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Differential Equations: An Introduction to Modern Methods and Applications
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- If the quantities x and y are related by the equation y=3x , then we say that y is __________ _________ to x and the constant of ____________ is 3.arrow_forwardIn each of Problems 1 through 8, express the general solution of the given system of equations in terms of real-valued functions:arrow_forwardeliminate the arbitrary constant xy2 = Cy+1arrow_forward
- Suppose C = 45+ 0.5t and L = 9 +2.5t represent the population (in thousands) of two cities, Clarksville and Lanesville, respectively. Determine the number of years it will take for their populations to be (a) equal, and (b) for Clarksville to have twice as many inhabitants as Lanesville. Also report the population of the towns for each situation. (a) In how many years will the population of Clarksville equal that of Lanesville? Number years What will be their populations? Number thousand peoplearrow_forward1)The sum of three consecutive multiples of 4 is 444. Find these multiples. [This is a problem on linear equations in one variable] 2.State the steps you will take to transform 3x + n = 7 to x = (1/3)[7- n]arrow_forwardSolve for x. state non-permissable values of the variables 1/x-2 = 1/4x+10arrow_forward
- Please solve for problem #3, thank you.arrow_forwardIf x = 3 and y = 7, then 1/x + 1/yarrow_forwardSuppose E = 185+2.5t and W = 5 +7.5t represent the population (in thousands) of two cities, Eastborough and Westborough, respectively. Determine the number of years it will take for their populations to be (a) equal, and (b) for Eastborough to have twice as many inhabitants as Westborough. Also report the population of the towns for each situation. (a) In how many years will the population of Eastborough equal that of Westborough? 36 Correct response: 36 years What will be their populations? 275 Correct response: 275 thousand people A graphical representation of the solution to part (a) is shown below. Population, thousands Westborough of people Eastborough 275 t, years 36 (b) In how many years will Eastborough have twice as many inhabitants as Westborough? Predict first: Viewing the above graph, the answer should be less Correct response: less than 36 years. In how many years will Eastborough have twice as many inhabitants as Westborough? Number years (TIP: Be sure this is consistent…arrow_forward
- On the basis of data from 1990 to 2006, the median income y in year x for men and women is approximated by the equations given below, where x = 0 corresponds to 1990 and y is in constant 2006 dollars. If these equations remain valid in the future, in what year will the median income of men and women be the same? Men: Women: -231x+2y=60,623 - 830x + 3y = 49,894 The median income of men and women will be the same in the yeararrow_forwardThe molarity of a solute in solution is defined to be the number of moles of solute per liter of solution (1 mole = 6.02 × 1023 molecules). If X is the molarity of a solution of sodium chloride (NaCl), and Y is the molarity of a solution of sodium carbonate (Na2CO3), the molarity of sodium ion (Na+)inasolution made of equal parts NaCl and Na2CO3 is given by M = 0.5X + Y. Assume X and Y are independent and normally distributed, and that X has mean 0.450 and standard deviation 0.050, and Y has mean 0.250 and standard deviation 0.025. a) What is the distribution of M? b) Find P(M > 0.5).arrow_forward1.Solve simultaneously for x and y xy = 9 and 25x - 2y -3 =0arrow_forward
- Algebra for College StudentsAlgebraISBN:9781285195780Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher:Cengage LearningCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning