calculus

posted by .

A fence 5 feet tall runs parallel to a tall building at a distance of 3 feet from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building?

  • calculus -

    draw a diagram. If the foot of the ladder is x feet from the fence, and the ladder reaches y feet up the wall, then we have

    x/5 = (x+3)/y
    y = 5 + 15/x

    if the length of the ladder is z,

    z^2 = (x+3)^2 + y^2
    = (x+3)^2 + (5 + 15/x)^2
    z = √((x+3)^2 + (5 + 15/x)^2)

    dz/dx = (x+3)(x^3-75) / <a bunch of nonzero junk>

    so, dz/dx=0 at x = -3 or ∛75

    z^2 = (3+∛75)^2 + (5+15/∛75)^2
    z = 11.19 feet

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    A fence 5 feet tall runs parallel to a tall building at a distance of 7 feet from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building?
  2. Calculus

    A fence 6 feet tall runs parallel to a tall building at a distance of 7 feet from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building?
  3. Math: Calculus

    A fence 6 feet tall runs parallel to a tall building at a distance of 2 feet from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building?
  4. Calculus

    A fence 2 feet tall runs parallel to a tall building at a distance of 6 feet from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building?
  5. Calculus

    A fence 4 feet tall runs parallel to a tall building at a distance of 6 feet from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building?
  6. calculus

    A fence 5 feet tall runs parallel to a tall building at a distance of 3 feet from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building?
  7. Calculus

    A fence 8 feet tall runs parallel to a tall building at a distance of 6 feet from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building?
  8. Calculus

    A fence 3 feet tall runs parallel to a tall building at a distance of 7 feet from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building?
  9. Calculus

    fence 3 feet tall runs parallel to a tall building at a distance of 7 feet from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building?
  10. Calculus

    A fence 4 feet tall runs parallel to a tall building at a distance of 2 feet from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building?

More Similar Questions