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#1 2016-06-05 08:02:27

Mathegocart
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Registered: 2012-04-29
Posts: 1,882

Quickies #3 Assorted Math

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.
061d7fd7208adb35149f52ef57990e317d73f23f.png

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.

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#2 2016-06-05 08:25:37

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

Re: Quickies #3 Assorted Math

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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#3 2016-06-05 12:24:51

Mathegocart
Member
Registered: 2012-04-29
Posts: 1,882

Re: Quickies #3 Assorted Math

bobbym wrote:

Hi;

Is there something you left out for 1)?

Is it incomplete?


The integral of hope is reality.

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#4 2016-06-05 13:52:34

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

Re: Quickies #3 Assorted Math

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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#5 2016-06-05 18:28:58

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

Re: Quickies #3 Assorted Math


{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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#6 2016-06-05 18:33:01

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

Re: Quickies #3 Assorted Math

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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#7 2016-06-05 19:38:11

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

Re: Quickies #3 Assorted Math

(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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#8 2016-06-06 02:08:34

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,592

Re: Quickies #3 Assorted Math

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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#9 2016-06-06 04:22:51

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

Re: Quickies #3 Assorted Math

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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#10 2016-06-06 08:33:18

Mathegocart
Member
Registered: 2012-04-29
Posts: 1,882

Re: Quickies #3 Assorted Math

Good job.


The integral of hope is reality.

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#11 2016-06-06 08:52:46

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

Re: Quickies #3 Assorted Math

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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#12 2016-06-06 11:20:09

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,592

Re: Quickies #3 Assorted Math

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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#13 2016-06-06 13:29:49

Mathegocart
Member
Registered: 2012-04-29
Posts: 1,882

Re: Quickies #3 Assorted Math

bobbym wrote:

Hi;

May I ask whom is giving you these problems?

I make them, bobbym.


The integral of hope is reality.

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#14 2016-06-06 14:19:40

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

Re: Quickies #3 Assorted Math

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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#15 2016-06-07 12:50:27

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,592

Re: Quickies #3 Assorted Math

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. smile

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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#16 2016-06-07 14:16:44

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

Re: Quickies #3 Assorted Math

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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#17 2016-06-07 14:27:09

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,592

Re: Quickies #3 Assorted Math

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.


"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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#18 2016-06-07 14:29:08

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

Re: Quickies #3 Assorted Math

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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#19 2016-06-07 14:42:18

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,592

Re: Quickies #3 Assorted Math

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


"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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#20 2016-06-07 14:47:27

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

Re: Quickies #3 Assorted Math

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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#21 2016-06-07 15:06:02

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,592

Re: Quickies #3 Assorted Math

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.


"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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#22 2016-06-07 15:08:42

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

Re: Quickies #3 Assorted Math

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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#23 2016-06-07 15:29:32

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,592

Re: Quickies #3 Assorted Math

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


"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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#24 2016-06-07 15:32:54

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

Re: Quickies #3 Assorted Math

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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#25 2016-06-07 15:37:25

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,592

Re: Quickies #3 Assorted Math

You have your specs on inside out!


"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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