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Relativity

The Relativistic Doppler shift

Consider a source of very short-duration electromagnetic pulses (e.g., a radar antenna) at rest at the origin of reference frame S. An observer moves in the x-direction at velocity v as seen in frame S. The observer is at rest in frame S’. Suppose a first pulse is sent at t = 0 when the observer is at position x = xo Further suppose the (n + 1)th pulse is sent out at t = nτ where  τ is the period.

  1. Carefully draw the Minkowski diagram (space-time diagram) for frame S identifying the two events representing the arrival of the first and (n + 1)th pulse at the observer.
  2. Find the time interval between those two pulses in the observer’s frame S’.
  3. And therefore find the frequency ν' in the observer’s frame in terms of the source frequency ν and the observer’s velocity factor β. This is the relativistic Doppler shift.

S’(2) is moving right with a speed v. S(1) is standing. At (X0,0) in S the first light is emitted. These events are the red circles in the S and S’ axes. At (X0 + ντ,τ) in S' the second light is emitted. These events are the blue circles in S and S’.  The interval is Δt= τ' in S' (the brown segment).  In S the interval is Δt = τ. Thus τ is the time between two consecutive emissions of light.

From the diagram we can immediately deduce that 

The speed v of S’ moving is 

To find tB, suppose one has a mirror at τ' that reflects back the light emitted at tA = τ towards S. This light arrives in S at tC  = K * τ' (from symmetry considerations). Therefore 

Therefore the speed of S’ is          

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      • Illuminate\Cache\Events\CacheHit (475μs)
      • Illuminate\Cache\Events\CacheHit (1.33ms)
      • Illuminate\Cache\Events\CacheHit (774μs)
      • Illuminate\Cache\Events\CacheHit (186μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (8.34ms)
      • Illuminate\Cache\Events\CacheHit (540μs)
      • Illuminate\Cache\Events\CacheHit (411μs)
      • Illuminate\Cache\Events\CacheHit (220μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (230μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (374μs)
      • Illuminate\Cache\Events\CacheHit (182μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (248μs)
      • Illuminate\Cache\Events\CacheHit (231μs)
      • Illuminate\Cache\Events\CacheHit (268μs)
      • Illuminate\Cache\Events\CacheHit (202μs)
      • Illuminate\Cache\Events\CacheHit (149μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (201μs)
      • Illuminate\Cache\Events\CacheHit (262μs)
      • Illuminate\Cache\Events\CacheHit (211μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (199μs)
      • Illuminate\Cache\Events\CacheHit (241μs)
      • Illuminate\Cache\Events\CacheHit (204μs)
      • Illuminate\Cache\Events\CacheHit (182μs)
      • Illuminate\Cache\Events\CacheHit (203μs)
      • Illuminate\Cache\Events\CacheHit (150μs)
      • Illuminate\Cache\Events\CacheHit (417μs)
      • Illuminate\Cache\Events\CacheHit (223μs)
      • Illuminate\Cache\Events\CacheHit (201μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
      • Illuminate\Cache\Events\CacheHit (141μs)
      • Illuminate\Cache\Events\CacheHit (250μs)
      • Illuminate\Cache\Events\CacheHit (151μs)
      • Illuminate\Cache\Events\CacheHit (8.92ms)
      • Illuminate\Cache\Events\CacheHit (438μs)
      • Illuminate\Cache\Events\CacheHit (270μs)
      • Illuminate\Cache\Events\CacheHit (509μs)
      • Illuminate\Cache\Events\CacheHit (248μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (523μs)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (205μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • creating: components.tutors-card (742μs)
      • composing: components.tutors-card (69μs)
      • Illuminate\Database\Events\StatementPrepared (7.46ms)
      • Illuminate\Database\Events\QueryExecuted (1.08ms)
      • Illuminate\Cache\Events\CacheMissed (247μs)
      • Illuminate\Cache\Events\CacheMissed (78μs)
      • Illuminate\Database\Events\StatementPrepared (2.53ms)
      • Illuminate\Database\Events\QueryExecuted (7.51ms)
      • eloquent.retrieved: App\Models\Subject (130μs)
      • eloquent.retrieved: App\Models\Subject (20μs)
      • eloquent.retrieved: App\Models\Subject (13μs)
      • eloquent.retrieved: App\Models\Subject (11μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (8μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (8μs)
      • eloquent.retrieved: App\Models\Subject (8μs)
      • eloquent.retrieved: App\Models\Subject (8μs)
      • eloquent.retrieved: App\Models\Subject (8μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (8μs)
      • eloquent.retrieved: App\Models\Subject (8μs)
      • eloquent.retrieved: App\Models\Subject (8μs)
      • eloquent.retrieved: App\Models\Subject (8μs)
      • eloquent.retrieved: App\Models\Subject (8μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (8μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (8μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (8μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (8μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (39μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (8μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (8μs)
      • eloquent.retrieved: App\Models\Subject (8μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (8μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (8μs)
      • eloquent.retrieved: App\Models\Subject (8μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • Illuminate\Database\Events\StatementPrepared (972μs)
      • Illuminate\Database\Events\QueryExecuted (1.2ms)
      • eloquent.retrieved: App\Models\SubjectCat (97μs)
      • eloquent.retrieved: App\Models\SubjectCat (18μs)
      • eloquent.retrieved: App\Models\SubjectCat (10μs)
      • eloquent.retrieved: App\Models\SubjectCat (10μs)
      • Illuminate\Cache\Events\KeyWritten (17.93ms)
      • Illuminate\Cache\Events\KeyWritten (1.63ms)
      • Illuminate\Cache\Events\CacheHit (3.94ms)
      • Illuminate\Cache\Events\CacheHit (835μs)
