Answer :
To solve the problem using the equation [tex]\( F = \frac{9}{5} C + 32 \)[/tex], where [tex]\( F \)[/tex] is the temperature in Fahrenheit and [tex]\( C \)[/tex] is the temperature in Celsius, we'll convert each given Celsius temperature to Fahrenheit. Let's go through each calculation step-by-step:
1. Convert 20°C to Fahrenheit:
- Start with the formula: [tex]\( F = \frac{9}{5} C + 32 \)[/tex]
- Substitute [tex]\( C = 20 \)[/tex]:
[tex]\[
F = \frac{9}{5} \times 20 + 32
\][/tex]
- Calculate the multiplication: [tex]\( \frac{9}{5} \times 20 = 36 \)[/tex]
- Add 32: [tex]\( 36 + 32 = 68 \)[/tex]
- So, 20°C is 68°F.
2. Convert 4°C to Fahrenheit:
- Start with the formula: [tex]\( F = \frac{9}{5} C + 32 \)[/tex]
- Substitute [tex]\( C = 4 \)[/tex]:
[tex]\[
F = \frac{9}{5} \times 4 + 32
\][/tex]
- Calculate the multiplication: [tex]\( \frac{9}{5} \times 4 = 7.2 \)[/tex]
- Add 32: [tex]\( 7.2 + 32 = 39.2 \)[/tex]
- So, 4°C is 39.2°F.
3. Convert 175°C to Fahrenheit:
- Start with the formula: [tex]\( F = \frac{9}{5} C + 32 \)[/tex]
- Substitute [tex]\( C = 175 \)[/tex]:
[tex]\[
F = \frac{9}{5} \times 175 + 32
\][/tex]
- Calculate the multiplication: [tex]\( \frac{9}{5} \times 175 = 315 \)[/tex]
- Add 32: [tex]\( 315 + 32 = 347 \)[/tex]
- So, 175°C is 347°F.
Conclusion on Proportionality:
The mathematical relationship given by the equation [tex]\( F = \frac{9}{5} C + 32 \)[/tex] is not proportional because it does not pass through the origin (0,0). It is a linear relationship with a non-zero y-intercept, specifically 32. Therefore, while the relationship is linear, it is not proportional.
Here are the temperatures converted:
- 20°C is 68°F.
- 4°C is 39.2°F.
- 175°C is 347°F.
1. Convert 20°C to Fahrenheit:
- Start with the formula: [tex]\( F = \frac{9}{5} C + 32 \)[/tex]
- Substitute [tex]\( C = 20 \)[/tex]:
[tex]\[
F = \frac{9}{5} \times 20 + 32
\][/tex]
- Calculate the multiplication: [tex]\( \frac{9}{5} \times 20 = 36 \)[/tex]
- Add 32: [tex]\( 36 + 32 = 68 \)[/tex]
- So, 20°C is 68°F.
2. Convert 4°C to Fahrenheit:
- Start with the formula: [tex]\( F = \frac{9}{5} C + 32 \)[/tex]
- Substitute [tex]\( C = 4 \)[/tex]:
[tex]\[
F = \frac{9}{5} \times 4 + 32
\][/tex]
- Calculate the multiplication: [tex]\( \frac{9}{5} \times 4 = 7.2 \)[/tex]
- Add 32: [tex]\( 7.2 + 32 = 39.2 \)[/tex]
- So, 4°C is 39.2°F.
3. Convert 175°C to Fahrenheit:
- Start with the formula: [tex]\( F = \frac{9}{5} C + 32 \)[/tex]
- Substitute [tex]\( C = 175 \)[/tex]:
[tex]\[
F = \frac{9}{5} \times 175 + 32
\][/tex]
- Calculate the multiplication: [tex]\( \frac{9}{5} \times 175 = 315 \)[/tex]
- Add 32: [tex]\( 315 + 32 = 347 \)[/tex]
- So, 175°C is 347°F.
Conclusion on Proportionality:
The mathematical relationship given by the equation [tex]\( F = \frac{9}{5} C + 32 \)[/tex] is not proportional because it does not pass through the origin (0,0). It is a linear relationship with a non-zero y-intercept, specifically 32. Therefore, while the relationship is linear, it is not proportional.
Here are the temperatures converted:
- 20°C is 68°F.
- 4°C is 39.2°F.
- 175°C is 347°F.
