Peirs

In the rectangle OABC, M is the midpoint of OA and N is the midpoint of AB. OB meets MC at P and NC at Q. Show that OP=PQ=QB Many Thanks

In the triangle OAB, OA = a and OB= b. Show that (a-b) times (a-b) = (a times a) + (b times b) - (2 times a times b). Hence prove the cosine rule Specifically the Cosine Rule part of question is difficult Thanks

the inside of a glass is in the shape of an inverted cone of depth 8cm and radius 4cm. Wine is poured into the glass at a rate of 4cm^3/s. Find the rate at which the depth of the wine in the glass is increasing when the depth is 6cm. Thanks

A hollow cone of base radius 10cm and height 10cm is held with its vertex downwards. The cone is initially empty when water is poured into it at the rate of (4pie) cm^3/s. Find the rate of increase in the depth of the water in the cone 18 second after pou...

A differential equation question Find the general solution to the equation (dy/dx)^2 + sinxcos^2x(dy/dx) - sin^4x = 0 Thanks