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, 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

Answer 1

We can find the answer by solving the two equations simultaneously.

equation 1: y = -0.4x^2 +3xequation 2: x + y = 10
We need to write equation to with y as the subject:equation 2: y = 10 - x

equation 1 = equation 2:
10 - x = -0.4x^2 + 3x0.4x^2 - 4x + 10 = 02x^2 - 20 + 50 = 0(2x - 10)(x - 5) = 0x = -10/2 or x = 5

But x >= 0 (the question says it's a height above the water), so x = 5

Substituting x = 5 into one of the equations:
y = 10 - x
y = 10 - 5
y = 5

So the answer is C

Answer 2

Answer:

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

$y=-0.4 x^2+3x$ (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

$x+y=10$  (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

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

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

$4x^2-40x+100=0$

$x^2-10 x+25=0$

$x^2-5x-5x+25=0$

$x(x-5)-5(x-5)=0$

$(x-5)(x-5)=0$

x-5=0 and x-5=0

x=5 and x=5

Then , substitute x=5 in equation y

Then we get

$y=-0.4(5)^2+3(5)$

$y=-10+15$

$y=5$

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

Option  C: 5 feet