Find the initial and final values of y(t), given the following transfer functions and assuming u(t) = -2 for t > 0. S-5 (i) gp(s) = 4s²+2s+10 y(t=0) = y(t=∞) = 4 (ii) gp(s) = s²+10 y(0) = y(∞) =
Q: dy Solve the differential equation dx 9y' Find an implicit solution and put your answer in the…
A: Step 1: solution Step 2:Step 3: Step 4:
Q: 7 and 11
A:
Q: @find the solution of D integral equation 4 0 4 (X) = 1 + ± 5 × U(+) at ∞ u(x) = 1/2 x + 1/1√ √ x 4…
A: Part (a) Part (b): Complete the Series to the Tenth TermThe series expansion given…
Q: Histogram and graphs : I need detailed answer with each single step, do not skip any calculations,…
A:
Q: 1. A space-ship is heading towards a planet, following the trajectory, -t r(t) = Ae¯² (5 cos(4t), 4…
A: Step 1:Position of the spaceship as a function of time:r(t)=Ae−t(5cos(4t),4sin(4t),−3sin(4t)) where…
Q: 2. Use a full truth table to determine whether or not each of the following pairs of sentences are…
A: I'll guide you through solving this problem step by step for both pairs of sentences.(i) ¬(A → B) ⇔?…
Q: Please help and explain for part a b c and d Thank you
A:
Q: Solve the initial value problem xy' -2y=x³ex, y(1) = e.
A: Step 1:Step 2: Step 3: Step 4:
Q: ank holds 600 gallons of a well-mixed solution of water and 50 lbs of salt. A salt solution 5…
A: Question 6:Given data:The tank initially holds 600 gallons of water and 50 lbs of salt.Salt solution…
Q: Solve 2y"-5y+3y=0, y(0) = 1, '(0) = 2.5 (Note: The characteristic equation does factor.) y(t) =
A: Step 1: The given differential equation is, 2y"-5y'+3y=0 It can be written as, 2D²y-5Dy+3y=0 (Here…
Q: Problem 3 In the assignment on Canvas, find a data set of measured temperatures T in Kelvin measured…
A:
Q: ween Lapla Solve the oDE Using Yang and Natural transforms Ody +y=1, 9(0) = 0 (2) "y-y=0,…
A: Step 1: Step 2: Step 3: Step 4:
Q: The initial cost of an investment is $70,000 and the discount rate (cost of capital) is 12%. The…
A: Total Present ValueNow, we sum up all the present…
Q: Pls help ASAP, pls show all work and steps. Pls circle the final answer.
A: Answer:Explanation:
Q: (3) A capsule made of two identical hemispheres of radius r cm, one at each end of a cylinder, is…
A: Step 1. Understand the problem: Our cone measures 12 cm in height and 9 cm in base radius. A…
Q: A pharmacist needs to prepare 60 mL of a 3.3 % w/v solution using a mixture of a 15 % w/v solution…
A: First, we need to understand the problem. We are given two solutions with different concentrations…
Q: Definition 1. If A and B are sets, then their symmetric difference is defined to be AAB (AB) U (BA)…
A:
Q: Q1/ What is the relationship between Laplace transform L[u(t)] = F(s) = est u(t)dt 0 and the…
A: 2.) Adomian Decomposition Method for the PDE uxx+u2−uyy2=0:The Adomian Decomposition Method (ADM)…
Q: Don't use chat gpt plz Solve 9.3 only Solve 9.3 please
A: (a) Extrinsically:For the 2-sphere S2 embedded in R3, we can calculate the Riemann curvature tensor…
Q: 4. Given the data points (0, 1), (1, 2), (2, 0) and (3,2), construct the quadratic spline…
A: .
Q: These question need to be solved using R with the given data, please do not provide AI solution ,…
A: Here's the combined R code for Bayesian hierarchical modeling of Math Scores, along with…
Q: Detalied solution by hand , no AI please.
A:
Q: Please calculate Show-me pass-to-pass
A: //The answer above is a possible detailed explanation of the question mentioned…
Q: Write a mathematical relationship between each transformation with the proof 1\sumudu and elzaki. 2/…
A: Step 1:
Q: Suppose that an odd function f has the additional symmetry that f(L = x) = f(x) - on the interval –L…
A: In summary:- An=0 for all n .- Bn=0 for all even n .
