The cost of laying power line underwater is 3 times that of underground. an island is 4km from the shore and a power station is at a distance of 8km from the point on the shore which is closest to the island. how should the power line be laid so that the cost is a minimum?

The pipeline should come ashore √2 km toward the power station from the point on shore closest to the island.

Step-by-step explanation:

Let d represent the distance from the power station to the point where the power line comes ashore. The relative cost of the line will be ...

c = 3√(4² +(8-d)²) +d

c = 3√(80 -16d +d²) +d

Differentiating c with respect to d and setting that to zero gives ...

dc/dd = 0 = (3/2)(2d-16)/√(80 -16d +d²) +1

Subtracting 1, multiplying by the denominator, and squaring both sides gives a quadratic that can be solved in the usual way. It reduces to ...

(d -8)² -2 = 0

d = 8±√2 . . . . . . . . only the root 8-√2 is useful

This tells us the pipeline should come ashore √2 km toward the power station from the point closest to the island.

the answer is 99.

6,250

step-by-step explanation:

to get the area, multiply 360 by 160.(57,600)

to find out how many bags of fertilizer it will take, first figure out how many square feet one bag can hold. divide 1000 by 8(125) to get the unit rate(how many square feet one pound of fertilizer can hold)and multiply it by 50(6250). if i haven't made a mistake, that is the answer.