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**Mathegocart****Member**- Registered: 2012-04-29
- Posts: 1,973

1) if x-(yz)=100, find the maximum value of x^3-y^2+z^2.

2) Find the product of ALL the numbers in this grid.

3) if ab = 100 and a^2 + b^2 = 200, find (a+b)^2.

4) How many computer pixels are required to cover a 9 meter radius sphere?

5) A man is driving his car at a constant speed of 36 km/hour. He gets shocked by seeing a boy standing on the road in front of his way and in order to save him starts applying brakes. The car decelerates at the rate of 5/6 m/s^2 and he stops right in front of the boy after 14 seconds. what was his reaction time (in seconds)?

6) The escape velocity of Earth and Bobbymland are 11. 2 km/h and 20 km/h, respectively. The mass of bobbymland is 20000 kg. What is the ratio of Earth's radius to Bobbymland's radius?

The integral of hope is reality.

May bobbym have a wonderful time in the pearly gates of heaven.

He will be sorely missed.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

Is there something you left out for 1)?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**Mathegocart****Member**- Registered: 2012-04-29
- Posts: 1,973

bobbym wrote:

Hi;

Is there something you left out for 1)?

Is it incomplete?

The integral of hope is reality.

May bobbym have a wonderful time in the pearly gates of heaven.

He will be sorely missed.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Thought there might be more because there does not seem to be a maxima.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**thickhead****Member**- Registered: 2016-04-16
- Posts: 1,086

**{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha{Gods rejoice at those places where ladies are respected.}**

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**thickhead****Member**- Registered: 2016-04-16
- Posts: 1,086

(2) The product has 655549440 factors.

**{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha{Gods rejoice at those places where ladies are respected.}**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,613

Hi thickhead;

I get 770515200, based on the same product as Bobby's, which I got from:

"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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**thickhead****Member**- Registered: 2016-04-16
- Posts: 1,086

*Last edited by thickhead (2016-06-06 04:24:15)*

**{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha{Gods rejoice at those places where ladies are respected.}**

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**Mathegocart****Member**- Registered: 2012-04-29
- Posts: 1,973

Good job.

The integral of hope is reality.

May bobbym have a wonderful time in the pearly gates of heaven.

He will be sorely missed.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

May I ask whom is giving you these problems?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,613

Hi thickhead;

I saw the factorial answer first and then checked it with the same diagonal method as yours.

From there I extracted the primes as , checked that against my factorial answer, and then applied (a+1)(b+1)(c+1)(...+1) to the exponents to get 770515200.And I also tried it in M, in various ways:

M gave an error message that I don't understand, but otherwise it all works.

*Last edited by phrontister (2016-06-07 13:38:30)*

"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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**Mathegocart****Member**- Registered: 2012-04-29
- Posts: 1,973

bobbym wrote:

Hi;

May I ask whom is giving you these problems?

I make them, bobbym.

May bobbym have a wonderful time in the pearly gates of heaven.

He will be sorely missed.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Then I will have to provide a warning. It is great fun to create your own problems but remember that it is also easy to invent problems that you or no one else can solve.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,613

Hi Bobby;

Did you look at the M code in my previous post? I added the 'DivisorSigma' function to the list, having come across it in M's 'Suggestions Bar' that pops up when you click somewhere on the output screen. Would've saved me the time working out how to sum divisors...but I don't really mind learning something new.

*Last edited by phrontister (2016-06-07 13:10:05)*

"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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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

I did not look at the divisor part but I used this to get the product.

`Times @@ (Table[Range[k, k + 9], {k, 1, 10}] // Flatten)`

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,613

That's a neat way of doing it!

I'd wanted to make a table and do a Times@@ on it, but couldn't get the table working.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

There is probably something shorter than mine.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,613

My symbolic version of the factorial method has about 15 fewer keypresses than yours.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Your product answer is very nice.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,613

Just stumbled across that. The idea popped into my head that there might be a symbol for product as there is with sigma for summation, and so I started looking.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

I knew there was such a command but never thought about using it.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,613

It certainly looks the part, and using it probably leads people into thinking that I know what I'm doing!

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

It looks like you do from here.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,613

You have your specs on inside out!

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