Answer:
4.2 or 15.8 metres
Step-by-step explanation:
We assume your model for the height of the water stream is supposed to be ...
h(x) = -0.15x^2 +3x
This will have a value of 10 when ...
-0.15x^2 +3x = 10
.15x^2 -3x +10 = 0 . . . . . subtract the left side to get standard form
For a quadratic equation of the form ...
ax² +bx +c = 0
The 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 15.8
The 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.
