A body cools in a surrounding which is at a constant temperature of ${\mathrm{\theta }}_0$. Assuming that it obeys Newton's law of cooling, its temperature $\mathrm{\theta }$ is plotted against time t. Tangents are drawn to the curve at the points A($\mathrm{\theta }$=$\mathrm{\theta }$₁) and B($\mathrm{\theta }$=$\mathrm{\theta }$₂). These tangents meet the time-axis at angles $\mathrm{\alpha }$₁ and $\mathrm{\alpha }$₂ as shown in the graph then:

1.  $\frac{\tan {\mathrm{\alpha }}_1}{\tan {\mathrm{\alpha }}_2}=\frac{{\mathrm{\theta }}_2}{{\mathrm{\theta }}_1}$

2.  $\frac{\tan {\mathrm{\alpha }}_1}{\tan {\mathrm{\alpha }}_2}=\frac{{\mathrm{\theta }}_1}{{\mathrm{\theta }}_2}$

3.  $\frac{\tan {\mathrm{\alpha }}_1}{\tan {\mathrm{\alpha }}_2}=\frac{{\mathrm{\theta }}_1-{\mathrm{\theta }}_0}{{\mathrm{\theta }}_2-{\mathrm{\theta }}_0}$

4.  $\frac{\tan {\mathrm{\alpha }}_1}{\tan {\mathrm{\alpha }}_2}=\frac{{\mathrm{\theta }}_2-{\mathrm{\theta }}_0}{{\mathrm{\theta }}_1-{\mathrm{\theta }}_0}$