(a) [5 points] using only the definition, find the laplace transform y (s) of y(t) = e a t where a is a constant. for what values of s does the laplace transform y (s) exist? (b) [10 points] solve, using laplace transforms, the initial value problem: y 00 − 4y 0 + 4y = 3, y(0) = 0, y0 (0) = 1.

Mary beth used the mapping rule to find the coordinates of a point that had been rotated 90° counterclockwise around the origin. examine the steps to determine whether she made an error. m (3, –6) is rotated 90° counterclockwise. (x, y) → (–y, x) 1. switch the x- and y-coordinates: (6, –3) 2. multiply the new x-coordinate by –1: (6(–1), –3) 3. simplify: (–6, –3) .

Points a, b, and c form a triangle. complete the statements to prove that the sum of the interior angles of triangle abc is 180

Which shows one way to determine the factors of 4x3 + x2 – 8x – 2 by grouping?