A Telephone Line Hangs Between Two Poles at 12 M $y=30 \cosh \left(\frac{x}{30}\right)-35$

question 75

Multiple Choice

A telephone line hangs between two poles at 12 m apart in the shape of the catenary $y=30 \cosh \left(\frac{x}{30}\right) -35$ , where x and y are measured in meters. Find the slope of this curve where it meets the right pole.

• A) \(\frac{\sinh 5}{6}\)
• B) \(\sinh \left(\frac{5}{6}\right)\)
• C) \(\sinh \left(\frac{1}{6}\right)\)
• D) \(\sinh 6\)
• E) \(\sinh \left(\frac{1}{5}\right)\)

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Definitions:

Opportunity Cost

The benefit missed out on when choosing one alternative over another, emphasizing the impact of choice on resource allocation.

Limited Resources

The finite availability of inputs such as labor, materials, and capital, which restricts production capabilities and economic growth.

Unlimited Wants

The concept in economics that human desires for goods and services exceed the available resources, leading to perpetual states of decision making and prioritization.

Economizing Behavior

The tendency of individuals or organizations to attempt to minimize costs or expenses and maximize value.