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E Portfolio Test

The document discusses the shape and properties of a catenary curve, which is the shape a hanging cable or chain takes under its own weight. It gives the equation y=1/2(e^x - e^-x) that defines the catenary curve. The domain is all real numbers and the range is all real numbers greater than or equal to 0. It is not invertible. It also provides an equation for the shape of the Gateway Arch in St. Louis, and asks to find the highest point on the arch by analyzing that equation.

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18 views1 page

E Portfolio Test

The document discusses the shape and properties of a catenary curve, which is the shape a hanging cable or chain takes under its own weight. It gives the equation y=1/2(e^x - e^-x) that defines the catenary curve. The domain is all real numbers and the range is all real numbers greater than or equal to 0. It is not invertible. It also provides an equation for the shape of the Gateway Arch in St. Louis, and asks to find the highest point on the arch by analyzing that equation.

Uploaded by

api-252993354
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as DOCX, PDF, TXT or read online on Scribd
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William L.

Ellis
02-23-15

E-portfolio test assignment


35. In Exercise 26 in Section 2.3, we stated that the cable of a suspension bridge
formed a parabola but that a free hanging cable did not. A free hanging cable forms
a catenary and its basic shape is given by

y=

1
2

( e

). Use your

calculator to graph this function. What are its domain and range? What is its end
behavior? Is it invertible? How do you think it is related to the function given in
Exercise 47 in Section 6.3 and the one given in the answer to Exercise 38 in Section
6.4? When flipped upside down, the catenary makes an arch. The Gateway Arch in
St. Louis, Missouri has the shape
y = 757.7

127.7
x
(e
)
2
127.7 +

127.7

where x and y are measured in feet and 315 x 315. Find the highest point on
the arch.

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