Is this cool with you?

bobbym · 2011-04-22 17:40:16

I think so.

gAr · 2011-04-22 17:42:35

Ok.

123ronnie321 · 2011-04-25 03:27:17

A continuation to the Bullfrog Problem(#562),

'B' solves the given problem (using the same information as given in post no. 562 ) for some value of probability p < 1/6 and the 2 values of n that he gets are 5/2 & 7/6. Is it possible that B has solved the problem correctly?

Last edited by 123ronnie321 (2011-04-27 02:07:58)

bobbym · 2011-04-25 14:03:49

Hi 123ronnie321;

Yes, I believe that all n = 7 / 6 to n = 2.5 and a little bit more than that have the same probability. I have a drawing but I can not upload it to the site.

bobbym · 2011-04-26 12:47:08

Hi 123ronnie321;

Are you clear on it now? If not what question would you like answered? I do not know what you are asking.

123ronnie321 · 2011-04-26 20:04:47

Hi bobbym,
Yes, I am clear with it now.
I will be back in some time with some drawings. I am a bit busy now.

bobbym · 2011-04-26 21:29:37

That is okay. I would like to see them.

123ronnie321 · 2011-04-27 02:07:06

Hi bobbym,

I am confused. I do not understand your statement although it appeared correct to me till yesterday-

I believe that all n = 7 / 6 to n = 2.5 and a little bit more than that have the same probability.

This is what i think ---- for probability p = 1/6 there will be only one solution n = sqrt(3)
and for a fixed probability p < 1/6 there will be exactly two solutions.

bobbym · 2011-04-27 16:54:47

Hi 123ronnie321;

When I get the drawing uploaded it will clear this up.

In the meantime, If you think of the two tangents as now going through the 1 meter circle of course points on the smaller circle's circumference are solutions but so are all the other points between them. They are also within 1 meter.

123ronnie321 · 2011-04-27 19:25:07

bobbym · 2011-04-27 19:39:24

Hi;

I am currently in the middle of trying to upload an image that should make it clear to both of us.

See the points p1, p2, p3, p4 they are all solutions for some n. All the points in between then and a little beyond have the 41.4 degrees , so they have the same probability and they are within 1 meter.

123ronnie321 · 2011-04-27 21:26:40

Hi Bobbym,
In your diagram, n = length of segment BP1 & n = length of segment BP3 are the only solutions for probability = 41.7/360. This is what i think. Am i right?

bobbym · 2011-04-27 21:32:46

Pick any two more points between P1 and P3 and P2 and P4 (and on BP2 and BP4 ) and they have a different n but the same probability because they are still 41.7 degrees. The red circle and the green circle represent two possible n's. You can make an infinite number of circles through B that fall inside of the blue circle ( 1 meter ).

Only 60 degrees has 1 unique answer that is why the poser picked it.

123ronnie321 · 2011-04-27 21:45:27

Hi Bobbym,
But if you pick any point between P1 and P3 and name it say P5 and then draw an arc centered at B passing through P5, you will find that the portion of arc inside the 1 meter circle subtends at B an angle greater than 41.7. Thus the probability will differ, wont it?

bobbym · 2011-04-27 21:57:42

Not from the two points they will all have the same angle. I am showing another drawing. Each red circle because the points are all on the same lines all have the same angle and therefore the same probability. Only the n's ( radii of each circle is different.) Angle GBH and angle EBF and angle P3 B P4 are all 41.7 degrees. So P3 and P4 and E and F and G and H are all solutions for different n.

You see each red circle represents all possible jumps for a particular n from B. The angle from B (41.7 degrees ) in those circles represents the probabilities. The area that is covered inside of the small 1 meter ( blue circle ) does not matter. Just as long as the angular measure of the circumference of each red circle is inside of the blue one.

Arc P1P2 is 41.7° of the smallest red circle shown and is inside of the blue circle so P1 and P2 are solutions.

Arc EF is 41.7° of the next red circle shown and is inside of the blue circle so E and F are solutions.

Arc GH is 41.7° of the next red circle shown and is inside of the blue circle so G and H are solutions.

Arc P3P4 is 41.7° of the largest red circle shown and is inside of the blue circle so P3 and P4 are solutions.

You can see now that we can make many circles each being a solution. The 60° problem was a tangent so you could only have one solution. The rest of the angles have none or an infinite number of solutions.

123ronnie321 · 2011-04-29 17:37:48

Hi Bobbym,

Thank you so much for your time!

bobbym · 2011-04-29 18:23:25

Hi 123ronnie321;

You are welcome. Thanks for looking at the problem.

bobbym · 2011-05-03 19:24:28

New problem!

Prove

A says) I got it!
B says) Yep!
C says) Me too!
D says) That is a tough one!
E says) Too easy!

gAr · 2011-05-03 23:09:28

Hi bobbym,

bobbym · 2011-05-03 23:18:33

Hi gAr;

Very good! Can you find an even simpler idea than those 2?

gAr · 2011-05-03 23:34:54

I thought I could get something from (a+b+c)^2, but couldn't get further.
I don't know!

bobbym · 2011-05-03 23:52:24

Hi gAr;

gAr · 2011-05-04 00:09:08

Hi bobbym,

That's nice too!

bobbym · 2011-05-04 00:10:17

Yes it is, but who the heck can see that!

gAr · 2011-05-04 00:16:15

but who the heck can see that!

bobbym!

Math Is Fun Forum

#576 2011-04-22 17:40:16

Re: Is this cool with you?

#577 2011-04-22 17:42:35

Re: Is this cool with you?

#578 2011-04-25 03:27:17

Re: Is this cool with you?

#579 2011-04-25 14:03:49

Re: Is this cool with you?

#580 2011-04-26 12:47:08

Re: Is this cool with you?

#581 2011-04-26 20:04:47

Re: Is this cool with you?

#582 2011-04-26 21:29:37

Re: Is this cool with you?

#583 2011-04-27 02:07:06

Re: Is this cool with you?

#584 2011-04-27 16:54:47

Re: Is this cool with you?

#585 2011-04-27 19:25:07

Re: Is this cool with you?

#586 2011-04-27 19:39:24

Re: Is this cool with you?

#587 2011-04-27 21:26:40

Re: Is this cool with you?

#588 2011-04-27 21:32:46

Re: Is this cool with you?

#589 2011-04-27 21:45:27

Re: Is this cool with you?

#590 2011-04-27 21:57:42

Re: Is this cool with you?

#591 2011-04-29 17:37:48

Re: Is this cool with you?

#592 2011-04-29 18:23:25

Re: Is this cool with you?

#593 2011-05-03 19:24:28

Re: Is this cool with you?

#594 2011-05-03 23:09:28

Re: Is this cool with you?

#595 2011-05-03 23:18:33

Re: Is this cool with you?

#596 2011-05-03 23:34:54

Re: Is this cool with you?

#597 2011-05-03 23:52:24

Re: Is this cool with you?

#598 2011-05-04 00:09:08

Re: Is this cool with you?

#599 2011-05-04 00:10:17

Re: Is this cool with you?

#600 2011-05-04 00:16:15

Re: Is this cool with you?

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