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Question Number 61612 by Tawa1 last updated on 05/Jun/19

Commented by MJS last updated on 05/Jun/19

a hanging rope forms  y=acosh (x/a)  if we put the towers  at x=±(d/2)

$$\mathrm{a}\:\mathrm{hanging}\:\mathrm{rope}\:\mathrm{forms} \\ $$$${y}={a}\mathrm{cosh}\:\frac{{x}}{{a}} \\ $$$$\mathrm{if}\:\mathrm{we}\:\mathrm{put}\:\mathrm{the}\:\mathrm{towers}\:\:\mathrm{at}\:{x}=\pm\frac{{d}}{\mathrm{2}} \\ $$

Commented by mr W last updated on 06/Jun/19

under the given condition the  distance between the towers must  be zero.

$${under}\:{the}\:{given}\:{condition}\:{the} \\ $$$${distance}\:{between}\:{the}\:{towers}\:{must} \\ $$$${be}\:{zero}. \\ $$

Commented by Tawa1 last updated on 06/Jun/19

How is it zero sir.  Please enlight me.

$$\mathrm{How}\:\mathrm{is}\:\mathrm{it}\:\mathrm{zero}\:\mathrm{sir}.\:\:\mathrm{Please}\:\mathrm{enlight}\:\mathrm{me}. \\ $$

Commented by Tawa1 last updated on 06/Jun/19

Zero look strange.

$$\mathrm{Zero}\:\mathrm{look}\:\mathrm{strange}. \\ $$

Commented by Tawa1 last updated on 06/Jun/19

And what condition sir

$$\mathrm{And}\:\mathrm{what}\:\mathrm{condition}\:\mathrm{sir} \\ $$

Commented by mr W last updated on 06/Jun/19

look at the picture:  the rope is 15m long.  both ends of the rope are 7.5 m above  the midpoint of the rope.  ⇒both ends of rope must be at the  same point, i.e. the two towers must  touch each other.

$${look}\:{at}\:{the}\:{picture}: \\ $$$${the}\:{rope}\:{is}\:\mathrm{15}{m}\:{long}. \\ $$$${both}\:{ends}\:{of}\:{the}\:{rope}\:{are}\:\mathrm{7}.\mathrm{5}\:{m}\:{above} \\ $$$${the}\:{midpoint}\:{of}\:{the}\:{rope}. \\ $$$$\Rightarrow{both}\:{ends}\:{of}\:{rope}\:{must}\:{be}\:{at}\:{the} \\ $$$${same}\:{point},\:{i}.{e}.\:{the}\:{two}\:{towers}\:{must} \\ $$$${touch}\:{each}\:{other}. \\ $$

Commented by mr W last updated on 06/Jun/19

this is not a good question.  it is a good question if the length of  rope is 25m, for example.

$${this}\:{is}\:{not}\:{a}\:{good}\:{question}. \\ $$$${it}\:{is}\:{a}\:{good}\:{question}\:{if}\:{the}\:{length}\:{of} \\ $$$${rope}\:{is}\:\mathrm{25}{m},\:{for}\:{example}. \\ $$

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