The temperature T at a distance, d meters from a heat source is inversely proportional to the square of the distance. When d=4 t=275 how do you find t when d=6?

Feb 23, 2018

$T = 122. \overline{2}$

Explanation:

$\text{the initial statement is } T \propto \frac{1}{d} ^ 2$

$\text{to convert to an equation multiply by k the constant}$
$\text{of variation}$

$\Rightarrow T = k \times \frac{1}{d} ^ 2 = \frac{k}{d} ^ 2$

$\text{to find k use the given condition}$

$\text{when } d = 4 , T = 275$

$T = \frac{k}{d} ^ 2 \Rightarrow k = T \times {d}^{2} = 275 \times 16 = 4400$

$\text{equation is } \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{T = \frac{4400}{d} ^ 2} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{when "d=6" then}$

$T = \frac{4400}{36} = 122. \overline{2}$