A barrier is being constructed to separate a body of water

1. The height above the ground of a suspended cable
   is given by h = 20 + cosh x where x is the distance measured from the centre of
   the suspended cable.

            Determine
the height of the cable 2.5m from the centre of the span.

• A barrier is being constructed to separate a
  body of water into two sections, section A and section B. Due to fluctuations
  in the tide the depth in metres of the water in the two sections can be modelled
  with the following equations.

   

,

Solve the above equations
and calculate when the height of the two sections become equal.

• Biodegradable materials such as geotextiles can
  be used for ground improvement and soil erosion control with a limited
  lifespan.

A polymer-based geotextile
is used to increase the maximum load per unit area that the ground on a
construction site can support. The increase in this maximum load per unit area
can be modelled by the equation:

            Where

 is measured
in Newtons per square metre,

           

 is the time
in years

1. If

    is initially
   5

    and after 2
   years it drops to half it’s original value, calculate the values of

    and B, rewriting the equation given with the
   values calculated.

2. How long will it take for the value of F to drop to 10% of it’s initial value?

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