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As One Approaches a Certain Sound Source, the Sound Intensity F(x)=2(x3)2+3(x3)92(x3)+30F ( x ) = - \frac { 2 ( x - 3 ) ^ { 2 } + 3 ( x - 3 ) - 9 } { 2 ( x - 3 ) + 30 }

question 342

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As one approaches a certain sound source, the sound intensity in arbitrary units increases according to the following function of time: F(x) =2(x3) 2+3(x3) 92(x3) +30F ( x ) = - \frac { 2 ( x - 3 ) ^ { 2 } + 3 ( x - 3 ) - 9 } { 2 ( x - 3 ) + 30 } . Starting at x=0x = 0 , when the source of sound is first sensed, how much time elapses until maximum sound intensity is felt? Round the result to the nearest hundredth.

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Definitions:

Myringoscope

An instrument used for examining the eardrum or tympanic membrane.

Otosclerosis

A condition in which abnormal bone growth around the stapes bone leads to hearing loss.

Labyrinthitis

An inner ear disorder that causes inflammation of the labyrinth, leading to vertigo and hearing loss.

Acoustic

Pertaining to sound or the science of sound, especially its production, transmission, and effects.

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