Answer to Question #304172 in Calculus for itz_perfect

Question #304172

A measure of how hot weather feels to an average person is the Apparent Temperature Index.

A model for this index is:


A = 0.885t − 22.4h + 1.20th − 0.544,


where A is the apparent temperature in degrees Celsius, t is the air temperature, and h is the

relative humidity in decimal form.

a) Find ∂A/∂t and ∂A/∂h when t = 300 and h = 0.80.


b) Which has a greater effect on A, air temperature or humidity? Explain.


1
Expert's answer
2022-03-02T13:10:28-0500

a)


A/t=0.885+1.20h\partial A/\partial t=0.885+1.20h

A/h=22.4+1.20t\partial A/\partial h=-22.4+1.20t

t=300,h=0.80t=300, h=0.80


A/t=0.885+1.20(0.80)=1.845\partial A/\partial t=0.885+1.20(0.80)=1.845

A/h=22.4+1.20(300)=337.6\partial A/\partial h=-22.4+1.20(300)=337.6

b)

Since A/h>A/t,|\partial A/\partial h|>|\partial A/\partial t|, then relative humidity has a a greater effect on A, than air temperature.




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