The Gateway Arch in St. Louis, Missouri was constructed using the hyperbolic cos

Question

The Gateway Arch in St. Louis, Missouri was constructed using the hyperbolic cosine function. The equation used for construction was

y=693.8597 - 68.7672cosh0.0100333x, -299.2239 <= x <= 299.2239

where x and y are measured in feet. Cross sections of ther arch are equilateral triangles, and (x,y) traces a path of the centers of mass of the cross section triangles. For each value of x, the area of the cross section is

A= 125.1406cosh0.0100333x

(a) How high above the ground is the center of the highest triangle?(At ground level, y = 0.)

(b) What is the height of the arch? (Hint: For an equilateral triangle, A = sqrt(3)c^2, where c is one-half the base of the triangle, and the center of mass of the triangle is located at two-thirds the height of the triangle.)

(c) How wide is the arch at ground level?
  

Explanation / Answer

The Gateway Arch in St. Louis, Missouri was constructed using the hyperbolic cos

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