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

'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'

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,922

Hi Agnishom

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

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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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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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,922

That is correct.

Here lies the reader who will never open this book. He is forever dead.

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

The knowledge of some things as a function of age is a delta function.

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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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,922

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

Here lies the reader who will never open this book. He is forever dead.

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

The knowledge of some things as a function of age is a delta function.

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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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,020

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

Bob

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

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,020

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: 15,922

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

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

The knowledge of some things as a function of age is a delta function.

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**scientia****Member**- Registered: 2009-11-13
- Posts: 224

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: 224

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: 224

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

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Got it! Happy New Year!

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

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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