Question

La temperatura a una distancia r del centro de una lámina está dada por T=40 (r2?2r) . La variación instantánea de la temperatura respecto a r está dada por:

Answer 1

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:

$T = 40 (r ^ 2 + 2r)$

Way 2:

$T = 40 (r ^ 2-2r)$

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:

$\frac {dT} {dr} = 40 \frac {d ((r ^ 2 + 2r))} {dr}$

$\frac {dT} {dr} = 40 (2r + 2)$

Rewriting

$\frac {dT} {dr} = 80r + 80$

For function 2:

$\frac {dT} {dr} = 40 \frac {d ((r ^ 2-2r))} {dr}$

$\frac {dT} {dr} = 40 (2r-2)$

Rewriting

$\frac {dT} {dr} = 80r-80$

Answer:

The instantaneous variation of the temperature with respect to r is given by:

Assuming function 1:

$\frac {dT} {dr} = 80r + 80$

Assuming Function 2:

$\frac {dT} {dr} = 80r-80$