Consider the Equation $u _ { xx } - u _ { t t } = 0$

question 27

Multiple Choice

Consider the equation $u _ { xx } - u _ { t t } = 0$ with conditions $\frac { d u } { d x } ( 0 , t ) = 0 , \frac { d u } { d x } = ( L , t ) = 0 , u ( x , 0 ) = f ( x ) , \frac { d u } { d t } ( 0 ) = 0$ . When separating variables with $u ( x , t ) = X ( x ) T ( t )$ , the resulting problems for $X , T$ are

• A) \(X ^ { \prime \prime } + \lambda X = 0 , X ^ { \prime } ( 0 ) = 0 , X ^ { \prime } ( L ) = 0 , T ^ { \prime \prime } + \lambda T = 0 , T ( 0 ) = 0\)
• B) \(X ^ { \prime \prime } - \lambda X = 0 , X ^ { \prime } ( 0 ) = 0 , X ^ { \prime } ( L ) = 0 , T ^ { \prime \prime } + \lambda T = 0 , T ^ { \prime } ( 0 ) = 0\)
• C) \(X ^ { \prime \prime } + \lambda X = 0 , X ^ { \prime } ( 0 ) = 0 , X ^ { \prime } ( L ) = 0 , T ^ { \prime \prime } + \lambda T = 0 , T ^ { \prime } ( 0 ) = 0\)
• D) \(X ^ { \prime \prime } + \lambda X = 0 , X ^ { \prime } ( 0 ) = 0 , X ^ { \prime } ( L ) = 0 , T ^ { \prime \prime } - \lambda T = 0 , T ^ { \prime } ( 0 ) = 0\)
• E) \(X ^ { \prime \prime } + \lambda X = 0 , X ^ { \prime } ( 0 ) = 0 , X ^ { \prime } ( L ) = 0 , T ^ { \prime \prime } + \lambda T = 0 , T ( 0 ) = f ( x )\)

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Definitions:

Work In Process Inventory

Work In Process Inventory consists of partially finished goods that are still undergoing manufacturing or production processes.

Predetermined Overhead Rate

A rate calculated before a period begins, used to allocate manufacturing overhead costs to individual units of production based on a particular activity base.

Moving Average Basis

Moving average basis is a method for evaluating or forecasting trends by averaging data points within a specific period to smooth out short-term fluctuations.

Actual Overhead Costs

The real, incurred expenses related to the indirect costs of operating a business, such as utilities, rent, and administrative expenses.