Consider the following initial-value problem. y' + 3y = f(t), y(0) = 0, where f(t) = t, 0 ≤ t < 1 0, t ≥ 1 Write the function f(t) in terms of unit step functions. Find the Laplace transform of the given function.

What values of x satisfy the inequality x^2-9x< 0? how is your answer shown on the graph?

If the scale factor between two circles is 2x/5y what is the ratio of their areas?

Mrs. avila is buying a wallpaper border to go on all of her kitchen walls. she wants to buy 5 extra feet of wallpaper border than she needs to be sure she has enough. she buys 55.5 feet of the border. the store owner selling the border uses the width of mrs. avila's kitchen to determine that the length of her kitchen must be 14.5 feet.