What do you think?

gAr · 2011-01-25 23:49:01

Whew! I thought I understood the question wrong when you asked that!
Congratulations Euler!!

Howardroark · 2011-01-26 02:00:29

Hi bobbym,

bobbym wrote:

Problem #12:
An urn contains 15 balls. There are only 2 different colors the balls can have, red and orange. There are at least 3 of each color in the urn. Picking 3 balls without replacement. the probability that all of the picked ones are red is the same as the probability that exactly one of them is orange. How many of the 15 balls are red?

bobbym · 2011-01-26 02:05:39

Hi Howardroark;

bobbym · 2011-01-28 16:22:54

New problem!

I want to get from (0,0) to (20,20) in a cartesian system. I want to use the shortest path of course. There is a big perfectly circular island with center at (10,9) with a radius of 6. What is the shortest distance to the destination, you cannot go through the interior of the circle.

A says ) 180 / 3 units is the shortest.
B says ) That is wrong.
C says ) My answer involves pi.
D says ) Mine too.

gAr · 2011-01-28 18:31:59

Hi bobbym,

bobbym · 2011-01-28 21:04:04

That is correct! Very good!

gAr · 2011-01-28 21:12:28

Nice one!

bobbym · 2011-01-28 21:40:15

Hi;

This is what I did, did you do something similar?

Drawing a tangent from (0,0) to the circle and from
(20 ,20) to the circle and following the arc of the circle between the two points of tangency.

gAr · 2011-01-28 21:51:50

Hi,

Yes, I did the same thing.
To convince myself it's the shortest path, I imagined an elastic string from (0,0) to (20,20), then slowly moved a circular obstacle against the string.

bobbym · 2011-01-28 22:06:12

It seems pretty obvious to me too. I used geogebra to draw it and played with bending the two lines. It became pretty obvious that the 2 tangents was the way to go.

bobbym · 2011-02-01 22:15:44

If you are allergic to formic acid please do not read this post. If you do and any allergic reaction occurs please see you physician immediately. No part of this post is to be ingested, if accidentally swallowed do not induce vomiting. That will occur naturally.

Now to the new problem!

http://en.wikipedia.org/wiki/Ant

3 ants start at point A ( 0,6 ). They run around the circle at 3 different speeds. Ant A travels at 10° per second. Ant B is slightly slower at 9° per second. Ant C is a slow poke he travels at only 4° per second. What is the earliest time that all 3 ants are out of sight of each other?

A says) Impossible to determine.
B says) I solved that once but do not remember how.
C says) Happens earliest at 216 seconds.
D says) I hate ants, let us wipe them all out.
E says) A is right.
F says) Never happens and I can prove it!

gAr · 2011-02-01 22:55:29

Hi bobbym,

What is the earliest time that all 3 ants are out of sight of each other?

Is it out of line-of-sight, as in : http://www.neoprogrammics.com/spheres/distance_to_horizon.php

Last edited by gAr (2011-02-01 22:57:07)

bobbym · 2011-02-01 23:14:18

Yes, that is correct. The ants eyes here are 1 unit high. Of course being upside down does not bother them.

gAr · 2011-02-02 01:30:41

Hi,

Agnishom · 2011-02-02 02:16:14

Can u give me any Idea when ants become out of sight

bobbym · 2011-02-02 03:16:28

Hi guys;

I am currently swamped with work please hold on until I can devote my full attention on the answer you gave.

Hi gAr;

I am getting 61.867 for the angle of line of sight.

gAr · 2011-02-02 03:56:57

Hi,

Isn't it (acos(6/7))⋅2 = 62.0054?

Last edited by gAr (2011-02-02 04:04:50)

bobbym · 2011-02-02 04:05:53

You are using that site for a sphere?

gAr · 2011-02-02 04:11:09

I did not use that site for calculation.
But how did you get your value?

bobbym · 2011-02-02 04:14:51

You might be right because I used geogebra. Set it to 10 digits. Remember ant A is 1 unit high bit so is ant B.

gAr · 2011-02-02 04:25:33

I get that value in geogebra too...

bobbym · 2011-02-02 04:31:05

Uh, oh looks like I have problem then! Can you tell me how you got it to measure the interior angle like that? When I do it it does the complementary angle of 298.13

gAr · 2011-02-02 04:35:40

It measures angle in counter clockwise direction.
If you measured angle[A,O,B], then try angle[B,O,A]

bobbym · 2011-02-02 04:42:20

Thanks a lot for that tip! But I am still getting 61.867. Is your line through g a tangent?

gAr · 2011-02-02 04:44:32

Yes, it is a tangent... Did you do something else?

Math Is Fun Forum

#476 2011-01-25 23:49:01

Re: What do you think?

#477 2011-01-26 02:00:29

Re: What do you think?

#478 2011-01-26 02:05:39

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#479 2011-01-28 16:22:54

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#480 2011-01-28 18:31:59

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#481 2011-01-28 21:04:04

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#482 2011-01-28 21:12:28

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