The power, say, P, generated by a water wheel of velocity V can be modeled by the system P P PV, V 1 V P2, where and are both positive Describe the qualitative behavior of this system as and vary and give physical interpretations of the results ...

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The power, say, P, generated by a water wheel of velocity V can be modeled by the

Question:

The power, say, P, generated by a water wheel of velocity V can be modeled by the system P˙ = −αP + PV, V˙ = 1 − βV − P2, where α and β are both positive. Describe the qualitative behavior of this system as α and β vary and give physical interpretations of the results.

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