGtjeEdPVUxoQWxqWmdNOUJTUjliTU5DeTJ4dHlSTmxNSm5IM3JwbmxXb3ljbk12M2VDdnVyNkxpYzQ0SkZTNzN0VGVJNi91OFpKZHl5aURRSE9UMDB3Z2twN3pXbVg1SzU0bURBdTFYZFZabHBCa2JkOWEiLCJtYWMiOiI3NDhjMjJkODlkYzJmOWQ2ZjJhN2ViMjU2NWFlYmQ3ZjQ5ZWQ1Njk4NTBkNDQxM2UwYjE2NDFlOGQ5MjYzZGVkIiwidGFnIjoiIn0%3D; expires=Wed, 16-Apr-2025 23:23:16 GMT; domain=.24houranswers.com; path=/; httponly24houranswers_session=eyJpdiI6IklEOW5xWjBBY2ZHWVhLcGM0anlHNmc9PSIsInZhbHVlIjoiS3ZKTTJONGx2OWs4cGtjeEdPVUxoQWxqWmdNOUJTUjliTU5DeTJ4dHlSTmxNSm5IM3JwbmxXb3ljbk12M2" ] ]
          session_attributes
          0 of 0
          array:6 [ "_token" => "VtWfe1sI1HJLirFI21HRBETIxoVbkSvrrUnt3HMx" "utm_source" => "direct" "redirectUrl" => "/college-homework-library/Engineering/Materials-Science/61779" "_previous" => array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/Engineering/Materials-Science/61779" ] "_flash" => array:2 [ "old" => [] "new" => [] ] "PHPDEBUGBAR_STACK_DATA" => [] ]