Application Example Homework Assignment – Part B 1. It is desired...

Question
Solution Preview

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

clc;
clear all;
Kc = [0.1 0.25 0.5 1];
T = 1;
D = 1;
d = D/T;
for i = 1:length(Kc)
G1(i) = tf([1 -1 0],[1 -1 Kc(i)*T],T,'TimeUnit','days');
G2(i) = tf(Kc(i)*[1 -1 0],[1 -1 Kc(i)*T 0],T,'TimeUnit','days');
end
figure;
subplot(2,2,1);step(G1(1));title('WIP for K_{c}=0.1');ylabel('Hours');
subplot(2,2,2);step(G1(2));title('WIP for K_{c}=0.25');ylabel('Hours');
subplot(2,2,3);step(G1(3));title('WIP for K_{c}=0.5');ylabel('Hours');
subplot(2,2,4);step(G1(4));title('WIP for K_{c}=0.5');ylabel('Hours');
figure;
subplot(2,2,1);step(G2(1));title('Capacity for K_{c}=0.1');ylabel('Hours/day');
subplot(2,2,2);step(G2(2));title('Capacity for K_{c}=0.25');ylabel('Hours/day');
subplot(2,2,3);step(G2(3));title('Capacity for K_{c}=0.5');ylabel('Hours/day');
subplot(2,2,4);step(G2(4));title('Capacity for K_{c}=0.5');;ylabel('Hours/day');
%%%%%%%
for i = 1:4
[w,zeta] = damp(G1(i));
fprintf('The Damping Ratio in the case of WIP with K_{c} = %f is %f\n',Kc(i),max([w,zeta] = damp(G2(i));
fprintf('The Damping Ratio in the case of Capacity with K_{c} = %f is %f\n',Kc(end
%%%%%%%
Kc = 0.25;
G1 = tf([1 -1
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
Solution.pdf
Purchase Solution
$25.00
Google Pay
Amazon
Paypal
Mastercard
Visacard
Discover
Amex
View Available Mathematics 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 Version794msRequest Duration45MBMemory UsageGET college-homework-library/{category}/{subject}/{id}Route
    • Booting (507ms)time
    • Application (286ms)time
    • 1 x Booting (63.92%)
      507ms
      1 x Application (36.08%)
      286ms
      • Illuminate\Routing\Events\Routing (866μs)
      • Illuminate\Routing\Events\RouteMatched (380μs)
      • Illuminate\Foundation\Events\LocaleUpdated (4.5ms)
      • eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (181μs)
      • eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (142μs)
      • Illuminate\Database\Events\ConnectionEstablished (927μs)
      • Illuminate\Database\Events\StatementPrepared (11.34ms)
      • Illuminate\Database\Events\QueryExecuted (1.33ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (311μs)
      • eloquent.booting: App\Models\Subject (92μs)
      • eloquent.booted: App\Models\Subject (61μs)
      • Illuminate\Database\Events\StatementPrepared (1.55ms)
      • Illuminate\Database\Events\QueryExecuted (1.25ms)
      • eloquent.retrieved: App\Models\Subject (116μs)
      • eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (114μs)
      • eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (58μs)
      • Illuminate\Database\Events\StatementPrepared (809μs)
      • Illuminate\Database\Events\QueryExecuted (933μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (85μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (20μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (12μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (11μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (10μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (9μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (8μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (11μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (8μs)
      • eloquent.booting: App\Models\SubjectCat (649μs)
      • eloquent.booted: App\Models\SubjectCat (61μs)
      • Illuminate\Database\Events\StatementPrepared (1.05ms)
      • Illuminate\Database\Events\QueryExecuted (965μs)
      • eloquent.retrieved: App\Models\SubjectCat (96μs)
      • Illuminate\Cache\Events\CacheHit (21.39ms)
      • Illuminate\Cache\Events\CacheMissed (205μs)
      • Illuminate\Database\Events\StatementPrepared (871μs)
