We solve the problem by means of the method of separation of variables. We have then: 2ty '= 4y 2t (dy / dt) = 4y t (dy / dt) = 2y (dy / y) = 2 (dt / t) integrating both sides: int (dy / y) = 2int (dt / t) Ln (y) = 2Ln (t) + c exp (Ln (y)) = exp (2Ln (t) + c) exp (Ln (y)) = exp (Ln (t ^ 2) + c) exp (Ln (y)) = exp (Ln (t ^ 2)) * exp (c) y = c * t ^ 2 ---> y (1) = - 2. -2 = c * (1) ^ 2 c = -2 then: y = -2 * t ^ 2 answer: c = -2 r = 2
The vertex angle of any triangle of the dodecagon formed by radii and a side is 360/12=30º. The half-length of the base of the triangle is sin15=0.2588 approx. Since there are 12 sides there are 24 half-sides in the perimeter=6.2117.
