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## Quiz of the Month (July 2007)

### Hector C. Parr

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#### SOLUTION TO LAST MONTH'S QUIZ

```   1.  45o,   45o,    90o
2.  50.8o, 100.4o, 28.8o```

Notes.

Q.1 Suppose the warning triangle has sides of length 2a.
It is easily seen that the dimensions of the shadow are as shown.

Q.2 Take x-y co-ordinates as shown.

Then point P can be found to be (1.2247a, 1.2247a)
So gradient of PR is 1.2247/0.2247 = 5.4504
and gradient of PQ is 1.2247/2.2247 = 0.5505

So slope of PR = tan-1(5.4504) = 79.60o
and slope of PQ = tan-1(0.5505) = 28.83o

(etc.)

#### THIS MONTH'S QUIZ

1. At what two times, exactly, between 12 o'clock and 2 o'clock, do the two pointers of a clock exchange positions?

2. At what two times, exactly, one time between 3 o'clock and 4 o'clock and the other between 5 o'clock and 6 o'clock, do the pointers of a clock exchange positions?

3. How many pairs of times are there between 12 noon and 12 midnight when the pointers of a clock exchange positions?

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