math

posted by .

A small resort is situated on an island that lies exactly 4 miles from , the nearest point to the island along a perfectly straight shoreline. 10 miles down the shoreline from is the closest source of fresh water. If it costs 1.5 times as much money to lay pipe in the water as it does on land, how far down the shoreline from should the pipe from the island reach land in order to minimize the total construction costs?

  • math -

    Draw a diagram, where
    R is the resort
    P is the named point on shore
    W is the water well
    L is the point on land where the pipe comes ashore

    RPL is a right triangle, where
    RP=4
    PL = x
    PW=10, so LW=10-x

    without loss of generality, we may assume the land cost is 1, so the total cost is

    c = 1.5√(16+x^2) + (10-x)
    dc/dx = 1.5x/√(16+x^2) - 1
    dc/dx = 0 when x = 8/√5 = 3.58

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus

    A lighthouse is built on an exposed reef, 5.5 miles off-shore. The shoreline is perfectly straight, and a town is located 6.5 miles downshore from the point on the shoreline nearest the lighthouse. The lighthouse keeper needs to go …
  2. calculus

    A lighthouse is built on an exposed reef, 5.5 miles off-shore. The shoreline is perfectly straight, and a town is located 6.5 miles downshore from the point on the shoreline nearest the lighthouse. The lighthouse keeper needs to go …
  3. Calculus

    A lighthouse is located on a small island 4 km away from the nearest point P on a straight shoreline. Its light makes 3 revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1.7 kilometers from …
  4. Calculus

    A small resort is situated on an island that lies exactly 6 miles from P, the nearest point to the island along a perfectly straight shoreline. 10 miles down the shoreline from P is the closest source of fresh water. If it costs 1.4 …
  5. Calculus

    A lighthouse is located on a small island 3 km away from the nearest point P on a straight shoreline and its light makes four revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from P?
  6. Calculus

    A lighthouse is located on a small island 4 km away from the nearest point P on a straight shoreline and its light makes three revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from P?
  7. Calculus

    A small resort is situated on an island that lies exactly 5 miles from P, the nearest point to the island along a perfectly straight shoreline. 10 miles down the shoreline from P is the closest source of fresh water. If it costs 1.5 …
  8. Calculus 1

    Related Rates: A lighthouse is located on a small island 4 km away from the nearest point P on a straight shoreline and its light makes two revolutions per minute. How fast is the beam of light moving along the shoreline when it is …
  9. Calculus 1

    A lighthouse is located on a small island 4 km away from the nearest point P on a straight shoreline and its light makes two revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from P?
  10. Calculus

    An island is 3 mi from the nearest point on a straight​ shoreline; that point is 6 mi from a power station​. A Utility company plans to lay electrical cable underwater from the island to the shore and then underground along …

More Similar Questions