Consider the Problem Replace $\frac { \partial ^ { 2 } u } { \partial x ^ { 2 } }$

question 11

Multiple Choice

Consider the problem $c ^ { 2 } \frac { \partial ^ { 2 } u } { \partial x ^ { 2 } } = \frac { \partial ^ { 2 } u } { \partial t ^ { 2 } } , u ( 0 , t ) = 0 , u ( 1 , t ) = 0 , u ( x , 0 ) = \sin ( \pi x ) , u _ { t } ( x , 0 ) = g ( x )$ . Replace $\frac { \partial ^ { 2 } u } { \partial x ^ { 2 } }$ with a central difference approximation with $h = 1 / 4$ and $\frac { \partial ^ { 2 } u } { \partial t ^ { 2 } }$ with a central difference approximation with $k = 1 / 3$ The resulting equation is

• A) \(c ^ { 2 } [ u ( x + h , t ) - 2 u ( x , t ) + u ( x - h , t ) ] / h ^ { 2 } = ( u ( x , t + k ) - u ( x , t ) + u ( x , t - k ) ) / k ^ { 2 }\)
• B) \(c ^ { 2 } [ u ( x + h , t ) - 2 u ( x , t ) + u ( x - h , t ) ] / h ^ { 2 } = ( u ( x , t + k ) - 2 u ( x , t ) + u ( x , t - k ) ) / k ^ { 2 }\)
• C) \(c ^ { 2 } [ u ( x + h , t ) - 2 u ( x , t ) + u ( x - h , t ) ] / h ^ { 2 } = ( u ( x , t + k ) - u ( x , t ) ) / k ^ { 2 }\)
• D) \(c ^ { 2 } [ u ( x + h , t ) - 2 u ( x , t ) + u ( x - h , t ) ] / h ^ { 2 } = ( u ( x , t + k ) + u ( x , t ) ) / k\)
• E) \(c ^ { 2 } [ u ( x + h , t ) - 2 u ( x , t ) + u ( x - h , t ) ] / h ^ { 2 } = ( u ( x , t + k ) - u ( x , t ) ) / k\)

Determine the present value of future cash flows to make informed investment decisions.

Understand and apply the concept of annual raises to predict future salary based on current salary and raise percentage.

Calculate how inflation affects the future cost of items.

Analyze the impact of waiting to invest on the achievement of financial goals.

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Definitions:

Uniform Commercial Code

A comprehensive set of laws governing commercial transactions in the United States, aimed at harmonizing the law among the states.

Sale of Goods

A transaction between a buyer and a seller involving the transfer of ownership of goods from one party to another for a price.

Secondary Obligation

A duty or liability that is dependent on the occurrence or non-occurrence of certain conditions or the failure to perform a primary obligation.

Promissory Estoppel

A legal principle that prevents a party from withdrawing a promise if the other party has significantly relied on that promise to their detriment, even if there is no formal contract.