      • Illuminate\Database\Events\QueryExecuted (3.06ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (97μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (22μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (14μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (13μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (12μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (12μs)
      • Illuminate\Database\Events\StatementPrepared (1.15ms)
      • Illuminate\Database\Events\QueryExecuted (2.16ms)
      • eloquent.retrieved: App\Models\Subject (95μs)
      • Illuminate\Cache\Events\KeyWritten (1.91ms)
      • Illuminate\Database\Events\StatementPrepared (9.65ms)
      • Illuminate\Database\Events\QueryExecuted (1.95ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (95μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (22μs)
      • Illuminate\Database\Events\StatementPrepared (1.92ms)
      • Illuminate\Database\Events\QueryExecuted (1.5ms)
      • Illuminate\Database\Events\StatementPrepared (4.85ms)
      • Illuminate\Database\Events\QueryExecuted (2.17ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (76μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (22μs)
      • Illuminate\Cache\Events\CacheHit (663μs)
      • creating: homework.show (740μs)
      • composing: homework.show (325μs)
      • creating: components.breadcrumbs (1.02ms)
      • composing: components.breadcrumbs (264μs)
      • Illuminate\Database\Events\StatementPrepared (2.63ms)
      • Illuminate\Database\Events\QueryExecuted (1.22ms)
      • eloquent.retrieved: App\Models\SubjectCat (102μs)
      • Illuminate\Cache\Events\CacheHit (6.61ms)
      • Illuminate\Cache\Events\CacheHit (247μs)
      • Illuminate\Cache\Events\CacheHit (341μs)
      • Illuminate\Cache\Events\CacheHit (365μs)
      • Illuminate\Cache\Events\CacheHit (216μs)
      • Illuminate\Cache\Events\CacheHit (168μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (340μs)
      • Illuminate\Cache\Events\CacheHit (498μs)
      • Illuminate\Cache\Events\CacheHit (890μs)
      • Illuminate\Cache\Events\CacheHit (335μs)
      • Illuminate\Cache\Events\CacheHit (259μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (832μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (206μs)
      • Illuminate\Cache\Events\CacheHit (401μs)
      • Illuminate\Cache\Events\CacheHit (222μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (260μs)
      • Illuminate\Cache\Events\CacheHit (310μs)
      • Illuminate\Cache\Events\CacheHit (237μs)
      • Illuminate\Cache\Events\CacheHit (165μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (212μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (164μs)
      • Illuminate\Cache\Events\CacheHit (202μs)
      • Illuminate\Cache\Events\CacheHit (173μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (328μs)
      • Illuminate\Cache\Events\CacheHit (201μs)
      • Illuminate\Cache\Events\CacheHit (163μs)
      • Illuminate\Cache\Events\CacheHit (195μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (296μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (232μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (402μs)
      • Illuminate\Cache\Events\CacheHit (209μs)
      • Illuminate\Cache\Events\CacheHit (229μs)
      • Illuminate\Cache\Events\CacheHit (216μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (158μs)
      • Illuminate\Cache\Events\CacheHit (2.32ms)
      • Illuminate\Cache\Events\CacheHit (223μs)
      • Illuminate\Cache\Events\CacheHit (645μs)
      • Illuminate\Cache\Events\CacheHit (253μs)
      • Illuminate\Cache\Events\CacheHit (215μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (231μs)
      • Illuminate\Cache\Events\CacheHit (300μs)
