There are two telephone poles. Each one is 100-feet tall. They are parallel and

Question

There are two telephone poles. Each one is 100-feet tall. They are parallel and and unknown distance apart. We're going to attach a 150-foot rope from the very top of one of the poles to the top of the other. This rope will, of course, droop down somewhat. That drooping rope of the rope is called a catenary, from the Latin word for chain. The question is: What must be the distance between the two poles, so that the lowest point of the catanary is 25-feet above the ground? The catenary equation is (if you need to use it): (you can use a=l for the rope, if you like) y = a cosh (x/a)=(ex/a +e-x/a) The formula is something unique to this class. You will not run into it again. It does have a purpose though. It is designed to determine whether or not anyone heeded one particular piece of advice I gave, on multiple occasions. Plot the following function, on the interval x=0 to x=5 f(x)= (x + 3)(x + 2)(X + 1)/(x2 + 3x + 2)-3

Explanation / Answer

y=cosh x y=75 feet 75=cosh x x= cosh^-1 75 x=5.01 feet the above function reduces to y = (x+2) -3 y= x-1 which can be easily plotted with slope 1 and passing through -1 on y axis

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