Step 1 :Given: focal length (f) = 13.9 cm, magnification (m) = +2.00
Step 2 :Use magnification formula: m = -v/u, so v = -2u
Step 3 :Substitute v in lens formula: 1/f = 1/u + 1/v, so 1/13.9 = 1/u - 1/(2u)
Step 4 :Solve for u: u = 6.95 cm
Step 5 :\(\boxed{6.95}\) cm is the distance between the nickel and the lens