Question

A power plant is located on a river that is 600 feet wide. To lay a new cable from the plant to a location in a city 1 mile downstream on the opposite side costs $175 per foot across the river and $100 per foot along the land. Suppose that the cable goes from the plant to a point Q on the opposite side that is x feet from the point P directly opposite the plant. Write a function C(x) that gives the cost of laying the cable in terms of the distance x. 1 mi city Cl 600 ft power plant

Answer 1

Answer:

C(x) = 175√(x² + 360000) + 528000 - 100x

Step-by-step explanation:

See the attachment below (Line PR = 1mile)

C(x) = Cost of Distance across the river + Cost of Distance along the land

Calculating Distance Across the river:

In triangle OPQ,The distance across the river is represented by line y

Line y is the hypothenus of the triangle

Pythagoras theorem states that:

if one angle of a triangle is 90 degrees, then the square of the length of the hypotenuse - the side opposite the right angle - is equal to the sum of the squares of the lengths of the other two sides.

So,

y² = x² + 600²

y² = x² + 360000

y = √(x² + 360000)

If it costs $175 per foot across the river then It'll cost

175 * √(x² + 360000) to lay cables across the river.

Calculating Distance along the land

Distance along the land is represented by line QR

Line QR = Line PR - PQ.

Where PR = 1 Miles (1 mile = 5280 feet)

So, PR = 5280

Line PQ = x

So, QR = 5280 - x

If it costs $100 per foot along the land,then it'll cost

100 * (5280 - x) to lay cables along the land

= 528000 - 100x

C(x) = 175√(x² + 360000) + 528000 - 100x