The Arch is an inverted (upside down) catenary curve, which means that it follows a hyperbolic trajectory. In fact, the central curve of the Arch can be modeled with the function y = 693.8597 – 68.6772 cosh(.0100333z) with x and y both in feet. Check out the graph of this function at desmos . Determine the maximum height of the Arch using this function and calculus (note the actual height is given as 630 feet, but this measures to the top surface of the Arch, while this function models the central curve, cutting through the middle of the structure).
The Arch is an inverted (upside down) catenary curve, which means that it follows a hyperbolic trajectory. In fact, the central curve of the Arch can be modeled with the function y = 693.8597 – 68.6772 cosh(.0100333z) with x and y both in feet. Check out the graph of this function at desmos . Determine the maximum height of the Arch using this function and calculus (note the actual height is given as 630 feet, but this measures to the top surface of the Arch, while this function models the central curve, cutting through the middle of the structure).
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:1. The Arch is an inverted (upside down) catenary curve, which means that it follows a hyperbolic trajectory. In fact, the central curve of the Arch can be modeled with the function
y = 693.8597 – 68.6772 cosh(.0100333x) with x and y both in feet. Check out the graph of this function at desmoS . Determine the maximum height of the Arch using this function and
calculus (note the actual height is given as 630 feet, but this measures to the top surface of the Arch, while this function models the central curve, cutting through the middle of the structure).
2. On July 14, 1964, McDonnell Douglas employee Percy Green staged a protest by climbing to a height of about 125 feet in order to bring attention to the need for greater numbers of minority workers on
the Arch construction site (see this article or this one 7 for more details). How steep is (i.e., what is the slope of) the Arch at the point to which Percy Green climbed in 1964 (125 feet above the
ground)? (hint: use wolframalpha, symbolab, or a TI calculator to determine the value of the inverse cosh).
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