      • Illuminate\Cache\Events\CacheHit (945μs)
      • Illuminate\Cache\Events\CacheHit (220μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (297μs)
      • Illuminate\Cache\Events\CacheHit (1.44ms)
      • Illuminate\Cache\Events\CacheHit (252μs)
      • Illuminate\Cache\Events\CacheHit (356μs)
      • Illuminate\Cache\Events\CacheHit (663μs)
      • Illuminate\Cache\Events\CacheHit (566μs)
      • Illuminate\Cache\Events\CacheHit (257μs)
      • Illuminate\Cache\Events\CacheHit (222μs)
      • Illuminate\Cache\Events\CacheHit (186μs)
      • Illuminate\Cache\Events\CacheHit (204μs)
      • Illuminate\Cache\Events\CacheHit (317μs)
      • Illuminate\Cache\Events\CacheHit (228μs)
      • Illuminate\Cache\Events\CacheHit (319μs)
      • Illuminate\Cache\Events\CacheHit (210μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheHit (213μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (201μs)
      • Illuminate\Cache\Events\CacheHit (480μs)
      • Illuminate\Cache\Events\CacheHit (571μs)
      • Illuminate\Cache\Events\CacheHit (1.26ms)
      • Illuminate\Cache\Events\CacheHit (636μs)
      • Illuminate\Cache\Events\CacheHit (210μs)
      • Illuminate\Cache\Events\CacheHit (213μs)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (206μs)
      • Illuminate\Cache\Events\CacheHit (164μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (215μs)
      • Illuminate\Cache\Events\CacheHit (304μs)
      • Illuminate\Cache\Events\CacheHit (202μs)
      • Illuminate\Cache\Events\CacheHit (231μs)
      • Illuminate\Cache\Events\CacheHit (257μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (206μs)
      • Illuminate\Cache\Events\CacheHit (226μs)
      • Illuminate\Cache\Events\CacheHit (199μs)
      • Illuminate\Cache\Events\CacheHit (164μs)
      • Illuminate\Cache\Events\CacheHit (186μs)
      • Illuminate\Cache\Events\CacheHit (161μs)
      • Illuminate\Cache\Events\CacheHit (289μs)
      • Illuminate\Cache\Events\CacheHit (818μs)
      • Illuminate\Cache\Events\CacheHit (226μs)
      • Illuminate\Cache\Events\CacheHit (335μs)
      • Illuminate\Cache\Events\CacheHit (296μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (276μs)
      • Illuminate\Cache\Events\CacheHit (641μs)
      • Illuminate\Cache\Events\CacheHit (327μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (258μs)
      • Illuminate\Cache\Events\CacheHit (163μs)
      • Illuminate\Cache\Events\CacheHit (205μs)
      • Illuminate\Cache\Events\CacheHit (247μs)
      • Illuminate\Cache\Events\CacheHit (1.02ms)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheHit (205μs)
      • Illuminate\Cache\Events\CacheHit (598μs)
      • Illuminate\Cache\Events\CacheHit (257μs)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (202μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (537μs)
      • Illuminate\Cache\Events\CacheHit (247μs)
      • Illuminate\Cache\Events\CacheHit (206μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (203μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (263μs)
      • Illuminate\Cache\Events\CacheHit (225μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (232μs)
      • Illuminate\Cache\Events\CacheHit (163μs)
      • Illuminate\Cache\Events\CacheHit (315μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • Illuminate\Cache\Events\CacheHit (236μs)
      • Illuminate\Cache\Events\CacheHit (162μs)
      • Illuminate\Cache\Events\CacheHit (297μs)
      • Illuminate\Cache\Events\CacheHit (295μs)
      • Illuminate\Cache\Events\CacheHit (257μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (278μs)
      • Illuminate\Cache\Events\CacheHit (200μs)
      • Illuminate\Cache\Events\CacheHit (398μs)
      • Illuminate\Cache\Events\CacheHit (210μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (255μs)
