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2 months ago

Which of the following ranges depicts the 2% tolerance range to the full 9 digits provided?

Engineering

1 answer:

Mrrafil [318]2 months ago

4 0

Answer:

Only option C fulfills the criteria.

Explanation:

A quantity's tolerance defines the allowable range of variation for that quantity.

To calculate this, we need to know the magnitude, with the closest value being the average. This average may be provided or can be found using the formula

x_average = ∑ $x_{i}$ / n

The error or tolerance is determined by comparing the current value with the average expressed as a percentage

Δx₁ = x₁ / x_average

tolerance = | 100 - Δx₁ 100 |

where bars denote absolute values

Let’s compute these values for each option.

x_average = (2.1700000 + 2.258571429) / 2

x_average = 2.2142857145

For x₁, we compute the fluctuation

Δx₁ = 2.17000 / 2.2142857145

Tolerance = 100 - 97.999999991

Tolerance = 2.000000001%

For x₂, we analyze the fluctuation

Δx₂ = 2.258571429 / 2.2142857145

Δx₂ = 1.02

tolerance = 100 - 102.000000009

tolerance = 2.000000001%

x_average = (2.2 + 2.29) / 2

x_average = 2.245

For x₁, we evaluate fluctuation

Δx₁ = 2.2 / 2.245

Δx₁ = 0.9799554

tolerance = 100 - 97.999

Tolerance = 2.00446%

For x₂, we measure fluctuation

Δx₂ = 2.29 / 2.245

Δx₂ = 1.0200445

Tolerance = 2.00445%

x_average = (2.211445 + 2.3) / 2

x_average = 2.2557225

Δx₁ = 2.211445 / 2.2557225 = 0.9803710

tolerance = 100 - 98.0371

tolerance = 1.96%

Δx₂ = 2.3 / 2.2557225 = 1.024624

tolerance = 100 - 101.962896

tolerance = 1.96%

x_average = (2.20144927 + 2.29130435) / 2

x_average = 2.24637681

Δx₁ = 2.20144927 / 2.24637681 = 0.98000043

tolerance = 100 - 98.000043

tolerance = 2.000002%

Δx₂ = 2.29130435 / 2.24637681 = 1.0200000017

tolerance = 2.0000002%

x_average = (2 + 2.3) / 2

x_average = 2.15

Δx₁ = 2 / 2.15 = 0.93023

tolerance = 100 - 93.023

tolerance = 6.98%

Δx₂ = 2.3 / 2.15 = 1.0698

tolerance = 6.97%

Examining these outcomes, it is evident that result E does not fall within the specified tolerance range, while the remaining values could align with the desired tolerance based on the required degree of precision. Thus, under stringent precision requirements, option C stands out as the only choice that meets the criteria.

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