Determine whether each of these proposed definitions is a valid recursive definition of a function f from the set of nonnegative integers to the set of integers. if f is well defined, find a formula for f(n) when n is a nonnegative integer and prove that your formula is valid. a) f(0) = 1, f(n) =−f(n−1) for n ≥ 1 b) f(0) = 1, f(1) = 0, f(2) = 2, f(n) = 2f(n−3) for n ≥ 3 c) f(0) = 0, f(1) = 1, f(n) = 2f(n+1) for n ≥ 2 d) f(0) = 0, f(1) = 1, f(n) = 2f(n−1) for n ≥ 1 e) f(0) = 2,f(n) = f(n−1)ifnisoddandn ≥ 1and f(n) = 2f(n−2) if n ≥ 2

step-by-step explanation:

a rhombus is a parallelogram enjoying his symmetry.

55.44 inches

step-by-step explanation:

part a. assuming a perfectly linear relationship, we can find the slope from the first two data points.

slope = m = (change in rainfall)/(change in years)

= (61.80 -62.33)/(2005 -2004) = -0.53/1 = -0.53

then the point-slope form of the equation of the line can be written as

y = m(x -h) +k . . . . . m = -0.53, (h, k) = (0, 62.33)

y = -0.53x +62.33 . . . x = years after 2004

part b. in 2017, x = 2017 -2004 = 13. then the predicted rainfall is

y = -0.53·13 +62.33 = 55.44 . . inches

the predicted rainfall in 2017 is 55.44 in.