10fg Per Question Per Hard Tricky Math - Topic

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Jun 5 2013 08:35pm

What is the maximum possible radius of a circle completely enclosed in a 4 dimensional hypercube with side length 1?

If we choose four points at random in R2, what is the probability that they will form a convex quadrilateral?

feanur

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#22

Jun 6 2013 03:54pm

Quote (Bojana @ Jun 5 2013 05:06pm)

adequate prefix 1/46
adequate suffix 1/27
adequate roll on the prefix for ar 1/11
adequate roll on the prefix for dmg 1/3
adequate roll on the suffix for life 1/5

total: 1/(46*27*11*3*5) = 1/204930 or about 0.000488% on a sc drop :mellow:

1/344,396 at iLvl 99
1/249,356 at iLvl 61

http://forums.d2jsp.org/topic.php?t=46086105&f=87

Derkaderk

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#23

Jun 6 2013 06:12pm

A fractal is formed by attaching to a sphere of radius 1 9 spheres of radius 1/3, to each of those spheres 9 spheres of radius 1/9, and to each of those 9 spheres of radius 1/27, so on and so forth forever. Show that the surface area is infinite.

Also

Find the surface area of the figure formed by attaching to a sphere of radius 1 9 spheres of radius 1/3, 9 spheres of radius 1/9, 9 spheres of radius 1/27 so on and so forth forever

CornMuffin

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#24

Jun 6 2013 10:51pm

Quote (Derkaderk @ Jun 6 2013 08:12pm)

This is an interesting question. I hope you don't mind if I offer a solution:

Part i:

The surface area of the figure formed from this fractal is
S = 4pi + 9(4pi(1/3)^2) + 9^2(4pi(1/3^2)^2+9^3(4pi(1/3^3)^2) + ...
This simplifies to
S = 4pi + 4pi + 4pi + ... = infinity

Part ii:

The surface area of the figure formed from this fractal is
S = 4pi + 9(4pi(1/3)^2) + 9(4pi(1/3^2)^2) + 9(4pi(1/3^3)^2) + ...
This simplifies to
S = 4pi + 4pi + 4pi(1/3) + 4pi(1/3^2) + ...
S = 4pi + sum (from i=0 to infinity) 4pi(1/3)^i
This sum is just a geometric series, where r=1/3 < 1 and so it is convergent

S = 4pi + 4pi/(1-1/3) = 4pi(1+1/(2/3)) = 4pi(1+3/2) = 4pi(5/2) = 10pi

thisisjeremy

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#25

Jun 8 2013 07:18pm

6-2+1=?

Remember PEMDAS

So is the answer 5 or 3?

carteblanche

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#26

Jun 8 2013 07:41pm

I'm still waiting on my fg.

russian

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#27

Jun 9 2013 01:12am

Quote (thisisjeremy @ Jun 8 2013 06:18pm)

6-2+1=?

Remember PEMDAS

So is the answer 5 or 3?

5, of course. Addition and subtraction have the same priority and are simply done in order.AS stands for "addition and subtraction", not "addition" and then "subtraction". Just like MD is for "multiplication and division", which are also done in a left-to-right order, not multiplication first.

Sealock

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#28

Jun 9 2013 01:26am

Quote (carteblanche @ Jun 5 2013 10:34am)

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice? (it DOES matter if you switch or not btw)

I hate it when people leave out information in the Monty Hall problem. You must specify that the host announces BEFORE you make your choice that he will be revealing a goat and giving you the option to switch later. Otherwise, it DOES NOT matter if you switch or not.

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