Real mathematics is about modeling situations that occur naturally,...

Question
Real mathematics is about modeling situations that occur naturally, and using the model to understand what is happening, or maybe to predict what will happen in the future.
The quadratic equation is often used in modeling. Quadratic functions and applications are a large part of the mathematics of the world around us. any general problem involving areas is a quadratic problem. The force of gravity, which basically holds the universe as we know it together, can be modeled with a quadratic function. The standard form of a quadratic function is y= ax² + bx+c.
In this project we are going to model the Ball Toss with a quadratic function. So at 30 number intervals, we draw 4 vertical lines extending from the eraser tray to the top of the marker board. cm We our the lines with their distances from the left most vertical line (which serves as the y-axis).Each the volunteers selects a line and stand facing it at close proximity to the board. Between the board and of volunteers, I toss the ball to the catcher. Each of the volunteers will mark the height above the eraser tray at which the ball crosses his/her line. We will measure and label the height from the eraser tray to the marks.
We have the following data: M(0,23.5); N(30,37.2); P(60,35.8); Q(90,19.3)
These ordered data represent a set of ordered pairs or a function. Since this function has an infinite number in x and y where x represents the first coordinate and y represents the second coordinate. We should pairs, we are going to find an equation that defines this function. So we should use an equation of the y-axis. create a coordinate plane by drawing a horizontal number line called the x-axis, and a vertical line called
1. In this specific model of ball toss
a) What does the x-axis represent?
b) What do the x-coordinates represent?
C) What do the y-coordinates represent?
2. Display your data in the coordinate plane or plot the points using a graph paper (Consider each square 10cm). Make sure you label the axis and the points.
3. Draw a smooth curve containing these points.
4. What shape does the graph have?
5. How does this shape open?
6. What kind of function this graph represents?
7. Write the standard form of the equation that represents this function.
8. Use the 3 points M (0, 23.5); N (30, 37.2) and P (60, 35.8) that verify the equation you wrote in question #7

a) (Remember equation Find to the find to quadratic show the coefficients all polynomial your work) of that the equation). predicts y (Round from X. your (Hint: answers you should to the resolve nearest a system ten of linear thousandths).
b) Is the leading coefficient positive or negative? work over before you continue).
c) Does your answer for question (8b) contradict with your answer for question (5)? (If yes, check your your answer to the nearest tenth). 9. a) What does the function say the height of the ball was when it was 120cm from the y-axis? (Round
b) What is the sign of this height?
c) What is the position of the ball to the eraser tray?
d) Write this ordered pairs and plot its point T on the graph.
10. a) At what values of X does the function say the ball should have hit the eraser tray? (Round the values of x to the nearest cm)
b) Display these points I and J on the graph and write their coordinates.
c) What are these points called?
11. a) At what distances from the y-axis was the ball 28 cm above the eraser tray?(Round your answers to the nearest cm)
b) Write these ordered pairs and plot their points R and S on the graph.
12. a) At what distance from the y-axis was the ball at its highest point?(Round your answer to the nearest cm).
b) What was the maximum height of the ball measured, of course, from the eraser tray? (Round your answer to the nearest cm).
c) What is the name of this highest point of the graph?
d) Write the coordinate of the highest point V and plot it on the graph.
