SOLUTION: A bridge is the shape of a parabola. It is 10 m wide and the highest point of the bridge is 6m above ground. A transport truck is 4.5 m tal and 3 m wide. The road is centered on th
Question 203530: A bridge is the shape of a parabola. It is 10 m wide and the highest point of the bridge is 6m above ground. A transport truck is 4.5 m tal and 3 m wide. The road is centered on the axis of symmetry and the transport truck must stay on its own side of the road. Will the trick fit under the bridge? Justify your decision. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A bridge is the shape of a parabola. It is 10 m wide and the highest point of
the bridge is 6m above ground. A transport truck is 4.5 m tal and 3 m wide.
The road is centered on the axis of symmetry and the transport truck must stay
on its own side of the road. Will the truck fit under the bridge?
Justify your decision.
:
Find the parabola equation using the form ax^2 + bx = y
x = 5; y = 6
25a + 5b = 6
and
x = 10; y = 0
100a + 10b = 0
:
Multiply the 1st equation by 2 and subtract from th above equation
100a + 10b = 0
50a + 10b = 12
----------------
50a = -12
a =
a = -.24
;
Find b using 100a + 10b = 0
100(-.24) + 10b = 0
-24 + 10b = 0
10b = 24
b = 2.4
:
The equation y = -.24x^2 + 2.4x which we can plot:
Assuming the truck will be just at the right of the centerline,
a 3 m wide truck will be at x = 8>
Find the height of the parabola where x = 8
y = -.24(8^2) + 2.4(8)
y = -15.36 + 19.2
y = +3.84, so 4.5 is too high
