Solve the given initial value problem using the method of Laplace transforms. Sketch the graph of the solution. y'' +y = 3u(t-4); y(0) = 0, y'(0) = 1 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. First, identify the appropriate Laplace transform(s) that should be applied to solve the given initial value problem. Select all that apply. e A. L{u(t-a)} = S B. £{eat} = - 1 □E. £{"}= s-a as [c. L{f''}(s) = s² L{f}(s) - sf(0) - f'(0) D. L{f'}(s) = s£{f}(s)-f(0) n! sn +1 Solve the given initial value problem. y(t) =

The acceleration of an object (in m/s²) is given by the function a(t) = 6 sin(t). The initial velocity of the object is v(0) 11 m/s. Round your answers to four decimal places. a) Find an equation v(t) for the object velocity. v(t) = = b) Find the object's displacement (in meters) from time 0 to time 3. meters c) Find the total distance traveled by the object from time 0 to time 3. meters

Find an equation for the linear function which has f (0.5) = 0.8 and f (0.8) = -0.3. f (x) =

y=f(x)=-3