      • Illuminate\Cache\Events\CacheHit (403μs)
      • Illuminate\Cache\Events\CacheHit (280μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (346μs)
      • Illuminate\Cache\Events\CacheHit (363μs)
      • Illuminate\Cache\Events\CacheHit (265μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (319μs)
      • Illuminate\Cache\Events\CacheHit (260μs)
      • Illuminate\Cache\Events\CacheHit (321μs)
      • Illuminate\Cache\Events\CacheHit (182μs)
      • Illuminate\Cache\Events\CacheHit (294μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (9.62ms)
      • Illuminate\Cache\Events\CacheHit (245μs)
      • Illuminate\Cache\Events\CacheHit (402μs)
      • Illuminate\Cache\Events\CacheHit (219μs)
      • Illuminate\Cache\Events\CacheHit (267μs)
      • Illuminate\Cache\Events\CacheHit (288μs)
      • Illuminate\Cache\Events\CacheHit (365μs)
      • Illuminate\Cache\Events\CacheHit (186μs)
      • Illuminate\Cache\Events\CacheHit (345μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (196μs)
      • Illuminate\Cache\Events\CacheHit (336μs)
      • Illuminate\Cache\Events\CacheHit (429μs)
      • Illuminate\Cache\Events\CacheHit (278μs)
      • Illuminate\Cache\Events\CacheHit (412μs)
      • Illuminate\Cache\Events\CacheHit (233μs)
      • Illuminate\Cache\Events\CacheHit (207μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (163μs)
      • Illuminate\Cache\Events\CacheHit (206μs)
      • Illuminate\Cache\Events\CacheHit (334μs)
      • Illuminate\Cache\Events\CacheHit (209μs)
      • Illuminate\Cache\Events\CacheHit (186μs)
      • Illuminate\Cache\Events\CacheHit (200μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (295μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (201μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (173μs)
      • Illuminate\Cache\Events\CacheHit (848μs)
      • Illuminate\Cache\Events\CacheHit (7.44ms)
      • Illuminate\Cache\Events\CacheHit (264μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (204μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
      • Illuminate\Cache\Events\CacheHit (217μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (208μs)
      • Illuminate\Cache\Events\CacheHit (227μs)
      • Illuminate\Cache\Events\CacheHit (216μs)
      • Illuminate\Cache\Events\CacheHit (168μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (291μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (173μs)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (165μs)
      • Illuminate\Cache\Events\CacheHit (200μs)
      • Illuminate\Cache\Events\CacheHit (173μs)
      • Illuminate\Cache\Events\CacheHit (1.23ms)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheHit (182μs)
      • Illuminate\Cache\Events\CacheHit (156μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (255μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (164μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (154μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (240μs)
      • Illuminate\Cache\Events\CacheHit (204μs)
      • Illuminate\Cache\Events\CacheHit (8.3ms)
      • Illuminate\Cache\Events\CacheHit (310μs)
      • Illuminate\Cache\Events\CacheHit (266μs)
      • Illuminate\Cache\Events\CacheHit (362μs)
      • Illuminate\Cache\Events\CacheHit (295μs)
      • Illuminate\Cache\Events\CacheHit (380μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (274μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (267μs)
      • Illuminate\Cache\Events\CacheHit (346μs)
      • Illuminate\Cache\Events\CacheHit (205μs)
      • Illuminate\Cache\Events\CacheHit (168μs)
      • Illuminate\Cache\Events\CacheHit (486μs)
      • Illuminate\Cache\Events\CacheHit (249μs)
      • Illuminate\Cache\Events\CacheHit (340μs)