      • Illuminate\Cache\Events\CacheHit (241μs)
      • Illuminate\Cache\Events\CacheHit (208μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (163μs)
      • Illuminate\Cache\Events\CacheHit (5.57ms)
      • Illuminate\Cache\Events\CacheHit (235μs)
      • Illuminate\Cache\Events\CacheHit (206μs)
      • Illuminate\Cache\Events\CacheHit (157μs)
      • Illuminate\Cache\Events\CacheHit (319μs)
      • Illuminate\Cache\Events\CacheHit (235μs)
      • Illuminate\Cache\Events\CacheHit (236μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (195μs)
      • Illuminate\Cache\Events\CacheHit (322μs)
      • Illuminate\Cache\Events\CacheHit (201μs)
      • Illuminate\Cache\Events\CacheHit (154μs)
      • Illuminate\Cache\Events\CacheHit (411μs)
      • Illuminate\Cache\Events\CacheHit (207μs)
      • Illuminate\Cache\Events\CacheHit (7.77ms)
      • Illuminate\Cache\Events\CacheHit (416μs)
      • Illuminate\Cache\Events\CacheHit (253μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (214μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • Illuminate\Cache\Events\CacheHit (236μs)
      • Illuminate\Cache\Events\CacheHit (182μs)
      • Illuminate\Cache\Events\CacheHit (195μs)
      • Illuminate\Cache\Events\CacheHit (160μs)
      • Illuminate\Cache\Events\CacheHit (290μs)
      • Illuminate\Cache\Events\CacheHit (257μs)
      • Illuminate\Cache\Events\CacheHit (214μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (158μs)
      • Illuminate\Cache\Events\CacheHit (234μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (1.35ms)
      • Illuminate\Cache\Events\CacheHit (779μs)
      • Illuminate\Cache\Events\CacheHit (462μs)
      • Illuminate\Cache\Events\CacheHit (200μs)
      • Illuminate\Cache\Events\CacheHit (220μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (201μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (199μs)
      • Illuminate\Cache\Events\CacheHit (529μs)
      • Illuminate\Cache\Events\CacheHit (350μs)
      • Illuminate\Cache\Events\CacheHit (203μs)
      • Illuminate\Cache\Events\CacheHit (7.04ms)
      • Illuminate\Cache\Events\CacheHit (230μs)
      • Illuminate\Cache\Events\CacheHit (361μs)
      • Illuminate\Cache\Events\CacheHit (207μs)
      • Illuminate\Cache\Events\CacheHit (202μs)
      • Illuminate\Cache\Events\CacheHit (162μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (157μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (159μs)
      • Illuminate\Cache\Events\CacheHit (292μs)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (199μs)
      • Illuminate\Cache\Events\CacheHit (255μs)
      • Illuminate\Cache\Events\CacheHit (573μs)
      • Illuminate\Cache\Events\CacheHit (204μs)
      • Illuminate\Cache\Events\CacheHit (210μs)
      • Illuminate\Cache\Events\CacheHit (2.84ms)
      • Illuminate\Cache\Events\CacheHit (383μs)
      • Illuminate\Cache\Events\CacheHit (394μs)
      • Illuminate\Cache\Events\CacheHit (277μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (399μs)
      • Illuminate\Cache\Events\CacheHit (199μs)
      • Illuminate\Cache\Events\CacheHit (216μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
      • Illuminate\Cache\Events\CacheHit (199μs)
      • Illuminate\Cache\Events\CacheHit (163μs)
      • Illuminate\Cache\Events\CacheHit (213μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (270μs)
      • Illuminate\Cache\Events\CacheHit (193μs)
      • Illuminate\Cache\Events\CacheHit (202μs)
      • Illuminate\Cache\Events\CacheHit (164μs)
      • Illuminate\Cache\Events\CacheHit (263μs)
      • Illuminate\Cache\Events\CacheHit (292μs)
      • Illuminate\Cache\Events\CacheHit (214μs)
      • Illuminate\Cache\Events\CacheHit (267μs)
      • Illuminate\Cache\Events\CacheHit (198μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • Illuminate\Cache\Events\CacheHit (612μs)
      • Illuminate\Cache\Events\CacheHit (212μs)
      • Illuminate\Cache\Events\CacheHit (209μs)
      • Illuminate\Cache\Events\CacheHit (162μs)
      • creating: components.tutors-card (773μs)
      • composing: components.tutors-card (65μs)
      • Illuminate\Database\Events\StatementPrepared (1.61ms)
      • Illuminate\Database\Events\QueryExecuted (1.75ms)
      • Illuminate\Cache\Events\CacheMissed (207μs)
      • Illuminate\Cache\Events\CacheMissed (89μs)
      • Illuminate\Database\Events\StatementPrepared (944μs)
      • Illuminate\Database\Events\QueryExecuted (3.22ms)
      • eloquent.retrieved: App\Models\Subject (100μs)
      • eloquent.retrieved: App\Models\Subject (19μs)
      • eloquent.retrieved: App\Models\Subject (12μs)
      • eloquent.retrieved: App\Models\Subject (11μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • Illuminate\Database\Events\StatementPrepared (27.72ms)
      • Illuminate\Database\Events\QueryExecuted (4.97ms)
      • eloquent.retrieved: App\Models\SubjectCat (124μs)
      • eloquent.retrieved: App\Models\SubjectCat (98μs)
      • Illuminate\Cache\Events\KeyWritten (4.8ms)
      • Illuminate\Cache\Events\KeyWritten (1.91ms)
      • Illuminate\Cache\Events\CacheHit (6.28ms)
      • Illuminate\Cache\Events\CacheHit (541μs)
      • Illuminate\Cache\Events\CacheHit (298μs)
      • Illuminate\Cache\Events\CacheHit (662μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (193μs)
      • Illuminate\Cache\Events\CacheHit (338μs)
      • Illuminate\Cache\Events\CacheHit (336μs)
      • Illuminate\Cache\Events\CacheHit (272μs)
      • Illuminate\Cache\Events\CacheHit (283μs)
      • Illuminate\Cache\Events\CacheHit (159μs)
      • Illuminate\Cache\Events\CacheHit (414μs)
      • Illuminate\Cache\Events\CacheHit (1.67ms)
      • Illuminate\Cache\Events\CacheHit (2.88ms)
      • Illuminate\Cache\Events\CacheHit (356μs)
      • Illuminate\Cache\Events\CacheHit (1.19ms)
      • Illuminate\Cache\Events\CacheHit (990μs)
      • Illuminate\Cache\Events\CacheHit (241μs)
      • Illuminate\Cache\Events\CacheHit (576μs)
      • creating: components.tutors-card (1.25ms)
      • composing: components.tutors-card (346μs)
      • Illuminate\Database\Events\StatementPrepared (8.51ms)
