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What is the value of the function f(x) = 3x - 1 when x = 2

Math Connects: Concepts, Skills, and Problem Solving Course 3 | 0th Edition | ISBN: 9780078740503 | Authors: Roger Day ISBN: 9780078740503 157

Solution for problem 7 Chapter 9

Math Connects: Concepts, Skills, and Problem Solving Course 3 | 0th Edition

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Math Connects: Concepts, Skills, and Problem Solving Course 3 | 0th Edition | ISBN: 9780078740503 | Authors: Roger Day

Math Connects: Concepts, Skills, and Problem Solving Course 3 | 0th Edition

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Problem 7

What is the value of the function f(x) = 3x - 1 when x = 2? A 3 B 5 C 6 D 8

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PRODUCTION and PERCEPTION of VOWELS: Part 1: Resonance Speech Sounds  Vowels: o Produced by relatively free air passage o Through the larynx and oral cavity o Nucleus of a syllable  Consonants: o One (or more) areas of vocal tract narrowed by some degree of constriction (partial or complete)  Three Sources of Speech Sounds 1. Nearly Periodic Complex Waves (fundamental frequency w/ harmonics on top of it) » Source = vocal fold vibration » All vowels, many consonants 2. Continuous Aperiodic Waves » Source = turbulent flow through a supraglottal constriction (noise) » Many consonants, such as /s/, /f/ 3. Transient Aperiodic Waves » Source = rapid pressure change » Some consonants such as /p/, /b/ Acoustic Theory of Speech Production AKA Source-Filter Theory » Assumptions: o What we hear coming out of someone’s mouth is the consequence of  The generation of a sound source  Filtering of that sound source via the vocal tract’s resonant properties o The source and filter (vocal tract) operate in a largely independent manner. o Different postures change the shape of the resonator. o Can use acoustic signal to gather info about vocal tract position/features. Spectral Characteristics of the Source  Sound from Larynx: Vibration rate determines fundamental frequency and harmonics Acoustic Characteristics of the Source:  IDEALIZED glottal volume velocity = volume of air flowing through the glottis as a function of time **better explained as a Triangular Wave  ACTUAL glottal volume velocity: o Speed and completeness of vocal fold closure affect roll-off. o In general, the low frequency harmonics dominate. Acoustic Theory of Speech Production  Vocal tract acts as a filter o is frequency dependent. o Certain frequencies of the source signal pass through the filter with greater amplitude than others. **Selected frequencies  Characteristics resonances  formants Vocal Tract Transfer Function: - Resonance characteristics of the vocal tract - Specifies the vowel - Example: Model the vocal tract like a uniform tube » “schwa” vowel Ə Rule: For a tube closed, at one end and open at the other, the natural resonant frequency = wavelength 4X the length of the tube. Tube Representation of Vocal Tract In the Model…  Glottis: ((with adducted vocal folds)) o Air particles vibrate LEAST effectively o Minimum velocity  o Maximum pressure o Node (meaning there’s minimum velocity + maximum pressure)  Lips: ((separated for vowel production)) o Air particles vibrate MOST effectively. o Maximum velocity  o Minimum pressure o Antinode  Some differences…  Vocal tract not a completely uniform cross-section  Oral cavity meets pharynx at 90 degree angle » Doesn’t matter acoustically Standing Wave Patterns  Rule: The vocal tract will resonate only at odd-numbered multiples of the lowest frequency.  Each resonant pattern is a standing wave = FORMANT Vowels - Supraglottal cavities are shaped by articulators - Formant values correspond roughly to articulatory postures. (will change the circumference of the tube)

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Chapter 9, Problem 7 is Solved
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Textbook: Math Connects: Concepts, Skills, and Problem Solving Course 3
Edition: 0
Author: Roger Day
ISBN: 9780078740503

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What is the value of the function f(x) = 3x - 1 when x = 2