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Autocatalytic Reaction In an autocatalytic reaction, one substance is converted into a second substance in such a way that the second substance catalyzes its own formation. This is the process by which trypsinogen is converted into the enzyme trypsin. The reaction starts only in the presence of some trypsin, and each molecule of trypsinogen yields 1 molecule of trypsin. The rate of formation of trypsin is proportional to the product of the amounts of the two substances present. Set up the
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CALCULUS+ITS APPLICATIONS
- Consider the mixing process shown in the figure. A mixing chamber initially contains 3 liters of a clear liquid. Clear liquid flows into the chamber at a rate of 10 liters per minute. A dye solution having a concentration of 0.4 kilograms per liter is injected into the mixing chamber at a constant rate of r liters per minute. When the mixing process is started, the well-stirred mixture is pumped from the chamber at a rate of 10 + r liters per minute. (a) Develop a mathematical model for the mixing process, Let Q represent the amount of dye in kilograms in the mixture. dQ 0.4r-(Q/3)(10+) kg/min dr (b) The objective is to obtain a dye concentration in the outflow mixture of 0.25 kilograms per liter. What injection rate r is required to achieve this equilibrium solution? L/min Would this equilibrium value of r be different if the fluid in the chamber at time I = 0 contained some dye? no (c) Assume the mixing chamber contains 3 liters of clear liquid at time t = 0. How many minutes will it…arrow_forwardConsider the mixing process shown in the figure. A mixing chamber initially contains 2 liters of a clear liquid. Clear liquid flows into the chamber at a rate of 10 liters per minute. A dye solution having a concentration of 0.4 kilograms per liter is injected into the mixing chamber at a constant rate of rr liters per minute. When the mixing process is started, the well-stirred mixture is pumped from the chamber at a rate of 10+r liters per minute.(a) Develop a mathematical model for the mixing process. Let Q represent the amount of dye in kilograms in the mixture.kg/min The objective is to obtain a dye concentration in the outflow mixture of 0.25 kilograms per liter. What injection rate r is required to achieve this equilibrium solution?L/min Assume the mixing chamber contains 2 liters of clear liquid at time t=0t=0. How many minutes will it take for the outflow concentration to rise to within 1% of the desired concentration of 0.25 kilograms per liter?arrow_forwardConsider the mixing process shown in the figure. A mixing chamber initially contains 3 liters of a clear liquid. Clear liquid flows into the chamber at a rate of 10 liters per minute. A dye solution having a concentration of 0.25 kilograms per liter is injected into the mixing chamber at a constant rate of r liters per minute. When the mixing process is started, the well-stirred mixture is pumped from the chamber at a rate of 10 + r liters per minute. (a) Develop a mathematical model for the mixing process. Let Q represent the amount of dye in kilograms in the mixture. dQ = 0 dt kg / min (b) The objective is to obtain a dye concentration in the outflow mixture of 0.1 kilograms per liter. What injection rate r is required to achieve this equilibrium solution? r = L/ min Would this equilibrium value of r be different if the fluid in the chamber at time t = 0 contained some dye? no (c) Assume the mixing chamber contains 3 liters of clear liquid at time t = 0. How many minutes will it take…arrow_forward
- Cotinine levels were measured in a group of smokers (n = 31, x = 172.48 ng/mL, s = 119.50 ng/mL) and a group of nonsmokers not exposed to tobacco smoke (n = 31, x = 16.35 ng/mL, s = 62.53 ng/mL). Cotinine is a metabolite of nicotine, meaning that when nicotine is absorbed by the body, cotinine is produced. Test the claim that the variation of cotinine in smokers is greater than the variation of cotinine in nonsmokers not exposed to tobacco smoke. Use a 0.01 significance level. • What is the critical value? A. 1.84 B. 2.39 C. 1.74 D. 2.20 • What is the test statistic and conclusion? A. 3.65; Reject Ho B. 3.65; Fail to reject Ho C. 3.07; Reject Ho D. 3.07; Fail to reject Hoarrow_forwardVerify that (AB)T = BTAT. 2 -2 4 -1 0 A = 1 1 and B = 1 3 STEP 1: Find (AB). (AB)T = STEP 2: Find ВТАТ. BTAT = %3D STEP 3: Are the results from Step 1 and Step 2 equivalent? Yes Noarrow_forwardThe Different Effects of Excitation and Inhibition in Neural Circuit (series #1)| Neural circuit consists of polysynaptic neural network, combination of excitatory and inhibitory neurons. This exercise helps to understand the effects of excitation and inhibition in the nervous system. Our body is dynamically active under physiology condition. As a result, there are basal levels of activity such as 70 beats/min of heart rate at resting condition. Either increased or decreased activities are relative to the baseline. The effects of excitation are easily understood---one neuron activates another neuron. However, when inhibition is introduced into circuits, analysis become more complicated. In fact, the numbers of inhibitory neurons in the circuit determine the final effect of the circuit, which can be excitation or inhibition, on the target organ or area. We assume all excitatory and inhibitory neurons are glutamate and GABA neurons, respectively, in this practice sheet. The glutamate and…arrow_forward
- 1 A tank originally contains 100 gal of fresh water. Then water containing lb of salt per gallon is poured into the tank at a rate of 2 2 gal/min, and the mixture is allowed to leave at the same rate. After 10 min the process is stopped, and fresh water is poured into the tank at a rate of 6 gal/min, with the mixture again leaving at the same rate. Find the amount of salt in the tank at the end of an additional 10 min. Round your answer to two decimal places. i 4.13 lbsarrow_forwardAt the centers of some stars, fluorine-19 can undergo a fusion reaction with a proton (a hydrogen-1 nucleus) to produce two different nuclei. One of the products is an alpha particle (a helium-4 nucleus). What is the other? Write down the reaction equation for this transformation. 19 o + 19 F + 1 8 16 0 + He 8. 19 F + Не 9 1 15 0 + He Не IH → 8 19 F + '0+ He He 17 Не F + 1 8. 4 Не 18 0 + F + 2 8.arrow_forwardy = (8+ x)-1/2, Find the Linearization at z = a. a = 8 L(z) =||arrow_forward
- The linear model da -2x, r(0) 300 dt describes decay of populations. Select one: O True O Falsearrow_forwardIntegration Techniques. Use variable y for initial substitutionarrow_forwardIn Exercises 7-14, balance the chemical equation for each reaction. 8. (This reaction takes place when a green plant converts carbon dioxide and water to glucose and oxygen during photosynthesis.)arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning