The amount of carbon-14 in an ancient artifact is decreasing at a rate of 15e^-0.00012t mg per year,
where t = 0 corresponds to the year 1900.
(a) how fast will the the amount of carbon-14 in the artifact be decreasing in the year 2000? show your work and answer in a complete sentence.
(b) by how much will the total amount of carbon-14 in the artifact decrease between 1900 and 2000? write down and evaluate a definite integral to answer this question. you must show your work in evaluating the integral; answer in a complete sentence.
(c) what is the average rate of change of the amount of carbon-14 in the artifact between 1900 and 2000? write down an expression involving a definite integral and evaluate the expression to answer this question. you don’t need to show your work in evaluating the expression; answer in a complete sentence.

Na food processing facility, a spherical container of inner radius r1 5 40 cm, outer radius r2 5 41 cm, and ther- mal conductivity k 5 1.5 w/m · k is used to store hot water and to keep it at 100°c at all times. to accomplish this, the outer surface of the container is wrapped with a 800-w electric strip heater and then insulated. the temperature of the inner surface of the container is observed to be nearly 120°c at all times. as- suming 10 percent of the heat generated in the heater is lost through the insulation, (a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the container, (b) obtain a relation for the variation of temperature in the container material by solving the differential equation, and (c) evaluate the outer surface tempera- ture of the container. also determine how much water at 100°c this tank can supply steadily if the cold water enters at 20°c.

How much force was applied to an object if was moved 2 meters and the work done on the object was 8 joules? a. 0.25 n b. 4 n c. 6 n d. 16 n

In a heat engine if 1000 j of heat enters the system the piston does 500 j of work, what is the final internal energy of the system if the initial energy was 2000 j? 1. write the equation 2.list out your known variables 3.plug the numbers into the equations 4.solve 5.write your solution statement that includes initial energy and final