A Lighthouse Is Located on a Small Island $3 \mathrm {~km}$

question 1

Multiple Choice

A lighthouse is located on a small island, $3 \mathrm {~km}$ away from the nearest point $P$ on a straight shoreline, and its light makes four revolutions per minute. How fast is the beam of light moving along the shoreline when it is $1 \mathrm {~km}$ from $P$ ?

• A) \(1900 \pi \mathrm { km } / \mathrm { h }\)
• B) \(2000 \pi \mathrm { km } / \mathrm { h }\)
• C) \(1800 \pi \mathrm { km } / \mathrm { h }\)
• D) \(1700 \pi \mathrm { km } / \mathrm { h }\)
• E) \(1600 \pi \mathrm { km } / \mathrm { h }\)

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Definitions:

Cournot Equilibrium Price

A concept in economics where firms reach a state in which each firm chooses the quantity to produce to maximize its profit, given the quantities chosen by other firms in the market.

Inverse Demand Function

A mathematical representation showing the relationship between the price of a good and the quantity demanded, expressed as price as a function of quantity.

Unit Cost

The cost incurred to produce, store, and sell one unit of a product or service.

Bertrand Model

An economic model that describes interactions between firms that compete by setting prices, assuming products are perfect substitutes.