1) You have been given the job of finding the specific heat capacit...

Question
1) You have been given the job of finding the specific heat capacity of two materials. You do two experiments, where you have both materials in thermal contact and equilibrium. For the first experiment and for material “Type 1” you have .5 kg, and for material “Type 2” you have .3 kg. In the first experiment, you measure 7.83 x 10⁴ joules lost (take joules lost to be a negative quantity) when the combined materials drop 90 degrees. In the second experiment, you have .2 kg of material 1 and .3 kg of material 2 and measure 2.55 x 10⁴ joules lost when the combined materials drop 50 degrees. What are the specific heat capacities (in SI units please) of the two materials? Assume that no phase change has taken place.

2) You have measured the total heat lost during cooling of a lava lake and it is 4.8 x 10¹² joules. The volume of the lava lake is 1000 cubic meters, and the density (assumed constant for this problem) is 3200 kg/m³. The temperature drop from liquidus to complete cooling was 1200 degrees. Assume that the value of the specific heat capacity for lava is 1000 (J/kg*K). What percentage of the total heat is due to the latent heat of crystallization? What is the value of the specific latent heat (J/kg)?

3) You have a cup of coffee with volume .0003 m³ that is initially 80⁰ and you bring it into a room that is that we will assume is held at 20⁰. The density of the coffee is 1000 (kg/m³) and the specific heat is 4184 (J/kg*K). What is the total amount of thermal energy (relative to the room temperature) in the coffee? Now if the cup of coffee loses heat at a constant rate of -20 (J/s), plot how the temperature of the coffee changes with time (assume that the coffee is well stirred and that once it hits room temp, the cooling stops). How long will it take to reach room temperature? How good was our assumption that the room was held at constant temperature during this process- assume that the room has a well mixed volume of 3 m x 3 m x 3 m, and that the density of air is 1.2 (kg/m³) and that the specific heat capacity of air is 1000 (J/kg*K).

4) Now instead of a coffee cup, assume that we have a popsicle at -10⁰. It has the same mass as the coffee. Given the same heat transfer rate (except this time it is heating up) how long will it take before it starts to melt? How long before it is all melted? How long before it comes to room temperature? Plot the temperature of the popsicle vs. time on the same plot as you made for the coffee. The specific heat for the popsicle while it is solid is 2108 (J/kg*K), and while liquid use the same value as the coffee. The latent heat is 3.34x105 (J/kg).

5) How many 75 Watt light bulbs could you light if you could gather all the geothermal energy coming out of 5 square kilometers of continental crust?

6) If radioactive decay is an important source of energy to power plate tectonics, are rates of plate motion speeding up, slowing down, staying constant? Why?

7) If the crust is 30 km thick, and the thermal conductivity is 2.5 (W/m*K) and the temperature at the Moho is 950 degrees C, what is the heat flow at the surface?
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.