      • Illuminate\Cache\Events\CacheHit (263μs)
      • Illuminate\Cache\Events\CacheHit (712μs)
      • Illuminate\Cache\Events\CacheHit (483μs)
      • Illuminate\Cache\Events\CacheHit (493μs)
      • Illuminate\Cache\Events\CacheHit (360μs)
      • Illuminate\Cache\Events\CacheHit (486μs)
      • Illuminate\Cache\Events\CacheHit (319μs)
      • Illuminate\Cache\Events\CacheHit (8.6ms)
      • Illuminate\Cache\Events\CacheHit (639μs)
      • Illuminate\Cache\Events\CacheHit (304μs)
      • Illuminate\Cache\Events\CacheHit (269μs)
      • Illuminate\Cache\Events\CacheHit (203μs)
      • Illuminate\Cache\Events\CacheHit (228μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (522μs)
      • Illuminate\Cache\Events\CacheHit (250μs)
      • Illuminate\Cache\Events\CacheHit (577μs)
      • Illuminate\Cache\Events\CacheHit (442μs)
      • Illuminate\Cache\Events\CacheHit (325μs)
      • Illuminate\Cache\Events\CacheHit (228μs)
      • Illuminate\Cache\Events\CacheHit (615μs)
      • Illuminate\Cache\Events\CacheHit (478μs)
      • Illuminate\Cache\Events\CacheHit (345μs)
      • Illuminate\Cache\Events\CacheHit (222μs)
      • Illuminate\Cache\Events\CacheHit (585μs)
      • Illuminate\Cache\Events\CacheHit (324μs)
      • Illuminate\Cache\Events\CacheHit (665μs)
      • Illuminate\Cache\Events\CacheHit (8.4ms)
      • Illuminate\Cache\Events\CacheHit (218μs)
      • Illuminate\Cache\Events\CacheHit (483μs)
      • Illuminate\Cache\Events\CacheHit (211μs)
      • Illuminate\Cache\Events\CacheHit (462μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (279μs)
      • Illuminate\Cache\Events\CacheHit (261μs)
      • Illuminate\Cache\Events\CacheHit (208μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (337μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheMissed (3.24ms)
      • Illuminate\Database\Events\StatementPrepared (2.52ms)
      • Illuminate\Database\Events\QueryExecuted (12.63ms)
      • eloquent.retrieved: App\Models\SubjectCat (116μs)
      • Illuminate\Cache\Events\KeyWritten (352μs)
      • Illuminate\Cache\Events\CacheHit (239μs)
      • Illuminate\Cache\Events\CacheHit (521μs)
      • Illuminate\Cache\Events\CacheHit (255μs)
      • Illuminate\Cache\Events\CacheHit (280μs)
      • Illuminate\Cache\Events\CacheHit (565μs)
      • Illuminate\Cache\Events\CacheHit (488μs)
      • Illuminate\Cache\Events\CacheHit (373μs)
      • Illuminate\Cache\Events\CacheHit (363μs)
      • Illuminate\Cache\Events\CacheHit (716μs)
      • Illuminate\Cache\Events\CacheHit (264μs)
      • Illuminate\Cache\Events\CacheHit (1.1ms)
      • Illuminate\Cache\Events\CacheHit (692μs)
      • Illuminate\Cache\Events\CacheHit (298μs)
      • Illuminate\Cache\Events\CacheHit (532μs)
      • Illuminate\Cache\Events\CacheHit (317μs)
      • Illuminate\Cache\Events\CacheHit (236μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • creating: site.layouts.app (1.68ms)
      • composing: site.layouts.app (77μs)
      • creating: components.canonical (4.42ms)
      • composing: components.canonical (107μs)
      • creating: components.open-graph (1.29ms)
      • composing: components.open-graph (1.75ms)
      • creating: site.headers.header (362μs)
      • composing: site.headers.header (92μs)
      • Illuminate\Cache\Events\CacheHit (9.28ms)
      • creating: components.footer (106μs)
      • composing: components.footer (92μs)
      • Illuminate\Cache\Events\CacheHit (1.31ms)
      • Illuminate\Cache\Events\CacheHit (351μs)
      • Illuminate\Cache\Events\CacheHit (281μs)
      • Illuminate\Cache\Events\CacheHit (204μs)
      • Illuminate\Cache\Events\CacheHit (198μs)
      • Illuminate\Cache\Events\CacheHit (517μs)
      • Illuminate\Cache\Events\CacheHit (211μs)
