Question

In a small town, the use of coal (W in tons/per

Answer 1

Answer:

i)W = 2500 / T

ii)  W = 500 Tons

iii) grad W(10°) = - 25î

iv) The formulation is not practical

Step-by-step explanation:

i)  Write an equation describing the use of coal

As use of coal is inversely proportional to the average monthly temperature

if  W is use of coal in tons/per month then

W(t)  =   k / T              where k is a constant of proportionality and T is the average temperature in degrees. We have to determine k from given conditions

k  =  ??   we know that when   T  =  25°    W = 100 tons  the by subtitution

W = k/T           100  =  k /25       k  =  2500 Tons*degree

Then final equation is:

W = 2500 / T

ii) Find the amount of coal when T = 5 degrees

W = 2500 / 5

W = 500 Tons

iii)

The inverse proportionality implies that W will decrease as T increase.

The vector gradient of W function is:

grad W  = DW(t)/dt î  

grad W  = - 2500/T² î

Wich agrees with the fact that W is decreasing.

And when T = 100°

grad W(10°) =  - 2500/ 100 î      ⇒  grad W(10°) = - 25î

iv) When T =  0  The quantity of coal tends to infinite and the previous formulation is not practical