Arc length

**amiv4** · October 8th 2008, 11:56 AM

A cable hangs between two poles of equal height and

feet apart.
At a point on the ground directly under the cable and

feet from the point on the ground halfway between the poles
the height of the cable in feet is

The cable weighs 17.3 pounds per linear foot.
Find the weight of the cable.

**shawsend** · October 8th 2008, 03:48 PM

Arc length is:

$L=\int_0^a \sqrt{1+(f'(x))^2} dx$

right? And $f(x)=10+0.4x^{3/2}$

So total cable length is $2\int_0^{18}\sqrt{1+(.4(1.5 x^{1/2})^2}dx$

**amiv4** · October 8th 2008, 05:18 PM

k i just wasnt sure about the limits. why is it 0 to 18

**shawsend** · October 9th 2008, 01:24 AM

Originally Posted by amiv4

k i just wasnt sure about the limits. why is it 0 to 18

Because f(x) measures the distance to the cable starting from the lowest point (call that the origin) and the two poles are 36 feet away.

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