      • Illuminate\Cache\Events\CacheHit (359μs)
      • Illuminate\Cache\Events\CacheHit (552μs)
      • Illuminate\Cache\Events\CacheHit (198μs)
      • Illuminate\Cache\Events\CacheHit (201μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • creating: components.forms.contact-us (234μs)
      • composing: components.forms.contact-us (156μs)
      • creating: components.forms.get-started (137μs)
      • composing: components.forms.get-started (66μs)
      • creating: components.forms.free-tool-download (872μs)
      • composing: components.forms.free-tool-download (86μs)
      • creating: components.forms.claim-free-worksheet (169μs)
      • composing: components.forms.claim-free-worksheet (71μs)
      • creating: components.forms.tutor-subscription-waitlist (97μs)
      • composing: components.forms.tutor-subscription-waitlist (61μs)
      • creating: components.forms.tutor-subscription-join (92μs)
      • composing: components.forms.tutor-subscription-join (62μs)
      • creating: components.forms.tutor-support (92μs)
      • composing: components.forms.tutor-support (143μs)
      • 320 x Illuminate\Cache\Events\CacheHit (22.07%)
        175ms
        11 x Illuminate\Database\Events\StatementPrepared (4.83%)
        38.35ms
        11 x Illuminate\Database\Events\QueryExecuted (3.67%)
        29.16ms
        1 x Illuminate\Foundation\Events\LocaleUpdated (0.57%)
        4.50ms
        1 x creating: components.canonical (0.56%)
        4.42ms
        2 x Illuminate\Cache\Events\CacheMissed (0.43%)
        3.44ms
        2 x Illuminate\Cache\Events\KeyWritten (0.29%)
        2.27ms
        1 x composing: components.open-graph (0.22%)
        1.75ms
        1 x creating: site.layouts.app (0.21%)
        1.68ms
        1 x creating: components.open-graph (0.16%)
        1.29ms
        1 x creating: components.breadcrumbs (0.13%)
        1.02ms
        1 x Illuminate\Database\Events\ConnectionEstablished (0.12%)
        927μs
        1 x creating: components.forms.free-tool-download (0.11%)
        872μs
        1 x Illuminate\Routing\Events\Routing (0.11%)
        866μs
        1 x creating: homework.show (0.09%)
        740μs
        1 x eloquent.booting: App\Models\SubjectCat (0.08%)
        649μs
        7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.06%)
        481μs
        13 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.05%)
        389μs
        1 x Illuminate\Routing\Events\RouteMatched (0.05%)
        380μs
        1 x creating: site.headers.header (0.05%)
        362μs
        1 x composing: homework.show (0.04%)
        325μs
        3 x eloquent.retrieved: App\Models\SubjectCat (0.04%)
        314μs
        1 x composing: components.breadcrumbs (0.03%)
        264μs
        1 x creating: components.forms.contact-us (0.03%)
        234μs
        2 x eloquent.retrieved: App\Models\Subject (0.03%)
        211μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.02%)
        181μs
        1 x creating: components.forms.claim-free-worksheet (0.02%)
        169μs
        1 x composing: components.forms.contact-us (0.02%)
        156μs
        1 x composing: components.forms.tutor-support (0.02%)
        143μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.02%)
        142μs
        1 x creating: components.forms.get-started (0.02%)
        137μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.01%)
        114μs
        1 x composing: components.canonical (0.01%)
        107μs
        1 x creating: components.footer (0.01%)
        106μs
        1 x creating: components.forms.tutor-subscription-waitlist (0.01%)
        97μs
        1 x eloquent.booting: App\Models\Subject (0.01%)
        92μs
        1 x composing: site.headers.header (0.01%)
