Question 1127352
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Make a graph of the tunnel with the origin at road level in the middle of the tunnel.  That makes the vertex the top of the tunnel, at (0,10); with the width of the tunnel being 20m, the edges of the tunnel at road level are at (-10,0) and (10,0).<br>
The equation of a parabola with vertex at (0,10) is<br>
{{{y = ax^2+10}}}<br>
To find the value of the constant a, use either edge of the tunnel at road level.<br>
{{{0 = a(10^2)+10}}}
{{{0 = 100a+10}}}
{{{100a = -10}}}
{{{a = -1/10}}}<br>
The equation of the parabola is<br>
{{{y = (-1/10)x^2+10}}}<br>
We want to know the value of x when the y value (the height of the truck) is 190cm = 1.9m.<br>
{{{1.9 = (-1/10)x^2+10}}}
{{{(1/10)x^2 = 10-1.9 = 8.1}}}
{{{x^2 = 81}}}
{{{x = 9}}}<br>
The truck can pass through the tunnel 9m from the center of the tunnel.<br>
The problem asks for the minimum distance from the edge of the tunnel that the truck can pass through; 9m from the center is 1m from the edge.<br>
ANSWER: The truck can pass through the tunnel 1m from the edge<br>
A graph....  Green line is the 1.9m height of the truck, showing that it can fit through the tunnel 9m from the center of the tunnel, which is 1m from the edge of the tunnel.<br>
{{{graph(400,200,-12,12,-2,12,(-1/10)x^2+10,1.9)}}}