Let y 00 + by0 + 2y = 0 be the equation of a damped vibrating spring with mass m = 1, damping coefficient b > 0, and spring constant k = 2. (a) Convert this second order equation into a system of two first order equations. (b) Express the eigenvalues for this system in terms of b. (c) Describe the stability of the equilibrium solution ~0 for b > 2 √ 2. Justify your claim with information about the eigenvalues of the matrix for the system. (d) Connect the behavior of solutions near an equilibrium of this type with the spring mass system with damping coefficient b > 2 √ 2 and explain why your answer for part (c) is (or is not) what one should expect.

Carmen begins her next painting on a rectangular canvas that is 82.7 cm long and has a area of 8,137.68 cm2. will the painting fit in a frame with an opening that is 82.7 cm long and 95 cm wide? explain

Which of the following is the true for f(x) = 5cos

Acaterer knows he will need 60, 50, 80, 40 and 50 dinner napkins on five successive evenings. he can purchase new napkins initially at 25 cents each, after which he can have dirty napkins laundered by a fast one-day laundry service (i. e., dirty napkins given at the end of the day will be ready for use the following day) at 15 cents each, or by a slow two-day service at 8 cents each or both. the caterer wants to know how many napkins he should purchase initially and how many dirty napkins should be laundered by fast and slow service on each of the days in order to minimize his total costs. formulate the caterer’s problem as a linear program as follows (you must state any assumptions you make): a. define all variables clearly. how many are there? b. write out the constraints that must be satisfied, briefly explaining each. (do not simplify.) write out the objective function to be minimized. (do not simplify.)