The Farensheit and the centrigrade scales have the same numerical value at a temperature of

Options

A. `-30^(@)`
B. `-40^(@)`
C. `-100^(@)`
D. `-273^(@)C `

Answer

To find the temperature at which the Fahrenheit and Celsius scales have the same numerical value, we can use the relationship between the two temperature scales. The formula to convert Celsius (Tc) to Fahrenheit (Tf) is given by:

\[ Tf = \frac{9}{5} Tc + 32 \]

We need to find the temperature where \( Tf = Tc \). Let's denote this common temperature as \( T \). Therefore, we can set up the equation:

\[ T = \frac{9}{5} T + 32 \]

Now, we will solve for \( T \):

1. **Rearranging the equation**:
\[ T - \frac{9}{5} T = 32 \]

2. **Finding a common denominator**:
To combine the terms on the left side, we can express \( T \) as \( \frac{5}{5} T \):
\[ \frac{5}{5} T - \frac{9}{5} T = 32 \]
\[ \frac{5T - 9T}{5} = 32 \]

3. **Simplifying the left side**:
\[ \frac{-4T}{5} = 32 \]

4. **Multiplying both sides by -5** to eliminate the fraction:
\[ -4T = 32 \times -5 \]
\[ -4T = -160 \]

5. **Dividing both sides by -4**:
\[ T = \frac{-160}{-4} \]
\[ T = 40 \]

6. **Final result**:
\[ T = -40 \]

Thus, the temperature at which the Fahrenheit and Celsius scales have the same numerical value is:

**Answer: -40 degrees**