The wind-chill index W is the perceived temperature when the actual temperature is T and the wind speed is v, so we can write W = f(T, v). Wind speed (km/h) 20 30 40 50 60 70 - 10 - 18 - 20 -21 - 22 -23 - 23 -15 -24 - 26 - 27 - 29 - 30 - 30 - 20 - 30 - 33 - 34 - 35 - 36 - 37 - 25 - 37 - 39 -41 -42 -43 -44 (a) Estimate the values of f(-15, 30) and fy(-15, 30). (Round your answers to two decimal places.) f(-15, 30) = ful-15, 30) = | What are the practical interpretations of these values? When the actual temperature is -15°C and the wind speed is 30 km/h, the apparent temperature rises vv by about X °C for every degree that the actual temperature rises. When the actual temperature is -15°C and the wind speed is 30 km/h, the apparent temperature decreases vv by about |× °C for every km/h that the wind speed increases. (b) In general, what can you say about the signs of aw/aT and aw/əv? For a fixed wind speed v, the values of the wind-chill index W increase vv as temperature T increases, so aw is positive For a fixed temperature T, the values of w decrease (or remain constant) as v increases is negative , so av v (c) What appears to be the value of the following limit? aw lim Actual temperature (3.)
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Given that the wind chill index W is the perceived temperature when actual temperature is T and wind speed is v and can be written as .
a)It is required to estimate and .
Use h=5 and obtain as,
Use h=5 and obtain as,
Thus, is approximately the average as,
Therefore, when actual temperature is and wind speed is 30 km/h the apparent temperature rises by for every degree that the actual temperature rises.
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