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STRUCTURE A quality control inspector at a bolt factory examines random bolts that come off the assembly line. All bolts being made must be a tolerance of 0.04 mm. The inspector is examining bolts that are to have a diameter of 6.5 mm.

Answer :

From an absolute value inequality, we have that:

  • The minimum diameter is 6.46 mm.
  • The maximum diameter is 6.54 mm.

  • The absolute value measures the distance of a point or a function to the origin.
  • One example of inequality is:

[tex]|f(x)| \leq a[/tex]

Which has solution:

[tex]-a \leq f(x) \leq a[/tex]

In this problem:

  • Bolts with a diameter of 6.5 mm, with a tolerance of 0.04 mm, thus the absolute value of the difference of the diameter D and 6.5 has to be of at most 0.04, that is:

[tex]|D - 6.5| \leq 0.04[/tex]

Applying the solution:

[tex]-0.04 \leq D - 6.5 \leq 0.04[/tex]

[tex]-0.04 \leq D - 6.5[/tex]

[tex]D - 6.5 \geq -0.04[/tex]

[tex]D \geq 6.46[/tex]

[tex]\leq D - 6.5 \leq 0.04[/tex]

[tex]D \leq 6.54[/tex]

  • The minimum diameter is 6.46 mm.
  • The maximum diameter is 6.54 mm.

A similar problem is given at https://brainly.com/question/24835634

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