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?

Answer 1

5 feet

Explanation:

Answer 2

5 feet

Explanation:

The path traveled by a bottlenose dolphin as it jumps out of water is modeled by the equation,

`y=-0.4x^2+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`

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.

`10-x=-0.4x^2+3x`

`-0.4x^2+4x-10=0`

`x=(-4\pm√(4^2-4(-10)(-0.4)))/(2(-0.4))`

`x=5\text{ feet }`

`y=5\text{ feet }`

Hence, The beam hit dolphin at 5 feet.