Precalculus 2014
56

 PAGE: 128 SET: Exercises PROBLEM: 56

The volume of the rectungular prism is .

Height of the tunnel is feet more than  of its width, hence height .

Length of the tunnel is feet more than  times of its width, .

Subustiute these values into the equation for volume of the tunnel .

The volume of the tunnel is  cubic feet.

Subustiute in the equation  and solve for .

The obtained polynomial equation is .

The above polynomial has sign variation. so , it has positive real zero.

Graph :

Draw the coordinate plane.

Graph the function .

Observe the graph:

The function touches the  axis at .

Synthetic Division:

The function is  .

Perform the synthetic division method by testing .

must be a positive value because ,the above polynomial has sign variation. so , it has posotive real zero.

Since only has positive real zero.Width of the tunnel is feet.

Therwfore width of the tunnel , feet.

Height of the tunnel, .

Length of the tunnel is .

Width of the tunnel is feet.

Height of the tunnel is feet.

Length of the tunnel is  feet.

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