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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. Explain in words each step to find the following question:



At what number(s) measures played would the sound level be at 80 decibels?

Respuesta :

MrRoyal

Answer:

The numbers of measure of music played are 1 and 7

Step-by-step explanation:

Given

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

Required

Solve for x when s = 80

Substitute 80 for x

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

Subtract 50 from both sides

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

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

Divide through by 10

[tex]\frac{30}{10}= \frac{10|x - 4| }{10}[/tex]

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

Reorder

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

This can be split into

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

Solve for x

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

[tex]x = 7[/tex] or [tex]x = 1[/tex]

Hence:

The numbers of measure of music played are 1 and 7

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