The curve for which f'(x) = ax, where a is a constant, is such that the tangent at (1,2) passes through the origin. find the gradient of this tangent and hence determine:
a) the value of a
b) the equation of the curve

Sam makes his sales calls according to a pattern. he travels either north or south depending on the calendar. some of his past trips were as follows: on february 17, april 24, june 10, september 19, and november 3 he drove north. on february 28, may 25, august 22, november 20, and december 18, he drove south. describe sams' pattern. in which direction will sam drive on oct4 and oct 24?

Find the area of a parallelogram with the given vertices. p(-2, -5), q(9, -5), r(1, 5), s(12, 5)

Asphere has a diameter of 10 in. what is the volume of the sphere?