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DIFFERENTIAL EQUATIONS-NEXTGEN WILEYPLUS
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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_forwardSolve for x and y on both problemsarrow_forwardIn 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_forward
- Solve when x(0)=2 and y(0)=3arrow_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
- 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_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
- Two new DVDS, a horror film and a comedy film, are released in the same week. The weekly number N of rentals decreases for the horror film and increases for the comedy film according to the models JN = 350 - 25x IN = Horror film 30 + 15x Comedy film where x represents the time (in weeks), with x = 1 corresponding to the first week of release. (a) After how many weeks will the numbers of DVDS rented for the two films be equal? weeks (b) Use a table to solve the system of equations numerically. Compare your result with that of part (a). Weeks, x N = 350 - 25x N = 30 + 15x 1 3 4 5 6. 7 8 10 The rentals are equal when x = weeks.arrow_forwardfind the general solution of the equationarrow_forwardQuestion 3 based on question 2arrow_forward
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