Clouds and Temperature As the altitude increases, both the air temperature and the dew poi...

Clouds and Temperature As the altitude increases, both the air temperature and the dew point decrease. As long as the air temperature is greater than the dew point, clouds will not form. Typically, the air temperature T cools at 19°F for the 1-mile increase in altitude and the dew point D decreases by 5.8°F for the 1-mile increase in altitude. (Source: A. Miller and R. Anthes, Meteorology.)

(a) Suppose the air temperature at ground level is 65°F. Write a formula for a linear function T that gives the air temperature at x miles high.

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(b) Suppose the dew point at ground level is 50°F. Write a formula for a linear function D that gives the dew point at x miles high.

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(c) Determine symbolically altitudes where clouds will not form.

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(d) Solve part (c) graphically.