Aspring with a spring constant 3 n/m is loaded with a 4 kg mass and allowed to reach equilibrium. it is then displaced 1 meter downward and released. suppose the mass experiences a damping force in newtons equal to 2 times the velocity at every point and an external force of f(t)=5sin(4t) driving the system. set up a differential equation that describes this system and find a particular solution to this non-homogeneous differential equation:

Michelle and julie work at a catering company. they need to bake 264 cookies for a birthday party that starts in a little over an hour and a half. each tube of cookie dough claims to make 36 cookies, but michelle eats about 1/5 of every tube and julie makes cookies that are 1.5 times as large as the recommended cookie size.it takes about 8 minutes to bake a container of cookies, but since julie's cookies are larger, they take 12 minutes to bake. a. how many tubes should each girl plan to bake? how long does each girl use the oven? b. explain your solution process what did you make? c. what assumptions did you make?

Rewrite the following quadratic functions in intercept or factored form. show your work. y = 9 + 12x + 4x^2

If f(x) = 2x + 8 and g(x) = x4, what is (gº)?