Letâ€™s talk about spinning plates! A juggler wants to perform a trick where he will...

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Physics

Letâ€™s talk about spinning plates! A juggler wants to perform a trick where he will spin three platesas long as possible. Suppose that a plate of type k starts the plate spinning trick by spinning at k rotations per second. Every plate slows down by one rotation persecond each second. Whenever needed, the juggler can increase thespin rate of a plate of type k,by krotationsper second. If the plateâ€™s speed is not increased before or at theinstant its spin rate reaches zero, it falls off its support andends the trick. The juggler can perform at most one â€œboostâ€ ofspeed to one plate at the end of each second during the trick.Determine the unordered triples (a,b,c)of positive integers such that the juggler can keep three plates,of types a,b,and c,spinning indefinitely.

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Note rps stands for rotations per second First a specific instance 1 rps plate slows down by 1 rps per second after one second it would lose 1 rps Thus after one second its speed is 1 rps1rps 0 2 rps plate two seconds before it falls 3 rps plate three seconds before it falls n rps plate n seconds before it falls Boosting The boost returns the 1 rps plate to 1 rps It returns 2 rps plate to 2 rpsit returns n rps plate to n rps The 1 rps plate definitely requires boost every second The 2 rps plate definitely requires boost every two seconds but can be See Answer

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