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# Solved: Solve each of these congruences using the modular

ISBN: 9780073383095 37

## Solution for problem 12E Chapter 4.4

Discrete Mathematics and Its Applications | 7th Edition

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Discrete Mathematics and Its Applications | 7th Edition

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Problem 12E

Solve each of these congruences using the modular inverses found in parts (b), (c), and (d) of Exercise 6.a) 34 x = 77 (mod 89)________________b) 144 x = 4 (mod 233)________________c) 200 x = 13 (mod 1001)

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Cinematography History Notes  Cinematography = motion-picture photography (writing in movement)  Photography = light writing; it is not continuous; captures a moment in image form; mimics vision  Vision = continuous; occurs when light rays (reflected from object) hit the eye’s retina and stimulate the perception of the object’s picture in the brain  Apparent Motion = gives an explanation to people’s perception of movement when viewing movies A Short History of the Cinematic Image  The Republic = written by Plato; about people who are trapped in a cave and think that the shadows hitting the cave wall are the real world  Leonardo da Vinci = described how a light source coming into a hole in a camera obscura projected an upside-down image on the opposite wall  Camera Obscura = dark room (the literal definition)  Magic Lantern = was utilized by showmen to make “phantasmagoria”  Etinne-Gaspard Robert = made mobile projections of ghosts and skeletons on columns of smoke (the most famous) 1820s-1880s: The Invention of Photography and the Prehistory of Cinema  Phenakistiscope (1832), Zoetrope (1834) = pre-cinematic contraptions; made illusions of movement Phenakistiscope Zoetrope  Louis- Jacques-Mande Daguerre = made known the first still photograph (1839)  Chronophotography = series of still pictures that recorded accumulative movement and developed the basis of cinematography  Eadweard Muybridge = experimented with still photographs  Zoopraxiscope (1879) = let moving pictures be projected for the first time 1890s-1920s: The Emergence and Refinement of Cinematography  Official Birth Date of Movies = December 28, 1895 (Lumiere Brothers showed ten short films at the Grand Café in Paris)  Lumiere Brothers joined two elements = ability to record a sequence of pictures on a transparent, flexible medium, and the capacity to project the sequence  First Movies = had a single moving image  Kinetoscopic Camera = patented by Thomas Edison (1891)  Early Edison Films = viewed by looking into a Kinetoscope  Kinetoscope = peep show machine  Eastman Kodak = primary manufacturer of film stock  Film Stock = has a flexible base or backing (such as light-sensitive emulsion and celluloid)  Nitrate Film Base = highly flammable; wouldn’t be replaced by safety film until 1952  Film Gauge = the width of the strip of film; standardized at 35mm (1909)  16mm was used by independent filmmakers  70mm = experimented with for effects  35mm = industry standard  1920s = frame rate increased from 16 to 24 frames per second (fps) (more definition and clarity)  Panchromatic Stock = responded to a full spectrum of colors; standard for black and white films (after 1926)  1927 = sound is introduced 1930s-1940s: Developments in Color, Wide-Angle, and Small-Guage Cinematography  1930s = color processes had evolved to colored stocks  Technicolor = would dominate until 1950s  Flowers and Trees (1932) = first to use Tehnicolor’s three-strip process  Tehnicolor’s three-strip process = recorded different colors separately  Wizard of Oz (1939) = used Tehnicolor’s three-strip process  Focal Length = the distance from the center of the lens to the point where light rays meet in a focus that is sharp  Wide-Angle lens = contain short focal length; a lens of less than 35mm  Telephoto = contain long focal length  Zoom = variable focus lens  Soft Style = main character or action is highlighted (filmmakers used gauzy fabrics and then special lenses to make this style)  Handheld Cameras = lightweight; used in WWII for newsreels and other things  Small Gauge Production = expanded  8mm film = made in 1932 for the unprofessional filmmaker  16mm = got an addition of sound and color 1950s-1960s: Widescreen, 3-D, and New Color Processes  Widescreen Processes = changed the shape and size of picture (changed ratio of width to height = aspect ratio; it widened)  Larger image = introduced so that cinema can be told apart from TV  CinemaScope = used anamorphic lens  Anamorphic Lens = compressed a wide angle view onto a 35mm film and then uncompressed it during projection with another such lens  Ways to distort or call attention to the picture: 1. Flares = made by directing strong light at the lens 2. Zooming = changing fast motion and focal length 3. Filters = transparent sheets of gels or glass placed in front of the lens 4. Telephoto Lenses = lenses containing a focal length of at least 75mm 1970s-1980s: Cinematography and Exhibition in the Age of the Blockbuster  1970s = Steadicam is introduced  Steadicam = lets the operator follow action quickly and smoothly  Visual Effects technology developed  IMAX = utilized a large film frame (runs film through the camera horizontally and at a higher speed); 1970s  1980s = camcorders developed  Consumer video and Broadcast = analog formats 1990s and Beyond: The Digital Era  First: digital technology for special effects and nonlinear editing systems is started by film industry  Digital Cinematography = alternative to 35mm film  Star Wars: Episode II - Attack of the Clones = first to be shot in HD (high-definition) digital video  Digital Technology = does not require processing in a laboratory and doesn’t utilize film stock  Digital Technology = has economic advantage of mobile and lightweight cameras  35mm Cinematography = has big cameras and lot of crew members  Digital Imaging disadvantages: 1. Depends on familiarity with the camera’s capabilities 2. The images are recorded and displayed in pixels 3. 35mm film frame has about ten million pixels (when converted to digital file) 4. Has less range 5. Lacks the tones and grain located in the film emulsion  2012 = digital projection surpassed 35mm film

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##### ISBN: 9780073383095

Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073383095. The answer to “Solve each of these congruences using the modular inverses found in parts (b), (c), and (d) of Exercise 6.a) 34 x = 77 (mod 89)________________b) 144 x = 4 (mod 233)________________c) 200 x = 13 (mod 1001)” is broken down into a number of easy to follow steps, and 37 words. Since the solution to 12E from 4.4 chapter was answered, more than 348 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Discrete Mathematics and Its Applications, edition: 7. This full solution covers the following key subjects: mod, Congruences, found, Inverses, exercise. This expansive textbook survival guide covers 101 chapters, and 4221 solutions. The full step-by-step solution to problem: 12E from chapter: 4.4 was answered by , our top Math solution expert on 06/21/17, 07:45AM.

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Solved: Solve each of these congruences using the modular