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| 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 
.
.gif)
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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