Using matrix method, solve the following system of equation:
x - 2y = 10, 2x + y + 3z = 8 and - 2y + z = 7.
If , prove that: x2 + y2 + z2 + 2xyz = 1
squaring on both sides,
P, Q and R reprsent switches in on position and P', Q' and R' represent switches in off position. Construct a switching circuit representing the polynomial PR + Q(Q' + R)(P + QR). Using Boolean algebra, simplify the polynomial expression and construct the simplified circuit.
A wire of length 50m is cut into two pieces. One piece of the wire is bent in the shape of a square and the other in the shape of a circle. What should be the length of each piece so that the combined area of the two is minimum.