Question

Yesterday's temperature at t hours past midnight was f(t)∘c . at noon the temperature was 20∘c . the first derivative, f′(t) , decreased all morning, reaching a low of 3∘c/hour at noon, then increased for the rest of the day. which of the following must be correct?

a) 3°C
b) 20°C
c) Cannot be determined
d) Insufficient information

Answer 1

When there is a 40.0°F decrease in temperature, the temperature decreases by approximately 4.444 degrees Celsius. Additionally, any change in temperature in Fahrenheit degrees is nine-fifths the change in Celsius degrees.

Step-by-step explanation:

The question asks about the decrease in temperature in degrees Celsius when there is a 40.0°F decrease in temperature. To convert Fahrenheit to Celsius, we use the formula: (°F - 32) * 5/9 = °C. Plugging in the values, we have: (40 - 32) * 5/9 = 4.444°C. Therefore, the temperature decreases by approximately 4.444 degrees Celsius.

The second part of the question asks to show that any change in temperature in Fahrenheit degrees is nine-fifths the change in Celsius degrees. Using the conversion formula mentioned earlier, we can see that a change of 1 degree Fahrenheit is equal to a change of 5/9 degrees Celsius. So, any change in Fahrenheit degrees is nine-fifths the change in Celsius degrees.