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.docx
Solution.pdf
Purchase Solution
$23.00
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 Version504msRequest Duration45MBMemory UsageGET college-homework-library/{category}/{subject}/{id}Route
    • Booting (304ms)time
    • Application (200ms)time
    • 1 x Booting (60.35%)
      304ms
      1 x Application (39.65%)
      200ms
      • Illuminate\Routing\Events\Routing (5.05ms)
      • Illuminate\Routing\Events\RouteMatched (682μs)
      • Illuminate\Foundation\Events\LocaleUpdated (7.05ms)
      • eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (258μs)
      • eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (236μs)
      • Illuminate\Database\Events\ConnectionEstablished (1.49ms)
      • Illuminate\Database\Events\StatementPrepared (14.53ms)
      • Illuminate\Database\Events\QueryExecuted (1.18ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (131μs)
      • eloquent.booting: App\Models\Subject (122μs)
      • eloquent.booted: App\Models\Subject (61μs)
      • Illuminate\Database\Events\StatementPrepared (2.02ms)
      • Illuminate\Database\Events\QueryExecuted (900μs)
      • eloquent.retrieved: App\Models\Subject (116μs)
      • eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (156μs)
      • eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (86μs)
      • Illuminate\Database\Events\StatementPrepared (676μs)
      • Illuminate\Database\Events\QueryExecuted (864μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (82μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (18μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (11μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (9μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (9μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (8μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (8μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (9μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (7μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (8μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (7μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (8μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (8μs)
      • eloquent.booting: App\Models\SubjectCat (540μs)
      • eloquent.booted: App\Models\SubjectCat (54μs)
      • Illuminate\Database\Events\StatementPrepared (731μs)
      • Illuminate\Database\Events\QueryExecuted (870μs)
      • eloquent.retrieved: App\Models\SubjectCat (130μs)
      • Illuminate\Cache\Events\CacheHit (14.13ms)
      • Illuminate\Cache\Events\CacheHit (1.91ms)
      • Illuminate\Database\Events\StatementPrepared (2.21ms)
      • Illuminate\Database\Events\QueryExecuted (946μs)
      • Illuminate\Database\Events\StatementPrepared (854μs)
      • Illuminate\Database\Events\QueryExecuted (860μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (137μs)
      • Illuminate\Database\Events\StatementPrepared (843μs)
      • Illuminate\Database\Events\QueryExecuted (1.04ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (50μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (17μs)
      • Illuminate\Cache\Events\CacheHit (744μs)
      • creating: homework.show (421μs)
      • composing: homework.show (179μs)
      • creating: components.breadcrumbs (347μs)
      • composing: components.breadcrumbs (225μs)
      • Illuminate\Database\Events\StatementPrepared (1.38ms)
      • Illuminate\Database\Events\QueryExecuted (843μs)
      • eloquent.retrieved: App\Models\SubjectCat (78μs)
      • Illuminate\Cache\Events\CacheMissed (7.86ms)
      • Illuminate\Database\Events\StatementPrepared (751μs)
      • Illuminate\Database\Events\QueryExecuted (1ms)
      • eloquent.retrieved: App\Models\SubjectCat (80μs)
      • Illuminate\Cache\Events\KeyWritten (550μs)
      • Illuminate\Cache\Events\CacheHit (351μs)
      • Illuminate\Cache\Events\CacheHit (269μs)
      • Illuminate\Cache\Events\CacheHit (209μs)
      • Illuminate\Cache\Events\CacheHit (275μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheHit (202μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (173μs)
      • Illuminate\Cache\Events\CacheHit (204μs)