      • Illuminate\Database\Events\QueryExecuted (11.47ms)
      • Illuminate\Cache\Events\CacheMissed (498μs)
      • Illuminate\Cache\Events\CacheMissed (130μs)
      • Illuminate\Database\Events\StatementPrepared (1.64ms)
      • Illuminate\Database\Events\QueryExecuted (4.52ms)
      • eloquent.retrieved: App\Models\Subject (121μs)
      • eloquent.retrieved: App\Models\Subject (22μs)
      • eloquent.retrieved: App\Models\Subject (13μs)
      • eloquent.retrieved: App\Models\Subject (12μs)
      • eloquent.retrieved: App\Models\Subject (44μs)
      • eloquent.retrieved: App\Models\Subject (12μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (24μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (11μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • Illuminate\Database\Events\StatementPrepared (913μs)
      • Illuminate\Database\Events\QueryExecuted (1.92ms)
      • eloquent.retrieved: App\Models\SubjectCat (171μs)
      • eloquent.retrieved: App\Models\SubjectCat (23μs)
      • eloquent.retrieved: App\Models\SubjectCat (14μs)
      • eloquent.retrieved: App\Models\SubjectCat (12μs)
      • eloquent.retrieved: App\Models\SubjectCat (11μs)
      • Illuminate\Cache\Events\KeyWritten (16.24ms)
      • Illuminate\Cache\Events\KeyWritten (2.31ms)
      • Illuminate\Cache\Events\CacheHit (1.88ms)
      • Illuminate\Cache\Events\CacheHit (947μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (193μs)
      • Illuminate\Cache\Events\CacheHit (209μs)
      • Illuminate\Cache\Events\CacheHit (343μs)
      • Illuminate\Cache\Events\CacheHit (259μs)
      • Illuminate\Cache\Events\CacheHit (261μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (276μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (331μs)
      • Illuminate\Cache\Events\CacheHit (394μs)
      • Illuminate\Cache\Events\CacheHit (327μs)
      • Illuminate\Cache\Events\CacheHit (380μs)
      • Illuminate\Cache\Events\CacheHit (668μs)
      • Illuminate\Cache\Events\CacheHit (198μs)
      • Illuminate\Cache\Events\CacheHit (277μs)
      • Illuminate\Cache\Events\CacheHit (566μs)
      • Illuminate\Cache\Events\CacheHit (223μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (159μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (294μs)
      • Illuminate\Cache\Events\CacheHit (241μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (200μs)
      • Illuminate\Cache\Events\CacheHit (5.92ms)
      • Illuminate\Cache\Events\CacheHit (294μs)
      • Illuminate\Cache\Events\CacheHit (227μs)
      • Illuminate\Cache\Events\CacheHit (199μs)
      • Illuminate\Cache\Events\CacheHit (168μs)
      • Illuminate\Cache\Events\CacheHit (237μs)
      • Illuminate\Cache\Events\CacheHit (275μs)
      • Illuminate\Cache\Events\CacheHit (219μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (440μs)
      • Illuminate\Cache\Events\CacheHit (228μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheHit (216μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (255μs)
      • Illuminate\Cache\Events\CacheHit (299μs)
      • Illuminate\Cache\Events\CacheHit (416μs)
      • Illuminate\Cache\Events\CacheHit (238μs)
      • Illuminate\Cache\Events\CacheHit (544μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (389μs)
      • Illuminate\Cache\Events\CacheHit (193μs)
      • Illuminate\Cache\Events\CacheHit (341μs)
      • Illuminate\Cache\Events\CacheHit (234μs)
      • Illuminate\Cache\Events\CacheHit (374μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (392μs)
      • Illuminate\Cache\Events\CacheHit (500μs)
      • Illuminate\Cache\Events\CacheHit (324μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (201μs)
      • Illuminate\Cache\Events\CacheHit (163μs)
      • Illuminate\Cache\Events\CacheHit (388μs)
      • Illuminate\Cache\Events\CacheHit (235μs)
      • Illuminate\Cache\Events\CacheHit (289μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • creating: site.blocks.subject-homework (2.39ms)
      • composing: site.blocks.subject-homework (24μs)
      • eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (144μs)
      • eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (218μs)
      • Illuminate\Database\Events\StatementPrepared (2.11ms)
      • Illuminate\Database\Events\QueryExecuted (4.49ms)
      • Illuminate\Database\Events\StatementPrepared (1.31ms)
      • Illuminate\Database\Events\QueryExecuted (2.22ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (110μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (21μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (14μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (12μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (99μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (18μs)
      • Illuminate\Database\Events\StatementPrepared (1.1ms)
      • Illuminate\Database\Events\QueryExecuted (1.26ms)
      • eloquent.retrieved: App\Models\Subject (102μs)
      • Illuminate\Database\Events\StatementPrepared (937μs)
      • Illuminate\Database\Events\QueryExecuted (1.08ms)
      • eloquent.retrieved: App\Models\SubjectCat (95μs)
      • creating: components.homework-blocks (769μs)
      • composing: components.homework-blocks (174μs)
      • creating: site.blocks.reviews (1.06ms)
      • composing: site.blocks.reviews (23μs)
      • creating: site.blocks.submit-homework (146μs)
      • composing: site.blocks.submit-homework (20μs)
      • creating: site.blocks.faq (113μs)
      • composing: site.blocks.faq (17μs)
      • eloquent.booting: App\Models\Twill\TwillFaq (138μs)
      • eloquent.booted: App\Models\Twill\TwillFaq (243μs)
      • eloquent.booting: App\Models\Twill\Slugs\TwillFaqSlug (316μs)
      • eloquent.booted: App\Models\Twill\Slugs\TwillFaqSlug (77μs)
      • Illuminate\Database\Events\StatementPrepared (3.72ms)
      • Illuminate\Database\Events\QueryExecuted (3.18ms)
      • eloquent.retrieved: App\Models\Twill\TwillFaq (300μs)
      • Illuminate\Database\Events\StatementPrepared (2.75ms)
      • Illuminate\Database\Events\QueryExecuted (3.25ms)
      • eloquent.retrieved: App\Models\Twill\Slugs\TwillFaqSlug (114μs)