Ans 3
Total mass of the coffee = 0.0003 × 1000 = 3 kg
Temp of the coffee = 80 degree
Room temp = 20 degree
Specific heat = 4184 j/kg.k
So total amount of heat in the coffee = 3 × 4184 × 60 = 753120 joules
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.docx
Purchase Solution
$60.00
Google Pay
Amazon
Paypal
Mastercard
Visacard
Discover
Amex
View Available Earth Science 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 Version460msRequest Duration45MBMemory UsageGET college-homework-library/{category}/{subject}/{id}Route
    • Booting (294ms)time
    • Application (166ms)time
    • 1 x Booting (63.98%)
      294ms
      1 x Application (36.01%)
      166ms
      • Illuminate\Routing\Events\Routing (1.41ms)
      • Illuminate\Routing\Events\RouteMatched (527μs)
      • Illuminate\Foundation\Events\LocaleUpdated (4.28ms)
      • eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (208μs)
      • eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (182μs)
      • Illuminate\Database\Events\ConnectionEstablished (917μs)
      • Illuminate\Database\Events\StatementPrepared (10.17ms)
      • Illuminate\Database\Events\QueryExecuted (1.19ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (86μs)
      • eloquent.booting: App\Models\Subject (56μs)
      • eloquent.booted: App\Models\Subject (47μs)
      • Illuminate\Database\Events\StatementPrepared (1.69ms)
      • Illuminate\Database\Events\QueryExecuted (934μs)
      • eloquent.retrieved: App\Models\Subject (113μs)
      • eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (130μs)
      • eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (71μs)
      • Illuminate\Database\Events\StatementPrepared (767μs)
      • Illuminate\Database\Events\QueryExecuted (817μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (60μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (14μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (13μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (11μs)
      • eloquent.booting: App\Models\SubjectCat (597μs)
      • eloquent.booted: App\Models\SubjectCat (87μs)
      • Illuminate\Database\Events\StatementPrepared (792μs)
      • Illuminate\Database\Events\QueryExecuted (883μs)
      • eloquent.retrieved: App\Models\SubjectCat (73μs)
      • Illuminate\Cache\Events\CacheHit (14.23ms)
      • Illuminate\Cache\Events\CacheMissed (796μs)
      • Illuminate\Database\Events\StatementPrepared (989μs)
      • Illuminate\Database\Events\QueryExecuted (2.91ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (77μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (14μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (8μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (7μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (6μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (6μs)
      • Illuminate\Database\Events\StatementPrepared (637μs)
      • Illuminate\Database\Events\QueryExecuted (958μs)
      • eloquent.retrieved: App\Models\Subject (101μs)
      • Illuminate\Cache\Events\KeyWritten (913μs)
      • Illuminate\Database\Events\StatementPrepared (1.92ms)
      • Illuminate\Database\Events\QueryExecuted (2.41ms)
      • Illuminate\Database\Events\StatementPrepared (784μs)
      • Illuminate\Database\Events\QueryExecuted (942μs)
      • Illuminate\Database\Events\StatementPrepared (612μs)
      • Illuminate\Database\Events\QueryExecuted (693μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (37μs)
      • Illuminate\Cache\Events\CacheHit (682μs)
      • creating: homework.show (388μs)
      • composing: homework.show (179μs)
      • creating: components.breadcrumbs (313μs)
      • composing: components.breadcrumbs (186μs)
      • Illuminate\Database\Events\StatementPrepared (1.31ms)
      • Illuminate\Database\Events\QueryExecuted (825μs)
      • eloquent.retrieved: App\Models\SubjectCat (66μs)
      • Illuminate\Cache\Events\CacheMissed (3.99ms)
      • Illuminate\Database\Events\StatementPrepared (2.32ms)
      • Illuminate\Database\Events\QueryExecuted (883μs)
      • eloquent.retrieved: App\Models\SubjectCat (73μs)
      • Illuminate\Cache\Events\KeyWritten (363μs)
      • Illuminate\Cache\Events\CacheHit (928μs)
      • Illuminate\Cache\Events\CacheHit (232μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (202μs)
      • Illuminate\Cache\Events\CacheHit (216μs)
      • Illuminate\Cache\Events\CacheHit (229μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (228μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (196μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheMissed (2.58ms)
      • Illuminate\Database\Events\StatementPrepared (742μs)
      • Illuminate\Database\Events\QueryExecuted (1.09ms)
      • eloquent.retrieved: App\Models\SubjectCat (74μs)
      • Illuminate\Cache\Events\KeyWritten (306μs)
      • Illuminate\Cache\Events\CacheHit (255μs)
      • Illuminate\Cache\Events\CacheHit (199μs)
      • Illuminate\Cache\Events\CacheHit (128μs)
      • Illuminate\Cache\Events\CacheHit (137μs)
