Consider the initial value problem y″+16y=48t, y(0)=3,y′(0)=7. take the laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. denote the laplace transform of y(t) by y(s). do not move any terms from one side of the equation to the other (until you get to part (b) below).

The average number of vehicles waiting in line to enter a parking lot can be modeled by the function f left parenthesis x right x squared over 2 left parenthesis 1 minus x right parenthesis endfraction , where x is a number between 0 and 1 known as the traffic intensity. find the rate of change of the number of vehicles waiting with respect to the traffic intensity for the intensities (a) xequals0.3 and (b) xequals0.6.

If you apply the below transformations to the square root parent function, f(x) = vx, what is the equation of the new function? • shift 12 units right. • shift seven units down.

Elena is paid a constant rate for each hour she works. the table shows the amounts of money that elena earned for various amounts of time that she worked.