      • eloquent.retrieved: App\Models\Twill\Slugs\TwillFaqSlug (24μs)
      • creating: components.faq-item (157μs)
      • composing: components.faq-item (161μs)
      • Illuminate\Database\Events\StatementPrepared (9.29ms)
      • Illuminate\Database\Events\QueryExecuted (1.47ms)
      • eloquent.retrieved: App\Models\Twill\TwillFaq (336μs)
      • Illuminate\Database\Events\StatementPrepared (6.99ms)
      • Illuminate\Database\Events\QueryExecuted (1.17ms)
      • eloquent.retrieved: App\Models\Twill\Slugs\TwillFaqSlug (761μs)
      • eloquent.retrieved: App\Models\Twill\Slugs\TwillFaqSlug (28μs)
      • creating: components.faq-item (117μs)
      • composing: components.faq-item (46μs)
      • Illuminate\Database\Events\StatementPrepared (2.99ms)
      • Illuminate\Database\Events\QueryExecuted (1.24ms)
      • eloquent.retrieved: App\Models\Twill\TwillFaq (361μs)
      • Illuminate\Database\Events\StatementPrepared (1.16ms)
      • Illuminate\Database\Events\QueryExecuted (1.99ms)
      • eloquent.retrieved: App\Models\Twill\Slugs\TwillFaqSlug (186μs)
      • creating: components.faq-item (108μs)
      • composing: components.faq-item (57μs)
      • Illuminate\Database\Events\StatementPrepared (9.86ms)
      • Illuminate\Database\Events\QueryExecuted (4.87ms)
      • eloquent.retrieved: App\Models\Twill\TwillFaq (214μs)
      • Illuminate\Database\Events\StatementPrepared (1.51ms)
      • Illuminate\Database\Events\QueryExecuted (3.41ms)
      • eloquent.retrieved: App\Models\Twill\Slugs\TwillFaqSlug (159μs)
      • creating: components.faq-item (152μs)
      • composing: components.faq-item (49μs)
      • creating: site.blocks.text-with-image (485μs)
      • composing: site.blocks.text-with-image (23μs)
      • creating: site.blocks.work-with-tutors (400μs)
      • composing: site.blocks.work-with-tutors (91μs)
      • creating: site.layouts.app (237μs)
      • composing: site.layouts.app (119μs)
      • creating: components.canonical (584μs)
      • composing: components.canonical (95μs)
      • creating: components.open-graph (407μs)
      • composing: components.open-graph (83μs)
      • creating: site.headers.header (333μs)
      • composing: site.headers.header (79μs)
      • Illuminate\Cache\Events\CacheHit (13.72ms)
      • creating: components.footer (110μs)
      • composing: components.footer (99μs)
      • Illuminate\Cache\Events\CacheHit (5.54ms)
      • Illuminate\Cache\Events\CacheHit (423μs)
      • Illuminate\Cache\Events\CacheHit (306μs)
      • Illuminate\Cache\Events\CacheHit (195μs)
      • Illuminate\Cache\Events\CacheHit (182μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheHit (450μs)
      • Illuminate\Cache\Events\CacheHit (663μs)
      • Illuminate\Cache\Events\CacheHit (786μs)
      • Illuminate\Cache\Events\CacheHit (460μs)
      • Illuminate\Cache\Events\CacheHit (208μs)
      • Illuminate\Cache\Events\CacheHit (219μs)
      • Illuminate\Cache\Events\CacheHit (195μs)
      • creating: components.forms.contact-us (476μs)
      • composing: components.forms.contact-us (195μs)
      • creating: components.forms.get-started (159μs)
      • composing: components.forms.get-started (72μs)
      • creating: components.forms.free-tool-download (104μs)
      • composing: components.forms.free-tool-download (110μs)
      • creating: components.forms.claim-free-worksheet (114μs)
      • composing: components.forms.claim-free-worksheet (68μs)
      • creating: components.forms.tutor-subscription-waitlist (98μs)
      • composing: components.forms.tutor-subscription-waitlist (60μs)
      • creating: components.forms.tutor-subscription-join (95μs)
      • composing: components.forms.tutor-subscription-join (60μs)
      • creating: components.forms.tutor-support (131μs)
      • composing: components.forms.tutor-support (66μs)
      • 493 x Illuminate\Cache\Events\CacheHit (26.42%)
        356ms
        36 x Illuminate\Database\Events\StatementPrepared (13.65%)
        184ms
        36 x Illuminate\Database\Events\QueryExecuted (10.87%)
        147ms
        13 x Illuminate\Cache\Events\KeyWritten (4.45%)
        60.04ms
        13 x Illuminate\Cache\Events\CacheMissed (1.05%)
        14.23ms
        1 x Illuminate\Routing\Events\Routing (0.67%)
        9.03ms
        6 x creating: components.tutors-card (0.44%)
        5.90ms
        1 x Illuminate\Foundation\Events\LocaleUpdated (0.22%)
        2.96ms
        2 x Illuminate\Database\Events\ConnectionEstablished (0.21%)
        2.82ms
        1 x creating: site.blocks.subject-homework (0.18%)
        2.39ms
        1 x eloquent.booting: App\Models\User\Tutor (0.15%)
        2.05ms
        20 x eloquent.retrieved: App\Models\SubjectCat (0.13%)
        1.77ms
        91 x eloquent.retrieved: App\Models\Subject (0.11%)
        1.51ms
        6 x eloquent.retrieved: App\Models\Twill\Slugs\TwillFaqSlug (0.09%)
        1.27ms
        4 x eloquent.retrieved: App\Models\Twill\TwillFaq (0.09%)
        1.21ms
        1 x creating: site.blocks.reviews (0.08%)
        1.06ms
        1 x creating: site.blocks.how-it-works (0.07%)
        956μs
        6 x composing: components.tutors-card (0.06%)
        834μs
        1 x creating: components.homework-blocks (0.06%)
        769μs
        1 x eloquent.retrieved: App\Models\Meta (0.05%)
        607μs
        1 x creating: components.canonical (0.04%)
        584μs
        1 x eloquent.booted: App\Models\User\Tutor (0.04%)
        569μs
        4 x creating: components.faq-item (0.04%)
        534μs
        1 x creating: site.blocks.text-with-image (0.04%)
        485μs
        1 x creating: components.forms.contact-us (0.04%)
        476μs
        1 x creating: components.open-graph (0.03%)
        407μs
        1 x creating: site.blocks.work-with-tutors (0.03%)
        400μs
        1 x eloquent.booting: App\Models\User\TutorAttributes\TutorDegree (0.03%)
        391μs
        1 x Illuminate\Routing\Events\RouteMatched (0.03%)
        382μs
        1 x creating: components.breadcrumbs (0.03%)
        373μs
        1 x creating: site.headers.header (0.02%)
        333μs
