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

#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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**noelevans****Member**- Registered: 2012-07-20
- Posts: 236

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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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,980

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

#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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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,980

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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,891

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 92,978

Hi;

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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

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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,891

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

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,891

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 92,978

Hi;

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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

#4. Rating: Difficult

*x* and *y* are real numbers satisfying

Find the maximum and minimum values of

.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 92,978

Hi scientia;

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 92,978

Hi;

**In mathematics, you don't understand things. You just get used to them.**

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

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

#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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,891

Hi scientia

*Last edited by anonimnystefy (2013-01-23 02:22:17)*

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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**Ivar Sand****Member**- Registered: 2013-01-22
- Posts: 14

*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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