      • Illuminate\Cache\Events\CacheHit (212μs)
      • Illuminate\Cache\Events\CacheHit (216μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheMissed (315μs)
      • Illuminate\Database\Events\StatementPrepared (1.6ms)
      • Illuminate\Database\Events\QueryExecuted (1.44ms)
      • eloquent.retrieved: App\Models\SubjectCat (90μs)
      • Illuminate\Cache\Events\KeyWritten (2.4ms)
      • Illuminate\Cache\Events\CacheHit (524μs)
      • Illuminate\Cache\Events\CacheHit (673μs)
      • Illuminate\Cache\Events\CacheHit (444μs)
      • Illuminate\Cache\Events\CacheHit (533μs)
      • Illuminate\Cache\Events\CacheHit (354μs)
      • Illuminate\Cache\Events\CacheHit (408μs)
      • Illuminate\Cache\Events\CacheHit (305μs)
      • Illuminate\Cache\Events\CacheMissed (534μs)
      • Illuminate\Database\Events\StatementPrepared (814μs)
      • Illuminate\Database\Events\QueryExecuted (1ms)
      • eloquent.retrieved: App\Models\SubjectCat (77μs)
      • Illuminate\Cache\Events\KeyWritten (362μs)
      • Illuminate\Cache\Events\CacheHit (246μs)
      • Illuminate\Cache\Events\CacheHit (202μs)
      • Illuminate\Cache\Events\CacheHit (214μs)
      • Illuminate\Cache\Events\CacheHit (287μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (210μs)
      • Illuminate\Cache\Events\CacheHit (411μs)
      • Illuminate\Cache\Events\CacheHit (286μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (211μs)
      • Illuminate\Cache\Events\CacheHit (310μs)
      • Illuminate\Cache\Events\CacheHit (208μs)
      • Illuminate\Cache\Events\CacheHit (269μs)
      • Illuminate\Cache\Events\CacheHit (259μs)
      • Illuminate\Cache\Events\CacheHit (159μs)
      • Illuminate\Cache\Events\CacheHit (290μs)
      • Illuminate\Cache\Events\CacheHit (198μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (148μs)
      • Illuminate\Cache\Events\CacheHit (244μs)
      • Illuminate\Cache\Events\CacheHit (251μs)
      • Illuminate\Cache\Events\CacheHit (285μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (220μs)
      • Illuminate\Cache\Events\CacheHit (214μs)
      • Illuminate\Cache\Events\CacheHit (193μs)
      • Illuminate\Cache\Events\CacheHit (160μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (155μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (153μs)
      • Illuminate\Cache\Events\CacheMissed (268μs)
      • Illuminate\Database\Events\StatementPrepared (731μs)
      • Illuminate\Database\Events\QueryExecuted (1.03ms)
      • eloquent.retrieved: App\Models\SubjectCat (82μs)
      • Illuminate\Cache\Events\KeyWritten (352μs)
      • Illuminate\Cache\Events\CacheHit (350μs)
      • Illuminate\Cache\Events\CacheHit (257μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (206μs)
      • Illuminate\Cache\Events\CacheHit (312μs)
      • Illuminate\Cache\Events\CacheHit (353μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
      • Illuminate\Cache\Events\CacheHit (223μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (312μs)
      • Illuminate\Cache\Events\CacheHit (307μs)
      • Illuminate\Cache\Events\CacheHit (226μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (283μs)
      • Illuminate\Cache\Events\CacheHit (203μs)
      • Illuminate\Cache\Events\CacheHit (303μs)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (210μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (229μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (237μs)
      • Illuminate\Cache\Events\CacheHit (239μs)
      • Illuminate\Cache\Events\CacheHit (281μs)
      • Illuminate\Cache\Events\CacheHit (221μs)
      • Illuminate\Cache\Events\CacheHit (227μs)
      • Illuminate\Cache\Events\CacheHit (325μs)
      • Illuminate\Cache\Events\CacheHit (344μs)
      • Illuminate\Cache\Events\CacheHit (207μs)
      • Illuminate\Cache\Events\CacheHit (288μs)
      • Illuminate\Cache\Events\CacheHit (327μs)
      • Illuminate\Cache\Events\CacheHit (219μs)
      • Illuminate\Cache\Events\CacheHit (182μs)
      • Illuminate\Cache\Events\CacheHit (207μs)
      • Illuminate\Cache\Events\CacheHit (173μs)
      • Illuminate\Cache\Events\CacheHit (217μs)
      • Illuminate\Cache\Events\CacheHit (144μs)
