Suppose you solved a second-order equation by rewriting it as a system and found two scalar solutions: y = e^5x and z = e^2x. think of the corresponding vector solutions y1 and y2 and use the wronskian to show that the solutions are linearly independent wronskian = det [ ] = these solutions are linearly independent because the wronskian is [ ] choose for all x.

In one day there are too high tides into low tides and equally spaced intervals the high tide is observed to be 6 feet above the average sea level after six hours passed a low tide occurs at 6 feet below the average sea level in this task you will model this occurrence using a trigonometric function by using x as a measurement of time assume the first high tide occurs at x=0. a. what are the independent and dependent variables? b. determine these key features of the function that models the tide: 1.amplitude 2.period 3.frequency 4.midline 5.vertical shift 6.phase shift c. create a trigonometric function that models the ocean tide for a period of 12 hours. d.what is the height of the tide after 93 hours?

Askate shop rents roller skates as shown on the table below. which graph and function models this situation?

What is the distance between the points (2, 5) and (5,9)?