Atelephone line hangs between two poles 14 m apart in the shape of the catenary , where and are measured in meters.
(a) find the slope of this curve where it meets the right pole.
(b) find the angle between the line and the pol

a) At x=14 the slope will be given by:

.

b) Then, the angle between the line and the pole will be:

where is the angle between the tangent to the catenary and the x-axis.

Explanation:

The catenary has the following general form:

a) The slope at any point will be given by the derivative of y.

At x=14:

.

b) The angle between the tangent to the catenary and the x-axis at a given point will be given by:

⇒

Then, the angle between the line and the pole will be:

.

object 2 because all the other ones are wrong