      • Illuminate\Cache\Events\CacheHit (144μs)
      • Illuminate\Cache\Events\CacheHit (148μs)
      • Illuminate\Cache\Events\CacheMissed (289μs)
      • Illuminate\Database\Events\StatementPrepared (634μs)
      • Illuminate\Database\Events\QueryExecuted (1.62ms)
      • eloquent.retrieved: App\Models\SubjectCat (66μs)
      • Illuminate\Cache\Events\KeyWritten (377μs)
      • Illuminate\Cache\Events\CacheHit (164μs)
      • Illuminate\Cache\Events\CacheHit (156μs)
      • Illuminate\Cache\Events\CacheHit (106μs)
      • Illuminate\Cache\Events\CacheHit (119μs)
      • Illuminate\Cache\Events\CacheHit (99μs)
      • Illuminate\Cache\Events\CacheHit (114μs)
      • Illuminate\Cache\Events\CacheHit (96μs)
      • Illuminate\Cache\Events\CacheMissed (220μs)
      • Illuminate\Database\Events\StatementPrepared (605μs)
      • Illuminate\Database\Events\QueryExecuted (1.05ms)
      • eloquent.retrieved: App\Models\SubjectCat (70μs)
      • Illuminate\Cache\Events\KeyWritten (357μs)
      • Illuminate\Cache\Events\CacheHit (281μs)
      • Illuminate\Cache\Events\CacheHit (234μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (232μs)
      • Illuminate\Cache\Events\CacheHit (218μs)
      • Illuminate\Cache\Events\CacheHit (201μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (307μs)
      • Illuminate\Cache\Events\CacheHit (217μs)
      • Illuminate\Cache\Events\CacheHit (207μs)
      • Illuminate\Cache\Events\CacheHit (132μs)
      • Illuminate\Cache\Events\CacheHit (910μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (203μs)
      • Illuminate\Cache\Events\CacheHit (127μs)
      • Illuminate\Cache\Events\CacheHit (140μs)
      • Illuminate\Cache\Events\CacheHit (158μs)
      • Illuminate\Cache\Events\CacheHit (141μs)
      • Illuminate\Cache\Events\CacheHit (103μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (148μs)
      • Illuminate\Cache\Events\CacheHit (149μs)
      • Illuminate\Cache\Events\CacheHit (137μs)
      • Illuminate\Cache\Events\CacheMissed (241μs)
      • Illuminate\Database\Events\StatementPrepared (536μs)
      • Illuminate\Database\Events\QueryExecuted (964μs)
      • eloquent.retrieved: App\Models\SubjectCat (69μs)
      • Illuminate\Cache\Events\KeyWritten (347μs)
      • Illuminate\Cache\Events\CacheHit (237μs)
      • Illuminate\Cache\Events\CacheHit (235μs)
      • Illuminate\Cache\Events\CacheHit (379μs)
      • Illuminate\Cache\Events\CacheHit (283μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (216μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (217μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (302μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (201μs)
      • Illuminate\Cache\Events\CacheHit (212μs)
      • Illuminate\Cache\Events\CacheHit (214μs)
      • Illuminate\Cache\Events\CacheHit (202μs)
      • Illuminate\Cache\Events\CacheHit (202μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
      • Illuminate\Cache\Events\CacheHit (196μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheHit (203μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheHit (200μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (250μs)
      • Illuminate\Cache\Events\CacheHit (227μs)
      • Illuminate\Cache\Events\CacheHit (220μs)
      • Illuminate\Cache\Events\CacheHit (230μs)
      • Illuminate\Cache\Events\CacheHit (219μs)
      • Illuminate\Cache\Events\CacheHit (193μs)
      • Illuminate\Cache\Events\CacheHit (199μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (160μs)
      • Illuminate\Cache\Events\CacheHit (207μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (208μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (199μs)
      • Illuminate\Cache\Events\CacheHit (243μs)
      • Illuminate\Cache\Events\CacheHit (335μs)
      • Illuminate\Cache\Events\CacheHit (209μs)
      • Illuminate\Cache\Events\CacheHit (221μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (263μs)
      • Illuminate\Cache\Events\CacheHit (341μs)
      • Illuminate\Cache\Events\CacheHit (238μs)
      • Illuminate\Cache\Events\CacheHit (230μs)
      • Illuminate\Cache\Events\CacheHit (210μs)
