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
