# Mathematics

Question 10

Use complex numbers to solve a parallel arrangement of impedances giving the answer in both Cartesian and polar form Use differential calculus to find the maximum/minimum for an engineering problem.

A sheet of metal is 340 mm x 225 mm and has four equal squares cut out at the corners so that the sides and edges can be turned up to form an open topped box shape.

Calculate:

(i) The lengths of the sides of the cut out squares for the volume of the box to be as big as possible.

(ii) The maximum volume of the box. Z Z1 Z2

Question 11

Using a graphical technique determine the single wave resulting from a combination of two waves of the same frequency and then verify the result using trig formulae.

A sheet of metal is 340 mm x 225 mm and has four equal squares cut out at the corners so that the sides and edges can be turned up to form an open topped box shape.

Calculate:

1. Using a vector or phasor diagram add the following waveforms together and present your answer in the form Vr = V sin(ωt+α).

Show all working including phasor diagrams.