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`