During a musical an orchestra is playing. As the music plays, the volume changes in the beginning of the piece can be modeled by the equation s = 10│x - 4│+ 50 where s represents the sound level in decibels and x represents the number of measures of music played. At what number(s) measures played would the sound level be at 80 decibels?

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elcharly64 elcharly64 · Answer 1 · 2020-10-08T20:53:26+02:00

Answer:

The sound level would be at 80 decibels at 1 or 7 number of measures played

Step-by-step explanation:

Equations with Absolute Values

We have the function s to represent the sound level in decibels:

[tex]s = 10|x - 4|+ 50[/tex]

Where x is the number of measures of the music played.

We are required to find the value of x that makes s=80 decibels. We have to find the equation:

[tex]10|x - 4|+ 50 =80[/tex]

Subtracting 50:

[tex]10|x - 4| =80-50[/tex]

[tex]10|x - 4| =30[/tex]

Dividing by 10:

[tex]|x - 4| =30/10=3[/tex]

[tex]|x - 4| =3[/tex]

For the absolute value be equal to 3, its argument could be positive or negative:

[tex]x-4=3[/tex]

Or

[tex]x-4=-3[/tex]

This leads us to two solutions:

[tex]x=3+4=7[/tex]

x=7

Or

[tex]x-4=-3[/tex]

[tex]x=4-3=1[/tex]

x=1

The sound level would be at 80 decibels at 1 or 7 number of measures played