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#1 2013-01-09 07:09:27

scientia
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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. )

#2 2013-01-09 09:27:57

noelevans
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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.

#3 2013-01-09 10:05:33

phrontister
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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

#4 2013-01-09 10:28:46

scientia
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Re: Scientia’s exercises

#2. Rating: Medium

Do there exist integers n such that 3n+7n is a perfect square?

Last edited by scientia (2013-01-09 10:29:46)

#5 2013-01-09 10:57:13

phrontister
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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

#6 2013-01-09 11:25:52

anonimnystefy
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Re: Scientia’s exercises

Hi scientia

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#7 2013-01-09 16:09:35

bobbym

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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.

#8 2013-01-09 21:53:40

scientia
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Re: Scientia’s exercises

anonimnystefy and bobbym:

Perfect! You got it right.

#3 Rating: Medium

Evaluate:

Last edited by scientia (2013-01-09 22:07:47)

#9 2013-01-09 22:20:48

anonimnystefy
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Re: Scientia’s exercises

Hi scientia

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

scientia
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#11 2013-01-10 02:01:48

anonimnystefy
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Re: Scientia’s exercises

Hi scientia

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#12 2013-01-10 03:59:01

bobbym

Online

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.

#13 2013-01-10 05:00:26

scientia
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Re: Scientia’s exercises

#4. Rating: Difficult

x and y are real numbers satisfying

Find the maximum and minimum values of
.

#14 2013-01-10 05:36:38

bobbym

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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.

scientia
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#16 2013-01-10 06:50:37

bobbym

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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.

#17 2013-01-11 22:48:26

scientia
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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.

#18 2013-01-14 22:58:57

scientia
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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.

#19 2013-01-24 01:21:32

anonimnystefy
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Re: Scientia’s exercises

Hi scientia

Last edited by anonimnystefy (2013-01-24 01:22:17)

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#20 2013-01-25 22:52:16

Ivar Sand
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Re: Scientia’s exercises

Last edited by Ivar Sand (2013-01-26 01:00:55)

I majored in Physics in 1976. Also, I studied mathematics and computer science. I work as a computer programmer. I am from Norway.

Nehushtan
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