SOLUTION: 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 temperatu

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Question 1074911: 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:
HI=-42.379 + 2.049T + 10.143R - 0.225TR - (6.838 x 10^-3)T^2 - 0.0548R^2 + (1.229 x 10^-3)T^2R + (8.528 x 10^-4)TR^2 - (1.990 x 10^-6)T^2R^2
where T is the air temperature in degrees Fahrenheit and R is the relative humidity (i.e R=55 if the relative humidity is 55%) the equation is valid only for air temperatures above 80 degrees Fahrenheit and a relative humidity above 40%
1. Write an equation that gives the heat index HI for any temperature T given a relative humidity of 100%. Round your coefficients to three decimal places.
2. On a warm day both the air temperature and the heat index are 85 degrees Fahrenheit. what is the relative humidity? Round any coefficients to three decimal places and give your answer to the nearest percent.
(I know its a lot but I'm stuck and need help thanks)
Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
HI=-42.379 + 2.049T + 10.143*100 - 0.225T*100 - (6.838 x 10^-3)T^2 - 0.0548*10000 + (1.229 x 10^-3)T^2*100 + (8.528 x 10^-4)T*10000- (1.990 x 10^-6)T^2*10000
HI=-42.379 + 2.049T + 1014.3 - ,22.5T - (6.838 x 10^-3)T^2 -548+ (1.229 x 10^-1)T^2 + 8.528T- (1.990 x 10^-2)T^2.
85=-42.379+174.165+10.143R-19.125R-49.406-0.055R^2+8.880R+0.072R^2-0.014R^2
85=82.38+0.003R^2-0.182R
0.003R^2-0.182R-2.62=0
quadratic formula
denominator is 0.006
0.182+/- sqrt (0.033124+4(0.003)(2.62); sqrt term is 0.03144, and root is 0.1773
0.182+/-0.1773 is 0.359 no negative root used
divide by 0.006 to get 59.83% or 60%.