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#1 2016-09-03 02:12:58

Mathegocart
Member
Registered: 2012-04-29
Posts: 1,792

Mathematics Challenges, #2

These questions are a compilation of physics-related mathematics problems. Enjoy!

1. In bobbym's lavish home, he has a triangular grandstand shown by Diagram 1.0:
CCFXLMI.png(A and a are the same length.)
Find where the center of mass is with calculus.

2. Bobbym is riding a sled on a gargantuan hill, and his speed is given by 29 - t^2 + t. How far will the valiant bobbym travel from t(time) =0 to when he stops at v =0?

3. What is the least positive integer with the property that the product of its digits is 5! ?

4.Find the sum of all the integers N > 1 with the properties that the each prime
factor of N is either 2, 3, or 5, and N is not divisible by any perfect cube greater
than 1.

5.If you roll six fair dice, let p be the probability that exactly three different numbers
appear on the upper faces of the six dice. If p = m/n where m and n are

relatively prime positive integers, find m + n.
5a. Say p is the probability that exactly four different numbers appear on the upper faces of the dice. How much smaller or larger is this probability?

6.Find the sum of all the digits in the decimal representations of all the positive
integers less than 10000.
7 Bobbym has some square tiles. Some of the tiles have side length 5 cm while
the others have side length 3 cm. The total area that can be covered by the
tiles is exactly 20124 cm squared.
. Find the least number of tiles that Bobbym can have.
8.Bobbym needed to address a letter to 27432 Mathematica Road. He remembered the
digits of the address, but he forgot the correct order of the digits, so he wrote
them down in random order. The probability that Bobbym got exactly two of the
four digits in their correct positions is m/n
, where m and n are relatively prime
positive integers. Find m + n.
9.Find the number of subsets of {1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 22} where the
elements in the subset add to 49.
10. There is a triangle where all sides of the triangle is 1, and Bobbym picks 3 points from the triangle's area. What is the probability that the area of the three points is greater than .4? All three points are distinct.


The integral of hope is reality.

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#2 2016-09-03 02:18:04

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,115

Re: Mathematics Challenges, #2

8) You mean 2 of the 5.


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 2016-09-03 02:21:17

Mathegocart
Member
Registered: 2012-04-29
Posts: 1,792

Re: Mathematics Challenges, #2

bobbym wrote:

8) You mean 2 of the 5.

Indeed.


The integral of hope is reality.

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#4 2016-09-03 02:25:18

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,115

Re: Mathematics Challenges, #2

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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#5 2016-09-03 04:41:16

thickhead
Member
Registered: 2016-04-16
Posts: 982

Re: Mathematics Challenges, #2



Last edited by thickhead (2016-09-03 05:08:45)


{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 2016-09-03 12:05:47

Mathegocart
Member
Registered: 2012-04-29
Posts: 1,792

Re: Mathematics Challenges, #2

bobbym wrote:

Hi;

Correct, verified.


The integral of hope is reality.

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#7 2016-09-03 12:06:59

Mathegocart
Member
Registered: 2012-04-29
Posts: 1,792

Re: Mathematics Challenges, #2

thickhead wrote:



Verified, correct.


The integral of hope is reality.

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#8 2016-09-03 15:44:49

thickhead
Member
Registered: 2016-04-16
Posts: 982

Re: Mathematics Challenges, #2

(8) I find the following 14 favorable cases
27324
27243
23427
22473
24237
22734
24372
23742
47322
37242
73422
32472
74232
42732
So the probability is p=14/60=7/30
Am I missing something?


{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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#9 2016-09-05 12:47:28

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,115

Re: Mathematics Challenges, #2

Nope, that is what I am getting too.


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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