Batch size 1
Total cost of chemicals
Total cost of preservatives
Total cost of production
r(t) = Σx(t)Σ = Σ t − sin(t) Σ
y(t) 1 − cos(t)
As an extension to this problem, we could consider the hypocycloid; a hypocycloid is the resulting curve traced by a point on the circumference of a circle that rolls without slip around the interior of another circle (see schematic). The position vector for a hypocycloid traced out by point P which sits on the circumference of a circle of radius r (with centre C), that rolls without slip on the circumference of the larger circle of radius R, is given by:
a) Explain (using words and mathematics) why the hypocycloid is a horizontal segment when R = 2r
b) Find vectors describing the velocity and acceleration of the point P on the hypocycloid for general values of r and R
c) When R = 2r, show that the acceleration of the hypocycloid is proportional to the distance of P from O .
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