PRINTABLE VERSION. Quiz 3. Question 1 Give the general solution to. f) None of the above. Question 2 Give the general solution to. 2/1/2016 Print Test

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1 PRINTABLE VERSION Question 1 Give the general solution to Quiz 3 Question 2 Give the general solution to 1/12

2 Question 3 + xy = 4 cos(3x) 3 Give the general solution to x 2 y 4 y 1/2. y 3/2 = 2x 2 sin(3x) + Cx 2 y 3/2 = 2x 2 sin(3x) + Cx 2 y 3/2 = 2x 2 sin(3x) + Cx 2 y 1/2 = 2x 2 sin(3x) + Cx 2 y 1/2 = 2x 2 sin(3x) + Cx 2 Question 4 Give the general solution to 2/12

3 Question 5 Give the general solution to Question 6 Give the family of orthogonal trajectories of the family of parabolas with vertical axis and vertex at the point ( 6, 3 ). 3/12

4 Question 7 A 1000 gallon tank, initially full of water, develops a leak at the bottom. Given that 200 gallons of water leak out in the first 10 minutes, find the amount of water, A(t), left in the tank t minutes after the leak develops if the water drains off at a rate proportional to the amount of water present. Question 8 4/12

5 An advertising company designs a campaign to introduce a new product to a metropolitan area of population 2 Million people. Let P(t) denote the number of people (in millions) who become aware of the product by time t. Suppose that P increases at a rate proportional to the number of people still unaware of the product. The company determines that no one was aware of the product at the beginning of the campaign, and that 40% of the people were aware of the product after 30 days of advertising. The number of people who become aware of the product at time t is: Question 9 Give the family of orthogonal trajectories of 5/12

6 Question 10 A calculator is required to obtain the final answer on this question. A solid metal sphere at room temperature 20 o C is dropped into a container of boiling water (100 o C). If the temperature of the sphere increases 5 o in 9 seconds, find the temperature of the ball after 18 seconds in the boiling water. (Assume the sphere obeys Newton's Law of Cooling.) Question 11 Give the family of orthogonal trajectories of 6/12

7 Question 12 Give the general solution to Question 13 Find a particular solution for given that y( 2) = /12

8 Question 14 Find a particular solution for given that y(0) = 3. Question 15 Find the general solution for 8/12

9 Question 16 Find the general solution for Question 17 The half life of a certain radioactive material is 3 days. The length 9/12 1

10 of time it will take for the material to decay to mass is 1 8 of its original ln 3 t = days 3 ln 8 t = 9 days t = 1 days 3 ln 2 t = days ln 8 8 ln 3 t = days ln 2 Question 18 A certain bacteria population obeys the population growth law. It is observed that the doubling time for the population is 3 hours. The length of time it will take for the population to increase to 4 times its original population is 4 ln 3 t = hours ln 2 2 t = hours 3 ln 3 t = hours 3 ln /12

11 t = 6 hours 3 ln 2 t = hours ln 4 Question 19 A certain bacteria population obeys the population growth law. Find the growth constant if the population at time t = t1 is 3 and the population at time t = t2 is 6. r = t 2 ln 6 t 1 ln 3 ln (2) r = t2 t1 ln (2) r = t1 t2 ln (1/2) r = t2 t1 ln 18 r = t2 t1 Question /12

12 A certain radioactive material loses half life of the material is 1 5 of its mass in 4 hours. The T = 4 ln 2 ln (4/5) ln (4/5) T = 4 ln 2 ln (4/5) T = 4 ln 2 T = 4 ln 2 ln (6/5) T = 4 ln 2 ln (4/5) 12/12