      • Illuminate\Cache\Events\CacheHit (113μs)
      • Illuminate\Cache\Events\CacheHit (131μs)
      • Illuminate\Cache\Events\CacheHit (138μs)
      • Illuminate\Cache\Events\CacheMissed (156μs)
      • Illuminate\Database\Events\StatementPrepared (567μs)
      • Illuminate\Database\Events\QueryExecuted (882μs)
      • eloquent.retrieved: App\Models\SubjectCat (65μs)
      • Illuminate\Cache\Events\KeyWritten (699μs)
      • Illuminate\Cache\Events\CacheHit (204μs)
      • Illuminate\Cache\Events\CacheHit (223μs)
      • Illuminate\Cache\Events\CacheHit (182μs)
      • Illuminate\Cache\Events\CacheHit (198μs)
      • Illuminate\Cache\Events\CacheHit (170μs)
      • Illuminate\Cache\Events\CacheHit (242μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (210μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
      • Illuminate\Cache\Events\CacheHit (253μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheHit (198μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (203μs)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheHit (210μs)
      • Illuminate\Cache\Events\CacheHit (186μs)
      • Illuminate\Cache\Events\CacheHit (204μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (221μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (293μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (212μs)
      • Illuminate\Cache\Events\CacheHit (221μs)
      • Illuminate\Cache\Events\CacheMissed (245μs)
      • Illuminate\Database\Events\StatementPrepared (627μs)
      • Illuminate\Database\Events\QueryExecuted (839μs)
      • eloquent.retrieved: App\Models\SubjectCat (70μs)
      • Illuminate\Cache\Events\KeyWritten (327μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheHit (214μs)
      • Illuminate\Cache\Events\CacheHit (195μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (170μs)
      • Illuminate\Cache\Events\CacheHit (229μs)
      • Illuminate\Cache\Events\CacheHit (159μs)
      • Illuminate\Cache\Events\CacheHit (210μs)
      • Illuminate\Cache\Events\CacheHit (226μs)
      • Illuminate\Cache\Events\CacheHit (217μs)
      • Illuminate\Cache\Events\CacheHit (205μs)
      • Illuminate\Cache\Events\CacheHit (235μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheHit (216μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (204μs)
      • Illuminate\Cache\Events\CacheHit (210μs)
      • Illuminate\Cache\Events\CacheHit (217μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (211μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (209μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (206μs)
      • Illuminate\Cache\Events\CacheHit (199μs)
      • Illuminate\Cache\Events\CacheHit (209μs)
      • Illuminate\Cache\Events\CacheHit (220μs)
      • Illuminate\Cache\Events\CacheHit (204μs)
      • Illuminate\Cache\Events\CacheHit (228μs)
      • Illuminate\Cache\Events\CacheHit (214μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (207μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (206μs)
      • Illuminate\Cache\Events\CacheHit (165μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (126μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheMissed (156μs)
      • Illuminate\Database\Events\StatementPrepared (545μs)
      • Illuminate\Database\Events\QueryExecuted (846μs)
      • eloquent.retrieved: App\Models\SubjectCat (87μs)
      • Illuminate\Cache\Events\KeyWritten (598μs)
      • Illuminate\Cache\Events\CacheHit (202μs)
      • Illuminate\Cache\Events\CacheHit (193μs)
      • Illuminate\Cache\Events\CacheHit (161μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (163μs)
      • Illuminate\Cache\Events\CacheHit (199μs)
      • Illuminate\Cache\Events\CacheHit (116μs)
      • Illuminate\Cache\Events\CacheMissed (121μs)
      • Illuminate\Database\Events\StatementPrepared (563μs)
      • Illuminate\Database\Events\QueryExecuted (745μs)
      • eloquent.retrieved: App\Models\SubjectCat (55μs)
      • Illuminate\Cache\Events\KeyWritten (1.33ms)
      • Illuminate\Cache\Events\CacheHit (220μs)
      • Illuminate\Cache\Events\CacheHit (204μs)
      • Illuminate\Cache\Events\CacheHit (173μs)
      • Illuminate\Cache\Events\CacheHit (242μs)
      • Illuminate\Cache\Events\CacheHit (212μs)
      • Illuminate\Cache\Events\CacheHit (204μs)
      • Illuminate\Cache\Events\CacheHit (207μs)
      • Illuminate\Cache\Events\CacheHit (193μs)
      • Illuminate\Cache\Events\CacheHit (160μs)
      • Illuminate\Cache\Events\CacheHit (207μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (840μs)
      • Illuminate\Cache\Events\CacheHit (170μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheHit (242μs)
      • Illuminate\Cache\Events\CacheHit (163μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheHit (163μs)
      • Illuminate\Cache\Events\CacheHit (173μs)
      • Illuminate\Cache\Events\CacheHit (156μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (164μs)
      • Illuminate\Cache\Events\CacheHit (173μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (165μs)