      • Illuminate\Cache\Events\CacheHit (151μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (229μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (145μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (116μs)
      • Illuminate\Cache\Events\CacheHit (123μs)
      • Illuminate\Cache\Events\CacheHit (225μs)
      • Illuminate\Cache\Events\CacheMissed (252μs)
      • Illuminate\Database\Events\StatementPrepared (709μs)
      • Illuminate\Database\Events\QueryExecuted (1.12ms)
      • eloquent.retrieved: App\Models\SubjectCat (111μs)
      • Illuminate\Cache\Events\KeyWritten (352μs)
      • Illuminate\Cache\Events\CacheHit (202μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (120μs)
      • Illuminate\Cache\Events\CacheHit (210μs)
      • Illuminate\Cache\Events\CacheHit (143μs)
      • Illuminate\Cache\Events\CacheHit (5.37ms)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (216μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (170μs)
      • Illuminate\Cache\Events\CacheHit (2.21ms)
      • Illuminate\Cache\Events\CacheHit (150μs)
      • Illuminate\Cache\Events\CacheHit (530μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (217μs)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (4.05ms)
      • Illuminate\Cache\Events\CacheHit (214μs)
      • Illuminate\Cache\Events\CacheHit (204μs)
      • Illuminate\Cache\Events\CacheHit (290μs)
      • Illuminate\Cache\Events\CacheHit (222μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (199μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (310μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheHit (205μs)
      • Illuminate\Cache\Events\CacheHit (153μs)
      • Illuminate\Cache\Events\CacheHit (203μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (316μs)
      • Illuminate\Cache\Events\CacheHit (199μs)
      • Illuminate\Cache\Events\CacheHit (118μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (306μs)
      • Illuminate\Cache\Events\CacheHit (293μs)
      • Illuminate\Cache\Events\CacheHit (222μs)
      • Illuminate\Cache\Events\CacheHit (212μs)
      • Illuminate\Cache\Events\CacheHit (248μs)
      • Illuminate\Cache\Events\CacheHit (211μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (201μs)
      • Illuminate\Cache\Events\CacheHit (173μs)
      • Illuminate\Cache\Events\CacheHit (293μs)
      • Illuminate\Cache\Events\CacheHit (196μs)
      • Illuminate\Cache\Events\CacheHit (220μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
      • Illuminate\Cache\Events\CacheHit (200μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (291μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
      • Illuminate\Cache\Events\CacheHit (205μs)
      • Illuminate\Cache\Events\CacheHit (159μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (279μs)
      • Illuminate\Cache\Events\CacheHit (208μs)
      • Illuminate\Cache\Events\CacheHit (158μs)
      • Illuminate\Cache\Events\CacheHit (195μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (164μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (160μs)
      • Illuminate\Cache\Events\CacheHit (202μs)
      • Illuminate\Cache\Events\CacheHit (186μs)
      • Illuminate\Cache\Events\CacheHit (199μs)
      • Illuminate\Cache\Events\CacheHit (221μs)
      • Illuminate\Cache\Events\CacheHit (205μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (198μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (213μs)
      • Illuminate\Cache\Events\CacheHit (173μs)
      • Illuminate\Cache\Events\CacheHit (238μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • Illuminate\Cache\Events\CacheHit (215μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (168μs)
      • Illuminate\Cache\Events\CacheHit (193μs)
      • Illuminate\Cache\Events\CacheHit (164μs)
      • Illuminate\Cache\Events\CacheHit (198μs)
      • Illuminate\Cache\Events\CacheHit (173μs)
      • Illuminate\Cache\Events\CacheMissed (350μs)
      • Illuminate\Database\Events\StatementPrepared (720μs)
      • Illuminate\Database\Events\QueryExecuted (980μs)
      • eloquent.retrieved: App\Models\SubjectCat (91μs)
      • Illuminate\Cache\Events\KeyWritten (379μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (273μs)
