# Question 3) A truck carrying a wide load is 4.8m high and 3.9m wide. What is the question of the truck's roofline? Question 4) Calculate the points intersection of the equation of tunnel (y =...

Question 3) A truck carrying a wide load is 4.8m high and 3.9m wide. What is the question of the truck's roofline?

Question 4) Calculate the points intersection of the equation of tunnel (y = (-16/18)x^2 + 8) and the equation of the truck (answer of question 3)

Question 5) Will the truck pass through the tunnel? Explain the answer.

Question 6) What is the maximum width of a truck 4.8m high, that can pass through the tunnel?

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### 1 Answer

A truck carrying a wide load is 4.8m high and 3.9m wide. The equation of the line along the roof line of the truck is that of a horizontal line and is given by the equation y = 3.9.

The truck passes through a tunnel which has a shape that can be described by the equation `y = (-16/18)x^2 + 8` . The points of intersection of the roof line and the tunnel can be determined by solving the equation:

`3.9 = (-16/18)x^2 + 8`

`-4.1 = (-16/18)*x^2`

`x = +-sqrt(4.1*(18/16))`

`x = +- sqrt 4.6125`

This gives the points of intersection as `(+sqrt 4.6125,3.9)` and `(-sqrt4.6125,3.9)`

The width of the load is 4.8 m. This will not pass through the tunnel.

The maximum width of the load that can pass through the tunnel is equal to `2*sqrt(4.6125) ~~ 4.295` m