For this, the first thing to do is to assume that the function of temperature with respect to r is written in one of the following ways:
Way 1:
[tex]T = 40 (r ^ 2 + 2r)[/tex]
Way 2:
[tex]T = 40 (r ^ 2-2r)[/tex]
To find the instant variation we must find the derivative of the temperature with respect to the distance r.
We have then:
For function 1:
[tex]\frac {dT} {dr} = 40 \frac {d ((r ^ 2 + 2r))} {dr}\\[/tex]
[tex]\frac {dT} {dr} = 40 (2r + 2)[/tex]
Rewriting
[tex]\frac {dT} {dr} = 80r + 80[/tex]
For function 2:
[tex]\frac {dT} {dr} = 40 \frac {d ((r ^ 2-2r))} {dr}[/tex]
[tex]\frac {dT} {dr} = 40 (2r-2)[/tex]
Rewriting
[tex]\frac {dT} {dr} = 80r-80[/tex]
Answer:
The instantaneous variation of the temperature with respect to r is given by:
Assuming function 1:
[tex]\frac {dT} {dr} = 80r + 80[/tex]
Assuming Function 2:
[tex]\frac {dT} {dr} = 80r-80[/tex]
