can I get the solution for these Special Topics in Physics: Mathematical Methods problems

Exercise 1. Size of a molecule [10 points] The size of an oil molecule can be estimated with the following experiment. A drop of oil spreads out on the surface of water until the thickness of the oil layer is on average equal to the length of an oil molecule (the molecules stand vertically on the water surface). a) Assume the oil drop has a mass of 8.4 . 107 kg and a density of 0.92 g/cm3. Once it has spread out it covers an area of 0.55 m. What is the length of an oil molecule? b) Assume additionally that the oil molecule has a mass of 150 u, where 1 u (one atomic unit) corresponds to 1.661 . 10 " kg. What cross section area does one such molecule occupy on average? Exercise 2. Mathematical induction [10 points] Prove the following relationship using mathematical induction: 13 + 23 + . . . + n3 - 43 - -12 (2+ 1)2 Exercise 3. Infinite circuit [10 points] In the following infinite ladder of 10 resistors, what is the resistance between points A and B? This measurement is indicated by the ohmmeter connected between these points. WWW WWW WWW B WWW WWW WWWExercise 4. [10 points] Choose and solve one of the following two exercises: Option 1: basic problem Simplify the expression 3 2 - 1 2 . 92 5-5 . 2- 2 . 45 3 1x 3.y 2 ) 272 5 - 2 . 2 - 2 . Option 2: advanced problem Evaluate V2 2 2 Note that a means a(6")