The heat index combines air temperature with relative humidi

The heat index combines air temperature with relative humidity to give an idea as to how hot it \"feels\" outside, in much the same way that the wind chill index links cold temperatures and wind speed. The National Weather Service uses the following equation to determine the heat index: H/ =-42.379 + 2.0497, + 1 0.1 43R-0.225 TR-(6.838 x 10-yr-00548P + ( 1.229 x 10-3)TR + (8,528 x1o-)TR2-(1 .990 × 10-6)T2R2 where T is the air temperature in , and R is the relative humidity (ie, R = 55 if the relative umidity is 55%). The equation is valid only for air temperatures above 80° F and relative humidities above 40%.

Solution

25)

T=85=HI

R=?

Substitute in the equation given

85 = -42.379+2.049(85)+10.143R-0.225(85)R-6.838x10^-3(85)²-0.0548R²+1.229(10^-3)85²R+(8.528x10^-4)85R²-1.990x10^-6(85²)R²

Simplify to get

85 = 82.381-R(-0.102)+R²(0.003)

Or 3R² +102R -2619 =0

R = 17.088 or -51.088

But R is valid only for humidities above 40%

Hence no valid solution for R