Using matrix method, solve the following system of equation:
x - 2y = 10, 2x + y + 3z = 8 and - 2y + z = 7.
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.
Find the equation of the parbola with latus-rectum joining points (4, 6) and (4, - 2).
The equation of parabola is given as:
(x - h)2 = 4p(y - k)
where, 4p is the length of latus rectum, which is equal to length of line segment joining the two given points (4, 6) and (4, - 2)
Length of latus rectum = 4p = = 8
p = 2
And focus is the mid-point of latus rectum, so focus: (4, 2)
since p =2, the vertex may be at a distance of 2 units left or right to the focus.
The vertex (h, k) be V(4, 2 + 2) = (4, 4)
The equation of the parabola may be
(x - 4)2 = 8(y - 4)
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.