      • Illuminate\Cache\Events\CacheHit (635μs)
      • Illuminate\Cache\Events\CacheHit (387μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (303μs)
      • Illuminate\Cache\Events\CacheHit (195μs)
      • Illuminate\Cache\Events\CacheHit (257μs)
      • Illuminate\Cache\Events\CacheHit (198μs)
      • Illuminate\Cache\Events\CacheHit (200μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (211μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheHit (255μs)
      • Illuminate\Cache\Events\CacheHit (196μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • creating: site.layouts.app (636μs)
      • composing: site.layouts.app (28μs)
      • creating: components.canonical (600μs)
      • composing: components.canonical (124μs)
      • creating: components.open-graph (292μs)
      • composing: components.open-graph (90μs)
      • creating: site.headers.header (330μs)
      • composing: site.headers.header (128μs)
      • Illuminate\Cache\Events\CacheHit (1.92ms)
      • creating: components.footer (71μs)
      • composing: components.footer (91μs)
      • Illuminate\Cache\Events\CacheHit (965μs)
      • Illuminate\Cache\Events\CacheMissed (555μs)
      • Illuminate\Database\Events\StatementPrepared (4.89ms)
      • Illuminate\Database\Events\QueryExecuted (1.17ms)
      • eloquent.retrieved: App\Models\SubjectCat (96μs)
      • Illuminate\Cache\Events\KeyWritten (483μs)
      • Illuminate\Cache\Events\CacheHit (409μs)
      • Illuminate\Cache\Events\CacheHit (228μs)
      • Illuminate\Cache\Events\CacheHit (213μs)
      • Illuminate\Cache\Events\CacheHit (322μs)
      • Illuminate\Cache\Events\CacheHit (206μs)
      • Illuminate\Cache\Events\CacheHit (408μs)
      • Illuminate\Cache\Events\CacheHit (639μs)
      • Illuminate\Cache\Events\CacheHit (231μs)
      • Illuminate\Cache\Events\CacheHit (335μs)
      • Illuminate\Cache\Events\CacheHit (257μs)
      • Illuminate\Cache\Events\CacheHit (230μs)
      • Illuminate\Cache\Events\CacheHit (201μs)
      • creating: components.forms.contact-us (313μs)
      • composing: components.forms.contact-us (262μs)
      • creating: components.forms.get-started (209μs)
      • composing: components.forms.get-started (89μs)
      • creating: components.forms.free-tool-download (142μs)
      • composing: components.forms.free-tool-download (78μs)
      • creating: components.forms.claim-free-worksheet (141μs)
      • composing: components.forms.claim-free-worksheet (233μs)
      • creating: components.forms.tutor-subscription-waitlist (153μs)
      • composing: components.forms.tutor-subscription-waitlist (80μs)
      • creating: components.forms.tutor-subscription-join (137μs)
      • composing: components.forms.tutor-subscription-join (76μs)
      • creating: components.forms.tutor-support (140μs)
      • composing: components.forms.tutor-support (75μs)
      • 312 x Illuminate\Cache\Events\CacheHit (19.57%)
        98.69ms
        18 x Illuminate\Database\Events\StatementPrepared (6.99%)
        35.23ms
        18 x Illuminate\Database\Events\QueryExecuted (3.74%)
        18.87ms
        10 x Illuminate\Cache\Events\CacheMissed (2.16%)
        10.88ms
        1 x Illuminate\Foundation\Events\LocaleUpdated (1.4%)
        7.05ms
        10 x Illuminate\Cache\Events\KeyWritten (1.18%)
        5.96ms
        1 x Illuminate\Routing\Events\Routing (1%)
        5.05ms
        1 x Illuminate\Database\Events\ConnectionEstablished (0.3%)
        1.49ms
        12 x eloquent.retrieved: App\Models\SubjectCat (0.21%)
        1.04ms
        1 x Illuminate\Routing\Events\RouteMatched (0.14%)
        682μs
        1 x creating: site.layouts.app (0.13%)
        636μs
        1 x creating: components.canonical (0.12%)
        600μs
        1 x eloquent.booting: App\Models\SubjectCat (0.11%)
        540μs
        1 x creating: homework.show (0.08%)
        421μs
        16 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.08%)
        396μs
        1 x creating: components.breadcrumbs (0.07%)
        347μs
        1 x creating: site.headers.header (0.07%)
        330μs
        1 x creating: components.forms.contact-us (0.06%)
        313μs
