- Webwork Math 2080 141 Homework06 1 Homework06 Problem 1 Previous Problem Problem List Next Problem Results For This Sub 1 (34.48 KiB) Viewed 38 times
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- Webwork Math 2080 141 Homework06 1 Homework06 Problem 1 Previous Problem Problem List Next Problem Results For This Sub 3 (56.09 KiB) Viewed 38 times
Results for this submission Entered 80 76 O Find the amount of salt in the tank after 1.5 hours amount 76 (kg) Answer Preview 80 Note: You can earn partial credit on this problem 76 0 Find the concentration of salt in the solution in the tank as time approaches infinity (Assume your tank is large enough to hold all the solution) concentration-0 kg/t) Result correct At least one of the answers above is NOT correct. (1 point) A tank contains 80 kg of salt and 2000 L of water. Pure water enters a tank at the rate 6 U/min. The solution is mixed and drains from the tank at the rate 3 Lin tal What is the amount of salt in the link initially? amount 80 gl incorect correct
At least one of the answers above is NOT correct (1 point) Susan finds an alien artifact in the desert, where there are temperature variations from a low in the 30s at night to a high in the 100s in the day. She is interested in how the artifact will respond to faster variations in temperature, so she kidnaps the artifact, takes it back to her lab (hotly pursued by the military police who patrol Area 51), and sticks it in an "oven-that is, a closed box whose temperature she can control precisely. Let 70) be the temperature of the artifact. Newton's law of cooling says that 7(r) changes at a rate proportional to the difference between the temperature of the environment and the temperature of the artifact. This says that there is a constant k, not dependent on time, such that T'k(E-T), where E is the temperature of the environment (the oven). Before collecting the artifact from the desert. Susan measured its temperature at a couple of times, and she has determined that for the allen artifact, k = 0,65. Susan preheats her oven to 90 degrees Fahrenheit (she has stubbornly refused to join the metric world). At time r=0 the oven is at exactly 90 degrees and is heating up, and the oven runs through a temperature cycle every 2x minutes, in which its temperature varies by 30 degrees above and 30 degrees below 90 degrees. Let Er) be the temperature of the oven after t minutes. EX)= 30sing-00 At timer 0, when the artifact is at a temperature of 60 degrees, she puts it in the oven. Let T() be the temperature of the artifact at timer. Then T(0) 60 (degrees) Witte a differential equation which models the temperature of the artifact. 19.5 T' =/(1.7) = Note: Use T rather than 7(r) since the latter confuses the computer. Don't enter units for this equation Solve the differential equation. To do this, you may find it helpful to know that if a is a constant, then sintet a²+1 e" (a sin(r)-cos(t))+C. T() 90-8.9102sint-13.708cost After Susan puts in the artifact in the n, the military police break in and take her away. Think about what happens to her artifact as 1oo and fill in the following sentence: For large values of r, even though the oven temperature varies between 60 and 120 degrees, the artifact varies from 73.65 Note: You can earn partial credit on this problem. to 102 degrees.