Question
QUESTION 1
1. When used at a wavelength of 1 micron, a telescope can resolve angles as small as 0.1 seconds of arc. How small an angle could the telescope resolve when used at a wavelength of 5 microns?
a. 0.02 seconds of arc
b. 0.004 seconds of arc
c. 0.5 seconds of arc
d. 0.25 seconds of arc

QUESTION 2
1. Which of the following is not likely to be an attribute of a good observing site?
a. dark sky
b. atmospheric stability
c. low elevation
d. low humidity

QUESTION 3
1. Telescope A has a mirror that is 10 times larger than the mirror of telescope B. Telescope A can resolve an angle as small as 0.1 seconds of arc. What is the smallest angle that can be resolved by telescope B?
a. 10 seconds of arc
b. 1 second of arc
c. 0.1 second of arc
d. 0.01 second of arc

QUESTION 4
1. Radio astronomers obtain great angular resolution by
a. observing at the longest wavelength possible.
b. using arrays of radio telescopes
c. observing objects when they are near the horizon.
d. observing an object with the same radio telescope for many years.

QUESTION 5
1. Which of the following kinds of photons are least energetic?
a. infrared
b. visible
c. ultraviolet
d. Xray

QUESTION 6
1. How does the light-gathering power of a 40 cm telescope compare to that of a 20 cm telescope?
a. they are the same
b. 2 times as great
c. 4 times as great
d. 8 times as great

QUESTION 7
1. In the laboratory, a spectral line of an element has a wavelength of 5000 Angstroms. What would be the measured wavelength of that line in the spectrum of a planet which is approaching at a velocity of 30 km/s? (The speed of light is 300,000 km/s.)
a. 4999.5 Angstroms
b. 4995 Angstroms
c. 5000.5 Angstroms
d. 5005 Angstroms

QUESTION 8
1. In the laboratory, an atom emits a spectral line at a wavelength of 400 nanometers. In the spectrum of a star, the same spectral line is found to have a wavelength of 410 nanometers. What can be said about the star?
a. It is hotter than the Sun.
b. It is moving toward the Earth.
c. It is moving away from the Earth
d. It contains elements that are not found on Earth.

QUESTION 9
1. A star is moving away from an observer at 1% of the speed of light. At what wavelength would the observer find an emission line which would occur at a wavelength of 6000 Angstroms if the star were at rest?
a. 6060 Angstroms
b. 6010 Angstroms
c. 6000 Angstroms
d. 5940 Angstroms

QUESTION 10
1. A TV satellite broadcasts at a frequency of 5000 MHz, (1 MHz = 1 million Hertz). What is the wavelength of this radiation?
a. 1000 cm
b. 5 million centimeters
c. 6 cm
d. 0.3 cm

QUESTION 11
1. The wavelength of a wave is 2 meters. The frequency of the wave is 2 Hz. What is the speed of the wave?
a. 16 m/s
b. 4 m/s
c. 64 m/s
d. 0.25 m/s

QUESTION 12
1. Which of the following forms of electromagnetic radiation has the longest wavelength?
a. visible
b. Xray
c. infrared
d. ultraviolet

QUESTION 13
1. The same telescope is used to obtain an image using light of the following wavelengths. Which of the images will have the poorest angular resolution?
a. blue
b. yellow
c. red
d. infrared

QUESTION 14
1. Which of the following is true about the frequency and velocity of electromagnetic waves?
a. The product of frequency and wavelength is the same for all such waves.
b. As frequency increases, wavelength increases.
c. Frequency is constant for all wavelengths.
d. Frequency and wavelength are independent of each other.

QUESTION 15
1. A particle of light is a
a. graviton.
b. proton.
c. spectrum.
d. photon.
e. angstrom.

QUESTION 16
1. Compared with infrared waves, radio waves
a. have higher energy.
b. are lower frequency.
c. take much longer to reach us from celestial objects.
d. have shorter wavelengths.

QUESTION 17
1. How does the speed of light in glass compare to the speed of light in a vacuum?
a. It is larger in glass.
b. It is larger in a vacuum.
c. Trick question, light can't travel in glass.
d. They are the same.

QUESTION 18
1. A telescope that uses a lens to bring radiation to a primary focus is called a:
a. radio telescope.
b. reflector.
c. refractor.
d. photometer.