        1 x creating: components.open-graph (0.06%)
        292μs
        1 x composing: components.forms.contact-us (0.05%)
        262μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.05%)
        258μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.05%)
        236μs
        1 x composing: components.forms.claim-free-worksheet (0.05%)
        233μs
        1 x composing: components.breadcrumbs (0.04%)
        225μs
        1 x creating: components.forms.get-started (0.04%)
        209μs
        1 x composing: homework.show (0.04%)
        179μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.03%)
        156μs
        1 x creating: components.forms.tutor-subscription-waitlist (0.03%)
        153μs
        1 x creating: components.forms.free-tool-download (0.03%)
        142μs
        1 x creating: components.forms.claim-free-worksheet (0.03%)
        141μs
        1 x creating: components.forms.tutor-support (0.03%)
        140μs
        1 x creating: components.forms.tutor-subscription-join (0.03%)
        137μs
        1 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.03%)
        131μs
        1 x composing: site.headers.header (0.03%)
        128μs
        1 x composing: components.canonical (0.02%)
        124μs
        1 x eloquent.booting: App\Models\Subject (0.02%)
        122μs
        1 x eloquent.retrieved: App\Models\Subject (0.02%)
        116μs
        1 x composing: components.footer (0.02%)
        91μs
        1 x composing: components.open-graph (0.02%)
        90μs
        1 x composing: components.forms.get-started (0.02%)
        89μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.02%)
        86μs
        1 x composing: components.forms.tutor-subscription-waitlist (0.02%)
        80μs
        1 x composing: components.forms.free-tool-download (0.02%)
        78μs
        1 x composing: components.forms.tutor-subscription-join (0.02%)
        76μs
        1 x composing: components.forms.tutor-support (0.01%)
        75μs
        1 x creating: components.footer (0.01%)
        71μs
        1 x eloquent.booted: App\Models\Subject (0.01%)
        61μs
        1 x eloquent.booted: App\Models\SubjectCat (0.01%)
        54μs
        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
      18 statements were executed, 3 of which were duplicates, 15 unique. Show only duplicated38.08ms
      • 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` = '41816' limit 1
        14.67mstwenty4_siteHomeworkLibraryController.php#97
        Bindings
        • 0: published
        • 1: 0
        • 2: 41816
        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 (2)
        1.1mstwenty4_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 (41816)
        950μstwenty4_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
        1.02mstwenty4_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_files` where `solutionslibrary_files`.`solutionlib_id` = 41816 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        1.02mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 41816
        • 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` = 41816 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'teaser' order by `order` asc, `id` asc
        1mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 41816
        • 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` = 41816 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'solution' order by `order` asc, `id` asc
        890μstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 41816
        • 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
        1.03mstwenty4_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` = 1 limit 1
        1.1mstwenty4_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
        2mstwenty4_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
        1.13mstwenty4_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
        1.68mstwenty4_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
        1.16mstwenty4_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
        910μstwenty4_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
