Question
Answer and show work:
The Gateway Arch in St. Louis was designed by architect Eero Saarinen and was constructed using the equation y = 211.488 - 20.96cosh (0.03291765x) for the central curve of the arch, where x and y are measured in meters and x 91.20 What is the height of the arch at its center? The city of St. Louis wishes to hang a banner on a wire stretched across the span between the leg of the Arch at a height of 50 meters. Help them determine the distance across the span at this height. If tanhx = 12/13 find the values of the other 5 hyperbolic functions at x.
Explanation / Answer
1)
a)Height at middle=maximum=211.488-20.96*cosh(0.03291765*0)
=190.528
b)y= 50
=>x=cosh^-1(161.488)/0.0329
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2)tanhx=12/13
coshx=13/5
sinhx=12/5
sechx=5/13
cosechx=5/13
cothx=13/12