Question

The wind-chill index is modeled by the function below where T is the temperature (°C) and v is the wind speed (km/h).
W = 13.12 + 0.6215T - 11.37v0.16 + 0.3965Tv0.16
When T = 13°C and v = 34 km/h, by how much would you expect the apparent temperature W to drop if the actual temperature decreases by 1°C? (Enter your answer to 1 decimal place.)
°C

What if the wind speed increases by 1 km/h?(Enter your answer to 2 decimal places.)
°C

Answer 1

is that v^0.16??

Answer 2

yes

Answer 3

and is the apparent temp the wind chill W?

Answer 4

yes

Answer 5

I was think I would have to find W with respect of T first, but I am not sure where the less 1 degree comes in

Answer 6

differentiate wrt T
dW/dT = 0.6215 + 0.3965 (v)^0.16
dW = [0.6215 + 0.3965 (v)^0.16] dT
dT=1
hence find dW

Answer 7

got it??

Answer 8

Depening on what class this is for, you may be supposed to do this with partial derivatives, but you can actually just plug in the given T and v, and compute an initial W, then change the T or v by the one unit as requested to get a final W, then just subtract to find the difference between W values.

Answer 9

yeah hes right

Answer 10

well yes i am suppose to use partial derivatives

Answer 11

then do as ive done....it should work...

Answer 12

I am....what about the dT=1 part?

Answer 13

dT is the change in actual temp, which is given to be 1 degree,

Answer 14

got it?

Answer 15

yes

Answer 16

ok....good luck fr the others