        1 x eloquent.booting: App\Models\Twill\Slugs\TwillFaqSlug (0.02%)
        316μs
        4 x composing: components.faq-item (0.02%)
        313μs
        1 x eloquent.booting: App\Models\Meta (0.02%)
        304μs
        6 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.02%)
        274μs
        6 x eloquent.retrieved: App\Models\User\Tutor (0.02%)
        270μs
        1 x creating: components.tutors-cards (0.02%)
        266μs
        1 x eloquent.booted: App\Models\Twill\TwillFaq (0.02%)
        243μs
        1 x creating: site.layouts.app (0.02%)
        237μs
        1 x composing: subjects.show (0.02%)
        235μs
        1 x eloquent.booting: App\Models\Subject (0.02%)
        231μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.02%)
        218μs
        1 x composing: components.breadcrumbs (0.01%)
        199μs
        1 x composing: components.forms.contact-us (0.01%)
        195μs
        1 x composing: components.homework-blocks (0.01%)
        174μs
        1 x creating: components.forms.get-started (0.01%)
        159μs
        1 x creating: site.blocks.subject-tutors (0.01%)
        148μs
        1 x creating: site.blocks.submit-homework (0.01%)
        146μs
        1 x composing: components.tutors-cards (0.01%)
        145μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.01%)
        144μs
        1 x eloquent.booting: App\Models\Twill\TwillFaq (0.01%)
        138μs
        1 x creating: components.forms.tutor-support (0.01%)
        131μs
        1 x creating: subjects.show (0.01%)
        122μs
        1 x eloquent.booted: App\Models\Subject (0.01%)
        121μs
        1 x composing: site.layouts.app (0.01%)
        119μs
        1 x creating: components.forms.claim-free-worksheet (0.01%)
        114μs
        1 x creating: site.blocks.faq (0.01%)
        113μs
        1 x composing: components.forms.free-tool-download (0.01%)
        110μs
        1 x creating: components.footer (0.01%)
        110μs
        1 x creating: components.forms.free-tool-download (0.01%)
        104μs
        1 x composing: components.footer (0.01%)
        99μs
        1 x creating: components.forms.tutor-subscription-waitlist (0.01%)
        98μs
        1 x composing: components.canonical (0.01%)
        95μs
        1 x creating: components.forms.tutor-subscription-join (0.01%)
        95μs
        1 x composing: site.blocks.work-with-tutors (0.01%)
        91μs
        1 x eloquent.booting: App\Models\SubjectCat (0.01%)
        87μs
        1 x composing: components.open-graph (0.01%)
        83μs
        1 x composing: site.headers.header (0.01%)
        79μs
        1 x eloquent.booted: App\Models\Twill\Slugs\TwillFaqSlug (0.01%)
        77μs
        1 x composing: components.forms.get-started (0.01%)
        72μs
        1 x composing: components.forms.claim-free-worksheet (0.01%)
        68μs
        1 x composing: components.forms.tutor-support (0%)
        66μs
        1 x eloquent.booted: App\Models\Meta (0%)
        64μs
        1 x composing: components.forms.tutor-subscription-waitlist (0%)
        60μs
        1 x composing: components.forms.tutor-subscription-join (0%)
        60μs
        1 x eloquent.booted: App\Models\SubjectCat (0%)
        57μs
        1 x eloquent.booted: App\Models\User\TutorAttributes\TutorDegree (0%)
        53μs
        1 x composing: site.blocks.how-it-works (0%)
        26μs
        1 x composing: site.blocks.subject-homework (0%)
        24μs
        1 x composing: site.blocks.reviews (0%)
        23μs
        1 x composing: site.blocks.text-with-image (0%)
        23μs
        1 x composing: site.blocks.subject-tutors (0%)
        21μs
        1 x composing: site.blocks.submit-homework (0%)
        20μs
        1 x composing: site.blocks.faq (0%)
        17μs
      34 templates were rendered
      • 1x subjects.showshow.blade.phpblade
      • 1x components.breadcrumbsbreadcrumbs.blade.phpblade
      • 1x site.blocks.how-it-workshow-it-works.blade.phpblade
      • 1x site.blocks.subject-tutorssubject-tutors.blade.phpblade
      • 1x components.tutors-cardstutors-cards.blade.phpblade
      • 6x components.tutors-cardtutors-card.blade.phpblade
      • 1x site.blocks.subject-homeworksubject-homework.blade.phpblade
      • 1x components.homework-blockshomework-blocks.blade.phpblade
      • 1x site.blocks.reviewsreviews.blade.phpblade
      • 1x site.blocks.submit-homeworksubmit-homework.blade.phpblade
      • 1x site.blocks.faqfaq.blade.phpblade
      • 4x components.faq-itemfaq-item.blade.phpblade
      • 1x site.blocks.text-with-imagetext-with-image.blade.phpblade
      • 1x site.blocks.work-with-tutorswork-with-tutors.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 subjects/{categoryUri}/{subjectUri?}
      middleware
      web, utm.parameters
      controller
      App\Http\Controllers\SubjectController@show
      namespace
      where
      as
      subjects.show
      file
      app/Http/Controllers/SubjectController.php:43-96
      36 statements were executed, 2 of which were duplicates, 34 unique. Show only duplicated256ms
      • Connection Establishedtwenty4_siteSubjectRepository.php#123
        Backtrace
        • 13. app/Repositories/SubjectRepository.php:123
        • 14. app/Http/Controllers/SubjectController.php:54
        • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
      • select * from `subjects` where `urlFriendlyTitle` = 'Relativity' limit 1
        19.77mstwenty4_siteSubjectRepository.php#123
        Bindings
        • 0: Relativity
        Backtrace
        • 15. app/Repositories/SubjectRepository.php:123
        • 16. app/Http/Controllers/SubjectController.php:54
        • 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
      • select * from `subject_cats` where `subject_cats`.`id` in (34)
        1.35mstwenty4_siteSubjectRepository.php#123
        Backtrace
        • 20. app/Repositories/SubjectRepository.php:123
        • 21. app/Http/Controllers/SubjectController.php:54
        • 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
      • select * from `subject_cats` where `subject_cats`.`id` = 34 limit 1
        2.7mstwenty4_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
        • 28. app/Http/Controllers/SubjectController.php:86
      • select * from `meta` where `meta`.`id` = 3 limit 1
        1.73mstwenty4_siteMetaService.php#118
        Bindings
        • 0: 3
        Backtrace
        • 19. app/Services/MetaService.php:118
        • 20. app/Services/MetaService.php:108
        • 21. app/Services/MetaService.php:81
        • 22. app/Http/Controllers/SubjectController.php:89
        • 23. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • Connection Establishedtwenty4_siteTutorRepository.php#40
        Backtrace
        • 13. app/Repositories/TutorRepository.php:40
        • 14. app/View/Components/TutorsCards.php:28
        • 15. app/View/Components/TutorsCards.php:22
        • 17. vendor/laravel/framework/src/Illuminate/Container/Container.php:929
        • 18. vendor/laravel/framework/src/Illuminate/Container/Container.php:770
      • select count(*) as aggregate from `users` where (`subjectsQualified` like '%|446|%' or `DSF_subjectsQualified` like '%|446|%' or `allsubjects` = 1) and `disable_profile` = 0 and `picture` != '' and `solutionrequestQualified` = 1 and `is_suspended` = 0 and `is_deactivated` = 0 and `status` != '' and `status` = 'tutor'
        24.11mstwenty4_siteTutorsCards.php#35
        Bindings
        • 0: %|446|%
        • 1: %|446|%
        • 2: 1
        • 3: 0
        • 4: 
        • 5: 1
        • 6: 0
        • 7: 0
        • 8: 
        • 9: tutor
        Backtrace
        • 15. app/View/Components/TutorsCards.php:35
        • 16. app/View/Components/TutorsCards.php:22
        • 18. vendor/laravel/framework/src/Illuminate/Container/Container.php:929
        • 19. vendor/laravel/framework/src/Illuminate/Container/Container.php:770
        • 20. vendor/laravel/framework/src/Illuminate/Foundation/Application.php:933
      • select * from `users` where (`subjectsQualified` like '%|446|%' or `DSF_subjectsQualified` like '%|446|%' or `allsubjects` = 1) and `disable_profile` = 0 and `picture` != '' and `solutionrequestQualified` = 1 and `is_suspended` = 0 and `is_deactivated` = 0 and `status` != '' and `status` = 'tutor' order by `completed_requests` desc limit 6 offset 0
        13.08mstwenty4_siteTutorsCards.php#35
        Bindings
        • 0: %|446|%
        • 1: %|446|%
        • 2: 1
        • 3: 0
        • 4: 
        • 5: 1
        • 6: 0
        • 7: 0
        • 8: 
        • 9: tutor
        Backtrace
        • 15. app/View/Components/TutorsCards.php:35
        • 16. app/View/Components/TutorsCards.php:22
        • 18. vendor/laravel/framework/src/Illuminate/Container/Container.php:929
        • 19. vendor/laravel/framework/src/Illuminate/Container/Container.php:770
        • 20. vendor/laravel/framework/src/Illuminate/Foundation/Application.php:933
      • select * from `tutor_degrees` where `tutor_degrees`.`tutor_id` = 76351 and `tutor_degrees`.`tutor_id` is not null order by `year` desc limit 1
        5.84mstwenty4_siteTutor.php#361
        Bindings
        • 0: 76351
        Backtrace
        • 18. app/Models/User/Tutor.php:361
        • 19. view::components.tutors-card:11
        • 21. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 22. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
      • select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1
        10.93mstwenty4_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
        9.13mstwenty4_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` = 10 limit 1
        8.38mstwenty4_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` = 36 limit 1
        9mstwenty4_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
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 42 limit 1
        1.27mstwenty4_siteSubject.php#100
        Bindings
        • 0: 42
        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 `tutor_degrees` where `tutor_degrees`.`tutor_id` = 69722 and `tutor_degrees`.`tutor_id` is not null order by `year` desc limit 1
        14.87mstwenty4_siteTutor.php#361
        Bindings
        • 0: 69722
        Backtrace
        • 18. app/Models/User/Tutor.php:361
        • 19. view::components.tutors-card:11
        • 21. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 22. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
      • select * from `subject_cats` where `subject_cats`.`id` = 31 limit 1
        1.18mstwenty4_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 `tutor_degrees` where `tutor_degrees`.`tutor_id` = 97466 and `tutor_degrees`.`tutor_id` is not null order by `year` desc limit 1
        6.02mstwenty4_siteTutor.php#361
        Bindings
        • 0: 97466
        Backtrace
        • 18. app/Models/User/Tutor.php:361
        • 19. view::components.tutors-card:11
        • 21. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 22. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
      • select * from `tutor_degrees` where `tutor_degrees`.`tutor_id` = 81676 and `tutor_degrees`.`tutor_id` is not null order by `year` desc limit 1
        7.34mstwenty4_siteTutor.php#361
        Bindings
        • 0: 81676
        Backtrace
        • 18. app/Models/User/Tutor.php:361
        • 19. view::components.tutors-card:11
        • 21. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 22. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
      • select `subjects`.*, `subject_cats`.`title` as `category_title`, `subject_cats`.`id` as `category_id` from `subjects` inner join `subject_cats` on `subject_cats`.`id` = `subjects`.`catID` where `subjects`.`id` in (16, 50, 130, 128, 136, 394, 114, 258, 354, 259, 344, 54, 490, 137, 115, 166, 355, 52, 395, 334, 135, 477, 34, 134, 2, 133, 1, 6, 10, 7, 3, 349, 9, 396, 66, 47, 73, 8, 347, 67, 48, 4, 401, 379, 397, 226, 446, 49)
        8.92mstwenty4_siteTutor.php#214
        Bindings
        • 0: 16
        • 1: 50
        • 2: 130
        • 3: 128
        • 4: 136
        • 5: 394
        • 6: 114
        • 7: 258
        • 8: 354
        • 9: 259
        • 10: 344
        • 11: 54
        • 12: 490
