Consider the optimization problem where A m × n , m ≥ n , and b m .

a. Show that the objective function for this problem is a quadratic function, and write down the gradient and Hessian of this quadratic.

b. Write down the fixed-step-size gradient algorithm for solving this optimization problem.

c. Suppose that Find the largest range of values for α such that the algorithm in part b converges to the solution of the problem.

At the olympic games, many events have several rounds of competition. one of these events is the men's 100-meter backstroke. the upper dot plot shows the times (in seconds) of the top 8 finishers in the final round of the 2012 olympics. the lower dot plot shows the times of the same 8 swimmers, but in the semifinal round. which pieces of information can be gathered from these dot plots? (remember that lower swim times are faster.) choose all answers that apply: a: the swimmers had faster times on average in the final round. b: the times in the final round vary noticeably more than the times in the semifinal round. c: none of the above.

Ascientist has 50 grams of a radioactive element. the amount of radioactive element remaining after t days can be determined using the equation (1) after two days the scientist receives a second shipment of 50 grams of the same element. the equation used to represent the amount of shipment 2 remaining after t days is 10) - 50 which of the following is an equivalent form of the expression for the amount remaining in shipment 2? what’s the answer?

Percent increase and decrease. original number: 45 new number: 18