        92μs
        1 x composing: components.footer (0.01%)
        92μs
        1 x creating: components.forms.tutor-subscription-join (0.01%)
        92μs
        1 x creating: components.forms.tutor-support (0.01%)
        92μs
        1 x composing: components.forms.free-tool-download (0.01%)
        86μs
        1 x composing: site.layouts.app (0.01%)
        77μs
        1 x composing: components.forms.claim-free-worksheet (0.01%)
        71μs
        1 x composing: components.forms.get-started (0.01%)
        66μs
        1 x composing: components.forms.tutor-subscription-join (0.01%)
        62μs
        1 x eloquent.booted: App\Models\Subject (0.01%)
        61μs
        1 x eloquent.booted: App\Models\SubjectCat (0.01%)
        61μs
        1 x composing: components.forms.tutor-subscription-waitlist (0.01%)
        61μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.01%)
        58μs
      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
      11 statements were executed, 4 of which were duplicates, 7 unique. Show only duplicated50.8ms
      • 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` = '50462' limit 1
        11.71mstwenty4_siteHomeworkLibraryController.php#97
        Bindings
        • 0: published
        • 1: 0
        • 2: 50462
        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 (229)
        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 (50462)
        900μstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1
        1.33mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 1
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 26. app/Http/Controllers/HomeworkLibraryController.php:105
        • 27. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 28. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 29. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
      • select * from `solutionslibrary` where `id` <> 50462 and `subject` = 229 and `status` = 'published' and `price` > 0 order by RAND() limit 6
        2.94mstwenty4_siteHomeworkLibraryRepository.php#30
        Bindings
        • 0: 50462
        • 1: 229
        • 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 (229)
        2.14mstwenty4_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` = 50462 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        8.37mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 50462
        • 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` = 50462 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'teaser' order by `order` asc, `id` asc
        1.91mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 50462
        • 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` = 50462 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'solution' order by `order` asc, `id` asc
        4.97mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 50462
        • 1: solution
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:80
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1
        1.35mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 1
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 32. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 33. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 34. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
        • 35. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • select * from `subject_cats` where `subject_cats`.`id` = 31 limit 1
        14.05mstwenty4_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
      App\Models\HomeworkLibrary\HomeworkLibraryFile
      13HomeworkLibraryFile.php
      App\Models\HomeworkLibrary\HomeworkLibrary
      7HomeworkLibrary.php
      App\Models\SubjectCat
      3SubjectCat.php
      App\Models\Subject
