The path traveled by a bottlenose dolphin as it jumps out of water is modeled by the equation y = −0.4x2 + 3x, 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 x + y = 10, at what height from the water's surface will the beam of light hit the dolphin?

2.7 feet

3 feet

5 feet

5.6 feet

Question

The path traveled by a bottlenose dolphin as it jumps out of water is modeled by the equation y = −0.4x2 + 3x, 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 x + y = 10, at what height from the water's surface will the beam of light hit the dolphin?

2.7 feet

3 feet 

5 feet

5.6 feet

directrix · Answer

I think that this diagram goes with this problem.

directrix · Answer

I can't say for sure but I think you can find the height by solving these two equations simultaneously: x + y = 10 y = −0.4x^2 + 3x Solve the equations online here: http://www.wolframalpha.com/ Enter this in the search field: y = −0.4x^2 + 3x, x + y = 10 @317K