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uysha [10]
3 years ago
13

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 he

ight 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?

Mathematics
1 answer:
Tamiku [17]3 years ago
8 0

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,

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=\dfrac{-4\pm\sqrt{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.

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