Answer
$x\gt 35.59$ meters
Work Step by Step
$T(x)=\frac{500,000}{x^2+400}$,
To solve for a range of distance at which the Temperature is less than 300 degrees Celsius.
$\frac{500,000}{x^2+400}\lt 300$, Multiply both sides by $x^2+400$.
$500,000\lt 300x^2+120,000$, Substracting $120,000$ from both sides.
$380,000\lt 300x^2$, dividing both sides by $300$ to Isolate the $x^2$.
$1266.67 \lt x^2$, Taking the square root of both sides.
$x\gt 35.59$.
Thus, The range of distance at which the Temperature is less than $300$ degrees Celsius is a distance of $x\gt 35.59$ meters.
