Question

6-6

6-17

6-18

please help me, how could solve these problems

In chemical kinetics and other types of rate processes, you frequently encounter with the initial condition m(0) == 2 6-4 B representing the interconversion of two species, A and B. The the scheme A rate equation for this interconversion can be written as dA/dt = -k\A + kąB, where k and kz are called rate constants. By conservation of mass, A(t)+B(t) = AoBo, where Aq = A(0) and Bọ = B(0). Solve the above equation for A(t) (8 and B(t). Show that Bea/Acq = k1/k2 = Keq - A large container contains 100 liters of a salt solution whose concentration is 20 grams per liter. A salt solution of concentration 2 grams per liter is added to 6-5 (b r cfVerity Equation Verify Equatio the container at a rate of 10 liters per minute, and the efflux from the container is Prove in both ca 5 liters per minute. Calculate the minimum amount of salt in the container and when it will occur. Assume that the solution is stirred vigorously so that it is cShow that A c C = (A+ B 16 maintained at a uniform concentration. 6-6 A large container contains 100 L of a 2.00 molar solution. Pure water is pumped into the container at a rate of 2.00 L s-, and the resulting solution (assumed to be homogeneous) is pumped out at a rate of 1.00 L s. How long will it take before 18 Show that A C = (A2 + trigonometric the solution in the container is less than 0.10 molar? 6-7 Find the general solutions of (a) y"(x)-yx)-2y(x) = 0 (b) y'(x)-6y (x)+9y(x) = 0 (c) y'(x)+4y'(x) +y(x) = 0 trigonomet 19 Use the res 20 Consider resistance system i find a second solution. x)+y(x) = 0, use reduction of order to 6-13 Prove that x(t) = cos ot oscillates with a frequency v=/27. Prove that x (r)= A cos ot +B sin ot oscillates with the same frequency, o/2T. solve the following initial value problems; -14 + a2x(t) = o (a) r d2x x(0) 0; x' (0)= vo +wx(t) = 0 x(0)= xo: x (0) = vo (b) d12 Prove in both cases that x(t) oscillates with frequency o/2t. Verify Equation 6.33. 6-15 Verify Equation 6.34. 6-16 Show that A cost + B sin t can be written as C sin (t +), where 6-17 C = (A2 B2)2 and = tan-'(A/B). Hint: Work backward from the trigonometric identity sin (a + B) = sin a cos B + cos a sin B. Show that A cost + B sin t can be written as C cos (t +), where 6-18 C = (A2+ B2) 1/2 and = tan'(-B/A). Hint: Work backward from the trigonometric identity cos (a + B) = cos a cos B- sina sin B mg 6-19. Use the result of Problem 6-18 to derive Equation 6.35 from Equation 6.34. 6-20 Consider a body falling from a height h, and suppose that it encounters a resistance proportional to its velocity. Show that Newton's equation for this system is (see Figure 6.10) Figure 6.10. The geometry to be used in Problem 6-20 dv d2x = + mg dt2 dx Y -V = g or dt dt

Answer 1

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