When Two Railroad Tracks Merge, the Overlapping Portions of the Tracks

question 176

Multiple Choice

When two railroad tracks merge, the overlapping portions of the tracks are in the shapes of circular arcs (see figure) .The radius of each arc r (in feet) and the angle $\theta$ are related by
$$\frac { x } { 2 } = 2 r \sin ^ { 2 } \frac { \theta } { 2 }$$
Write a formula for x in terms of cos $\theta$ .

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Definitions:

Balance Column

A column in ledgers or financial statements showing the difference between debits and credits.

Account Entry

An accounting record that logs a financial transaction in the books of accounts, impacting the balance sheet and/or income statement.

Debt Ratio

A financial ratio that measures the extent of a company’s leverage, computed by dividing total liabilities by total assets.

Financial Leverage

The use of borrowed funds to increase the potential return of an investment, which also increases the risk.