Canadian Open Mathematics Challenge 2007

Problem:

1. If a = 15 and b = -9, what is the value of a2 + 2ab + b2 ?
2. A circular wind power generator turns at a rate of 30 complete revolutions per
minute. Through how many degrees does it turn in one second ?

Solution ?

Solution 1
If a = 15 and b = -9, then a2 + 2ab + b2 = (a + b)2 = (15 + (-9))2= 62 = 36.

Solution 2
Since there are 60 seconds in a minute, the wind power generator turns
30/60=1/2 of a revolution each second.
Since a full revolution is 360o, then the generator turns 1
2(360o) = 180o each second.
(Alternatively, the generator turns through 30×360o in one minute, so through 30×360o÷60 =180o in one second)




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