      • Illuminate\Cache\Events\CacheHit (216μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheMissed (177μs)
      • Illuminate\Database\Events\StatementPrepared (695μs)
      • Illuminate\Database\Events\QueryExecuted (783μs)
      • eloquent.retrieved: App\Models\SubjectCat (75μs)
      • Illuminate\Cache\Events\KeyWritten (295μs)
      • Illuminate\Cache\Events\CacheHit (1.1ms)
      • Illuminate\Cache\Events\CacheHit (226μs)
      • Illuminate\Cache\Events\CacheHit (165μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheHit (156μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (173μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (163μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (161μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (157μs)
      • Illuminate\Cache\Events\CacheHit (173μs)
      • Illuminate\Cache\Events\CacheHit (153μs)
      • Illuminate\Cache\Events\CacheHit (240μs)
      • Illuminate\Cache\Events\CacheHit (158μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheHit (155μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheHit (153μs)
      • Illuminate\Cache\Events\CacheHit (173μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (170μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (158μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (157μs)
      • Illuminate\Cache\Events\CacheHit (205μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (205μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (164μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (272μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (161μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (159μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (156μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (158μs)
      • Illuminate\Cache\Events\CacheHit (203μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (193μs)
      • Illuminate\Cache\Events\CacheHit (182μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (165μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (160μs)
      • Illuminate\Cache\Events\CacheHit (200μs)
      • Illuminate\Cache\Events\CacheHit (168μs)
      • Illuminate\Cache\Events\CacheHit (225μs)
      • Illuminate\Cache\Events\CacheHit (149μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (159μs)
      • Illuminate\Cache\Events\CacheMissed (262μs)
      • Illuminate\Database\Events\StatementPrepared (896μs)
      • Illuminate\Database\Events\QueryExecuted (1.13ms)
      • eloquent.retrieved: App\Models\SubjectCat (71μs)
      • Illuminate\Cache\Events\KeyWritten (1.46ms)
      • Illuminate\Cache\Events\CacheHit (207μs)
      • Illuminate\Cache\Events\CacheHit (218μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (241μs)
      • Illuminate\Cache\Events\CacheHit (209μs)
      • Illuminate\Cache\Events\CacheHit (224μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (161μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (158μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (159μs)
      • Illuminate\Cache\Events\CacheHit (196μs)
      • Illuminate\Cache\Events\CacheHit (155μs)
      • Illuminate\Cache\Events\CacheHit (182μs)
      • Illuminate\Cache\Events\CacheHit (162μs)
      • Illuminate\Cache\Events\CacheHit (893μs)
      • Illuminate\Cache\Events\CacheHit (164μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (196μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (196μs)
      • Illuminate\Cache\Events\CacheHit (195μs)
      • Illuminate\Cache\Events\CacheHit (182μs)
      • Illuminate\Cache\Events\CacheHit (265μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (161μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (157μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (161μs)
      • Illuminate\Cache\Events\CacheHit (199μs)
      • Illuminate\Cache\Events\CacheHit (156μs)
      • Illuminate\Cache\Events\CacheHit (213μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheHit (227μs)
      • Illuminate\Cache\Events\CacheHit (159μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (155μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (158μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (158μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (170μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (156μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (159μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (159μs)
      • Illuminate\Cache\Events\CacheHit (186μs)
      • Illuminate\Cache\Events\CacheHit (154μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (156μs)
      • Illuminate\Cache\Events\CacheHit (168μs)
      • Illuminate\Cache\Events\CacheHit (196μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheHit (155μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (155μs)
      • Illuminate\Cache\Events\CacheHit (173μs)
      • Illuminate\Cache\Events\CacheHit (153μs)
      • Illuminate\Cache\Events\CacheHit (173μs)
      • Illuminate\Cache\Events\CacheHit (156μs)
      • Illuminate\Cache\Events\CacheHit (207μs)
