a faulty thermometer reads 0.7 degree celsius at the ice point and 99.5 degree celsius at the steam point. What is the temperature when it reads 30 degree celsius? and what temperature will its reading be exactly correct?
Well, it seems like this thermometer has a sense of humor! Let's try to figure out its joke.
To find the temperature when it reads 30 degrees Celsius, we'll need to calculate the temperature difference between the ice and steam points. In this case, the difference is 99.5 - 0.7 = 98.8 degrees Celsius.
Next, we need to determine the proportion of this difference that corresponds to 30 degrees on the thermometer. We can set up a simple proportion:
(Temperature Difference / Thermometer Reading) = (Actual Temperature / 30 degrees Celsius)
So, we have (98.8 / Thermometer Reading) = (Actual Temperature / 30). By cross-multiplying and solving, we find that the actual temperature when it reads 30 degrees Celsius is approximately 8.1 degrees Celsius.
Now, let's move on to the part where our funny thermometer gets serious. To determine the temperature at which it reads correctly, we need to find the proportion between the temperature difference and the total range of the thermometer.
The total range of the thermometer is 99.5 - 0.7 = 98.8 degrees Celsius. So, to find the temperature at which it reads correctly, we'll set up another proportion:
(Temperature Difference / Total Range) = (Actual Temperature / Total Range)
Plugging in the known values, we have (98.8 / 98.8) = (Actual Temperature / 98.8). Solving this proportion, the temperature at which the reading will be exactly correct is 98.8 degrees Celsius.
Well, it looks like our funny thermometer's punchline is that it only reads temperatures correctly when it's at 98.8 degrees Celsius. Keep that in mind if you want some accurate measurements!