        1.13mstwenty4_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
        1.02mstwenty4_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
        5.23mstwenty4_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\HomeworkLibrary\HomeworkLibraryFile
      16HomeworkLibraryFile.php
      App\Models\SubjectCat
      12SubjectCat.php
      App\Models\HomeworkLibrary\HomeworkLibrary
      1HomeworkLibrary.php
      App\Models\Subject
      1Subject.php
          _token
          SP8zJCBHAcueo3UrIVijNrZ6EbSPHGaMo2uso72q
          utm_source
          direct
          redirectUrl
          /college-homework-library/Mathematics/Algebra/41816
          _previous
          array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/Mathematics/Alg...
          _flash
          array:2 [ "old" => [] "new" => [] ]
          PHPDEBUGBAR_STACK_DATA
          []
          path_info
          /college-homework-library/Mathematics/Algebra/41816
          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=1-67f6ca0b-372025f34c192a35297fbe76" ] "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 => "18.221.200.48" ] "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, 09 Apr 2025 19:27:08 GMT" ] "set-cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6IlIzb1F4WXdnYXJqb3Q0dkNCSUIxSmc9PSIsInZhbHVlIjoielVPeDdxak5kRVp2anI0UXJsWHR3aHI0RnJhK3FvZ0FncnI1VDlyTUg0QXI4NkgwalFwZTIvaGFibTZ5WHlwSHhXdEx0b0pwVnNvQ24wY2gvL240eVB5aWhyYU5iRGhWSXlqdi9SaGppMzlCYkh0ai9qL21wL0Z1NU82dnpHK3ciLCJtYWMiOiI1MjEwOTc4ZDFlODI1NTYzMDU3NzFmY2Y2MDE1OGQ4ZDdkZDFlNTYxN2Q0NDg2MGEyNGIzODYyZTE3ZTVkMDE4IiwidGFnIjoiIn0%3D; expires=Wed, 09 Apr 2025 21:27:08 GMT; Max-Age=7200; path=/; domain=.24houranswers.com; samesite=laxXSRF-TOKEN=eyJpdiI6IlIzb1F4WXdnYXJqb3Q0dkNCSUIxSmc9PSIsInZhbHVlIjoielVPeDdxak5kRVp2anI0UXJsWHR3aHI0RnJhK3FvZ0FncnI1VDlyTUg0QXI4NkgwalFwZTIvaGFibTZ5WHlwSHhXdEx0b" 1 => "24houranswers_session=eyJpdiI6IlVRNzBBdVBqcnR3YmJSOVRwbGZaY1E9PSIsInZhbHVlIjoiblUxUkRkZkxVMzg0ZDM4U1JVTXJRdTFJc1A5MVVMQitFdHh0Zy9KQzdaYVNtakdUNVlwQU4zQ0hzQzJkbG1ZNWhSc09jL01PWjZScEc3NlA2U1pHYkFhRDZ3aHBrbXIvSkxkcU5VcWxsM2NiN0t2TnhnYnVWZ1lHUzFFYmNLWlciLCJtYWMiOiJkNTBlMWZiZWJhOTJhZjc5Y2UwMmZkNWRmMDk5MmY0NmZiMTMzYzI2ZGQxY2E3Y2Q1YmU0NWM3OThmNWM2YzYzIiwidGFnIjoiIn0%3D; expires=Wed, 09 Apr 2025 21:27:08 GMT; Max-Age=7200; path=/; domain=.24houranswers.com; httponly; samesite=lax24houranswers_session=eyJpdiI6IlVRNzBBdVBqcnR3YmJSOVRwbGZaY1E9PSIsInZhbHVlIjoiblUxUkRkZkxVMzg0ZDM4U1JVTXJRdTFJc1A5MVVMQitFdHh0Zy9KQzdaYVNtakdUNVlwQU4zQ0hzQzJkbG" ] "Set-Cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6IlIzb1F4WXdnYXJqb3Q0dkNCSUIxSmc9PSIsInZhbHVlIjoielVPeDdxak5kRVp2anI0UXJsWHR3aHI0RnJhK3FvZ0FncnI1VDlyTUg0QXI4NkgwalFwZTIvaGFibTZ5WHlwSHhXdEx0b0pwVnNvQ24wY2gvL240eVB5aWhyYU5iRGhWSXlqdi9SaGppMzlCYkh0ai9qL21wL0Z1NU82dnpHK3ciLCJtYWMiOiI1MjEwOTc4ZDFlODI1NTYzMDU3NzFmY2Y2MDE1OGQ4ZDdkZDFlNTYxN2Q0NDg2MGEyNGIzODYyZTE3ZTVkMDE4IiwidGFnIjoiIn0%3D; expires=Wed, 09-Apr-2025 21:27:08 GMT; domain=.24houranswers.com; path=/XSRF-TOKEN=eyJpdiI6IlIzb1F4WXdnYXJqb3Q0dkNCSUIxSmc9PSIsInZhbHVlIjoielVPeDdxak5kRVp2anI0UXJsWHR3aHI0RnJhK3FvZ0FncnI1VDlyTUg0QXI4NkgwalFwZTIvaGFibTZ5WHlwSHhXdEx0b" 1 => "24houranswers_session=eyJpdiI6IlVRNzBBdVBqcnR3YmJSOVRwbGZaY1E9PSIsInZhbHVlIjoiblUxUkRkZkxVMzg0ZDM4U1JVTXJRdTFJc1A5MVVMQitFdHh0Zy9KQzdaYVNtakdUNVlwQU4zQ0hzQzJkbG1ZNWhSc09jL01PWjZScEc3NlA2U1pHYkFhRDZ3aHBrbXIvSkxkcU5VcWxsM2NiN0t2TnhnYnVWZ1lHUzFFYmNLWlciLCJtYWMiOiJkNTBlMWZiZWJhOTJhZjc5Y2UwMmZkNWRmMDk5MmY0NmZiMTMzYzI2ZGQxY2E3Y2Q1YmU0NWM3OThmNWM2YzYzIiwidGFnIjoiIn0%3D; expires=Wed, 09-Apr-2025 21:27:08 GMT; domain=.24houranswers.com; path=/; httponly24houranswers_session=eyJpdiI6IlVRNzBBdVBqcnR3YmJSOVRwbGZaY1E9PSIsInZhbHVlIjoiblUxUkRkZkxVMzg0ZDM4U1JVTXJRdTFJc1A5MVVMQitFdHh0Zy9KQzdaYVNtakdUNVlwQU4zQ0hzQzJkbG" ] ]
          session_attributes
          0 of 0
          array:6 [ "_token" => "SP8zJCBHAcueo3UrIVijNrZ6EbSPHGaMo2uso72q" "utm_source" => "direct" "redirectUrl" => "/college-homework-library/Mathematics/Algebra/41816" "_previous" => array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/Mathematics/Algebra/41816" ] "_flash" => array:2 [ "old" => [] "new" => [] ] "PHPDEBUGBAR_STACK_DATA" => [] ]