Find the values of x that will make p=o

Question

The amount of a particular pollutant p from a power plant in the air above the plant depends on the wind speed x, among other things, with the relationship between p and x approximated by p=36-0.04x^2, with x in miles per hour. Find the values of x that will make p=o. What does p=0 mean in the application?

Answer 1

p=36-0.04x², so when p=0, 36-0.04x²=0, 0.04x²=36. Take the square root of each side: 0.2x=6, divide through by 0.2, x=6/0.2=30 mph. x=-30 mph also satisfies the equation because -30 and 30 squared is the same number 900. The sign is the direction of the wind, so the wind can be blowing either way, but at magnitude 30 mph the amount of pollutant is reduced to zero.