Question

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 1

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:

$|f(x)| \leq a$

Which has solution:

$-a \leq f(x) \leq a$

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:

$|D - 6.5| \leq 0.04$

Applying the solution:

$-0.04 \leq D - 6.5 \leq 0.04$

$-0.04 \leq D - 6.5$

$D - 6.5 \geq -0.04$

$D \geq 6.46$

$\leq D - 6.5 \leq 0.04$

$D \leq 6.54$

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

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