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Question Number 85709 by otchereabdullai@gmail.com last updated on 24/Mar/20

Answered by MJS last updated on 24/Mar/20

we had this many times before the posts are 50, the cable is 80, the space under the cable is 10 ⇒ the effective height of the poles is 40 ⇒ the distance between them is 0

$$\mathrm{we}\:\mathrm{had}\:\mathrm{this}\:\mathrm{many}\:\mathrm{times}\:\mathrm{before} \\ $$$$\mathrm{the}\:\mathrm{posts}\:\mathrm{are}\:\mathrm{50},\:\mathrm{the}\:\mathrm{cable}\:\mathrm{is}\:\mathrm{80},\:\mathrm{the}\:\mathrm{space} \\ $$$$\mathrm{under}\:\mathrm{the}\:\mathrm{cable}\:\mathrm{is}\:\mathrm{10} \\ $$$$\Rightarrow \\ $$$$\mathrm{the}\:\mathrm{effective}\:\mathrm{height}\:\mathrm{of}\:\mathrm{the}\:\mathrm{poles}\:\mathrm{is}\:\mathrm{40}\:\Rightarrow \\ $$$$\mathrm{the}\:\mathrm{distance}\:\mathrm{between}\:\mathrm{them}\:\mathrm{is}\:\mathrm{0} \\ $$

Commented by otchereabdullai@gmail.com last updated on 24/Mar/20

thanks prof mjs

$$\mathrm{thanks}\:\mathrm{prof}\:\mathrm{mjs} \\ $$

Commented by otchereabdullai@gmail.com last updated on 24/Mar/20

prof mjs please at this stage will the poles be together?

$$\mathrm{prof}\:\mathrm{mjs}\:\mathrm{please}\:\mathrm{at}\:\mathrm{this}\:\mathrm{stage}\:\mathrm{will}\:\mathrm{the}\: \\ $$$$\mathrm{poles}\:\mathrm{be}\:\mathrm{together}? \\ $$

Commented by MJS last updated on 24/Mar/20

yes. forget the curve. forget the length of the cable at first. the cable must go down from the left pole, vertically 40 meters. it must go up to the right pole, again vertically 40 meters. ⇒ it must be 80 meters at least. now remember the length of the cable is exactly 80 meters. ⇒ it′s hanging down vertically from both poles, there′s no length left ⇒ the poles must be together

$$\mathrm{yes}.\:\mathrm{forget}\:\mathrm{the}\:\mathrm{curve}.\:\mathrm{forget}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{cable}\:\mathrm{at}\:\mathrm{first}. \\ $$$$\mathrm{the}\:\mathrm{cable}\:\mathrm{must}\:\mathrm{go}\:\mathrm{down}\:\mathrm{from}\:\mathrm{the}\:\mathrm{left}\:\mathrm{pole}, \\ $$$$\mathrm{vertically}\:\mathrm{40}\:\mathrm{meters}.\:\mathrm{it}\:\mathrm{must}\:\mathrm{go}\:\mathrm{up}\:\mathrm{to}\:\mathrm{the} \\ $$$$\mathrm{right}\:\mathrm{pole},\:\mathrm{again}\:\mathrm{vertically}\:\mathrm{40}\:\mathrm{meters}.\:\Rightarrow \\ $$$$\mathrm{it}\:\mathrm{must}\:\mathrm{be}\:\mathrm{80}\:\mathrm{meters}\:\mathrm{at}\:\mathrm{least}.\:\mathrm{now}\:\mathrm{remember} \\ $$$$\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{the}\:\mathrm{cable}\:\mathrm{is}\:\mathrm{exactly}\:\mathrm{80}\:\mathrm{meters}. \\ $$$$\Rightarrow\:\mathrm{it}'\mathrm{s}\:\mathrm{hanging}\:\mathrm{down}\:\mathrm{vertically}\:\mathrm{from}\:\mathrm{both} \\ $$$$\mathrm{poles},\:\mathrm{there}'\mathrm{s}\:\mathrm{no}\:\mathrm{length}\:\mathrm{left}\:\Rightarrow\:\mathrm{the}\:\mathrm{poles}\:\mathrm{must} \\ $$$$\mathrm{be}\:\mathrm{together} \\ $$

Commented by otchereabdullai@gmail.com last updated on 24/Mar/20

God richly bless you i appreciate your time prof

$$\mathrm{God}\:\mathrm{richly}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{i}\:\mathrm{appreciate}\:\mathrm{your} \\ $$$$\mathrm{time}\:\mathrm{prof} \\ $$

Commented by MJS last updated on 24/Mar/20

you′re welcome

$$\mathrm{you}'\mathrm{re}\:\mathrm{welcome} \\ $$

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