HW017 closes 12 14 2024 at 11 59pm EST Myat Thu mxt5693 Section 8 This PDF is available for convenience Assignments must be submitted within WeBWorK for credit Problem 1 2 points The differential equation dy dx 7 2 x 21 y 6 xy Solve the differential equation dy dx x 49y Problem 3 2 points has an implicit general solution of the form F x y K In fact because the differential equation is separable we can define the solution curve implicitly by a function in the form F x y G x H y K 1 Find an implicit solution and put your answer in the following form constant Help help formulas 2 Find the equation of the solution through the point x y 7 1 Your equation must describe a sin gle curve y f x with the domain of f as large as possible Help help equations Find such a solution and then give the related func tions requested F x y G x H y 3 Find the equation of the solution through the point x y 0 4 Your answer should be of the form y f x Help help equations Problem 2 2 points Find the solution to dy dt 8y y 7 3 satisfying y Problem 4 2 points Solve the separable differential equation cid 112 11x 8y x2 1 0 dy dx Subject to the initial condition y 0 10 y Problem 5 2 points Find an equation of the curve that satisfies dy dx 117yx12 and whose y intercept is 4 y x Problem 6 2 points Find the particular solution of the differential equation dy dx y cos x 3 cos x satisfying the initial condition y 0 5 Answer y Your answer should be a function of x Math 140 Fall 2024 Amos Ong Page 1 Problem 7 2 points Find the particular solution of the differential equation x 4 e 2y dy dx satisfying the initial condition y 4 ln 4 y Your answer should be a function of x Problem 8 2 points An unknown radioactive element decays into non radioactive substances In 940 days the radioactivity of a sample decreases by 62 percent a What is the half life of the element half life days b How long will it take for a sample of 100 mg to decay to 59 mg time needed days Problem 10 2 points A bacteria culture grows with constant relative growth rate The bacteria count was 784 after 2 hours and 117649 after 6 hours Answer the following questions 1 What is the relative growth rate Answer k 2 What was the initial size of the culture Answer P0 3 Find an expression for the number of bacteria after t hours Answer P t 4 Find the number of cells after 4 hours Answer 5 When will the population reach 1000000 Answer in hours t Problem 9 2 points A bacteria culture starts with 700 bacteria and grows at a rate proportional to its size After 3 hours there will be 2100 bacteria a Express the population after t hours as a function of t population function of t b What will be the population after 5 hours c How long will it take for the population to reach 2370 Problem 11 2 points A thermometer is taken from a room where the temper ature is 22oC to the outdoors where the temperature is 8oC After one minute the thermometer reads 7oC a What will the reading on the thermometer be after 5 more minutes b When will the thermometer read 7oC minutes after it was taken to the out doors Generated by WeBWorK The WeBWorK Project openwebwork org Problem 12 2 points For this problem T is the variable for the temperature k is the growth constant or constant of proportionality and is positive Newton s Law of cooling states that the temperature of an object changes at a rate proportional to the difference of the temperature of the surrounding medium and the temperature of the object If the temperature of the sur rounding medium is 320 F write a differential equation to model the situation 0 Differential equation This is a separable differential equation T k Integrating both sides with respect to t using C as the constant of integration we get The temperature of the object is given by T Generated by WeBWorK The WeBWorK Project openwebwork org