Consider an equation of motion given by x+x(t) = e x(0) = 2. 8. Find the (total) response. (A) 1+e-2t (D) (t 1)e-t+36 (B) e-t+te-2 (Et+2)e-t (C) (t-1)e-t (F) 2t²+3t+1 9. Find the forced response. (A) te-t (D) +1-e-2 (B) 2-2e-t (E) 2e-t (C) (t 1)e+e-21 (F) 4te +e-21
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please epelain this problem its labled as 2 different problem but its both for the given equation and they are closely related
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- Grazing Rabbits and Sheep This is a continuation of Exercise 21. In addition to the kangaroos, the major grazing mammals of Australia include merino sheep and rabbits. For sheep, the functional response is S=2.82.8e0.01V, and for rabbits, it is H=0.20.2e0.008V, Here S and H are the daily intake measured in pounds, and v is the vegetation biomass measured in pounds per acre. a. Find the satiation level for sheep and that for rabbits. b. One concern in the management of rangelands is whether the various species of grazing animals are forced to complete for food. It is thought that competition will not be a problem if the vegetation biomass level provides at least 90 of the satiation level for each species. What biomass level guarantees that competition between sheep and rabbits will not be problem?z1(x) = 3x2+xex, z2(x) = xex-x2 are solutions of a second order, linear nonhomogeneousequation L[y] = f(x). y1(x) = x4is a solution of the corresponding reduced equationL[y] = 0. The general solution of L[y] = f(x) is:A mixing tank A 500-liter (L) tank is filled with pure water. Attime t = 0, a salt solution begins flowing into the tank at a rate of5 L/min. At the same time, the (fully mixed) solution flows outof the tank at a rate of 5.5 L/min. The mass of salt in grams in thetank at any time t Ú 0 is given byM(t) = 250(1000 - t)(1 - 10-30(1000 - t)10)and the volume of solution in the tank is given byV(t) = 500 - 0.5t.a. Graph the mass function and verify that M(0) = 0.b. Graph the volume function and verify that the tank is emptywhen t = 1000 min.c. The concentration of the salt solution in the tank (in g/L) isgiven by C(t) = M(t)>V(t). Graph the concentration functionand comment on its properties. Specifically, what are C(0)and lim t-S1000- C(t)?d. Find the rate of change of the mass M′(t), for 0 <, t < 1000.e. Find the rate of change of the concentration C′(t), for0 < t < 1000.f. For what times is the concentration of the solution increasing?Decreasing?
- can someone help me with this question? In a certain country, a population census was carried out in 1990 and its population turned out to be 8 million inhabitants, then another census was carried out in 2015 and its population turned out to be 14 million inhabitants. Use the population model of Malthus, to obtain the population in millions of inhabitants of the country, in the year 2060.equation differential partialSolve the next cauchy problem.pq − 3xy − 2u= 0,u= 15y,x = 5.PART A (full explanation plz) Certain populations that are present in a given habitat and are related in such a way that one species, known as the prey, has an ample food supply and the other species, known as the predator, feeds on the prey. This situation can be modeled with a system of differential equations known as the predator-prey or Lotka-Volterra equations. A solution of this system of equations is a pair of functions R (t ) and V (t) that describe the populations of the prey and predator as functions of time. Usually, it is impossible to find explicit formulas for R and V so graphical methods are used to analyze the equations. (1) Suppose that the populations of aphids and ladybugs are modeled with a system of Lotka- Volterra equations given below dA/dt=2A(1-0.0001A)-0.01AL dL/dt= -.5L+.0001AL where A(t) is the aphid population at time t and L(t)is the ladybug population at time t. a) In the absence of ladybugs, what does the model predict about the aphids?
- Differential Equations a) f(t)= 3t^2-e^t b) f(t)=2√t-t^4 c) f(t)= t if 0 ≤ t <2; f(t)= 2 if t ≥ 21. The population of Normal, Illinois grows proportionally to its population at time t. At an initial population of 1500, it grows at a rate of 12% over 9 years. What is the value of the proportionality constant?a. 0.01259/yrb. 0.004435/yrc. 0.004856/yrd. 0.00767/yr 2. What is the population of Normal, Illinois in 30 years?a. 2188 peopleb. 3655 peoplec. 2643 peopled. 5553 people 3. A sample of organic origin was tested to determine its approximate age. About 52% of its C-14 had decayed. Use a half life value of 5730 years to determine how old the sample is.a. 6067.37 yearsb. 11,136 yearsc. 8219 yearsd. 17,527 years 4. A prehistoric artifact was recently found off the coast of Borneo. Based on carbon dating, approximately 88% of the C-14 remained. Use the half-life of C-14 as 5,730 years. What is the approximate age of the artifact?a. 1057 yearsb. 2489 yearsc. 5406 yearsd. 3819 years 5. A 400-L tank initially contains 40 kg of KCl. There is an incoming flow rate of 8 L/min of a 2 kg…Using Gaussian elimination: Y2-1.96845y1+0-0.015625=0 Y3-1.96845y2+y1-0.015625=0 1.96845y3+y2-0.015625=0 Answer: Y1 = -0.002584 Y2 = 0.005152 Y3 = 0.002584 Show how to get the answer
- part B plz and if possible part C Certain populations that are present in a given habitat and are related in such a way that one species, known as the prey, has an ample food supply and the other species, known as the predator, feeds on the prey. This situation can be modeled with a system of differential equations known as the predator-prey or Lotka-Volterra equations. A solution of this system of equations is a pair of functions R (t ) and V (t) that describe the populations of the prey and predator as functions of time. Usually, it is impossible to find explicit formulas for R and V so graphical methods are used to analyze the equations. (1) Suppose that the populations of aphids and ladybugs are modeled with a system of Lotka- Volterra equations given below dA/dt=2A(1-0.0001A)-0.01AL dL/dt= -.5L+.0001AL where A(t) is the aphid population at time t and L(t)is the ladybug population at time t. a) In the absence of ladybugs, what does the model predict about the aphids? b) Identify…Weather is notoriously difficult to predict. Models are subject to chaotic motion and must consider the initial conditions. The famous butterfly effect states that if a butterfly flaps its wings in Tahiti, that small event might cause a hurricane to hit Texas. This leads us to the following model: suppose that weather at time t is always between 0 and 1 and is governed by x_(t+1)=〖4x〗_t (1-x_t ). For x_0 = 0.2 and x_0 = 0.2000001, determine x_1; x_2;… x_50. Assume values for x closer to zero represent mild weather, and closer to 1 represent extreme weather. How do your calculations illustrate the butterfly effect? Support your answer with graphs. Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.Weather is notoriously difficult to predict. Models are subject to chaotic motion and must consider the initial conditions. The famous butterfly effect states that if a butterfly flaps its wings in Tahiti, that small event might cause a hurricane to hit Texas. This leads us to the following model: suppose that weather at time t is always between 0 and 1 and is governed by x_(t+1)=〖4x〗_t (1-x_t ). For x_0 = 0.2 and x_0 = 0.2000001, determine x_1; x_2;… x_50. Assume values for x closer to zero represent mild weather, and closer to 1 represent extreme weather. How do your calculations illustrate the butterfly effect? Support your answer with graphs.