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**Mathegocart****Member**- Registered: 2012-04-29
- Posts: 1,965

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:

(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.

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

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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**Mathegocart****Member**- Registered: 2012-04-29
- Posts: 1,965

bobbym wrote:

8) You mean 2 of the 5.

Indeed.

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;

**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

*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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**Mathegocart****Member**- Registered: 2012-04-29
- Posts: 1,965

bobbym wrote:

Hi;

Correct, verified.

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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**Mathegocart****Member**- Registered: 2012-04-29
- Posts: 1,965

thickhead wrote:

Verified, correct.

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

He will be sorely missed.

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

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

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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