Consider a set of points (i,)nci such that zo< function s defined by s(x) = s(e ) for x e[,, 1where the s, are (of course) cubic polynomials (3.3) in, and a piecewise cubic polynomial (a) wnte down all the conditions to be satısfied for s to be a natural cubic spline (b) the function s 1s defined by 3-3 2 (3 so() si (x) if 0 2 f 2 4 s() = 12r236) is s a natural cubic spline? justify your answer

Astone is dropped with no initial velocity from the top of a cliff and hits the ground a time of 3.9 s later. what is the height of the cliff, in units of meters? you may assume that air resistance is negligible. give the answer as a positive number question 15 a figure skater is rotating at a rate of 200 revolutions per minute. what is the angular speed, in units of rad/s? 200 o 20.9 12000 o 3.33

The radius of a sphere is increasing at a rate of 9 cm/ sec. find the radius of the sphere when the volume and the radius of the sphere are increasing at the same numerical rate.

Which statement best explains why the overall charge on an atom is zero?