      2Subject.php
          _token
          pmSFTvXlZ2nspHNg2TxVfqjBCUBKli74gkbvkemR
          utm_source
          direct
          redirectUrl
          /college-homework-library/Mathematics/Control-Theory/50462
          _previous
          array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/Mathematics/Con...
          _flash
          array:2 [ "old" => [] "new" => [] ]
          PHPDEBUGBAR_STACK_DATA
          []
          path_info
          /college-homework-library/Mathematics/Control-Theory/50462
          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=1-67ff6520-5653c1cc32b4586175735346" ] "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 => "52.14.35.155" ] "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 08:06:56 GMT" ] "set-cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6IjYwSXU5ejVoODVvOEthS3FYVDU0VkE9PSIsInZhbHVlIjoiQy85V296SVBXVnpzb1J3ZElxR3R0VTAvQloxUFpCZjd5c1hObElxem9jY1AwbUJQcFBPQTVkQSt3cHgvY3ZtS3NaTGxUaHI5S3NyUGwyTEZMVzhUbkt2Tm1wdU1yK2tnNEpNQnlhTW1RRER1eXFBaFFoclVCb0dOOW0ybHhiQysiLCJtYWMiOiJlNzA4ZjFiODEwNzMxNTY5YjNhNmVkODRmODM1NGY4YWIxODFmN2U5MDg3NjJjZWZlNTVhYjE2Njk2ZDVlY2Q0IiwidGFnIjoiIn0%3D; expires=Wed, 16 Apr 2025 10:06:56 GMT; Max-Age=7200; path=/; domain=.24houranswers.com; samesite=laxXSRF-TOKEN=eyJpdiI6IjYwSXU5ejVoODVvOEthS3FYVDU0VkE9PSIsInZhbHVlIjoiQy85V296SVBXVnpzb1J3ZElxR3R0VTAvQloxUFpCZjd5c1hObElxem9jY1AwbUJQcFBPQTVkQSt3cHgvY3ZtS3NaTGxUa" 1 => "24houranswers_session=eyJpdiI6Ik15akVIY2NMck5CZ3Y2Qlo0ZU51TEE9PSIsInZhbHVlIjoiUTN2M1g2MDJPbWVLbXdTVEZwYWJHeWdYeEVRN21XNmRKek11am5PL2pVa29raXpIWHhXMktYbG1JVkRibEtrVE95ak82S24rTFFlMmVOWFl5RDJDVnV2VFVOUEJ6YVlrVnNWMnFzaXREOWZxNnhSVEpJYWNtTFZpc0YwZ3RaV2YiLCJtYWMiOiIzMzkxZmQ5MmVjMjkyNTc5ZGU2MGVkOGViMzRjNDc0YzEwZjNmNDkzM2FhYjhhYmU0MDBjYWMwNDhiMjE5YzU1IiwidGFnIjoiIn0%3D; expires=Wed, 16 Apr 2025 10:06:56 GMT; Max-Age=7200; path=/; domain=.24houranswers.com; httponly; samesite=lax24houranswers_session=eyJpdiI6Ik15akVIY2NMck5CZ3Y2Qlo0ZU51TEE9PSIsInZhbHVlIjoiUTN2M1g2MDJPbWVLbXdTVEZwYWJHeWdYeEVRN21XNmRKek11am5PL2pVa29raXpIWHhXMktYbG1JVkRibE" ] "Set-Cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6IjYwSXU5ejVoODVvOEthS3FYVDU0VkE9PSIsInZhbHVlIjoiQy85V296SVBXVnpzb1J3ZElxR3R0VTAvQloxUFpCZjd5c1hObElxem9jY1AwbUJQcFBPQTVkQSt3cHgvY3ZtS3NaTGxUaHI5S3NyUGwyTEZMVzhUbkt2Tm1wdU1yK2tnNEpNQnlhTW1RRER1eXFBaFFoclVCb0dOOW0ybHhiQysiLCJtYWMiOiJlNzA4ZjFiODEwNzMxNTY5YjNhNmVkODRmODM1NGY4YWIxODFmN2U5MDg3NjJjZWZlNTVhYjE2Njk2ZDVlY2Q0IiwidGFnIjoiIn0%3D; expires=Wed, 16-Apr-2025 10:06:56 GMT; domain=.24houranswers.com; path=/XSRF-TOKEN=eyJpdiI6IjYwSXU5ejVoODVvOEthS3FYVDU0VkE9PSIsInZhbHVlIjoiQy85V296SVBXVnpzb1J3ZElxR3R0VTAvQloxUFpCZjd5c1hObElxem9jY1AwbUJQcFBPQTVkQSt3cHgvY3ZtS3NaTGxUa" 1 => "24houranswers_session=eyJpdiI6Ik15akVIY2NMck5CZ3Y2Qlo0ZU51TEE9PSIsInZhbHVlIjoiUTN2M1g2MDJPbWVLbXdTVEZwYWJHeWdYeEVRN21XNmRKek11am5PL2pVa29raXpIWHhXMktYbG1JVkRibEtrVE95ak82S24rTFFlMmVOWFl5RDJDVnV2VFVOUEJ6YVlrVnNWMnFzaXREOWZxNnhSVEpJYWNtTFZpc0YwZ3RaV2YiLCJtYWMiOiIzMzkxZmQ5MmVjMjkyNTc5ZGU2MGVkOGViMzRjNDc0YzEwZjNmNDkzM2FhYjhhYmU0MDBjYWMwNDhiMjE5YzU1IiwidGFnIjoiIn0%3D; expires=Wed, 16-Apr-2025 10:06:56 GMT; domain=.24houranswers.com; path=/; httponly24houranswers_session=eyJpdiI6Ik15akVIY2NMck5CZ3Y2Qlo0ZU51TEE9PSIsInZhbHVlIjoiUTN2M1g2MDJPbWVLbXdTVEZwYWJHeWdYeEVRN21XNmRKek11am5PL2pVa29raXpIWHhXMktYbG1JVkRibE" ] ]
          session_attributes
          0 of 0
          array:6 [ "_token" => "pmSFTvXlZ2nspHNg2TxVfqjBCUBKli74gkbvkemR" "utm_source" => "direct" "redirectUrl" => "/college-homework-library/Mathematics/Control-Theory/50462" "_previous" => array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/Mathematics/Control-Theory/50462" ] "_flash" => array:2 [ "old" => [] "new" => [] ] "PHPDEBUGBAR_STACK_DATA" => [] ]