In Separating Variables, Using $u ( r , \theta ) = R ( r ) \Theta ( \theta )$

question 20

Multiple Choice

In separating variables, using, $u ( r , \theta ) = R ( r ) \Theta ( \theta )$ , in the equation $\frac { \partial ^ { 2 } u } { \partial r ^ { 2 } } + \frac { 2 } { r } \frac { \partial u } { \partial r } + \frac { 1 } { r ^ { 2 } } \frac { \partial ^ { 2 } u } { \partial \theta ^ { 2 } } + \frac { \cot \theta } { r ^ { 2 } } \frac { \partial u } { \partial \theta } = 0$ , the resulting equation for $R$ and is

• A) \(r ^ { 2 } R ^ { \prime \prime } + 2 r R ^ { \prime } - \lambda R = 0\)
• B) \(r ^ { 2 } R ^ { \prime \prime } - 2 r R ^ { \prime } - \lambda R = 0\)
• C) \(r R ^ { \prime \prime } + 2 r R ^ { \prime } - \lambda r R = 0\)
• D) \(r R ^ { \prime \prime } + 2 R ^ { \prime } - \lambda r R = 0\)
• E) \(r ^ { 2 } R ^ { \prime \prime } - 2 r R ^ { \prime } - \lambda r R = 0\)

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Definitions:

Conversion Costs

The combined costs of direct labor and manufacturing overhead, representing the expenses to convert raw materials into finished goods.

Cost Per Equivalent Unit

A calculation used in process costing, dividing the total cost by the number of units produced to determine the cost per unit.

Conversion Costs

Costs required to convert raw materials into finished products, usually including direct labor and manufacturing overhead.

Conversion Costs

The costs required to convert raw materials into finished goods, which typically include direct labor and manufacturing overhead.