Water from a hose is sprayed on a fire burning at a height of 10 m up the side of a wall. If the function h(x) = -0.15t^2 + 3x, where x is the horizontal distance from the fire, in metres, models the height of the water, h(x), also in metres. How far back does the firefighter have to stand in order to put out the fire?PLEASE ANSWER ASAP WILL GIVE BRAINLIEST

Accepted Solution

Answer:   4.2 or 15.8 metresStep-by-step explanation:We assume your model for the height of the water stream is supposed to be ...   h(x) = -0.15x^2 +3xThis will have a value of 10 when ...   -0.15x^2 +3x = 10   .15x^2 -3x +10 = 0 . . . . . subtract the left side to get standard formFor a quadratic equation of the form ...   ax² +bx +c = 0The solutions are given by the "quadratic formula:"[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]The above equation matches the template with a=0.15, b=-3, c=10. Putting these values into the formula gives ...[tex]x=\dfrac{-(-3)\pm\sqrt{(-3)^2-4\cdot 0.15\cdot 10}}{2\cdot 0.15}=\dfrac{3\pm\sqrt{3}}{0.3}\\\\x=10\pm\dfrac{10}{3}\sqrt{3}[/tex]   x ≈ 4.2 or 15.8The firefighter can stand at 4.2 metres or 15.8 metres from the fire to get the water to arrive at the building 10 metres up.