QuestionFind the max and min diameters of bolts with a target of $6.5 \mathrm{~mm}$ and tolerance of $0.04 \mathrm{~mm}$ .

Studdy Solution

STEP 1

Assumptions1. The desired diameter of the bolts is6.5 mm. . The tolerance is0.04 mm, which means the actual diameter can be0.04 mm more or less than the desired diameter.
3. We need to find the maximum and minimum diameters of the bolts that will pass inspection.

STEP 2

We can write an absolute value equation to represent the situation. The difference between the actual diameter and the desired diameter should be less than or equal to the tolerance.
|Actual\, diameter - Desired\, diameter| \leqolerance

STEP 3

Now, plug in the given values for the desired diameter and the tolerance to write the equation.
$|Actual\, diameter -6.5\, mm| \leq0.04\, mm$

STEP 4

The absolute value equation can be rewritten as a compound inequality. The actual diameter minus the desired diameter is between -0.04 mm and0.04 mm.
$-0.04\, mm \leq Actual\, diameter -6.\, mm \leq0.04\, mm$

STEP 5

Now, we can solve the compound inequality for the actual diameter. First, add.5 mm to all parts of the inequality.
$-0.04\, mm +.5\, mm \leq Actual\, diameter \leq0.04\, mm +.5\, mm$

STEP 6

Perform the addition to find the minimum and maximum diameters.
$6.46\, mm \leq Actual\, diameter \leq6.54\, mm$ The maximum and minimum diameters of bolts that will pass his inspection are6.54 mm and6.46 mm, respectively.

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