Answer :
To determine the rate of change in Fahrenheit for the increasing temperature of water, you can follow these steps:
1. Understand the Background: The formula for converting a temperature from Celsius (°C) to Fahrenheit (°F) is:
[tex]\[
F = \frac{9}{5}C + 32
\][/tex]
2. Identify the Given Information:
- The temperature of the water is increasing at a rate of 0.4 degrees Celsius per second.
3. Determine How Rates are Affected:
- Since we're interested in the rate of change from Celsius to Fahrenheit, focus on the conversion factor [tex]\(\frac{9}{5}\)[/tex] because the "+32" part of the formula doesn't affect changes in temperature (it's a constant offset).
4. Calculate the Rate of Change:
- Multiply the given rate of change in Celsius (0.4 degrees per second) by the conversion factor ([tex]\(\frac{9}{5}\)[/tex]):
[tex]\[
\text{Rate of change in Fahrenheit} = 0.4 \times \frac{9}{5} = 0.72
\][/tex]
5. Apply to Both Temperatures:
- Since the rate of change is constant, the starting temperature (whether it's 50°C or 75°C) doesn’t affect the rate at which the Fahrenheit temperature changes.
Thus, the rate of change in Fahrenheit is 0.72 degrees Fahrenheit per second for both starting temperatures of 50°C and 75°C.
1. Understand the Background: The formula for converting a temperature from Celsius (°C) to Fahrenheit (°F) is:
[tex]\[
F = \frac{9}{5}C + 32
\][/tex]
2. Identify the Given Information:
- The temperature of the water is increasing at a rate of 0.4 degrees Celsius per second.
3. Determine How Rates are Affected:
- Since we're interested in the rate of change from Celsius to Fahrenheit, focus on the conversion factor [tex]\(\frac{9}{5}\)[/tex] because the "+32" part of the formula doesn't affect changes in temperature (it's a constant offset).
4. Calculate the Rate of Change:
- Multiply the given rate of change in Celsius (0.4 degrees per second) by the conversion factor ([tex]\(\frac{9}{5}\)[/tex]):
[tex]\[
\text{Rate of change in Fahrenheit} = 0.4 \times \frac{9}{5} = 0.72
\][/tex]
5. Apply to Both Temperatures:
- Since the rate of change is constant, the starting temperature (whether it's 50°C or 75°C) doesn’t affect the rate at which the Fahrenheit temperature changes.
Thus, the rate of change in Fahrenheit is 0.72 degrees Fahrenheit per second for both starting temperatures of 50°C and 75°C.
