An object of mass 10 kg is released from rest 3000 m above the ground and allowed to fall under the influence of gravity. assuming the force due to air resistance is proportional to the velocity of the object with proportional constant b=50 n-sec/m, determine the equation of motion of the object. when will the object strike the ground? assume that the acceleration due to gravity is 9.81 m/sec^2 and let x(t) represent the distance the object has fallen in t seconds.

6x + 3y = -6 2x + y = -2 a. x = 0, y = -2 b. infinite solutions c. x = -1, y = 0 d. no solution

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.)

The experience c-0.25c can be used to find the cost of an item on sale for 25% off which expression beloit equivalent to c-0.25c