circuits check attachment

Demonstralte by analysing the circuit that the inverse of a function can be generated by placing the function in the feedback loop of the op-amp. In the diagram, a logarithmic amplifier has been placed in the feedback loop. The output of the log amplifier is Vb=log(Va). complete question with pic in attached doc file

Prove that the R-2R ladder network shown in the diagram has an output Vo of 2.5V

Prove that the R-2R ladder network shown in the diagram has an output Vo of 2.5V see attachment for pic

Prove that the circuit will give a weighted sum of the two voltages V1 and V2.

Prove that the circuit will give a weighted sum of the two voltages V1 and V2.

Finding a Spring Constant

Assuming negligible friction, what spring constant would be needed by the spring in a "b-b gun" to fire a 10g pellet to a height of 100m if the spring is initially compressed 10cm?

Work Done

A 70 kg cart is pushed 50m with a constant velocity upon a 45degree frictionless incline. fid the work done on the cart(assume 10 m/s^2 gor gravity). Express in scientific notation and in joules.