Relationship Between Celsius and Fahrenheit Scales:
The relationship between temperature changes on the Celsius scale (\( \Delta C \)) and the Fahrenheit scale (\( \Delta F \)) is given by:
\[ \Delta F = \Delta C \times 1.8 \]
Calculate the Change in Fahrenheit:
Given \( \Delta C = 40^\circ C \),
we can find \( \Delta F \) as follows:
\[ \Delta F = 40 \times 1.8 = 72^\circ F \]
Conclusion:
The increase in temperature on the Fahrenheit scale corresponding to a \( 40^\circ C \) increase is \( 72^\circ F \).
Let $ P_n = \alpha^n + \beta^n $, $ n \in \mathbb{N} $. If $ P_{10} = 123,\ P_9 = 76,\ P_8 = 47 $ and $ P_1 = 1 $, then the quadratic equation having roots $ \alpha $ and $ \frac{1}{\beta} $ is: