For ,at startpunkt, r= a and when , at A, . And we are told that the distance between the points, which is the difference between those two, is 86,23: . When , point B, [tex]r= ae^{2b\pi}. The distance between startpunkt and B, we are told, is 7541: ae^{2b\pi}- a= 7541. Solve those two equations for a and b.

As for the arclength, the general formula, given that x(t) and y(t) are functions of the parameter t, isAnd how do i find the length ?

Regards

Jacob

Here, since this is given in terms of r and so you need and as well as the fact that . That is, and .

The derivatives messy but the formula reduces nicely (since ) to

which is easy to integrate:

to find the arclength between and the startpunkt, evaluate that at the two points and subtract:

set that equal to 3000 and solve for .