Question

A particular thermocouple measures the temperature during a chemical reaction. The accuracy of this thermocouple is $0.05^{\circ} \mathrm{C}$. For an experiment, the technician wants to keep the temperature at $22^{\circ} \mathrm{C}$. The acceptable temperature readings for this reaction will satisfy $$ |T-22| \leq 0.05 $$ where $T$ is the temperature reading in degrees Celsius. Find the acceptable temperature readings for this chemical reaction.

Name: Problem 46, Chapter 2: Intermediate Algebra: Connecting Concepts through Applications
Uploaded: 2022-03-15T00:05:47-08:00
Duration: 37 s
Channel: James Kiss

   A particular thermocouple measures the temperature during a chemical reaction. The accuracy of this thermocouple is $0.05^{\circ} \mathrm{C}$. For an experiment, the technician wants to keep the temperature at $22^{\circ} \mathrm{C}$. The acceptable temperature readings for this reaction will satisfy $$ |T-22| \leq 0.05 $$ where $T$ is the temperature reading in degrees Celsius. Find the acceptable temperature readings for this chemical reaction.

Intermediate Algebra: Connecting Concepts through Applications

Mark Clark; Cynthia… 2nd Edition

Chapter 2, Problem 46

Instant Answer

Solved by Expert James Kiss

03/15/2022

Step 1

The absolute value of $T - 22$ is less than or equal to $0.05$. This means that the temperature reading $T$ can be at most $0.05$ degrees Celsius above or below $22$ degrees Celsius. Show more…

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A particular thermocouple measures the temperature during a chemical reaction. The accuracy of this thermocouple is $0.05^{\circ} \mathrm{C}$. For an experiment, the technician wants to keep the temperature at $22^{\circ} \mathrm{C}$. The acceptable temperature readings for this reaction will satisfy $$ |T-22| \leq 0.05 $$ where $T$ is the temperature reading in degrees Celsius. Find the acceptable temperature readings for this chemical reaction.

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Key Concepts

Absolute Value Inequality

An absolute value inequality, such as |x - a| ? b, describes all values of x that are within a distance b from the central value a. This concept is fundamental in many areas of mathematics and science as it models scenarios where deviations from a target value are bounded by an acceptable limit.

Measurement Error Tolerance

Measurement error tolerance refers to the allowable deviation from a target or specified value when taking measurements. It represents the precision of an instrument and indicates the range within which the measured value can vary while still being considered accurate or acceptable.

Interval Notation

Interval notation is a mathematical representation used to describe a set of numbers lying between two endpoints. When solving inequalities, such as an absolute value inequality, the result is often expressed in interval notation to clearly define the continuous range of acceptable values.

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