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## #1 2013-01-08 08:09:27

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

### Scientias 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
Member
Registered: 2012-07-20
Posts: 236

### Re: Scientias 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
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,509

### Re: Scientias 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
Member
Registered: 2009-11-13
Posts: 224

### Re: Scientias 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
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,509

### Re: Scientias 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: 16,018

### Re: Scientias 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
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,739

### Re: Scientias 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: Scientias 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: 16,018

### Re: Scientias 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
Member
Registered: 2009-11-13
Posts: 224

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## #11 2013-01-09 03:01:48

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,018

### Re: Scientias 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
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,739

### Re: Scientias 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: Scientias 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
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,739

### Re: Scientias 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

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## #16 2013-01-09 07:50:37

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,739

### Re: Scientias 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
Member
Registered: 2009-11-13
Posts: 224

### Re: Scientias exercises

#5. Rating: Easy

Let A and B be finite sets with m and n elements respectively, and suppose :AB is a mapping. If  is injective (one-to-one), show that mn.

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## #18 2013-01-13 23:58:57

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

### Re: Scientias exercises

#6. Rating: Medium

Let A and B be finite sets with m and n elements respectively, and suppose :AB is a mapping. If  is surjective (onto), show that mn.

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## #19 2013-01-23 02:21:32

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,018

### Re: Scientias 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
Member
Registered: 2013-01-22
Posts: 14

### Re: Scientias 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 work as a computer programmer. I am from Norway.

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## #21 2013-03-09 09:08:10

Nehushtan
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Registered: 2013-03-09
Posts: 883
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