## dryicegrl 4 years ago 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

1. him1618

is that v^0.16??

2. dryicegrl

yes

3. him1618

and is the apparent temp the wind chill W?

4. dryicegrl

yes

5. dryicegrl

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

6. him1618

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

7. him1618

got it??

8. 3pwood

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.

9. him1618

yeah hes right

10. dryicegrl

well yes i am suppose to use partial derivatives

11. him1618

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

12. dryicegrl

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

13. him1618

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

14. him1618

got it?

15. dryicegrl

yes

16. him1618

ok....good luck fr the others

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