QUESTION 19
1. How many 4 meter telescopes would be required to match the light gathering power of a 16 meter telescope?
a. 2
b. 4
c. 16
d. 64

QUESTION 20
1. The focal ratio of a lens or mirror is the ratio of its
a. focal length to diameter.
b. diameter to thickness.
c. magnification to diameter.
d. focal length to thickness.
1 points   
QUESTION 21
1. Which of the following forms of electromagnetic waves (or photons) has the greatest energy?
a. visible
b. Xray
c. infrared
d. ultraviolet

QUESTION 22
1. Which of the following are NOT electromagnetic waves?
a. radio waves
b. optical light
c. Xrays
d. gravitational waves

QUESTION 23
1. Why do X-ray telescopes have to be placed in space satellites?
a. They are too sensitive to terrestial radiation.
b. They are too dangerous for astronomers to operate on the ground.
c. The Earth's atmosphere absorbs cosmic Xrays.
d. There is too much scattered sunlight in the Earth's atmosphere.
e. The mirrors for X-ray telescopes are too large to operate on ground.

QUESTION 24
1. Suppose a source of electromagnetic waves is moving toward us at 2% of the speed of light. What can be said of the wavelength of the waves we receive from the source?
a. They are blueshifted by 2%.
b. They are redshifted by 2%.
c. They are blueshifted by 4%.
d. They are redshifted by 4%.

QUESTION 25
1. The product of the wavelength and frequency of a wave is equal to
a. the speed of the wave.
b. the energy of the wave.
c. the distance between crests of the wave.
d. the temperature of the wave.

QUESTION 26
1. Suppose you want to determine if there is any methane gas on a newly discovered planet. You need to equip your telescope with a
a. CCD.
b. photographic plate holder.
c. spectrometer.
d. space probe can't determine anything about gases without travelling there.

QUESTION 27
1. At what wavelength will the spectrum of a perfect black body with a temperature of 6,204 Kelvin peak, assuming that a perfect black body at 6000 Kelvin has a spectrum that peaks exactly at 500 nm? Express your answer in nm to the nearest whole nm. (Use the values given in this question to calculate your answer...)

QUESTION 28
1. An "isotope" is a nucleus:
a. ...which carries no net charge.
b. ...with a number of neutrons added or removed.
c. ...which cannot absorb radiation.
d. ...with a number of protons added or removed.
e. ...which carries a net charge.

QUESTION 29
1. Star A has 2 times the surface temperature and 0.8 times the radius of Star B. What is the ratio of the luminosity of Star A to the luminosity of Star B? (Indicate your answer to an accuracy of 0.1).

QUESTION 30
1. If a star is receding (moving away from us) at a speed of 1% of the speed of light, at what wavelength would a spectral line with a laboratory wavelength of 459 nm be observed? Express your answer in nm to the nearest 0.1 nm.

QUESTION 31
1. An "ion" is an atom or molecule:
a. ...with a number of neutrons added or removed.
b. ...with a number of protons added or removed to the nucleus.
c. ...which cannot absorb radiation.
d. ...which carries a net charge.
e. ...which carries no net charge.
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.

