Build a Diff. equation that expresses the phenomenon . Newton's law of cooling and heating, write the model. . Diffusion of a disease considering that, in a population of “N” people, two infected people arrive

Build a Diff. equation that expresses the phenomenon . Newton's law of cooling and heating, write the model. . Diffusion of a disease considering that, in a population of “N” people, two infected people arrive

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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Finding the work done in stretching or compressing a spring. Hooke's Law for Springs. According to Hooke's law, the force required to compress or stretch a spring from an equilibrium position is given by F(x) = kr, for some constant k. The value of k (measured in force units per unit length) depends on the physical characteristics of the spring. The constant k is called the spring constant and is always positive. Part 1. Suppose that it takes a force of 17 N to compress a spring 0.3 m from the equilibrium position. Find the force function, F(x), for the spring described. F(x) = Part 2. Setup the integral that will give the work required to stretch the spring 0.6 m from the equilibrium position. W = Part 3. Calculate the work done by the force described above. W = Note: enter your answer using values correct to three decimal places.
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LESSON 9 A quantitative look at the fish population Now you'll study the same fish population as in Lesson 8, but this time you'll answer some quantitative questions. Recall that the fish population, p(t), satisfies the DE p' = p = 0.2p² -0.7, (fishpop) where p is measured in thousands of kilograms and t is in weeks. The above DE has two equilibrium populations, p₁=0.8 and p₂ = 4.2, both of which are constant solutions of the equation. Since they're solutions, no other solution can cross through them; this can be seen by applying the Existence and Uniqueness Theorem (see your text) to the problem. Thus, the other solutions either approach them asymptotically as t-, or move away from them. Your phase line plot from the last lesson should show this. Task 1. Use the Euler approximation method with a reasonable step size to answer the following questions. 1. If p(0) = 6 (i.e., 6,000 kg), what is the population after 10 weeks? 2. How close is this to the equilibrium point it's approaching?…
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X- 36.000 9-1.456 Step 3. After compleling the table, present following computations and the interpretation. Calculate the correlation coetticient Ir). using the working formula: o The sign or integer before the value just interprets the value as either directly or inversely proportional. Just consider the rounded-off value il it is equal to I or 0. o If the computedr>0, it means that there is a perfect correlation between the variables. Therefore, there will be a need to continue solving for the slope and y intercept, No further calculations will be made it r
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Find kurtosis by using quartile deviation(formula given in picture).
Question content area top Part 1 The federal government has developed the body mass index (BMI) to determine ideal weights. A person's BMI is directly proportional to his or her weight in pounds and inversely proportional to the square of his or her height in inches. (A BMI of 19 to 25 corresponds to a healthy weight.) A 6-foot-tall person weighing 177 lb has BMI 24. Find the BMI (to the nearest whole number) of a person whose weight is 170 lb and whose height is 69 in. Question content area bottom Part 1 The BMI is enter your response here. (Type a whole number.)