Answer:
5 feet
Step-by-step explanation:
The path traveled by a bottlenose dolphin as it jumps out of water is modeled by the equation,
[tex]y=-0.4x^2+3x[/tex]
where y is the height above water and x is the horizontal distance in feet.
If a beam of light is shone upward at an angle modeled by the equation
[tex]x+y=10[/tex]
A beam of light hit the dolphin.
So, line must be intersect path of dolphin.
Using substation method,
Substitute y=10-x into dolphin equation.
[tex]10-x=-0.4x^2+3x[/tex]
[tex]-0.4x^2+4x-10=0[/tex]
[tex]x=\dfrac{-4\pm\sqrt{4^2-4(-10)(-0.4)}}{2(-0.4)}[/tex]
[tex]x=5\text{ feet }[/tex]
[tex]y=5\text{ feet }[/tex]
Hence, The beam hit dolphin at 5 feet.
