Problem 1: (2 points) The temperature-humidity index I (or humidex, for short) is the perceived air temperature when the actual temperature is T and the relative humidity is h, so we can write I = f(T, h). The fol- lowing table of values of I is an excerpt from a table compiled by the National Oceanic & Atmospheric Administration. Table 3 Apparent temperature as a function of temperature and humidity Relative humidity (%) Actual temperature (°F) h 20 30 40 50 60 70 T 80 77 78 79 81 82 83 85 82 84 86 88 90 93 90 87 90 93 96 100 106 95 93 96 101 107 114 124 100 99 104 110 120 132 144 (a) What is the value of f(95, 70)? What is its meaning? (b) For what value of h is f(90, h) = 100? (c) For what value of T is f(T, 50) = 88? (d) What are the meanings of the functions I = f(80, h) and I = f(100, h)? Compare the behavior of these two functions of h.
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We need to find the value of f(95, 70). From the table, we can see that when the temperature T is 95 and the relative humidity h is 70, the humidex value is 124. So, f(95, 70) = 124. Show more…
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Table 3 Apparent temperature as a function of temperature and humidity Relative humidity (%) h 20 30 40 50 60 70 T 80 77 78 79 81 82 83 85 82 84 86 88 90 93 90 87 90 93 96 100 106 95 93 96 101 107 114 124 100 99 104 110 120 132 144 (a) What is the value of f(95, 70)? What is its meaning? (b) For what value of h is f(90, h) = 100? (c) For what value of T is f(T, 50) = 88? (d) What are the meanings of the functions I = f(80, h) and I = f(100, h)? Compare the behavior of these two functions of h.
Adi S.
The temperature-humidity index I (or humidex, for short) is the perceived air temperature when the actual temperature is T and the relative humidity is h, so we can write I = f(T, h). The following table of values of I is an excerpt from a table compiled by the National Oceanic & Atmospheric Administration. Apparent temperature as a function of temperature and humidity Relative humidity (%) h 20 30 40 50 60 70 T 80 77 78 79 81 82 83 Actual temperature (F) 85 82 84 86 88 90 93 90 87 90 93 96 100 106 95 93 96 101 107 114 124 100 99 104 110 120 132 144 (a) What is the value of f(95, 70)? What is its meaning? From the table, f(95, 70) = , which means that when the actual temperature is 95°F and the relative humidity is 70%, the perceived air temperature is approximately °F. (b) For what value of h is f(80, h) = 78? % (c) For what value of T is f(T, 50) = 88? °F (d) What are the meanings of the functions I = f(80, h) and I = f(95, h)? Compare the behavior of these two functions of h. I = f(80, h) means that T is fixed at and h is allowed to vary, resulting in a function of h that gives the humidex values for different relative humidities when the actual temperature is °F. Similarly, I = f(95, h) is a function of one variable that gives the humidex values for different relative humidities when the actual temperature is °F. Looking at the rows of the table corresponding to T = 80 and T = 95, we see that f(80, h) ---Select--- at a relatively constant rate of approximately 1°F per 10% relative humidity, while f(95, h) ---Select--- more quickly (at first with an average rate of change of 3°F per 10% relative humidity) and at ---Select--- rate (approximately 10°F per 10% relative humidity for larger values of h).
Madhur L.
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