The position of an object at time t is given by s(t) = -1 - 13t. Find the instantaneous velocity at t = 8 by finding the derivative (you must use the limit of the difference quotient). Show all work.

An automobile assembly line operation has a scheduled mean completion time, μ, of 12 minutes. the standard deviation of completion times is 1.6 minutes. it is claimed that, under new management, the mean completion time has decreased. to test this claim, a random sample of 33 completion times under new management was taken. the sample had a mean of 11.2 minutes. assume that the population is normally distributed. can we support, at the 0.05 level of significance, the claim that the mean completion time has decreased under new management? assume that the standard deviation of completion times has not changed.

The perimeter of a rectangle is 42 inches. if the width of the rectangle is 6 inches, what is the length

Find the condition that the zeros of the polynomial f(x) = x^3+3px^2+3px+r may be in a.p.