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Two boats depart from a port located at (–10, 0) in a coordinate system measured in kilometers, and they travel in a positive x-direction. the first boat follows a path that can be modeled by a quadratic function with a vertex at (0, 5), and the second boat follows a path that can be modeled by a linear function and passes through the point (10, 4). at what point, besides the common starting location of the port, do the paths of the two boats cross? (–6, 0.8) (–6, 3.2) (6, 3.2) (6, 0.8)

Respuesta :

CastleRook
To get the points at which the two boats meet we need to find the equations that model their movement:
Boat A:
vertex form of the equation is given by:
f(x)=a(x-h)^2+k
where:
(h,k) is the vertex, thus plugging our values we shall have:
f(x)=a(x-0)^2+5
f(x)=ax^2+5
when x=-10, y=0 thus
0=100a+5
a=-1/20
thus the equation is:
f(x)=-1/20x^2+5

Boat B
slope=(4-0)/(10+10)=4/20=1/5

thus the equation is:
1/5(x-10)=y-4
y=1/5x+2

thus the points where they met will be at:
1/5x+2=-1/20x^2+5
solving for x we get:
x=-10 or x=6
when x=-10, y=0
when x=6, y=3.2
Answer is (6,3.2)

The answer is C. (6,3.2) on Edg ;))

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