Let c be a positive number. A differential equation of the form dy dt = ky1 + c where k is a positive constant, is called a doomsday equation because the exponent in the expression ky1 + c is larger than the exponent 1 for natural growth. (a) Determine the solution that satisfies the initial condition y(0) = y0. (b) Show that there is a finite time t = T (doomsday) such that lim t → T − y(t) = [infinity]. y(t) → [infinity] as 1 − cy0ckt → , that is, as t → cy0ck . Define T = cy0ck . Then lim t → T − y(t) = [infinity]. (c) An especially prolific breed of rabbits has the growth term ky1.01. If 2 such rabbits breed initially and the warren has 14 rabbits after three months, then when is doomsday? (Round your answer to two decimal places.) months

The focus of a parabola is (-4,-5) and its directrix is y=-1 find the equation

Which of the following statements are true? (select all that apply.) a quasi-static process is one in which the system is never far from being in equilibrium. when a system can go from state 1 to state 2 by several different processes, the amount of heat absorbed by the system will be the same for all processes. the internal energy of a given amount of an ideal gas depends only on its absolute temperature. when a system can go from state 1 to state 2 by several different processes, the work done on the system will be the same for all processes. when a system can go from state 1 to state 2 by several different processes, the change in the internal energy of the system will be the same for all processes. for any substance that expands when heated, its cp is greater than its cv.

Great freights a local shipping company, bases its charges on the weight of the items being shipped. in addition to changing 0.40$ per pound, great freights also charges a one-time fee of 10$ to set up a customers account.