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**Question 1: ** How to find the angle between the two hands of the clock at a given time?

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,609

Hi Agnishom

The angle is |h*30°-(m/2)*11°-(s/120)*11°|

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Sorry, it had been too stupid question

** A clock is set right at 7 am. The clock gains 10 minutes in 24 hrs. What will the approximate time when the clock indicates 1 pm on the following day? **

Is it 12:47:30 pm?

*Last edited by Agnishom (2012-12-31 01:53:18)*

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,609

That is correct.

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Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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Now, how do I show that the hands of the clock come in right angles 22 times?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,609

They do not. They are at right angles much more times. 46 times, I would say...

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Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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Then 22 is the number of what?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,471

Maybe that is for 90 measured clockwise (the rest 270) ?

Bob

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**bob bundy****Moderator**- Registered: 2010-06-20
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Changed my mind. I think it is 22.

00.15

0045

01.15 and a bit

01.45 and a bit

.......

2 per hour

but as the hour hand advances you loose the last hour

so 11 hours at 2 per hour.

Stefy: Is your clock a 24 hour one? ie 23 x 2 = 46

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,609

Actually, it is neither. We need to be given a time period on which we count the right angles...

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**scientia****Member**- Registered: 2009-11-13
- Posts: 222

I think the problem is for a 12-hour period. The simplest way is to count how many times the hands are at right angles in every hourly.

00:00 to 01:00 2

01:00 to 02:00 2

02:00 to 03:00 2 (including 3 o'clock)

03:00 to 04:00 1

04:00 to 05:00 2

05:00 to 06:00 2

06:00 to 07:00 2

07:00 to 08:00 2

08:00 to 09:00 2 (including 9 o'clock)

09:00 to 10:00 1

10:00 to 11:00 2

11:00 to 12:00 2

The hands are at right angles twice every hourly except for the hours 03:0004:00 and 09:0010:00. So it's 22 times every twelve hours.

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**scientia****Member**- Registered: 2009-11-13
- Posts: 222

Oh, here's the math.

The angular velocity of the minute hand is 6° per minute and that of the hour hand 0.5° per minute. The difference in their angular velocities is therefore 5.5° per minute. Starting at twelve o'clock, the time taken for the hands to be first at right angles with each other is 90/5.5 minutes. Thereafter the minute hand has to turn through 180° to be next at right angles with the hour hand; the time taken for this is 180/5.5 minutes. If is the time in minutes at which the hands are perpendicular for the th time after twelve o'clock, we have the formula:

There are 720 minutes in half a day. The largest integer

for which is .Happy New Year!

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**scientia****Member**- Registered: 2009-11-13
- Posts: 222

And these are the times at which the hands are perpendicular (using 12-hour notation):

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Got it! Happy New Year!

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'You have made another human being happy. There is no greater accomplishment.' -bobbym

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