1) the height of the tunnel is maximum at point (0, 36)
2) the height of the tunnel is zero at points (6, 0) and (-6, 0)
What is an equation?
"It is a mathematical statement which consists of equal symbol between two algebraic expressions."
For given question,
The height of tunnel is given by an equation [tex]y=-x^{2}+36[/tex]
where x is the horizontal distance from the center of the opening of the tunnel.
We need to find the points where the height of the tunnel is maximum and where the height of the tunnel is zero feet.
When the height of the tunnel is zero feet, then the equation would be,
[tex]0=-x^{2}+36[/tex]
We solve above equation to find the value of x.
[tex]\Rightarrow -x^{2}+36=0\\\\\Rightarrow -x^2=-36\\\\\Rightarrow x^2=36\\\\\Rightarrow x=\pm 6[/tex]
This means the height of the tunnel is zero at points (6, 0) and (-6, 0)
The height of the tunnel is maximum, when x = 0.
so, the equation becomes,
[tex]y=0+36\\\\y=36~feet[/tex]
This means, the height of the tunnel is maximum at point (0, 36)
Therefore, 1) the height of the tunnel is maximum at point (0, 36)
2) the height of the tunnel is zero at points (6, 0) and (-6, 0)
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