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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
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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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#10 2013-01-10 02:01:07
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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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#12 2013-01-10 03:59:01
- bobbym
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Re: Scientia’s exercises
Hi;
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#15 2013-01-10 06:16:06
- 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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#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:A→B is a mapping. If ƒ is injective (one-to-one), show that m ≤ n.
#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:A→B is a mapping. If ƒ is surjective (onto), show that m ≥ n.
#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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#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.
#21 2013-03-10 08:08:10
- Nehushtan
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Re: Scientia’s exercises
Holding on to anger is like drinking poison and expecting the other person to die.