      • Illuminate\Cache\Events\CacheHit (215μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (161μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (159μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (160μs)
      • Illuminate\Cache\Events\CacheHit (225μs)
      • Illuminate\Cache\Events\CacheHit (153μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheHit (149μs)
      • Illuminate\Cache\Events\CacheHit (165μs)
      • Illuminate\Cache\Events\CacheHit (151μs)
      • Illuminate\Cache\Events\CacheHit (236μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (163μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (152μs)
      • Illuminate\Cache\Events\CacheMissed (173μs)
      • Illuminate\Database\Events\StatementPrepared (785μs)
      • Illuminate\Database\Events\QueryExecuted (735μs)
      • eloquent.retrieved: App\Models\SubjectCat (82μs)
      • Illuminate\Cache\Events\KeyWritten (347μs)
      • Illuminate\Cache\Events\CacheHit (1.07ms)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (163μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (159μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (193μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (205μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (163μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (158μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • creating: site.layouts.app (465μs)
      • composing: site.layouts.app (28μs)
      • creating: components.canonical (488μs)
      • composing: components.canonical (156μs)
      • creating: components.open-graph (229μs)
      • composing: components.open-graph (78μs)
      • creating: site.headers.header (311μs)
      • composing: site.headers.header (76μs)
      • Illuminate\Cache\Events\CacheHit (2.56ms)
      • creating: components.footer (78μs)
      • composing: components.footer (112μs)
      • Illuminate\Cache\Events\CacheHit (952μs)
      • Illuminate\Cache\Events\CacheMissed (332μs)
      • Illuminate\Database\Events\StatementPrepared (849μs)
      • Illuminate\Database\Events\QueryExecuted (868μs)
      • eloquent.retrieved: App\Models\SubjectCat (83μs)
      • Illuminate\Cache\Events\KeyWritten (1.58ms)
      • Illuminate\Cache\Events\CacheHit (251μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheHit (208μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (353μs)
      • Illuminate\Cache\Events\CacheHit (363μs)
      • Illuminate\Cache\Events\CacheHit (217μs)
      • Illuminate\Cache\Events\CacheHit (213μs)
      • Illuminate\Cache\Events\CacheHit (206μs)
      • Illuminate\Cache\Events\CacheHit (219μs)
      • Illuminate\Cache\Events\CacheHit (216μs)
      • creating: components.forms.contact-us (206μs)
      • composing: components.forms.contact-us (165μs)
      • creating: components.forms.get-started (120μs)
      • composing: components.forms.get-started (81μs)
      • creating: components.forms.free-tool-download (98μs)
      • composing: components.forms.free-tool-download (65μs)
      • creating: components.forms.claim-free-worksheet (99μs)
      • composing: components.forms.claim-free-worksheet (63μs)
      • creating: components.forms.tutor-subscription-waitlist (134μs)
      • composing: components.forms.tutor-subscription-waitlist (65μs)
      • creating: components.forms.tutor-subscription-join (99μs)
      • composing: components.forms.tutor-subscription-join (64μs)
      • creating: components.forms.tutor-support (96μs)
      • composing: components.forms.tutor-support (62μs)
      • 311 x Illuminate\Cache\Events\CacheHit (17.27%)
        79.50ms
        20 x Illuminate\Database\Events\StatementPrepared (6.14%)
        28.26ms
        20 x Illuminate\Database\Events\QueryExecuted (4.64%)
        21.37ms
        11 x Illuminate\Cache\Events\CacheMissed (1.95%)
        8.99ms
        11 x Illuminate\Cache\Events\KeyWritten (1.79%)
        8.23ms
        1 x Illuminate\Foundation\Events\LocaleUpdated (0.93%)
        4.28ms
        1 x Illuminate\Routing\Events\Routing (0.31%)
        1.41ms
        1 x Illuminate\Database\Events\ConnectionEstablished (0.2%)
        917μs
        12 x eloquent.retrieved: App\Models\SubjectCat (0.19%)
        874μs
        1 x eloquent.booting: App\Models\SubjectCat (0.13%)
        597μs
        1 x Illuminate\Routing\Events\RouteMatched (0.11%)
        527μs
        1 x creating: components.canonical (0.11%)
        488μs
        1 x creating: site.layouts.app (0.1%)
        465μs
        1 x creating: homework.show (0.08%)
        388μs
        1 x creating: components.breadcrumbs (0.07%)
        313μs
        1 x creating: site.headers.header (0.07%)
        311μs
        1 x creating: components.open-graph (0.05%)
        229μs
        2 x eloquent.retrieved: App\Models\Subject (0.05%)
        214μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.05%)
        208μs
        1 x creating: components.forms.contact-us (0.04%)
        206μs
        7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.04%)
        204μs
        1 x composing: components.breadcrumbs (0.04%)