Q: Initially 10 grams of salt are dissolved into 35 liters of water. Brine with concentration of salt 4…
A: Given,x(t)=140−130e−7tNow, to find the amount of time needed to have exactly 25 g of salt,Put x(t)…
Q: Classify al critical points of the functions as well
A: Combine like terms:−2x3+9x2−5x−2=0Step 4: Solve the Cubic EquationThis is the same cubic…
Q: Solve y"-y-12y= 0, y(0) = -2, y'(0) = -1 y(t) =
A:
Q: Please do by hand , not include chatgpt, i need all graphs and visualizations.
A: Assessing the Impact of Dietary Habits on Health OutcomesData Visualization1. Histograms for Daily…
Q: 1. Let A = (-∞, -2], B = (-3,8], C = (5,25) and U = R. Find An B, AUC, C \ B. 2. Prove that AU(BNC)…
A: Problem 1: Set OperationsGiven:A = (-∞, -2]B = (-3, 8]C = (5, 25)U = ℝ (the set of all real…
Q: 12. Let W be the subspace of R4 spanned by the vectors, u₁ = (1, 2, 5, 3), u₂ = ալ (2, 3, 1, −4), u3…
A: Form a matrix with the given vectors as rows:[ 1 -2 5 -3] [ 2 3 1 -4] [ 2 8 -3 -5] 2.…
Q: Don't use chat gpt
A:
Q: Pls help ASAP, pls show all work and steps. Pls circle the final answer.
A:
Q: (3) The power line is strung between A and B which are on the same horizontal plane. The tension…
A: The magnitude of the tension force T = 200 lbThe angleθ = tan⁻¹(30 / 4.5)θ = 81.47°The tension force…
Q: Solve and show all calculations Exercise 2314
A: Step 1:Step 2:Step 3:
Q: Exercise 2.7.4. Give an example of each or explain why the request is impos- sible referencing the…
A:
Q: Calculate the Wronskian of y = 3, y2 = 6x and y3 = -18 +6 W(z) b) Are the functions y₁ = 3, y2 = 6x,…
A: a) Calculate the Wronskian W(x) of the functions:Given:y1=3y2=6xy3=−18x+6The Wronskian of three…
Q: Plz don't use chat gpt plz Solve correctly
A: Step 1:Step 2:
Q: PLEASE DO NOT USE AI
A: 1 . Domain of Analyticity - (a) f(z) = sin z : Since sine is an entire function (i .e . ,…
Q: Don't use chat gpt It Chatgpt means downvote
A: Least Squares Fit for Trigonometric FunctionProblem: Fit the function We want to fit a trigonometric…
Q: Two vectors a and b have the components, in meters, ax = +3.2, ay = +1.6, bx = +0.5, by = +4.5.…
A: Given:A. The vector a have components ax = +3.2 m, ay = +1.6 mIn component form, the vector a can be…
Q: Ex 49: Show that if u is a subspace of V then u= Span (W)
A: Step 1 Step 2
Q: 1: Prove the directed version of Veblen's Theorem : A directed graph admits a decomposition into…
A: 1st question: Proof OutlineTo prove Veblen's Theorem, we will demonstrate both directions of the…
Q: Problem 1 Find a basis for the kernel and the image of the following maps. Also find the dimension…
A: Step 1:Step 2: Step 3: Step 4:
Q: Y prime is the first derivative of y , find the integral of y prime to find y , show step by step…
A: .
Q: Please solve and show all steps and work.
A:
Q: The demand for subassembly S is 120 units in week 7. Each unit of S requires 1 unit of T and 2 units…
A: We must first dissect the demand for subassembly S into its components (T and U), and then into the…
Q: 10. Determine the sequence generated by each of the following exponential generating func- tions. a)…
A:
Q: U2 6. Is the set of all polynomials with integer coefficients a subspace of the set of all…
A: Problem 6No, the set of all polynomials with integer coefficients is not a subspace of the set of…
Q: Tim Urban, owner/manager of Urban's Motor Court in Key West, is considering outsourcing the daily…
A: 1.Let X be the crossover point. Not outsourcing = OutsourcingFixed cost + Variable cost per room…
Please help with i and ii.
