The Fibonacci series can be computed as follows, F(n) = F(n 1) + F(n 2) (1) In class, we showed how this can be done in O(log n) computation time. Now suppose that the de nition is changed in the following way, F0(n) = F0(n 1) + F0(n 2) + F0(n 3) + F0(n 4) (2) Can F0(n) be computed in O(log n)? If yes, please show how it can be done. If no, show a counterexample where this fails. Please provide your rationale for both. Assume that F0(0) = 0; F0(1) = 1; F0(2) = 1; F0(3) = 1.

Three out of five seniors remain undecided about a college major at the end of their senior year.

The volume v and paper surface area a of a conical paper cup are given by where r is the radius of the base of the cone and h is the height of the cone. a. by eliminating h, obtain the expression for a as a function of r and v. b. create a user-de ned function that accepts r as the only argument and computes a for a given value of v. declare v to be global within the function. c. for v ! 10 in.3 , use the function with the fminbnd function to compute the value of r that minimizes the area a. what is the corresponding value of the height h? investigate the sensitivity of the solution by plotting v versus r. how much can r vary about its optimal value before the area increases 10 percent above its minimum value?

Lucas put a lot of thought into the design for his company's new white paper. he made sure to include repeating design elements such as color schemes and decorative images. his goal was to a. add symmetry b. create a unified publication c. provide consistency d. save money