Good morning answers user. I am working on this math (Differential Equations) homework. Please help me with the rest of th
Posted: Mon Jul 11, 2022 12:50 pm
Good morning answers user. I am working on this math (DifferentialEquations) homework. Please help me with the rest of the questionsI attached down below. Please work on it carefully and make sure itis 100% right because it is worth many points. You do not have toshow work just give me the right answer. I will upvote if I get itright and down vote if it is incorrect.
1. (1 point) A thermometer is taken from a room where the temperature is 22°C to the outdoors, where the temperature is -6°C. After one minute the thermometer reads 12°C. (a) What will the reading on the thermometer be after 4 more minutes? (b) When will the thermometer read -5°C? 2. minutes after it was taken to the outdoors. Sunset Lake is stocked with 1200 rainbow trout and after 1 year the population has grown to 3900. Assuming logistic growth with a carrying capacity of 12000, find the growth constant k, and determine when the population will increase to 6100. yr-1 k = The population will increase to 6100 after years.
(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 T(t) be the temperature of the artifact. Newton's law of cooling says that T(t) 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 alien artifact, k = 0.6. Susan preheats her oven to 90 degrees Fahrenheit (she has stubbornly refused to join the metric world). At time t = 0 the oven is at exactly 90 degrees and is heating up, and the oven runs through a temperature cycle every 2 minutes, in which its temperature varies by 35 degrees above and 35 degrees below 90 degrees. Let E(t) be the temperature of the oven after t minutes. E(t) = At time t = 0, when the artifact is at a temperature of 40 degrees, she puts it in the oven. Let T(t) be the temperature of the artifact at time t. Then 7(0) = Write a differential equation which models the temperature of the artifact. T' = f(t, T) = Note: Use T rather than T(t) 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 1 -eat (a sin(t) cos(t)) + C. a² + 1 sin(t)eat dt = T(t) = - After Susan puts in the artifact in the oven, the military police break in and take her away. Think about what happens to her artifact as t→∞ and fill in the following sentence: For large values of t, even though the oven temperature varies between 55 and 125 degrees, the artifact varies from to degrees. (degrees)
- Good Morning Chegg User I Am Working On This Math Differential Equations Homework Please Help Me With The Rest Of Th 1 (61.81 KiB) Viewed 32 times
- Good Morning Chegg User I Am Working On This Math Differential Equations Homework Please Help Me With The Rest Of Th 2 (159.7 KiB) Viewed 32 times
(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 T(t) be the temperature of the artifact. Newton's law of cooling says that T(t) 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 alien artifact, k = 0.6. Susan preheats her oven to 90 degrees Fahrenheit (she has stubbornly refused to join the metric world). At time t = 0 the oven is at exactly 90 degrees and is heating up, and the oven runs through a temperature cycle every 2 minutes, in which its temperature varies by 35 degrees above and 35 degrees below 90 degrees. Let E(t) be the temperature of the oven after t minutes. E(t) = At time t = 0, when the artifact is at a temperature of 40 degrees, she puts it in the oven. Let T(t) be the temperature of the artifact at time t. Then 7(0) = Write a differential equation which models the temperature of the artifact. T' = f(t, T) = Note: Use T rather than T(t) 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 1 -eat (a sin(t) cos(t)) + C. a² + 1 sin(t)eat dt = T(t) = - After Susan puts in the artifact in the oven, the military police break in and take her away. Think about what happens to her artifact as t→∞ and fill in the following sentence: For large values of t, even though the oven temperature varies between 55 and 125 degrees, the artifact varies from to degrees. (degrees)