The wind-chill index W is the perceived temperature when the actual temperature is T and the wind speed is v, so we can write W = f(T, v). Estimate the values of fT(−15, 50) and fv(−15, 50).

V 20 30 40 50 60 70

T
−10 −18 −20 −21 −22 −23 −23
−15 −25 −26 −27 −29 −30 −30
−20 −30 −33 −34 −35 −36 −37
−25 −37 −39 −41 −42 −43 −44

value of Ft(-15,50) = 1.3

Value of Fv(-15,50) = -0.15

Step-by-step explanation:

W = perceived temperature

T = actual temperature

W = f( T,V)

Estimate the values of  ft ( -15,50) and  fv(-15,50)

calculate the Linear approximation of   f at(-15,50)

(-15,50) =  

from the table take h = 5, -5

 =

= 1.4

therefore the average value of

This means that when the Temperature is -15⁰c and the 40 km/h the  value of Ft (-15,40) = 1.3

calculate the linear approximation of

from the table take h = 10, -10

 =

 =  = -0.1

therefore the average value of

This means that when the temperature = -15⁰c and the wind speed is 40 km/h the temperature will decrease by 0.15⁰c

w = f(T,v)

   = -27 + 1.3(T+15) - 0.15(v-40)

   = -27 + 1.3T + 19.5 - 0.15v + 6

   = 1.3T - 0.15v -1.5  

calculate the linear approximation

 = -0.15