 Pre-Calculus Problem

Subject Mathematics Pre-Calculus

Question

Cost of Laying Cable. S represents the position of a power relay station located on a straight coastal highway, and M shows the location of a marine biology experimental station on a nearby island. A cable is to laid connecting the relay station at S with the experimental station at M via the point Q that lines on the x-axis between O and S. If the cost of running the cable on land is \$3 per running foot and the cost of running cable under water is \$5 per running foot, find an expression in terms of x that gives the total of laying the cable. Use this expression to find the total cost when x=1500 and when x =2500.

y (feet)
|M (0,3000)
|
|__________ _______>x (feet)
0 | Q(x,0) S(10,000,0)

Solution Preview

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Total Cost =3 MQ +5 SQ Using distance formula
=3 sqrt(x^2 + 9000000) + 5*10000
at x = 1500 ,...

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