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

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

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. tongue)

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#2 2013-01-08 10:27:57

noelevans
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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: 3,843

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: 222

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: 3,843

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: The Foundation
Registered: 2011-05-23
Posts: 15,315

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

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#7 2013-01-08 17:09:35

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,400

Re: Scientia’s exercises

Hi;


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#8 2013-01-08 22:53:40

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

Re: Scientia’s exercises

anonimnystefy and bobbym:

Perfect! You got it right. up


#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: The Foundation
Registered: 2011-05-23
Posts: 15,315

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

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#10 2013-01-09 03:01:07

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

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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,315

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

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#12 2013-01-09 04:59:01

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,400

Re: Scientia’s exercises

Hi;


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#13 2013-01-09 06:00:26

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

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
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,400

Re: Scientia’s exercises

Hi scientia;


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#15 2013-01-09 07:16:06

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

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,400

Re: Scientia’s exercises

Hi;


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#17 2013-01-10 23:48:26

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

Re: Scientia’s exercises


#5. Rating: Easy

Let A and B be finite sets with m and n elements respectively, and suppose ƒ:AB is a mapping. If ƒ 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: 222

Re: Scientia’s exercises

#6. Rating: Medium

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

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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,315

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

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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
Member
From: London
Registered: 2013-03-09
Posts: 611
Website

Re: Scientia’s exercises


150 books currently added on Goodreads

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