Q2/ The following system of equations is designed to determine concentrations (thec's in g/m²) in a series of coupled reactors as a function of the amount of mass input toeach reactor (the right-hand sides in g/day),... (1)703-30₁-0₂=-34201-602-03-38. (2)***C₂-8c₁-2c3-20=... (3)Using Jacobi's method for the first three iterations to determine the required.

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Answered: Q2/ The following system of equations…

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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Demand for a certain kind of SUV obeys the following equation,D(x, y) = 22,000 − 1 2 √ x − 5(0.6y − 10)3/2 where x is the price per car in dollars, y is the cost of gasoline per litre, and D is the number of cars.Suppose that the price of the car and the price of gasoline t years from now obey the following equations:x = 50,200 + 300t, y = 132 + 5 √ t What will the rate of change of the demand be (with respect to time) 3 years from now?
A pool has a volume of 1000?3. At time ? = 0 the pool is empty. We then fill the pool with water at a constant speed ? = 2.4 ?3 per minute. At the same time, water leaks out of the pool at a rate that is at all times proportional to the volume of water. The proportionality constant is ? = 3 ∙10^−3 ?????? − 1. Let ? (?) be the volume of water in the pool t minutes after we started filling water in the pool.a) Set up a differential equation that ? (?) must satisfy.b) Solve the equation by the integrative factor method.c) Find when the pool is half full.
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(a) Suppose we create a model of the height of a shrub (Y) based on the amount of bacteria in the soil (X1) and whether the plant is located in partial or full sun (X2). Height is measured in cm, bacteria is measured in thousand per ml of soil (so 1000 is 1 unit), and type of sun = sun and type of sun = between shrubs with a 5500 bacteria and those with a 4000 bacteria count. Assuming the sun is the 0 if the plant is in partial 1 if the plant is in full sun. What will be the height difference on average same for both. (b) Let's say after a few training steps your model is in this state: Y = 33 + 4.6 * X1+8* X2. Explain what the effect of the plant being in sun vs. partial shade will have on the average height of the shrub if there are no bacteria in the soil, based on the model.
A pasta company with a blue box produces 1,400 tons of semolina pasta per day. The pasta is fed into a machine as a large, loose dough and then squeezed through a bronze die to form a desired shape. As the pasta is squeezed through the die, the volume of space it takes up decreases while the mass remains constant, and thus the resulting shape is more dense. If m is the constant mass of the pasta in grams and V is the volume of the pasta in mL, then the density p is given by p= - m (a) If the mass remains constant while the volume changes with time, find dp dt (b) Suppose the mass of the pasta is 80g, the density is 0.8 g/mL, and the volume is decreasing at a rate of 400 mL/sec. How fast is the density of the pasta changing at that moment? mL · sec
A firm produces output y from inputs x1 and x2 whose prices are given as w1 = 1 and w2 = 1 respectively. The production function is y = x11/2 x21/2 a) Write the Lagrangian function b) Find the firm’s cost function If you could write out the steps to the first part about how you got the function, that would be great. It would help me understand it.

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