Step by step
Solved in 2 steps with 2 images
- The Lotka-Volterra equations are often used to model the links between a particular population of prey organisms and a population of predatory organisms. In a particular ecosystem u is used to represent the number of predatory organisms and v to represent the number of prey organisms. Suppose the growth rate uv of the predatory organisms is f(u,v) = - 0.5u + and of the prey organisms is g(u,v) = 6v – 10uv. 100 (a) Show that if u = 0.6 and v = 50, then f (u,v) = 0, and g(u,v) = 0. (The populations are said to be in equilibrium.) %D %3D f(u,v) (b) Find the linear approximation of the vector valued function h:(u,v)→ if u is close to 0.6 and v is g(u,v) close to 50. (a) Evaluate f(u,v) at u = 0.6 and v = 50, f(0.6, 50) = (Type an integer.)(1 point) Find the function y of t which is the solution of 64y" - 25у %3D 0 yı (0) = 1, (0) = 0. with initial conditions %3D Yi = Find the function y, of t which is the solution of 64y" - 25у %3D 0 with initial conditions y2 (0) = 0, , (0) = 1. %3D Y2 = Find the Wronskian W(t) = W(y , y2). W (t) : Remark: You can find W by direct computation and use Abel's theorem as a check. You should find that W is not zero and so yı and y, form a fundamental set of solutions of 64y" – 25y = 0.An antibiotic is administered intravenouslyinto the bloodstream at a constant rate r. As the drug flowsthrough the patient’s system and acts on the infection that is present,it is removed from the bloodstream at a rate proportional tothe amount in the bloodstream at that time. Since the amount ofblood in the patient is constant, this means that the concentrationy = y(t) of the antibiotic in the bloodstream can be modeled bythe differential equation dy/dt = r - ky, k > 0 and constant. If y(0) = y0, find the concentration y(t) at any time t.
- Solve the initial-value problem for y as a function of x. (16 - x²) dy - y = x +4 X +9 = 1, y(0) = 9 XConsider a monopolist who produces aluminium and faces a demand given by: (please see attached photo). The monopolist's costs are C(q) = 2q(a) Obtain the equilibrium of this industry and the monopolist's market power. Consider now an aluminium recycling industry. The aluminium available in period "t" can be recycled in the following period "t+1". Let "x" belongs to [0,1] be the fraction of aluminium recycled. The recycling cost is C(x) = x/(1-x). Consider a 2-period model "t" belongs to {1,2} in which the recycling industry is competitive. Consider a discount factor (d = 0.8).(b) Obtain the equilibrium in the aluminium market in each period and the market power of the monopolist. (c) Does the existence of a recycling industry improve the welfare of society? If so, how much would the government be willing to contribute to develop this industry?(d) What would be expected to happen with qt when "t" is a continuous variable. In particular, what would happen in the long run? ("t" -->…A particular region has a rabbit population of 1600. Two foxes are introduced to control the population of rabbits. Following this, the number of rabbits decreases according to the formula R(t) = 1700 – Aekt. - where A and k are constants, and R(t) is the number of rabbits in the region t years after the introduction of the foxes. (a) Given that the population of rabbits drops by one quarter after 5 years, find the values of A and k. (b) Following this model, how long will it take for the rabbits to become extinct? Give your answer to two decimal places. (c) Let F(t) be the number of foxes in the region t years after their introduction. If dF = 0.7F(t), dt find the time at which the rate of decrease of the rabbit population is equal to the rate of increase of the fox population, correct to two decimal places. dR dF Hint. Note that and represent the rates of change of the rabbit and fox dt dt populations respectively. (d) Identify any problems with this model.
- Assume that N(t) denotes the density of an insect species at time t and P(t) denotes the density of its predator at time t. The insect species is an agricultural pest, and its predator is used as a biological control agent. Their dynamics are given below by the system of differential equations. Complete parts (a) through (c). dN = 7N - 5PN dt dP = 4PN - P dt ..... (a) Explain why dN = 7N describes the dynamics of the insect in the absence of the predator. dt If there are no predators present, then P(t) = for all t. Substitute P = in the given differential dN equations to get dt So in the absence of the predators, the above equation describes the dynamics of the insect population. dN Solve the equation, dt N(t) = (Type an expression using t as the variable.) Describe what happens to the insect population in the absence of the predator. In the absence of the predator, the insect populationsolve part (b) (iii)test the stability of dp/dt=cp(1-p)-ep. Given that p represents the fraction of islands occupied, 0 < p < 1. Let c represent the colonization rate and e represent the extinction rate. p1=0 and p2=1 - e/c, test the stability of p1 p2, graphically, through the first derivative test. Explicitly write d(dp/dt)/dp.
- A population grows from an initial size of 10 people to an amount P(t), given by P(t) = 10(3+0.5t + t), where t is measured in years from 1996. Find the acceleration in the population t years from 1996. O A. 60t people per year OB. 60 people per year Oc. 30t people per year? OD. (5+30t) people per yearA 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) = kghelp