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

#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: 4,081

"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: 224

#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: 4,081

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: 15,922

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: 95,982

Hi;

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

**If it ain't broke, fix it until it is.**

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

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: 15,922

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: 224

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,922

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: 95,982

Hi;

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

**If it ain't broke, fix it until it is.**

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

#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: 95,982

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.**

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 95,982

Hi;

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

**If it ain't broke, fix it until it is.**

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

#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: 224

#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: 15,922

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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