A little help with a math problem....

[Taygoo]

Originally Posted by Letum

Just thinking out loud.....

Can they be worked out as simultaneous?

b must be less than 0.2 and more than 0.1

I can not say yet.

I have tried to do this..
86,23+1 = a*e^b*180

75,41-1=a*e^b360

and i get

a= 102,259 b=-0,000883

[Taygoo]

I go to sleep now.

Don't stay up all night for this. And thx for trying

[VipertheSniper]

I'm beginning to understand now.

[Letum]

Also need some sleep.
Will try again tomorrow if no one else has.

[Taygoo]

VipertheSniper..

Yea from the startpoint to A there is 86.23 m and from the startpoint to B there is 75.41 m

[Letum]

Good news!

The values are:

a=30
b=0.2

The function is:

30*e^(0.2*t)

To prove:
"When he has revolved around 180 degrees he is 86.23 meters from where he started."

Therefor:
a*e^(b*t)=86.23-a
30*e^(0.2*1pi)=86.23-30
30*e^(0.2*pi)=56.2336863

and

"after 360 degrees he is 75.41 meters where he started."

Therefor:
a*e^(b*t)=75.41+a
30*e^(0.2*2pi)=75.41+a
30*e^(0.2*2pi)=105.4075687


Second part coming soon. Ask if you need any more details.

[Onkel Neal]

Good work, I ran this past my daughter and two of her genius friends, they came up with the same thing:

This is what both Steven and Parag said after looking at the problem.


a = 29.99803486
b = 0.2000111295
theta = 14.88037659 (in radians)
r = 588.3798861 (m)

Note that if you want to describe the location with polar coordinates, you would use r = 14.88037659 - 4*pi = 2.314005976 instead.

ok, here is how i arrived at my answer:

First of all, at theta = 0, r = a. Therefore, the starting point is a. Now, using the information given we can write these two equations: A = a - 86.23 and B = a + 75.41.

We can write two more equations using the facts that at 180 degrees (pi) we are at point A and at 360 degrees (2*pi) we are at point B: A = -a*e^(pi*b) and B = a*e^(2*pi*b). Note that the first equation is negative to match the figure (A is on the negative x-axis).

At this point we have four equations and four unknowns. Solving for the unknowns yields the following: a = 29.99803486 and b = 0.2000111295 (A and B are not important)


Now, we must use arc length to find theta. We will use the following formula: s = [a*e^(b*theta)*(1+b^2)^(1/2)]/b. The formula can be derived using the general formula for arc length (involves a bit of calculus).

Anyway, using that formula (s = 3000 according to the problem), we get theta = 14.88037659 radians. Now, we can use the original ... Read Moreformula for a logarithmic spiral (r = a*e^(b*theta)) to solve for r. Doing so, we get r = 588.3798861 meters. As I said before, the exact location of the treasure can be expressed in the polar coordinates r = 588.3798861 m and theta = 2.314005976 radians.

After reading the explanation, it now seems so obvious (haha, no, not really!)

[Raptor1]

Hmm, good timing, them posts...almost too good...

[Onkel Neal]

Lol, Letum beat me to it.

[AVGWarhawk]

Now I see it. Clear as mud

[Letum]

Originally Posted by Neal Stevens

Lol, Letum beat me to it.

Ahh, but you did it the correct way.
I got the function through a hard trial and error/educated guess slog and then
started the calculus integration for the second part.

[Letum]

Neal, is your daughter sure about the second bit?

I find 3000m to be at ~13.76 radians...(4.38pi).
It may well be me that is wrong tho...I'm very much on the edge of my depth.

[Taygoo]

Thx for that..

i did some math, but never got these numbers

[Taygoo]

Letum good work..

I will try to use the result.

Do we agree that the start point is (a,0)
And therefore (0,0) is -a from the startpoint?

Neal

Nice to have a good family.. I say many thx to them.. give them a ice from me...:-)

[Task Force]

Ooooah god this thread is hard to understand.