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Question Number 71593 by TawaTawa last updated on 17/Oct/19

Answered by mr W last updated on 17/Oct/19

Commented by mr W last updated on 17/Oct/19

$$y=a\cosh \frac{x}{a}$$$$s=a\sinh \frac{x}{a}$$$$a+30=a\cosh \frac{b}{a}$$$$40=a\sinh \frac{b}{a}$$$${(a+30)}^2-{40}^2=a^2$$$$60a+{30}^2-{40}^2$$$$\Rightarrow a=\frac{{40}^2-{30}^2}{60}=\frac{70}{6}$$$$\sinh \frac{b}{a}=\frac{40}{a}=\frac{24}{7}$$$$\Rightarrow b=\frac{70}{6}{\sinh }^{-1}\frac{24}{7}$$$$\Rightarrow ?=2b=\frac{70}{3}{\sinh }^{-1}\frac{24}{7}=45.4$$$$$$$$generally:$$$$b=\frac{{\sinh }^{-1}\frac{2sh}{s^2-h^2}}{\frac{2sh}{s^2-h^2}}\times s$$

Commented by TawaTawa last updated on 17/Oct/19

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.\mathrm{Thanks}\mathrm{for}\mathrm{your}\mathrm{time}$$

Commented by TawaTawa last updated on 17/Oct/19

$$\mathrm{Thanks}\mathrm{sir}.\mathrm{God}\mathrm{bless}\mathrm{you}$$

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