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#1 2013-01-08 08:09:27
- scientia
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- Registered: 2009-11-13
- Posts: 224
Scientias exercises
#1. Rating: Easy
A window cleaner carries a uniform 60-lb ladder 15 ft long, at one end of which a bucket of water weighing 40 lb is hung. At what point must he support the ladder to carry it horizontally? Where is the center of gravity of his load?
(This problem is taken from chapter 4 of The Prime of Miss Jean Brodie by Muriel Spark. 
)
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#2 2013-01-08 10:27:57
- noelevans
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- Registered: 2012-07-20
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Re: Scientias exercises
Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).
LaTex is like painting on many strips of paper and then stacking them to see what picture they make.
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#3 2013-01-08 11:05:33
- phrontister
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- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,880
Re: Scientias exercises
"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson
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#4 2013-01-08 11:28:46
- scientia
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- Registered: 2009-11-13
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Re: Scientias exercises
#2. Rating: Medium
Do there exist integers n such that 3[sup]n[/sup]+7[sup]n[/sup] is a perfect square?
Last edited by scientia (2013-01-08 11:29:46)
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#5 2013-01-08 11:57:13
- phrontister
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- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,880
Re: Scientias exercises
Hi scientia,
"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson
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#6 2013-01-08 12:25:52
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
Re: Scientias exercises
Hi scientia
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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#7 2013-01-08 17:09:35
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Scientias exercises
Hi;
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#8 2013-01-08 22:53:40
- scientia
- Member
- Registered: 2009-11-13
- Posts: 224
Re: Scientias exercises
anonimnystefy and bobbym:
Perfect! You got it right. 
#3 Rating: Medium
Evaluate:
Last edited by scientia (2013-01-08 23:07:47)
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#9 2013-01-08 23:20:48
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
Re: Scientias exercises
Hi scientia
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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#10 2013-01-09 03:01:07
- scientia
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- Registered: 2009-11-13
- Posts: 224
Re: Scientias exercises
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#11 2013-01-09 03:01:48
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
Re: Scientias exercises
Hi scientia
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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#12 2013-01-09 04:59:01
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Scientias exercises
Hi;
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#13 2013-01-09 06:00:26
- scientia
- Member
- Registered: 2009-11-13
- Posts: 224
Re: Scientias exercises
#4. Rating: Difficult
x and y are real numbers satisfying
Find the maximum and minimum values of
.
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#14 2013-01-09 06:36:38
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Scientias exercises
Hi scientia;
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#15 2013-01-09 07:16:06
- scientia
- Member
- Registered: 2009-11-13
- Posts: 224
Re: Scientias exercises
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#16 2013-01-09 07:50:37
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Scientias exercises
Hi;
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#17 2013-01-10 23:48:26
- scientia
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- Registered: 2009-11-13
- Posts: 224
Re: Scientias exercises
#5. Rating: Easy
Let A and B be finite sets with m and n elements respectively, and suppose :A→B is a mapping. If is injective (one-to-one), show that m ≤ n.
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#18 2013-01-13 23:58:57
- scientia
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- Registered: 2009-11-13
- Posts: 224
Re: Scientias exercises
#6. Rating: Medium
Let A and B be finite sets with m and n elements respectively, and suppose :A→B is a mapping. If is surjective (onto), show that m ≥ n.
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#19 2013-01-23 02:21:32
- anonimnystefy
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- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
Re: Scientias exercises
Hi scientia
Last edited by anonimnystefy (2013-01-23 02:22:17)
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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#20 2013-01-24 23:52:16
- Ivar Sand
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- Registered: 2013-01-22
- Posts: 16
Re: Scientias exercises
Last edited by Ivar Sand (2013-01-25 02:00:55)
I majored in Physics in 1976. Also, I studied mathematics and computer science. I worked as a computer programmer. I became a pensioner in 2016. I am from Norway.
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