In the vicinity of a bonfire the temperature T in C at a dis

In the vicinity of a bonfire the temperature T (in °C) at a distance of x meters from the center of the fire is given by T(x) = 500,000 x^2 + 400 . At what range distances from the fire\'s center is the temperature less than 330°C?

(Assume x is positive.Round your values to one decimal place. Enter your answer using Interval Notation.)

Solution

T(x) = 500,000 /(x^2 + 400)

T(x) < 330 deg

330 > 500,000/( x^2 + 400)

330x^2 + 132000 > 500,000

330x^2 >4868000

x^2 >14751.51

(x^2 - 14751.51) >0

we get x < -121.456 and x > 121.456

x shall be positive , so x > 121.456

Solution x > 121.5 metres