According to the Michaelis-Menten equation, when an enzyme is combined with a substrate of concentration s (inmillimolars), the reaction rate (in micromolars/min) isAsR(s)(A, K constants)K + s(a) Find the limiting reaction rate as the concentration s approaches o by computing lim,. R(s).(Use symbolic notation and fractions where needed.)limiting reaction rate:(b) Find the reaction rate R(K).(Use symbolic notation and fractions where needed.)R(K) =(c) For a certain reaction, K = 1.150 mM and A = 0.200. For which concentration s is R(s) equal to 75% of its limiting value?(Use decimal notation. Give your answer to three decimal places.)S =mM

Given that Rs=AsK+s where A,K are constants Now, we have to find the limiting reaction rate as the…

Answered: According to the Michaelis-Menten…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A large tank contains 140 litres of water in which 20 grams of salt is dissolved. Brine containing 15 grams of salt per litre is pumped into the tank at a rate of 6 litres per minute. The well mixed solution is pumped out of the tank at a rate of 3 litres per minute. (a) Find an expression for the amount of water in the tank after t minutes. (b) Let x(t) be the amount of salt in the tank after t minutes. Which of the following is a differential equation for x(t)? (A) (E) (I) dt 90 || 3 x(t) 140 + 3t 6 (B) d 6 x(t) 140 + 3t 3 x(t) 140 + 6t dt dx dx 3 = 90 − x(1) (F) = 18 - 1*(7) (G) = 18 - dt dt 140 x(t) (C) dx dt = 18 3 x(t) 140 + 6t 6 x(t) 140 + 6t (D) (H) dx = 90 3 140 x(t) 6 x(t) 140 + 3t
(b) Towns A and B are 12 km apart. A cyclist leaves A and travels to B at an average speed of y km/h. From B, he returns immediately to A with an average speed reduced by 2 km/h. (i) Find, in terms of y, the time taken for the journey from A to B. (ii) Find, in terms of y, the time taken for the return journey. (iii) Given that the total time spent to travel from A toB and back to A is 5 hours, write an equation satisfied by y. (iv) Solve the equation written in part (iii). (v) Give a simple reason why one of the values of y obtained in part (iv) is not valid.
With t in years, the formulas for balances of two bank accounts, in dollars, are: f(t) = 1100(1.05)t and g(t) = 1500e0.05t(a) Describe the balance of the account modeled by f.(b) Describe the balance of the account modeled by g. State the effective annual yield.(c) What continuous rate has the same effective growth rate as the rate at which f(t) grows?
The volume, Vm³, of liquid in a container is given by V = (3h² + 4) ³ - 8, where h m is the depth of the liquid. Which of the following is/are true? Liquid is leaking from the container. It is observed that, when the depth of the liquid is 1 m, the depth is decreasing at a rate of 0.5 m per hour. The rate at which the volume of liquid in the container is decreasing at the instant when the depth is 1 m is 4.5√7. dV 6h√3h² +4. dh dV The value of at h = 1 mis 9√7. Non of the above is true. d²v 9h√3h² +4. dh2 = 2
A tank contains 1,000 L of pure water. Brine that contains 0.05 kg of salt per liter of water enters the tank at a rate of 5 L/min. Brine that contains 0.04 kg of salt per liter of water enters the tank at a rate of 10 L/min. The solution is kept thoroughly mixed and drains from the tank at a rate of 15 L/min. Let y(t) be the amount of salt (in kg) in the tank after t minutes. (a) Find the rate of change of amount of salt in the tank after t minutes. dy dt kg min How much salt is in the tank when t = 0? y(0) How much salt (in kg) is in the tank after t minutes? y = = kg (b) How much salt (in kg) is in the tank after 50 minutes? (Round the answer to one decimal place.) y(50) = kg
Water containing 0.5 lb/gal of salt enters a tank at a rate of 2 gal/min and leaves the tank at a rate of 3 gal/min. Suppose the tank initially contains 300 gallons of water and 60 lb of salt. (a) Set up an ODE for the amount of salt in the tank, x(t). b)solve it c)Sketch an accurate solution for x(t). Don't omit details.

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