1. c. 0.5 seconds of arc
2. c. low elevation
3. b. 1 second of arc
4. b. using arrays of radio telescopes
5. a. infrared
This is only a preview of the solution.
Please use the purchase button to see the entire solution.
By purchasing this solution you'll be able to access the following files:
Solution.pdf
Purchase Solution
$45.00
Google Pay
Amazon
Paypal
Mastercard
Visacard
Discover
Amex
View Available Astronomy 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 Version957msRequest Duration45MBMemory UsageGET college-homework-library/{category}/{subject}/{id}Route
    • Booting (653ms)time
    • Application (304ms)time
    • 1 x Booting (68.24%)
      653ms
      1 x Application (31.76%)
      304ms
      • Illuminate\Routing\Events\Routing (775μs)
      • Illuminate\Routing\Events\RouteMatched (335μs)
      • Illuminate\Foundation\Events\LocaleUpdated (1.88ms)
      • eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (224μs)
      • eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (148μs)
      • Illuminate\Database\Events\ConnectionEstablished (971μs)
      • Illuminate\Database\Events\StatementPrepared (9.96ms)
      • Illuminate\Database\Events\QueryExecuted (1.92ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (119μs)
      • eloquent.booting: App\Models\Subject (75μs)
      • eloquent.booted: App\Models\Subject (55μs)
      • Illuminate\Database\Events\StatementPrepared (2.2ms)
      • Illuminate\Database\Events\QueryExecuted (2.93ms)
      • eloquent.retrieved: App\Models\Subject (126μs)
      • eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (131μs)
      • eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (925μs)
      • Illuminate\Database\Events\StatementPrepared (2.29ms)
      • Illuminate\Database\Events\QueryExecuted (1.13ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (97μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (21μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (12μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (11μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (11μs)
      • eloquent.booting: App\Models\SubjectCat (906μs)
      • eloquent.booted: App\Models\SubjectCat (57μs)
      • Illuminate\Database\Events\StatementPrepared (640μs)
      • Illuminate\Database\Events\QueryExecuted (3.61ms)
      • eloquent.retrieved: App\Models\SubjectCat (133μs)
      • Illuminate\Cache\Events\CacheHit (33.57ms)
      • Illuminate\Cache\Events\CacheMissed (2.48ms)
      • Illuminate\Database\Events\StatementPrepared (2.22ms)
      • Illuminate\Database\Events\QueryExecuted (2.6ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (95μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (23μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (14μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (12μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (12μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (11μs)
      • Illuminate\Database\Events\StatementPrepared (709μs)
      • Illuminate\Database\Events\QueryExecuted (7.23ms)
      • eloquent.retrieved: App\Models\Subject (115μs)
      • Illuminate\Cache\Events\KeyWritten (1.36ms)
      • Illuminate\Database\Events\StatementPrepared (2.97ms)
      • Illuminate\Database\Events\QueryExecuted (1.6ms)
      • Illuminate\Database\Events\StatementPrepared (1.03ms)
      • Illuminate\Database\Events\QueryExecuted (1.01ms)
      • Illuminate\Database\Events\StatementPrepared (685μs)
      • Illuminate\Database\Events\QueryExecuted (1.06ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (79μs)
      • Illuminate\Cache\Events\CacheHit (477μs)
      • creating: homework.show (265μs)
      • composing: homework.show (111μs)
      • creating: components.breadcrumbs (410μs)
      • composing: components.breadcrumbs (138μs)
      • Illuminate\Database\Events\StatementPrepared (1.52ms)
      • Illuminate\Database\Events\QueryExecuted (1.24ms)
      • eloquent.retrieved: App\Models\SubjectCat (115μs)
      • Illuminate\Cache\Events\CacheHit (8.79ms)
      • Illuminate\Cache\Events\CacheHit (454μs)
      • Illuminate\Cache\Events\CacheHit (896μs)
      • Illuminate\Cache\Events\CacheHit (204μs)
      • Illuminate\Cache\Events\CacheHit (204μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheHit (254μs)
      • Illuminate\Cache\Events\CacheHit (305μs)
      • Illuminate\Cache\Events\CacheHit (218μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • Illuminate\Cache\Events\CacheHit (398μs)
      • Illuminate\Cache\Events\CacheHit (195μs)
      • Illuminate\Cache\Events\CacheHit (313μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (224μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • Illuminate\Cache\Events\CacheHit (203μs)
      • Illuminate\Cache\Events\CacheHit (186μs)
      • Illuminate\Cache\Events\CacheHit (198μs)
      • Illuminate\Cache\Events\CacheHit (322μs)
      • Illuminate\Cache\Events\CacheHit (262μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (201μs)
      • Illuminate\Cache\Events\CacheHit (158μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (336μs)
      • Illuminate\Cache\Events\CacheHit (209μs)
      • Illuminate\Cache\Events\CacheHit (203μs)
      • Illuminate\Cache\Events\CacheHit (261μs)
      • Illuminate\Cache\Events\CacheHit (182μs)
      • Illuminate\Cache\Events\CacheHit (290μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (333μs)
      • Illuminate\Cache\Events\CacheHit (2.52ms)
      • Illuminate\Cache\Events\CacheHit (1.08ms)
      • Illuminate\Cache\Events\CacheHit (236μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • Illuminate\Cache\Events\CacheHit (198μs)
      • Illuminate\Cache\Events\CacheHit (170μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (164μs)
      • Illuminate\Cache\Events\CacheHit (284μs)
      • Illuminate\Cache\Events\CacheHit (209μs)
      • Illuminate\Cache\Events\CacheHit (204μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (349μs)
      • Illuminate\Cache\Events\CacheHit (413μs)
      • Illuminate\Cache\Events\CacheHit (219μs)
      • Illuminate\Cache\Events\CacheHit (3.15ms)
      • Illuminate\Cache\Events\CacheHit (2.26ms)
      • Illuminate\Cache\Events\CacheHit (501μs)
      • Illuminate\Cache\Events\CacheHit (396μs)
      • Illuminate\Cache\Events\CacheHit (384μs)
      • Illuminate\Cache\Events\CacheHit (226μs)
      • Illuminate\Cache\Events\CacheHit (173μs)
      • Illuminate\Cache\Events\CacheHit (1.27ms)
      • Illuminate\Cache\Events\CacheHit (1.6ms)
      • Illuminate\Cache\Events\CacheHit (332μs)
      • Illuminate\Cache\Events\CacheHit (284μs)
      • Illuminate\Cache\Events\CacheHit (229μs)
      • Illuminate\Cache\Events\CacheHit (337μs)
      • Illuminate\Cache\Events\CacheHit (588μs)
      • Illuminate\Cache\Events\CacheHit (1.59ms)
      • Illuminate\Cache\Events\CacheHit (233μs)
      • Illuminate\Cache\Events\CacheHit (186μs)
      • Illuminate\Cache\Events\CacheHit (205μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (199μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheHit (199μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (211μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheHit (207μs)
      • Illuminate\Cache\Events\CacheHit (212μs)
      • Illuminate\Cache\Events\CacheHit (215μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (385μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheHit (196μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (168μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (160μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (157μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (170μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (160μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (260μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (173μs)
      • Illuminate\Cache\Events\CacheHit (161μs)
      • Illuminate\Cache\Events\CacheHit (214μs)
      • Illuminate\Cache\Events\CacheHit (165μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (201μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (186μs)
      • Illuminate\Cache\Events\CacheHit (318μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (236μs)
      • Illuminate\Cache\Events\CacheHit (193μs)
      • Illuminate\Cache\Events\CacheHit (165μs)
      • Illuminate\Cache\Events\CacheHit (917μs)
      • Illuminate\Cache\Events\CacheHit (163μs)
      • Illuminate\Cache\Events\CacheHit (201μs)
      • Illuminate\Cache\Events\CacheHit (162μs)
      • Illuminate\Cache\Events\CacheHit (301μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (170μs)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (202μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (201μs)
      • Illuminate\Cache\Events\CacheHit (161μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (164μs)
      • Illuminate\Cache\Events\CacheHit (229μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (155μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (170μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (173μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (162μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (160μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (156μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (155μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (155μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (284μs)
      • Illuminate\Cache\Events\CacheHit (354μs)
      • Illuminate\Cache\Events\CacheHit (200μs)
      • Illuminate\Cache\Events\CacheHit (297μs)
      • Illuminate\Cache\Events\CacheHit (418μs)
      • Illuminate\Cache\Events\CacheHit (674μs)
      • Illuminate\Cache\Events\CacheHit (201μs)
      • Illuminate\Cache\Events\CacheHit (237μs)
      • Illuminate\Cache\Events\CacheHit (269μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (153μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (159μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (154μs)
      • Illuminate\Cache\Events\CacheHit (412μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (317μs)
      • Illuminate\Cache\Events\CacheHit (282μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (154μs)
      • Illuminate\Cache\Events\CacheHit (512μs)
      • Illuminate\Cache\Events\CacheHit (173μs)
      • Illuminate\Cache\Events\CacheHit (251μs)
      • Illuminate\Cache\Events\CacheHit (272μs)
      • Illuminate\Cache\Events\CacheHit (196μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheHit (152μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheHit (299μs)
      • Illuminate\Cache\Events\CacheHit (8.27ms)
      • Illuminate\Cache\Events\CacheHit (289μs)
      • Illuminate\Cache\Events\CacheHit (204μs)
      • Illuminate\Cache\Events\CacheHit (157μs)
      • Illuminate\Cache\Events\CacheHit (262μs)
      • Illuminate\Cache\Events\CacheHit (161μs)
      • Illuminate\Cache\Events\CacheHit (264μs)
      • Illuminate\Cache\Events\CacheHit (165μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • Illuminate\Cache\Events\CacheHit (328μs)
      • Illuminate\Cache\Events\CacheHit (384μs)
      • Illuminate\Cache\Events\CacheHit (214μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (170μs)
      • Illuminate\Cache\Events\CacheHit (274μs)
      • Illuminate\Cache\Events\CacheHit (168μs)
      • Illuminate\Cache\Events\CacheHit (222μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (161μs)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (156μs)
      • Illuminate\Cache\Events\CacheHit (1.13ms)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (14.19ms)
      • Illuminate\Cache\Events\CacheHit (234μs)
      • Illuminate\Cache\Events\CacheHit (204μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
      • Illuminate\Cache\Events\CacheHit (195μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (212μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (157μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (157μs)
      • Illuminate\Cache\Events\CacheHit (2.1ms)
      • Illuminate\Cache\Events\CacheHit (212μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (1.56ms)
      • Illuminate\Cache\Events\CacheHit (242μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (204μs)
      • Illuminate\Cache\Events\CacheHit (157μs)
      • Illuminate\Cache\Events\CacheHit (186μs)
      • Illuminate\Cache\Events\CacheHit (17.92ms)
      • Illuminate\Cache\Events\CacheHit (1.01ms)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (163μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (156μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (158μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (186μs)
      • Illuminate\Cache\Events\CacheHit (193μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheHit (159μs)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (162μs)
      • Illuminate\Cache\Events\CacheHit (10.3ms)
      • Illuminate\Cache\Events\CacheHit (6.05ms)
      • Illuminate\Cache\Events\CacheHit (321μs)
      • Illuminate\Cache\Events\CacheHit (202μs)
      • Illuminate\Cache\Events\CacheHit (205μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (204μs)
      • Illuminate\Cache\Events\CacheHit (163μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (152μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (153μs)
      • Illuminate\Cache\Events\CacheHit (1.46ms)
      • Illuminate\Cache\Events\CacheHit (284μs)
      • Illuminate\Cache\Events\CacheHit (480μs)
      • Illuminate\Cache\Events\CacheHit (381μs)
      • Illuminate\Cache\Events\CacheHit (585μs)
      • Illuminate\Cache\Events\CacheHit (255μs)
      • Illuminate\Cache\Events\CacheHit (441μs)
      • Illuminate\Cache\Events\CacheHit (139μs)
      • Illuminate\Cache\Events\CacheHit (144μs)
      • Illuminate\Cache\Events\CacheHit (268μs)
      • Illuminate\Cache\Events\CacheHit (8.5ms)
      • Illuminate\Cache\Events\CacheHit (308μs)
      • Illuminate\Cache\Events\CacheHit (246μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (234μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (313μs)
      • Illuminate\Cache\Events\CacheHit (341μs)
      • Illuminate\Cache\Events\CacheHit (271μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (511μs)
      • Illuminate\Cache\Events\CacheHit (7.29ms)
      • Illuminate\Cache\Events\CacheHit (392μs)
      • Illuminate\Cache\Events\CacheHit (9.69ms)
      • Illuminate\Cache\Events\CacheHit (282μs)
      • Illuminate\Cache\Events\CacheHit (265μs)
      • Illuminate\Cache\Events\CacheHit (407μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (153μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (155μs)
      • Illuminate\Cache\Events\CacheHit (170μs)
      • Illuminate\Cache\Events\CacheHit (242μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (156μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (148μs)
      • creating: site.layouts.app (526μs)
      • composing: site.layouts.app (21μs)
      • creating: components.canonical (529μs)
      • composing: components.canonical (367μs)
      • creating: components.open-graph (226μs)
      • composing: components.open-graph (82μs)
      • creating: site.headers.header (261μs)
      • composing: site.headers.header (72μs)
      • Illuminate\Cache\Events\CacheHit (10.94ms)
      • creating: components.footer (213μs)
      • composing: components.footer (124μs)
      • Illuminate\Cache\Events\CacheHit (1.02ms)
      • Illuminate\Cache\Events\CacheHit (301μs)
      • Illuminate\Cache\Events\CacheHit (240μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • Illuminate\Cache\Events\CacheHit (159μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (317μs)
      • Illuminate\Cache\Events\CacheHit (388μs)
      • Illuminate\Cache\Events\CacheHit (398μs)
      • Illuminate\Cache\Events\CacheHit (265μs)
      • Illuminate\Cache\Events\CacheHit (415μs)
      • Illuminate\Cache\Events\CacheHit (215μs)
      • Illuminate\Cache\Events\CacheHit (411μs)
      • creating: components.forms.contact-us (277μs)
      • composing: components.forms.contact-us (172μs)
      • creating: components.forms.get-started (172μs)
      • composing: components.forms.get-started (90μs)
      • creating: components.forms.free-tool-download (107μs)
      • composing: components.forms.free-tool-download (69μs)
      • creating: components.forms.claim-free-worksheet (103μs)
      • composing: components.forms.claim-free-worksheet (67μs)
      • creating: components.forms.tutor-subscription-waitlist (99μs)
      • composing: components.forms.tutor-subscription-waitlist (66μs)
      • creating: components.forms.tutor-subscription-join (98μs)
      • composing: components.forms.tutor-subscription-join (64μs)
      • creating: components.forms.tutor-support (130μs)
      • composing: components.forms.tutor-support (73μs)
      • 321 x Illuminate\Cache\Events\CacheHit (23.47%)
        225ms
        10 x Illuminate\Database\Events\QueryExecuted (2.54%)
        24.33ms
        10 x Illuminate\Database\Events\StatementPrepared (2.53%)
        24.23ms
        1 x Illuminate\Cache\Events\CacheMissed (0.26%)
        2.48ms
        1 x Illuminate\Foundation\Events\LocaleUpdated (0.2%)
        1.88ms
        1 x Illuminate\Cache\Events\KeyWritten (0.14%)
        1.36ms
        1 x Illuminate\Database\Events\ConnectionEstablished (0.1%)
        971μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.1%)
        925μs
        1 x eloquent.booting: App\Models\SubjectCat (0.09%)
        906μs
        1 x Illuminate\Routing\Events\Routing (0.08%)
        775μs
        1 x creating: components.canonical (0.06%)
        529μs
        1 x creating: site.layouts.app (0.05%)
        526μs
        1 x creating: components.breadcrumbs (0.04%)
        410μs
        1 x composing: components.canonical (0.04%)
        367μs
        1 x Illuminate\Routing\Events\RouteMatched (0.03%)
        335μs
        7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.03%)
        286μs
        1 x creating: components.forms.contact-us (0.03%)
        277μs
        1 x creating: homework.show (0.03%)
        265μs
        1 x creating: site.headers.header (0.03%)
        261μs
        2 x eloquent.retrieved: App\Models\SubjectCat (0.03%)
        248μs