        186μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.04%)
        182μs
        1 x composing: homework.show (0.04%)
        179μs
        1 x composing: components.forms.contact-us (0.04%)
        165μs
        1 x composing: components.canonical (0.03%)
        156μs
        5 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.03%)
        135μs
        1 x creating: components.forms.tutor-subscription-waitlist (0.03%)
        134μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.03%)
        130μs
        1 x creating: components.forms.get-started (0.03%)
        120μs
        1 x composing: components.footer (0.02%)
        112μs
        1 x creating: components.forms.claim-free-worksheet (0.02%)
        99μs
        1 x creating: components.forms.tutor-subscription-join (0.02%)
        99μs
        1 x creating: components.forms.free-tool-download (0.02%)
        98μs
        1 x creating: components.forms.tutor-support (0.02%)
        96μs
        1 x eloquent.booted: App\Models\SubjectCat (0.02%)
        87μs
        1 x composing: components.forms.get-started (0.02%)
        81μs
        1 x composing: components.open-graph (0.02%)
        78μs
        1 x creating: components.footer (0.02%)
        78μs
        1 x composing: site.headers.header (0.02%)
        76μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.02%)
        71μs
        1 x composing: components.forms.free-tool-download (0.01%)
        65μs
        1 x composing: components.forms.tutor-subscription-waitlist (0.01%)
        65μs
        1 x composing: components.forms.tutor-subscription-join (0.01%)
        64μs
        1 x composing: components.forms.claim-free-worksheet (0.01%)
        63μs
        1 x composing: components.forms.tutor-support (0.01%)
        62μs
        1 x eloquent.booting: App\Models\Subject (0.01%)
        56μs
        1 x eloquent.booted: App\Models\Subject (0.01%)
        47μs
        1 x composing: site.layouts.app (0.01%)
        28μs
      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, 4 of which were duplicates, 16 unique. Show only duplicated35.53ms
      • 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` = '22471' limit 1
        10.55mstwenty4_siteHomeworkLibraryController.php#97
        Bindings
        • 0: published
        • 1: 0
        • 2: 22471
        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 (243)
        990μstwenty4_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 (22471)
        1.02mstwenty4_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` = 2 limit 1
        1.09mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 2
        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` <> 22471 and `subject` = 243 and `status` = 'published' and `price` > 0 order by RAND() limit 6
        3.19mstwenty4_siteHomeworkLibraryRepository.php#30
        Bindings
        • 0: 22471
        • 1: 243
        • 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 (243)
        960μstwenty4_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` = 22471 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        2.4mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 22471
        • 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` = 22471 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'teaser' order by `order` asc, `id` asc
        1.11mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 22471
        • 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` = 22471 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'solution' order by `order` asc, `id` asc
        800μstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 22471
        • 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` = 2 limit 1
        1.03mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 2
        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
        2.74mstwenty4_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
        1.15mstwenty4_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
        1.03mstwenty4_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
        980μstwenty4_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
        940μstwenty4_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
        890μstwenty4_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
        1.01mstwenty4_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
        1.43mstwenty4_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
        1.1mstwenty4_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
        1.12mstwenty4_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
      5HomeworkLibraryFile.php
      App\Models\Subject
      2Subject.php
          _token
          GlohqVviupo1JJS8HFWTBGHo4lYzKKcLheKBzz0K
          utm_source
          direct
          redirectUrl
          /college-homework-library/Earth-Science/Geology/22471
          _previous
          array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/Earth-Science/G...
