In each of problems 1 through a. draw a direction field for the given differential equation. b. based on an inspection of the direction field, describe how solutions behave for large t. c. find the general solution of the given differential equation, and use it to determine how solutions behave as t → [infinity]2. y'-2y=t2 e2t3. y'+y=te to the -t+14. y'+(1/t)/y=3cos2t, t> 05. y'-2y=3e to the t9. 2y'+y=3t10. ty'-y=t squared to the -t, t> 012. 2y'+y=3t squared

In the figure shown below, m < 40 and ab =8. which equation could be used to find 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?

Cal's go cart has a gas tank with the dimensions shown below. he uses a gas can that holds 11 gallon of gas, to fill the go cart tank. 11 gallon = 231 inches^3 how many full gas cans will it take to fill the go cart's gas tank?