        2 x eloquent.retrieved: App\Models\Subject (0.03%)
        241μs
        6 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.02%)
        231μs
        1 x creating: components.open-graph (0.02%)
        226μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.02%)
        224μs
        1 x creating: components.footer (0.02%)
        213μs
        1 x creating: components.forms.get-started (0.02%)
        172μs
        1 x composing: components.forms.contact-us (0.02%)
        172μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.02%)
        148μs
        1 x composing: components.breadcrumbs (0.01%)
        138μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.01%)
        131μs
        1 x creating: components.forms.tutor-support (0.01%)
        130μs
        1 x composing: components.footer (0.01%)
        124μs
        1 x composing: homework.show (0.01%)
        111μs
        1 x creating: components.forms.free-tool-download (0.01%)
        107μs
        1 x creating: components.forms.claim-free-worksheet (0.01%)
        103μs
        1 x creating: components.forms.tutor-subscription-waitlist (0.01%)
        99μs
        1 x creating: components.forms.tutor-subscription-join (0.01%)
        98μs
        1 x composing: components.forms.get-started (0.01%)
        90μs
        1 x composing: components.open-graph (0.01%)
        82μs
        1 x eloquent.booting: App\Models\Subject (0.01%)
        75μs
        1 x composing: components.forms.tutor-support (0.01%)
        73μs
        1 x composing: site.headers.header (0.01%)
        72μs
        1 x composing: components.forms.free-tool-download (0.01%)
        69μs
        1 x composing: components.forms.claim-free-worksheet (0.01%)
        67μs
        1 x composing: components.forms.tutor-subscription-waitlist (0.01%)
        66μs
        1 x composing: components.forms.tutor-subscription-join (0.01%)
        64μs
        1 x eloquent.booted: App\Models\SubjectCat (0.01%)
        57μs
        1 x eloquent.booted: App\Models\Subject (0.01%)
        55μs
        1 x composing: site.layouts.app (0%)
        21μs
      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
      10 statements were executed, 4 of which were duplicates, 6 unique. Show only duplicated33.89ms
      • 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` = '50017' limit 1
        10.85mstwenty4_siteHomeworkLibraryController.php#97
        Bindings
        • 0: published
        • 1: 0
        • 2: 50017
        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 (473)
        2.85mstwenty4_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 (50017)
        2.48mstwenty4_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` = 42 limit 1
        3.36mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 42
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 26. app/Http/Controllers/HomeworkLibraryController.php:105
        • 27. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 28. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 29. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
      • select * from `solutionslibrary` where `id` <> 50017 and `subject` = 473 and `status` = 'published' and `price` > 0 order by RAND() limit 6
        2.69mstwenty4_siteHomeworkLibraryRepository.php#30
        Bindings
        • 0: 50017
        • 1: 473
        • 2: published
        • 3: 0
        Backtrace
        • 14. app/Repositories/HomeworkLibraryRepository.php:30
        • 15. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 16. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 18. app/Repositories/HomeworkLibraryRepository.php:39
        • 19. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `subjects` where `subjects`.`id` in (473)
        7.21mstwenty4_siteHomeworkLibraryRepository.php#30
        Backtrace
        • 19. app/Repositories/HomeworkLibraryRepository.php:30
        • 20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 21. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 23. app/Repositories/HomeworkLibraryRepository.php:39
        • 24. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 50017 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        1.42mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 50017
        • 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` = 50017 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'teaser' order by `order` asc, `id` asc
        990μstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 50017