          _flash
          array:2 [ "old" => [] "new" => [] ]
          PHPDEBUGBAR_STACK_DATA
          []
          path_info
          /college-homework-library/Earth-Science/Geology/22471
          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=1-67f71ae9-6ec41bc8341529ab1ae02e39" ] "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 => "18.218.183.7" ] "content-length" => array:1 [ 0 => "" ] "content-type" => array:1 [ 0 => "" ] ]
          request_cookies
          []
          
          response_headers
          0 of 0
          array:5 [ "content-type" => array:1 [ 0 => "text/html; charset=UTF-8" ] "cache-control" => array:1 [ 0 => "no-cache, private" ] "date" => array:1 [ 0 => "Thu, 10 Apr 2025 01:12:10 GMT" ] "set-cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6ImIxK3gwd1BLK0h5TzE1QWhpRUc5ZFE9PSIsInZhbHVlIjoiTW1TR2xQUituVkxzQ2RQVU50c2dDaThId3UrN2trOTc1U1lPVXF0aGs4WGdPMklRZ3dRVnJVQlFCQ0Y3Y2l2Q0FpNXQrMU9tK0FrUWJoMkxXWk94MHNiQWVmOGlWdEVCbGZVbHN5RmtLMHRFb0RCTjN1ak5IS2hpSTlpZVFXOGsiLCJtYWMiOiIyNjNlY2ZlYWFjN2VmZmM3YTQ3MjJiOTdkZTY0NTlmYmEyZDIxYjA3ZDgxMzhhYTFlZjg4NmIyNjhhMGY1ZTVmIiwidGFnIjoiIn0%3D; expires=Thu, 10 Apr 2025 03:12:10 GMT; Max-Age=7200; path=/; domain=.24houranswers.com; samesite=laxXSRF-TOKEN=eyJpdiI6ImIxK3gwd1BLK0h5TzE1QWhpRUc5ZFE9PSIsInZhbHVlIjoiTW1TR2xQUituVkxzQ2RQVU50c2dDaThId3UrN2trOTc1U1lPVXF0aGs4WGdPMklRZ3dRVnJVQlFCQ0Y3Y2l2Q0FpNXQrM" 1 => "24houranswers_session=eyJpdiI6ImtpYnBDbDRNVUNqdnlTakxjcDgvMmc9PSIsInZhbHVlIjoiVDdhWStYN2dxc3dLZW5OdlB2QWpzNjVPZ2VaSHJEZ1AvUExiRVRrTVlkY2twanUwanhBNnJlYTNQaE5JL0VJeW9DekFrMzQ5M25KNmdBVi9BaUtwVnBHbncybkRPV0pyME1Nekc0cXJLMVY0WjhYN2t1d3QxbUNEazRob2NUOVgiLCJtYWMiOiI2MWUzZDU2NDhiMmM5MTQwNGQwMzFkMGViMDczY2M4MjVlNmQzMzYyZTAzNmQ3YzllOTQwNTZmZDUwNTExM2JkIiwidGFnIjoiIn0%3D; expires=Thu, 10 Apr 2025 03:12:10 