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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_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 magnesium chloride (MgCl2), and Y is the molarity of a solution of ferric chloride (FeCl3), the molarity of chloride ion (Cl−) in a solution made of equal parts of the solutions of MgCl2 and FeCl3 is given by M = X + 1.5Y. Assume that X has mean 0.125 and standard deviation 0.05, and that Y has mean 0.350 and standard deviation 0.10. Find μM.arrow_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 magnesium chloride (MgCl2), and Y is the molarity of a solution of ferric chloride (FeCl3), the molarity of chloride ion (Cl−) in a solution made of equal parts of the solutions of MgCl2 and FeCl3 is given by M = X + 1.5Y. Assume that X has mean 0.125 and standard deviation 0.05, and that Y has mean 0.350 and standard deviation 0.10 .Assuming X and Y to be independent, find σM.arrow_forward
- The 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_forwardIf a and ß are the roots of the equation x² – 3x + 4 = 0, the equation whose roots are a? + a + 1 and B² + B + 1 is (a) x' - 6x + 19 = 0 (b) х? + 6х - 37 %3D 0 (c) x' + 6x - 19 = 0 (d) x² - 6x + 37 = 0 If a, and B, are the roots of the equation 3x? - 2x – 5 = 0 and a, and B, are the roots of the equation 2x² + x - 7 = 0, the equation whose roots are (a,a, + B,B,) and (a,ß, + a,B,) is (a) 36x? – 12x + 911 = 0 (b) 9х* - 91х + 11 %3D0 (c) 36x? + 12x - 911 = 0 (d) 9x² + 91x – 19 = 0 3x-2 If a and B are the roots of the equation 7X- 3 5x 1 = 4, 1 isarrow_forward(5x + 3y = 1 (5x- y = 13arrow_forward
- In a certain region, about 6% of a city's population moves to the surrounding suburbs each year, and about 2% of the suburban population moves into the city. In 2020, there were 9,750,000 residents in the city and 900,000 residents in the suburbs. Set up a difference equation that describes this situation, where x is the initial population in 2020. Then estimate the populations in the city and in the suburbs two years later, in 2022. (Ignore other factors that might influence the population sizes.) Set up a difference equation that describes this situation, where x is the initial population in 2020. x₁ = Mx0 = (Type an integer or decimal for each matrix element. Do not perform the calculation.)arrow_forwardIf x = (1/2)a + (2/3)b + (3/4)c c=(12x-6a- /9arrow_forwardfind the general solution of the equationarrow_forward
- Solve when x(0)=2 and y(0)=3arrow_forwardSolve for x and y on both problemsarrow_forwardIf an antibiotic is taken orally, only a fraction of the antibiotic is actually absorbed in the bloodstream. This fraction is called bioavailability of the dose. Suppose that for a specific antibiotic, when a mg is taken orally, only 50% of the dose is absorbed, that is the bioavailability can be expressed as 2 I. Now, if h mg of antibiotic enters the bloodstream, the amount eventually absorbed at the site of the infection 4h is g(h) = mg. h+ 4 !! Finally, if g mg is absorbed into the site of the infection, the number of surviving bacteria is given by 3000 f(9) = CFU (colony forming units). %3D 9+g? a) If a dose of 8 mg is given orally, compute the amount of antibiotic absorbed at the site of infection. An er: mg. Round to 1 decimal place as needed. b) If an amount of 7 mg enters the bloodstream, compute the amount that is eventaully absorbed at the site of the infection. Answer: mg. Round to1 decimal place as needed. c) If a dose of 6 mg is injected directly into the bloodstream…arrow_forward
- Algebra for College StudentsAlgebraISBN:9781285195780Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher:Cengage LearningCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning