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, the beam of light will hit the dolphin at what height from the surface of the water?

a.) 2.7 feet
b.) 3 feet
c.) 5 feet
d.) 5.6 feet

C.5 feet

Step-by-step explanation:

We are given that path traveled by a bottlenose  dolphin it jumps out of water is modeled by the equation

(Equation I)

Where y is the height above water  and x is the horizontal distance in feet

If  a beam of light is shown upward at angle modeled by the equation

 (Equation II)

We have to find the height of dolphin from the surface of the water when the beam of light will hit the dolphin

Substitute the value of y in equation II

Then we get

x-5=0 and x-5=0

x=5 and x=5

Then , substitute x=5 in equation y

Then we get

Hence, the height of dolphin from the surface of water when the beam of light hit the dolphin=5 feet

Option  C: 5 feet

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