GMT; Max-Age=7200; path=/; domain=.24houranswers.com; httponly; samesite=lax24houranswers_session=eyJpdiI6ImtpYnBDbDRNVUNqdnlTakxjcDgvMmc9PSIsInZhbHVlIjoiVDdhWStYN2dxc3dLZW5OdlB2QWpzNjVPZ2VaSHJEZ1AvUExiRVRrTVlkY2twanUwanhBNnJlYTNQaE5JL0" ] "Set-Cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6ImIxK3gwd1BLK0h5TzE1QWhpRUc5ZFE9PSIsInZhbHVlIjoiTW1TR2xQUituVkxzQ2RQVU50c2dDaThId3UrN2trOTc1U1lPVXF0aGs4WGdPMklRZ3dRVnJVQlFCQ0Y3Y2l2Q0FpNXQrMU9tK0FrUWJoMkxXWk94MHNiQWVmOGlWdEVCbGZVbHN5RmtLMHRFb0RCTjN1ak5IS2hpSTlpZVFXOGsiLCJtYWMiOiIyNjNlY2ZlYWFjN2VmZmM3YTQ3MjJiOTdkZTY0NTlmYmEyZDIxYjA3ZDgxMzhhYTFlZjg4NmIyNjhhMGY1ZTVmIiwidGFnIjoiIn0%3D; expires=Thu, 10-Apr-2025 03:12:10 GMT; domain=.24houranswers.com; path=/XSRF-TOKEN=eyJpdiI6ImIxK3gwd1BLK0h5TzE1QWhpRUc5ZFE9PSIsInZhbHVlIjoiTW1TR2xQUituVkxzQ2RQVU50c2dDaThId3UrN2trOTc1U1lPVXF0aGs4WGdPMklRZ3dRVnJVQlFCQ0Y3Y2l2Q0FpNXQrM" 1 => "24houranswers_session=eyJpdiI6ImtpYnBDbDRNVUNqdnlTakxjcDgvMmc9PSIsInZhbHVlIjoiVDdhWStYN2dxc3dLZW5OdlB2QWpzNjVPZ2VaSHJEZ1AvUExiRVRrTVlkY2twanUwanhBNnJlYTNQaE5JL0VJeW9DekFrMzQ5M25KNmdBVi9BaUtwVnBHbncybkRPV0pyME1Nekc0cXJLMVY0WjhYN2t1d3QxbUNEazRob2NUOVgiLCJtYWMiOiI2MWUzZDU2NDhiMmM5MTQwNGQwMzFkMGViMDczY2M4MjVlNmQzMzYyZTAzNmQ3YzllOTQwNTZmZDUwNTExM2JkIiwidGFnIjoiIn0%3D; expires=Thu, 10-Apr-2025 03:12:10 GMT; domain=.24houranswers.com; path=/; httponly24houranswers_session=eyJpdiI6ImtpYnBDbDRNVUNqdnlTakxjcDgvMmc9PSIsInZhbHVlIjoiVDdhWStYN2dxc3dLZW5OdlB2QWpzNjVPZ2VaSHJEZ1AvUExiRVRrTVlkY2twanUwanhBNnJlYTNQaE5JL0" ] ]
          session_attributes
          0 of 0
          array:6 [ "_token" => "GlohqVviupo1JJS8HFWTBGHo4lYzKKcLheKBzz0K" "utm_source" => "direct" "redirectUrl" => "/college-homework-library/Earth-Science/Geology/22471" "_previous" => array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/Earth-Science/Geology/22471" ] "_flash" => array:2 [ "old" => [] "new" => [] ] "PHPDEBUGBAR_STACK_DATA" => [] ]