The beam of light hit the dolphin at the common point that is the solution of a system:
[tex] \left\{\begin{array}{l}
y=-0.4x^2+3x \\
x+y=10
\end{array}
\right. [/tex].
From the second equation express y: y=10-x and substitute it into the first equation:
[tex] 10-x=-0.4x^2+3x,\\ 10-x+0.4x^2-3x=0,\\ 0.4x^2-4x+10=0,\\ 4x^2-40x+100=0,\\ x^2-10x+25=0,\\ (x-5)^2=0,\\ x=5 [/tex].
Therefore, the horizontal distance in feet is x=5 ft and the height above water is y=10-5=5 ft.
Answer: the beam of light hit the dolphin at 5 ft above water