        • 13: 137
        • 14: 115
        • 15: 166
        • 16: 355
        • 17: 52
        • 18: 395
        • 19: 334
        • 20: 135
        • 21: 477
        • 22: 34
        • 23: 134
        • 24: 2
        • 25: 133
        • 26: 1
        • 27: 6
        • 28: 10
        • 29: 7
        • 30: 3
        • 31: 349
        • 32: 9
        • 33: 396
        • 34: 66
        • 35: 47
        • 36: 73
        • 37: 8
        • 38: 347
        • 39: 67
        • 40: 48
        • 41: 4
        • 42: 401
        • 43: 379
        • 44: 397
        • 45: 226
        • 46: 446
        • 47: 49
        Backtrace
        • 14. app/Models/User/Tutor.php:214
        • 15. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 16. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 18. app/Models/User/Tutor.php:216
        • 24. app/Models/User/Tutor.php:267
      • select * from `subject_cats` where `subject_cats`.`id` in (1, 3, 10, 34)
        1.44mstwenty4_siteTutor.php#214
        Backtrace
        • 19. app/Models/User/Tutor.php:214
        • 20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 21. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 23. app/Models/User/Tutor.php:216
        • 29. app/Models/User/Tutor.php:267
      • select * from `tutor_degrees` where `tutor_degrees`.`tutor_id` = 155241 and `tutor_degrees`.`tutor_id` is not null order by `year` desc limit 1
        2.31mstwenty4_siteTutor.php#361
        Bindings
        • 0: 155241
        Backtrace
        • 18. app/Models/User/Tutor.php:361
        • 19. view::components.tutors-card:11
        • 21. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 22. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
      • select `subjects`.*, `subject_cats`.`title` as `category_title`, `subject_cats`.`id` as `category_id` from `subjects` inner join `subject_cats` on `subject_cats`.`id` = `subjects`.`catID` where `subjects`.`id` in (259, 401, 325, 14, 226, 501, 89, 446, 269)
        3.28mstwenty4_siteTutor.php#214
        Bindings
        • 0: 259
        • 1: 401
        • 2: 325
        • 3: 14
        • 4: 226
        • 5: 501
        • 6: 89
        • 7: 446
        • 8: 269
        Backtrace
        • 14. app/Models/User/Tutor.php:214
        • 15. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 16. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 18. app/Models/User/Tutor.php:216
        • 24. app/Models/User/Tutor.php:267
      • select * from `subject_cats` where `subject_cats`.`id` in (3, 34)
        31.83mstwenty4_siteTutor.php#214
        Backtrace
        • 19. app/Models/User/Tutor.php:214
        • 20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 21. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 23. app/Models/User/Tutor.php:216
        • 29. app/Models/User/Tutor.php:267
      • select * from `tutor_degrees` where `tutor_degrees`.`tutor_id` = 89695 and `tutor_degrees`.`tutor_id` is not null order by `year` desc limit 1
        11.55mstwenty4_siteTutor.php#361
        Bindings
        • 0: 89695
        Backtrace
        • 18. app/Models/User/Tutor.php:361
        • 19. view::components.tutors-card:11
        • 21. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 22. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
      • select `subjects`.*, `subject_cats`.`title` as `category_title`, `subject_cats`.`id` as `category_id` from `subjects` inner join `subject_cats` on `subject_cats`.`id` = `subjects`.`catID` where `subjects`.`id` in (459, 142, 18, 144, 30, 293, 294, 250, 211, 212, 210, 133, 1, 6, 127, 123, 70, 124, 41, 223, 401, 325, 479, 14, 379, 226, 327, 501, 89, 446, 269, 259)
        5.02mstwenty4_siteTutor.php#214
        Bindings
        • 0: 459
        • 1: 142
        • 2: 18
        • 3: 144
        • 4: 30
        • 5: 293
        • 6: 294
        • 7: 250
        • 8: 211
        • 9: 212
        • 10: 210
        • 11: 133
        • 12: 1
        • 13: 6
        • 14: 127
        • 15: 123
        • 16: 70
        • 17: 124
        • 18: 41
        • 19: 223
        • 20: 401
        • 21: 325
        • 22: 479
        • 23: 14
        • 24: 379
        • 25: 226
        • 26: 327
        • 27: 501
        • 28: 89
        • 29: 446
        • 30: 269
        • 31: 259
        Backtrace
        • 14. app/Models/User/Tutor.php:214
        • 15. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 16. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 18. app/Models/User/Tutor.php:216
        • 24. app/Models/User/Tutor.php:267
      • select * from `subject_cats` where `subject_cats`.`id` in (1, 3, 5, 34, 42)
        2.09mstwenty4_siteTutor.php#214
        Backtrace
        • 19. app/Models/User/Tutor.php:214
        • 20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 21. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 23. app/Models/User/Tutor.php:216
        • 29. app/Models/User/Tutor.php:267
      • select count(*) as aggregate from `solutionslibrary` where exists (select * from `subjects` where `solutionslibrary`.`subject` = `subjects`.`id`) and `subject` = 446 and `status` = 'published' and `price` > 0
        5.29mstwenty4_siteHomeworkBlocks.php#27
        Bindings
        • 0: 446
        • 1: published
        • 2: 0
        Backtrace
        • 15. app/View/Components/HomeworkBlocks.php:27
        • 16. vendor/laravel/framework/src/Illuminate/View/Component.php:102
        • 17. view::site.blocks.subject-homework:4
        • 19. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • select * from `solutionslibrary` where exists (select * from `subjects` where `solutionslibrary`.`subject` = `subjects`.`id`) and `subject` = 446 and `status` = 'published' and `price` > 0 order by `purchase_count` desc limit 6 offset 0
        2.15mstwenty4_siteHomeworkBlocks.php#27
        Bindings
        • 0: 446
        • 1: published
        • 2: 0
        Backtrace
        • 15. app/View/Components/HomeworkBlocks.php:27
        • 16. vendor/laravel/framework/src/Illuminate/View/Component.php:102
        • 17. view::site.blocks.subject-homework:4
