SUBSIM Radio Room Forums - A little help with a math problem....

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Quote:

Originally Posted by Letum (Post 1125940)

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

I go to sleep now.

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

I'm beginning to understand now.

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

VipertheSniper..

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

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.

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

Quote:

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!) :haha:

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

Lol, Letum beat me to it.

Now I see it. Clear as mud:up::o

Quote:

Originally Posted by Neal Stevens (Post 1126395)

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.

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.

Thx for that..

i did some math, but never got these numbers

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...:-):D

Ooooah god this thread is hard to understand.:dead: