Consider the differential equation y'' − y' − 30y = 0. Verify that the functions e−5x and e6x form a fundamental set of solutions of the differential equation on the interval (−[infinity], [infinity]). The functions satisfy the differential equation and are linearly independent since the Wronskian W (e−5x, e6x) = ?

On a architect's drawing of a house, 1 inche representa 1.5

The height of a birch tree, f(x), in inches, after x months is shown in the graph below. how much does the birch tree grow per month, and what will be the height of the birch tree after 10 months? a. the birch tree grows 1 inch per month. the height of the birch tree will be 16 inches after 10 months. b. the birch tree grows 2 inches per month. the height of the birch tree will be 26 inches after 10 months. c. the birch tree grows 3 inches per month. the height of the birch tree will be 36 inches after 10 months. d. the birch tree grows 2 inches per month. the height of the birch tree will be 24 inches after 10 months.

Ateam of runners is needed to run a 1 2 -mile relay race. if each runner must run 1 4 mile, how many runners will be needed?