        • 19. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • select * from `subjects` where `subjects`.`id` in (446)
        1.17mstwenty4_siteHomeworkBlocks.php#27
        Backtrace
        • 20. app/View/Components/HomeworkBlocks.php:27
        • 21. vendor/laravel/framework/src/Illuminate/View/Component.php:102
        • 22. view::site.blocks.subject-homework:4
        • 24. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 25. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • select * from `subject_cats` where `subject_cats`.`id` in (34)
        1.25mstwenty4_siteHomeworkBlocks.php#27
        Backtrace
        • 25. app/View/Components/HomeworkBlocks.php:27
        • 26. vendor/laravel/framework/src/Illuminate/View/Component.php:102
        • 27. view::site.blocks.subject-homework:4
        • 29. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 30. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • select * from `twill_faqs` where exists (select * from `twill_faq_slugs` where `twill_faqs`.`id` = `twill_faq_slugs`.`twill_faq_id` and `slug` = 'can-you-help-me-with-my-homework-in-less-than-24-hours' and `active` = 1 and `locale` = 'en' and `twill_faq_slugs`.`deleted_at` is null) and `twill_faqs`.`deleted_at` is null limit 1
        5.55mstwenty4_siteFaqItem.php#15
        Bindings
        • 0: can-you-help-me-with-my-homework-in-less-than-24-hours
        • 1: 1
        • 2: en
        Backtrace
        • 15. app/View/Components/FaqItem.php:15
        • 16. vendor/laravel/framework/src/Illuminate/View/Component.php:102
        • 17. view::site.blocks.faq:7
        • 19. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • select * from `twill_faq_slugs` where `twill_faq_slugs`.`twill_faq_id` in (1) and `twill_faq_slugs`.`deleted_at` is null
        3.07mstwenty4_siteFaqItem.php#15
        Backtrace
        • 20. app/View/Components/FaqItem.php:15
        • 21. vendor/laravel/framework/src/Illuminate/View/Component.php:102
        • 22. view::site.blocks.faq:7
        • 24. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 25. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • select * from `twill_faqs` where exists (select * from `twill_faq_slugs` where `twill_faqs`.`id` = `twill_faq_slugs`.`twill_faq_id` and `slug` = 'can-you-help-me-with-my-examquiztest' and `active` = 1 and `locale` = 'en' and `twill_faq_slugs`.`deleted_at` is null) and `twill_faqs`.`deleted_at` is null limit 1
        9.45mstwenty4_siteFaqItem.php#15
        Bindings
        • 0: can-you-help-me-with-my-examquiztest
        • 1: 1
        • 2: en
        Backtrace
        • 15. app/View/Components/FaqItem.php:15
        • 16. vendor/laravel/framework/src/Illuminate/View/Component.php:102
        • 17. view::site.blocks.faq:24
        • 19. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • select * from `twill_faq_slugs` where `twill_faq_slugs`.`twill_faq_id` in (2) and `twill_faq_slugs`.`deleted_at` is null
        7.39mstwenty4_siteFaqItem.php#15
        Backtrace
        • 20. app/View/Components/FaqItem.php:15
        • 21. vendor/laravel/framework/src/Illuminate/View/Component.php:102
        • 22. view::site.blocks.faq:24
        • 24. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 25. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • select * from `twill_faqs` where exists (select * from `twill_faq_slugs` where `twill_faqs`.`id` = `twill_faq_slugs`.`twill_faq_id` and `slug` = 'how-much-will-it-cost' and `active` = 1 and `locale` = 'en' and `twill_faq_slugs`.`deleted_at` is null) and `twill_faqs`.`deleted_at` is null limit 1
        1.29mstwenty4_siteFaqItem.php#15
        Bindings
        • 0: how-much-will-it-cost
        • 1: 1
        • 2: en
        Backtrace
        • 15. app/View/Components/FaqItem.php:15
        • 16. vendor/laravel/framework/src/Illuminate/View/Component.php:102
        • 17. view::site.blocks.faq:41
        • 19. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • select * from `twill_faq_slugs` where `twill_faq_slugs`.`twill_faq_id` in (3) and `twill_faq_slugs`.`deleted_at` is null
        1.16mstwenty4_siteFaqItem.php#15
        Backtrace
        • 20. app/View/Components/FaqItem.php:15
        • 21. vendor/laravel/framework/src/Illuminate/View/Component.php:102
        • 22. view::site.blocks.faq:41
        • 24. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 25. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • select * from `twill_faqs` where exists (select * from `twill_faq_slugs` where `twill_faqs`.`id` = `twill_faq_slugs`.`twill_faq_id` and `slug` = 'what-kind-of-payments-do-you-accept' and `active` = 1 and `locale` = 'en' and `twill_faq_slugs`.`deleted_at` is null) and `twill_faqs`.`deleted_at` is null limit 1
        12.52mstwenty4_siteFaqItem.php#15
        Bindings
        • 0: what-kind-of-payments-do-you-accept
        • 1: 1
        • 2: en
        Backtrace
        • 15. app/View/Components/FaqItem.php:15
        • 16. vendor/laravel/framework/src/Illuminate/View/Component.php:102
        • 17. view::site.blocks.faq:58
        • 19. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • select * from `twill_faq_slugs` where `twill_faq_slugs`.`twill_faq_id` in (4) and `twill_faq_slugs`.`deleted_at` is null
        2.37mstwenty4_siteFaqItem.php#15
        Backtrace
        • 20. app/View/Components/FaqItem.php:15
        • 21. vendor/laravel/framework/src/Illuminate/View/Component.php:102
        • 22. view::site.blocks.faq:58
        • 24. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 25. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      App\Models\Subject
      91Subject.php
      App\Models\SubjectCat
      20SubjectCat.php
      App\Models\User\Tutor
      6Tutor.php
      App\Models\HomeworkLibrary\HomeworkLibrary
      6HomeworkLibrary.php
      App\Models\Twill\Slugs\TwillFaqSlug
      6TwillFaqSlug.php
      App\Models\Twill\TwillFaq
      4TwillFaq.php
      App\Models\Meta
      1Meta.php
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          request_cookies
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