Gateway Arch in St. Louis was constructed using the equation

Question

y=211.49-20.96cosh(0.03291765x)
where |x|<=91.20
a) what is the height at its center in meters
b) At what points is height 70m (2 values of x)
c) what is the slope of arch at points in part b

Answer 1

a) well, cosh(0) = 1
b)
211.49-20.96cosh(0.03291765x) = 70
20.96cosh(0.03291765x) = 141.49
cosh(0.03291765x) = 6.75
x = arccosh(6.75)/0.03291765
c)
y' = -(20.96)(0.03291765x)sinh(0.03291765x)
so, just plug in the values from (b).
Use the graphs's symmetry to eliminate one calculation.

Answer 2

465