Question

A person walking along a dock drags a boat by a 10-meter rope. The boat travels along a path known as tractrix (see figure). The equation of this path is given below. 10 Tractrix 10 y10 In 10 V100- V100 x and x (a) What are the slopes of this path when x 9? (Round your answers to three decimal places.) y'(3) -3.179 y'(9) 98.33 (b) What does the slope of the path approach as 10? - 0 Need Help? Read It Talk to a Tutor

Answer 1

Given l00-x lo0-x d'y dt The slope of the path at any Point is We get diff w.t NOu 00- io n 00-X 00- cy dri 0 dx A the ake os diffesenttation, det 0o B 00-x and A get dy To dnlA) d 1 d1 dB 10 dA dx dy - 2 B dY Replace back the values, To gt d( oo ) I00- d 10* dy 2100-X d I00- ose 2uottent sule, (10 00- - 2 % x (-2x) 200- dy \oa-x dt f 100- dy 00- X-001 100- 19 duy foo- o+Oo- 100-

dy -oox 공- 001 VI00- dx 0o-X 100% dy - da t00- dy 00-x dy OO dx a00-x 100-1 dy dy hope 0f the path When That dy -3.1797 3 -3.180 Sope of the Path When That dy dx 19 -O.4343