        • 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` = 50017 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'solution' order by `order` asc, `id` asc
        900μstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 50017
        • 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` = 42 limit 1
        1.14mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 42
        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
      App\Models\HomeworkLibrary\HomeworkLibrary
      7HomeworkLibrary.php
      App\Models\HomeworkLibrary\HomeworkLibraryFile
      6HomeworkLibraryFile.php
      App\Models\Subject
      2Subject.php
      App\Models\SubjectCat
      2SubjectCat.php
          _token
          X4kxCRKXI91qzE6Eibaqqp9KDoGQ87oAzbNuo6eN
          utm_source
          direct
          redirectUrl
          /college-homework-library/Astronomy/Astronomy-Other/50017
          _previous
          array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/Astronomy/Astro...
          _flash
          array:2 [ "old" => [] "new" => [] ]
          PHPDEBUGBAR_STACK_DATA
          []
          path_info
          /college-homework-library/Astronomy/Astronomy-Other/50017
          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=1-67fc3562-23545c8654bc933a5b819d41" ] "host" => array:1 [ 0 => "staging.dev.24houranswers.com" ] "x-forwarded-port" => array:1 [ 0 => "443" ] "x-forwarded-proto" => array:1 [ 0 => "https" ] "x-forwarded-for" => array:1 [ 0 => "3.145.200.81" ] "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 => "Sun, 13 Apr 2025 22:06:26 GMT" ] "set-cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6IjlZY055eVdwNnlVY3NlelNmb0MwZ1E9PSIsInZhbHVlIjoiazdIQ3B1NUsyWU5USHhOQkFvVm5uZGFTVWJpSzJOUmJZdzN4Wm1IM1BrcTZoYy9rU082bjFxdDd0ZDlGOWVZSWxKeExuTWNwcDZ0dFhCM0hRbExnRXlNQmljRDJLbERDMmoxYmExRUFIci9UeGd3VTVZczNtdDd6bWhPRnNma2kiLCJtYWMiOiI2MjFiMzkyMDFlNjNlMWUwMWZkZjgzNjVkM2ZmOGJjNGRhNmY0NDY2OTZjMTllYWRkY2FmMWM0NTZmZmFkMWQ3IiwidGFnIjoiIn0%3D; expires=Mon, 14 Apr 2025 00:06:27 GMT; Max-Age=7200; path=/; domain=.24houranswers.com; samesite=laxXSRF-TOKEN=eyJpdiI6IjlZY055eVdwNnlVY3NlelNmb0MwZ1E9PSIsInZhbHVlIjoiazdIQ3B1NUsyWU5USHhOQkFvVm5uZGFTVWJpSzJOUmJZdzN4Wm1IM1BrcTZoYy9rU082bjFxdDd0ZDlGOWVZSWxKeExuT" 1 => "24houranswers_session=eyJpdiI6InMvOEgrdFpVK0xxdWpGMmF3ZlJmc1E9PSIsInZhbHVlIjoib2tETjU5MHoxMnB4aStGOHNsU20xalE2cjkzYytMcEZGVXN0aElVNXQybGFPam42QU5ySXJyVnh4WE0zYlJVdGRtTXdCUm53ZU1CZHg4c3ZhQVBtTHYyZmtsY2hNeTZNdjJzY0g1cWcrOXBWMTVJeXVJcHBFTUw3cHpoalBWK04iLCJtYWMiOiJhNTNkNTcwMjFiYzQ0N2ViNWMzZmFkMmI1NDIwZGY5MWY3YjY3Mjk1NGU0Njg2ODRlOGVhZmI1N2ExM2U4M2EyIiwidGFnIjoiIn0%3D; expires=Mon, 14 Apr 2025 00:06:27 GMT; Max-Age=7200; path=/; domain=.24houranswers.com; httponly; samesite=lax24houranswers_session=eyJpdiI6InMvOEgrdFpVK0xxdWpGMmF3ZlJmc1E9PSIsInZhbHVlIjoib2tETjU5MHoxMnB4aStGOHNsU20xalE2cjkzYytMcEZGVXN0aElVNXQybGFPam42QU5ySXJyVnh4WE0zYl" ] "Set-Cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6IjlZY055eVdwNnlVY3NlelNmb0MwZ1E9PSIsInZhbHVlIjoiazdIQ3B1NUsyWU5USHhOQkFvVm5uZGFTVWJpSzJOUmJZdzN4Wm1IM1BrcTZoYy9rU082bjFxdDd0ZDlGOWVZSWxKeExuTWNwcDZ0dFhCM0hRbExnRXlNQmljRDJLbERDMmoxYmExRUFIci9UeGd3VTVZczNtdDd6bWhPRnNma2kiLCJtYWMiOiI2MjFiMzkyMDFlNjNlMWUwMWZkZjgzNjVkM2ZmOGJjNGRhNmY0NDY2OTZjMTllYWRkY2FmMWM0NTZmZmFkMWQ3IiwidGFnIjoiIn0%3D; expires=Mon, 14-Apr-2025 00:06:27 GMT; domain=.24houranswers.com; path=/XSRF-TOKEN=eyJpdiI6IjlZY055eVdwNnlVY3NlelNmb0MwZ1E9PSIsInZhbHVlIjoiazdIQ3B1NUsyWU5USHhOQkFvVm5uZGFTVWJpSzJOUmJZdzN4Wm1IM1BrcTZoYy9rU082bjFxdDd0ZDlGOWVZSWxKeExuT" 1 => "24houranswers_session=eyJpdiI6InMvOEgrdFpVK0xxdWpGMmF3ZlJmc1E9PSIsInZhbHVlIjoib2tETjU5MHoxMnB4aStGOHNsU20xalE2cjkzYytMcEZGVXN0aElVNXQybGFPam42QU5ySXJyVnh4WE0zYlJVdGRtTXdCUm53ZU1CZHg4c3ZhQVBtTHYyZmtsY2hNeTZNdjJzY0g1cWcrOXBWMTVJeXVJcHBFTUw3cHpoalBWK04iLCJtYWMiOiJhNTNkNTcwMjFiYzQ0N2ViNWMzZmFkMmI1NDIwZGY5MWY3YjY3Mjk1NGU0Njg2ODRlOGVhZmI1N2ExM2U4M2EyIiwidGFnIjoiIn0%3D; expires=Mon, 14-Apr-2025 00:06:27 GMT; domain=.24houranswers.com; path=/; httponly24houranswers_session=eyJpdiI6InMvOEgrdFpVK0xxdWpGMmF3ZlJmc1E9PSIsInZhbHVlIjoib2tETjU5MHoxMnB4aStGOHNsU20xalE2cjkzYytMcEZGVXN0aElVNXQybGFPam42QU5ySXJyVnh4WE0zYl" ] ]
          session_attributes
          0 of 0
          array:6 [ "_token" => "X4kxCRKXI91qzE6Eibaqqp9KDoGQ87oAzbNuo6eN" "utm_source" => "direct" "redirectUrl" => "/college-homework-library/Astronomy/Astronomy-Other/50017" "_previous" => array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/Astronomy/Astronomy-Other/50017" ] "_flash" => array:2 [ "old" => [] "new" => [] ] "PHPDEBUGBAR_STACK_DATA" => [] ]