The Boundary Value Problem $r \frac { d ^ { 2 } u } { d r ^ { 2 } } + 2 \frac { d u } { d r } = 0 , u ( a ) = u _ { 0 } , u ( b ) = u _ { 1 }$

question 39

Multiple Choice

The boundary value problem $r \frac { d ^ { 2 } u } { d r ^ { 2 } } + 2 \frac { d u } { d r } = 0 , u ( a ) = u _ { 0 } , u ( b ) = u _ { 1 }$ is a model for the temperature distribution between two concentric spheres of radii $a$ and $b$ , with $a < b$ .The solution of this problem is

• A) \(u = c _ { 2 } + c _ { 1 } / r \text {, where } c _ { 1 } = a b \left( u _ { 1 } - u _ { 0 } \right) / ( b - a ) \text { and } c _ { 2 } = \left( u _ { 1 } b - u _ { 0 } a \right) / ( b - a )\)
• B) \(u = c _ { 2 } + c _ { 1 } / r \text {, where } c _ { 1 } = \left( u _ { 1 } b - u _ { 0 } a \right) / ( b - a ) \text { and } c _ { 2 } = a b \left( u _ { 1 } - u _ { 0 } \right) / ( b - a )\)
• C) \(u = c _ { 2 } - c _ { 1 } / r , \text { where } c _ { 1 } = a b \left( u _ { 1 } - u _ { 0 } \right) / ( b - a ) \text { and } c _ { 2 } = a b \left( u _ { 1 } b - u _ { 0 } a \right) / ( b - a )\)
• D) \(u = c _ { 2 } - c _ { 1 } / r \text {, where } c _ { 1 } = \left( u _ { 1 } b - u _ { 0 } a \right) / ( b - a ) \text { and } c _ { 2 } = a b \left( u _ { 1 } - u _ { 0 } \right) / ( b - a )\)
• E) none of the above

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Definitions:

Observational Learning

The process of learning behaviors by watching and imitating others, also known as modeling or social learning.

Headstands

An inversion exercise where one balances on their head with the feet pointing upwards; often practiced in yoga.

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Learning that occurs by observing the reinforcement or punishment of another person's behavior.

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A system used to reinforce positive behavior, where individuals earn tokens for demonstrating desirable actions that can later be exchanged for rewards.