Josh wants to know the length of a tunnel built through a mountain. To do so, he makes the measurements shown in the figure below. Use these measurements to find the length of the tunnel.

Josh wants to know the length of a tunnel built through a mountain. To do so, he makes the measurements shown in the figure below. Use these measurements to find the length of the tunnel.85°267m132m?Carry your intermediate computations to at least four decimal places.Round your answer to the nearest tenth of a meter.meters CheckSave For LaterSubmit Assignment

The cross-sectional view of a tunnel is shown on the axes below. The line [AB] representsa vertical wall located at the left side of the tunnel. The height, in metres, of the tunnel abovethe horizontal ground is modelled by y = -0.1 x 3 + 0.8 x 2 , 2 ≤ x ≤ 8 , relative to an origin O.yx2 4 6 8246A108EBCDOPoint A has coordinates (2 , 0), point B has coordinates (2 , 2.4), and point C hascoordinates (8 , 0).(a) (i) Find dy___dx .(ii) Hence find the maximum height of the tunnel. [6](b) Find the height of the tunnel when(i) x = 4 .(ii) x = 6 . [3](c) Use the trapezoidal rule, with three intervals, to estimate the cross-sectional area ofthe tunnel. [3](d) (i) Write down the integral which can be used to find the cross-sectional area ofthe tunnel.(ii) Hence find the cross-sectional area of the tunnel. [4]

Samantha is building a rectangular garden with a fence around it. If the length of the garden is 15𝑚 and the width is 10𝑚, what is the total length of the fence required?150𝑚300𝑚50𝑚

A surveyor needs to find the length from point A to point C across a lake as shown in the figure below. The measurements of which of the following angles and side lengths are sufficient for the surveyor to determine the length of 𝐴𝐶‾AC  using only the law of sines?

Two trains, X and Y, while traveling towards each other on different tracks, they enter a tunnel that is as long as the combined length of both trains. Train X is 135 meters long, and train Y is 151 meters long. After 10 seconds, the two trains meet inside the tunnel. If their speeds are in a ratio of 5:6, how much length (in m) of train X is still outside the tunnel when it meets train Y?