AP Calc

posted by .

When a chain hangs under its own weight, its shape is catenary. The equation of a catenary with a vertex on the y-axis is y=e^x+e^-x. Find the length of the chain from x=-2 to x=2. Then use the same technique from Problem #8(Previous AP calc problem I posted) to find the length of the parabola with the same vertex and endpoints.

I go the first part that asks to find the length to be 12.225, but I don't understand what the next part is asking or how to do it!

  • AP Calc -

    when x = 0, middle, y = e^0 + e^-0 = 2

    when x = 2 or -2 (end) y = e^2 + 1/e^2
    = 7.524

    so parabola has vertex at (0, 2)
    and goes through (-2, 7.524 ) and (-2,7.524)

    we might as well move this down weo so the vertex is at the origin
    vertex at (0,0)
    (2, 5.524) and (-2, 5.524)
    so form is
    y = a x^2 + b x
    b is 0 because symmetric about y axis
    (even function)
    y = a x^2
    when x = 2, y = 5.524
    5.524 = a (4)
    a = 1.381
    so our parabola is
    y = 1.381 x^2
    now use your technique (I do not know which you are using) to find the length of y = 1.381 x^2 from 0 to 2 and double that for -2 to + 2

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    complete the table that shows the length of the chain formed when rings are liked in a staright line 1)number of rings 1 length of chain 16mm 2)number of rings 2 length of chain 30m 3)number of rings 3 length of chain 44m 4)number …
  2. physics

    A big brass lantern hangs from three chains as shown below. The chain C1 is at an angle of 50.0 deg below the horizontal, while the chain C2 makes an angle of 60.0 deg with the vertical. These two chains join at knot K and the lantern …
  3. physics

    a chain that can support 2000 N is suspended between two trees. a 200 kg motor hangs from the middle. the slack in the chain makes the half slant upward 20 degrees. will the chain break?
  4. physics

    To protect her new two-wheeler, Iroda Bike buys a length of chain. She finds that its linear density is 0.61 lb/ft. If she wants to keep its weight below 1.8 lb, what length of chain is she allowed?
  5. Physics

    A large uniform chain is hanging from the ceiling, supporting a block of mass 48kg. The mass of the chain itself is 15 kg, and the length of the chain is 2.6 m. The acceleration of gravity is 9.81 m/s^2 Find the tension in the chain …
  6. Newton's law

    7. A uniform flexible chain of length l, with weight per unit length lamba, passes over a small, frictionless, massless pulley. It is released from a rest position with a length of chain x hanging from one side and a length l-x from …
  7. math calc 2

    a 30 m chain hangs vertically from a cylinder attached to a winch. assume there is no friction in the system and that the chain has a density of 5 kg/m. how much work is required to wind the entire chain onto the cylinder using the …
  8. Calc BC

    When a chain hangs under its own weight, its shape is a catenary (from the Latin word for chain). The equation of a catenary with a vertex on the y-axis is . Find the length of the chain from . Then use the same technique from Problem …
  9. physics

    Two uniform planks, each of mass m = 4.41 kg and length L = 2.11 m, are connected by a hinge at the top and by a chain of negligible mass attached at their centers, as shown in the figure. The assembly will stand upright, in the shape …
  10. Pre-Calculus

    The Gateway Arch in St. Louis, Missouri is not a parabola but a shape known as a catenary. The name is given to the shaoe formed by the Graph of the hyperbolic cosine (cosh). The arch has a height of 625 feet andna span of 600 feet. …

More Similar Questions