If the temperature is increased by `1""^(@)C`, then the increase in Fahrenheit scale will be

Options

A. `(5)/(9)""^(@)F`
B. `(9)/(5)""^(@)F`
C. `(1)/(5)""^(@)F`
D. `(1)/(9)""^(@)F`

Explanation

To find the increase in the Fahrenheit scale when the temperature is increased by 1°C, we can follow these steps:

### Step 1: Understand the relationship between Celsius and Fahrenheit
The relationship between Celsius (°C) and Fahrenheit (°F) can be expressed with the formula:
\[ °F = \frac{9}{5} °C + 32 \]

### Step 2: Determine the change in Fahrenheit for a change in Celsius
When the temperature increases by 1°C, we want to find out how much this corresponds to in Fahrenheit. We can use the derivative of the Fahrenheit formula with respect to Celsius to find the rate of change.

### Step 3: Calculate the change
The change in Fahrenheit (Δ°F) for a change in Celsius (Δ°C) can be derived from the formula:
\[ \Delta °F = \frac{9}{5} \Delta °C \]
Substituting Δ°C = 1°C:
\[ \Delta °F = \frac{9}{5} \times 1 = \frac{9}{5} °F \]

### Step 4: Convert to decimal
Calculating \(\frac{9}{5}\):
\[ \frac{9}{5} = 1.8 \]
Thus, when the temperature increases by 1°C, the increase in Fahrenheit is:
\[ \Delta °F = 1.8°F \]

### Conclusion
Therefore, the increase in the Fahrenheit scale when the temperature is increased by 1°C is **1.8°F**.

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