Sure, let's carefully work through this problem step-by-step.
### Given Data
1. The temperature measured by the faulty thermometer is [tex]\(28.2^\circ C\)[/tex].
2. The upper fixed point of the faulty thermometer is [tex]\(98.4^\circ C\)[/tex], whereas the correct upper fixed point for Celsius should be [tex]\(100^\circ C\)[/tex].
3. The lower fixed point of the faulty thermometer is [tex]\(1.2^\circ C\)[/tex], whereas the correct lower fixed point for Celsius should be [tex]\(0^\circ C\)[/tex].
### Steps to Find the Correct Temperature
1. Define the correct fixed point values:
- Correct upper fixed point: [tex]\(100^\circ C\)[/tex]
- Correct lower fixed point: [tex]\(0^\circ C\)[/tex]
2. Calculate the slope of the faulty thermometer:
[tex]\[
\text{slope} = \frac{\text{correct upper fixed point} - \text{correct lower fixed point}}{\text{faulty upper fixed point} - \text{faulty lower fixed point}}
\][/tex]
[tex]\[
\text{slope} = \frac{100 - 0}{98.4 - 1.2}
\][/tex]
3. Substitute the given values:
[tex]\[
\text{slope} = \frac{100}{98.4 - 1.2} = \frac{100}{97.2}
\][/tex]
4. Simplify the slope:
[tex]\[
\text{slope} \approx 1.02880658436214
\][/tex]
5. Calculate the correct temperature using the slope and the faulty temperature:
[tex]\[
\text{Correct temperature} = \text{slope} \times (\text{faulty temperature} - \text{faulty lower fixed point})
\][/tex]
[tex]\[
\text{Correct temperature} = 1.02880658436214 \times (28.2 - 1.2)
\][/tex]
[tex]\[
\text{Correct temperature} = 1.02880658436214 \times 27.0
\][/tex]
6. Perform the final calculation:
[tex]\[
\text{Correct temperature} \approx 27.77777777777778^\circ C
\][/tex]
### Conclusion
The correct temperature of the object is approximately [tex]\(27.78^\circ C\)[/tex].
