# Canadian Open Mathematics Challenge 2007

**Problem:**

1. If a = 15 and b = -9, what is the value of a^{2} + 2ab + b^{2} ?

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 a^{2} + 2ab + b^{2} = (a + b)^{2} = (15 + (-9))^{2}= 6^{2} = 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 360^{o}, then the generator turns 1

2(360^{o}) = 180^{o} each second.

(Alternatively, the generator turns through 30×360^{o} in one minute, so through 30×360^{o}÷60 =180^{o} in one second)

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