When Two Railroad Tracks Merge,the Overlapping Portions of the Tracks $$\frac { x } { 2 } = 2 r \sin ^ { 2 } \frac { \theta } { 2 }$$

question 40

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 θ are related by​ $$\frac { x } { 2 } = 2 r \sin ^ { 2 } \frac { \theta } { 2 }$$ ​ Write a formula for x in terms of cos θ.​ ​

• A)​ \(x = r \left( 1 - \cos \frac { \theta } { 2 } \right)\)
• B)​ \(x = r ( 1 - \cos \theta )\)
• C) \(x = 2 r ( 1 - \cos \theta )\) ​
• D) \(x = 2 r ( 1 + \cos \theta )\) ​
• E) \(x = 2 r \left( 1 - \cos \frac { \theta } { 2 } \right)\) ​

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Definitions:

Very Elastic

A description of a demand or supply curve which shows that the quantity demanded or supplied changes significantly as price changes.

Unit Elastic

A situation in which a one percent change in price causes an equal percentage change in quantity demanded or supplied.

Very Inelastic

Describes a situation where the demand or supply for a product is barely affected by changes in the price.

Calculate Elasticity

entails determining the degree to which the quantity demanded or supplied of a good changes in response to a change in its price.