Solve the second order non-homogeneous differential equation y" – 2y' – 3y = 3t2 + 4t -5, y = 9, y'(0) = -4 5. using the table of laplace transforms (appendix e), find the laplace transforms of the following functions: a. f(t) = 6e-57 +e3+ + 5t3 - 9 b. f(t) = 4 cos(4t) - 9 sin(4t) + 2cos (100) c. f(t) = e3+ + cos(6t) - eicos (6t) 6. find the inverse transform f(t) for each of the given functions f(s) using the method of partial fractions a. f(s) = b. f(s) = **

The hawaiian alphabet has 12 letters. how many permutations are posible for each number of letters?

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.

Idon’t understand! use slope intercept form to solve: through: (2,5) slope= undefined