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The formula for wind chill C (in degrees Fahrenheit) is given by C = 35.74 + 0.6215T − 35.75v0.16 + 0.4275Tv0.16 where v is the wind speed in miles per hour and T is the temperature in degrees Fahrenheit. The wind speed is 21 ± 3 miles per hour and the temperature is 8° ± 3°. Use dC to estimate the maximum possible propagated error (round your answer to four decimal places) and relative error in calculating the wind chill (round your answer to two decimal places).† dC = __________. ° dC/ C =_________

User Mruf
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2 Answers

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Final answer:

The provided question's information is insufficient to calculate the propagated error (dC) or relative error (dC/C) in the wind chill calculation without additional data or assumptions. However, for a temperature drop of 40.0 Fahrenheit degrees, the corresponding decrease in Celsius is 4.4444°C.

Step-by-step explanation:

Estimation of Propagated Error in Wind Chill Calculation

To estimate the maximum possible propagated error and relative error in calculating the wind chill, we need to use the given formula for wind chill C and the rules for propagation of uncertainty. The wind chill formula is repeated as follows: C = 35.74 + 0.6215T − 35.75v^0.16 + 0.4275Tv^0.16, where v is the wind speed in miles per hour and T is the temperature in degrees Fahrenheit. The uncertainty in wind speed is ± 3 mph, and the uncertainty in temperature is ± 3°F.

To find dC, the error in the wind chill, we partially differentiate the wind chill formula with respect to T and v and then use the uncertainties in them. However, the question doesn't provide enough information to conduct this differentiation, and hence we cannot calculate dC or the relative error dC/C without additional information or assumptions.

Wind chill factors serve as a reminder of convection's efficiency at transferring heat compared to conduction. For example, the wind chill effect makes 0°C air flying at 15.0 m/s feel as cold as still air at about -18°C.

For the temperature conversion, a temperature drop of 40.0 Fahrenheit degrees implies a drop in Celsius degrees which can be calculated using the formula below:

ΔC = (ΔF - 32) × 5/9

Applying the formula to a 40.0 Fahrenheit degree drop:

ΔC = (40.0 - 32) × 5/9

ΔC = 4.4444 Celsius degrees (rounded to four decimal places)

User Mclaughj
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Answer: dC = 2.6379

C = - 11.912

Relative error = 22.14%

Step-by-step explanation:

Please find the attached file for the solution

The formula for wind chill C (in degrees Fahrenheit) is given by C = 35.74 + 0.6215T-example-1
User Cocoapriest
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