1. Why do you think steady-state's are called steady-state's? Hint. Consider the problem da dt where x* is a steady-state of the function f (x). 2. What does a steady-state represent biologically? = f(x), x(0) = x*,
Q: E=2*10^5 I=30000 L=600 W=25 y = dy dx W 120EIL = 120 FIL (-5X² + 6(³X²-1²) ū assume as р 38, P = =…
A:
Q: b) Hence or otherwise prove that there do not exist three consecutive integer values of n for which…
A: We need to show that , there does not exists three consecutive integer values of n for which 29n+5…
Q: Define R as the region bounded above by the graph of f(x) = 3x - x² and below by the x-axis over the…
A: To find the volume of the solid of revolution formed by revolving R around the y-axis .
Q: Write the equation of the line that represents the linear approximation to the following function at…
A: The linear approximation: L(x) for a function f(x) at x=a is defined by the formula:…
Q: Discuss the continuity of the functions f and g. (x, y) = (0, 0) (x, y) = (0, 0) (x, y) = (0, 0) (x,…
A: Here given function as fx, y=x8-y8x4+y4x, y≠0, 00x, y=0, 0 and gx, y=x8-y8x4+y4x, y≠0, 06x, y=0, 0
Q: Modified TRUE or FALSE. Write Tolits if statement is true and Tol if statement is fa statement,…
A: 3. If the sun is a planet then 3 is even. 4. "Apple is a fruit." is a tautology We have to check…
Q: Solve y" - 2y + y = 12e³t y(0) = -1 y'(0) = 0
A:
Q: Solve the heat equation u = 12u, 'XX' u(x,0)=(x-8). 8 ○ Au(x, t) = 2/7/7 | e-120²₁ sin[(x-8)]d w. 2A…
A: Introduction: The heat equation is a very important partial differential equation. The method of…
Q: I. Modified TRUE or FALSE. Write Tolits if statement is true and Tol if statement is false. For…
A: Introduction: We can determine whether an argument is true or false based upon the rules of…
Q: Delete recessive rows and columns from the following matrix game: 4-31-2 4-40-2 -1 23 2 0 05 2 O A.…
A: Option B
Q: Find the four fourth roots of 7+27 and express the roots in polar form. [A] 1.64 cis 3.99°, 1.64 cis…
A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…
Q: 2. Determine the Maclaurin Series (5th approximation) of the function defined by f(x) = sinx. a.…
A: Maclareen series is taylor series about zero i.e. a =0…
Q: Choose all of the correct answers for each of the following: Consider the relationship R between two…
A: A] For one to one relationship both Entity E1 and E2 have direct relation. You can make any table…
Q: ind parametric equations for the tangent line to the curve with the given parametric equations at…
A: In this question, the concept of Parametric Equation is applied. Parametric Equation Parametric…
Q: Let f(x) = tan x. (1) Approximate f by a Taylor polynomial with degree n = 3 at the number a = 0.…
A: Given that fx=tanx To approximate the the function f by the Taylor polynomial with degree n = 3 and…
Q: Find both the vector equation and the parametric equations of the line through (0,0,0) that is…
A:
Q: The sum of the measures of the angles of n-sided polygon can be solved using the formula S = (n −…
A: We have S=n-2180
Q: Solve the given initial-value problem. y(x) = y" + 6y'7y = 11e²x, y(0) = 1, y'(0) = 1 -7.x 11e2x 7e…
A:
Q: I. Modified TRUE or FALSE. Write Tolits if statement is true and Tol if statement is false. For…
A:
Q: ell ау dy - 6 dy + ay dx 1. 3x 6e³x + 7e-²- log 2
A: We have to find the general solution of the given non-homogeneous linear differential equation.…
Q: Define R as the region bounded above by the graph of f(x) = x and below by the graph of g(x) = x²…
A:
Q: Let y = n=0 y' - 7y +11 x³ = 0, y(1)=4. Find 03. a3 03 = a3 None 269 3 268 3 271 3 a (x-1)" be the…
A: We have given a differential equation , y' - 7y + 11x3 = 0 with y1 = 4 Let y = ∑n=0∞ anx-1n be…
Q: The area of the region bounded by the function f(x) = + 3, lines x = −2, x = 2 and the x — axis is…
A:
Q: Lucia checked her online bank statement which shows the current balance is $381.23, pending…
A:
Q: Find a differential equation whose general solution is y = c₁est + c₂e-2t. = 0
A: given general solution : y=c1e8t+c2e-2t
Q: Let X be a normed space. (a) If E₁ is open in X and E₂ C X, then E₁ + E₂ is open in X. Proof: (a)…
A: It is given that X be a normed space, E1 is open in X and E2 be any subset of X. We have to explain…
Q: Make a generalization if tbe patterns discovered from the answers on the table.
A: Introduction: In mathematics and number theory, the Fibonacci sequence is one of the most important…
Q: Question # 44: Consider the following data set generated by a function, f (x) X f (x) 0.0 0.2 0.4…
A: Let us assign variables to the data points. For the given values of x we have, x0=0, x1=0.2, x3=0.4…
Q: Q3/ Solve the following Second order differential equations. 1- d²y dy - 3x - 12x 3 = dx dx² -
A:
Q: Solve the initial value problem 25y" - 40y' + 16y = 0, y(0) = 2, y'(0) = 3. y(t): How does the…
A: We have given a initial value problem , 25y'' - 40y' + 16y = 0 , y0 = 2 , y'0 = 3 First we will…
Q: 5. Write two propositions p and q in the form of complete sentences. Then formulate the compound…
A:
Q: - State and prove the convergence order of Newton's approach:
A:
Q: . Using Green's theorem, show that the area of a plane region in polar coordinate is 1 $ C r²do.…
A:
Q: Let P2 be the vector space of all polynomials of degree ≤ 2 with coefficients in R, and S= {1 + 2x,…
A: The basis for the vector space P2 is 1, x, x2. We have to write the matrix form for the set S. We…
Q: Find the Taylor or McLaurin series for the following functions f(x) = xe-*, a=0
A: Here f(x)=xe-x,a=0. We find the Maclaurin series of f(x).
Q: I. Modified TRUE or FALSE. Write Tolits if statement is true and Tol if statement is false. For…
A: Introduction: The validity of an argument depends upon the truth value of its conclusion. The…
Q: Find the Wronskian of two solutions of the differential equation t²y" — t(t − 2)y' + (t − 5)y = 0…
A:
Q: Find the volume V of the solid below the paraboloid z = 4-x² - y² and above the following region. R=…
A:
Q: Problem 5. Consider the recurrence T(n)= T(n-1) + (n). Prove that T(n) is (n²).
A:
Q: نموذجD1 (Q1)-A-State(First fundamental theorem) and Show that :(Z₂0 /(10).+..) (Z₁0+10 +10)
A: As per the policy, we are solving first question. Please repost the question and specify which…
Q: 2. Find the value of the line integral e F. dr without using Green's Theorem, where 1 F(x, y) = (x +…
A:
Q: Find the volume of the given solid over the indicated region of integration. f(x,y)=2x+2y+7;…
A: We find required volume of given region.
Q: An anthropologist can use linear functions to estimate the height of a male or female, given the…
A: The length of the humerus x is in centimeters. We have to find the height of a male and a female if…
Q: (B): If A = 2i + 3j - 4k; R = 3-4j+5k and C=i+j-k, find: (UU)Ã. (B+C)and (A + B). (iv) (3A+48).C…
A:
Q: A swimming pool has the shape of a box with the base that measures 20m by 17m and a uniform depth of…
A: Introduction: The work done by a force is the scalar product of the force and the displacement that…
Q: 5. Determine whether the series converges or diverges. b. Σ... (1+2n)" a ΤΟ n=1
A:
Q: Find the Wronskian of two solutions of the differential equation t²y" — t(t − 2)y' + (t − 5)y = 0…
A:
Q: Solve the initial value problem y" +0.2y +0.01y = 0; y(0) = 0, y/(0) = 2
A: We will 1st find roots of characteristic equation . depending upon type of roots of characteristic…
Q: -** Find the solution set in c Z² + 2i(32i) = 3Z
A:
Q: Find the general solution of the differential equation dy (x > 0). dx = 2x cos(x) The general…
A:
Step by step
Solved in 2 steps
- Please answer this question using the assumptions from the Solow Model In a country, the production function in terms of output per capita, y, and capital per labor, k, is y = k(12) The fraction of output saved, s, is 25% and the depreciation rate, δ, is 0.05. Assume that the population does not grow. What is the steady-state of capital per worker, k*, and output per worker, y*? What happens to the steady-state values if the population growth rate rises to 5%? By how much would the country have to increase its savings rate in b) in order to reach the same levels of steady-state values as in a)? Does the country’s growth rate increase in c) compared to a)? how?Suppose that we use K(C) = k C (for some constant k) instead of a Michaelis-Menten growth rate, in the chemostat model. (a) Find a change of variables so that only one parameter remains. (b) Find the steady state(s). Express it (them) in terms of the original parameters. Determine conditions on parameters so that a positive steady state exists, and explain intuitively why these conditions make sense. (c) Compare the conditions you just obtained with the ones that we got in the MM case. (d) Determine the stability of the positive steady state, if it existsFind the equilibrium solution for P. Furthermore determine whether P is initially increasing faster if the initial population is 120 or 200.
- Consider a population of tuna T that is growing logistically according to the equation: T'=0.1T(1-T/1000) What are the equilibrium values?The current toll for the use of a certain toll road is $2.50. A study conducted by the state highway department determined that, with a toll of p dollars, q cars will use the road each day, where q = 60,000e-0.5p. 1. Compute the elasticity of demand at p = 2.5. 2. Is demand elastic or inelastic at p = 2.5? 3. If the state increases the toll slightly, will the revenue increase or decrease?give an example of a function that is not a dirichlet function and justify
- It is observed that a certain bacteria culture has a relative growth rate of 12% per hour, but in the presence of an antibiotic the relative growth rate is reduced to 5% per hour. The initial number of bacteria in the culture is 22. Find the projected population after 24 hours for the following conditions.(a) No antibiotic is present, so the relative growth rate is 12%.(b) An antibiotic is present in the culture, so the relative growth rate is reduced to 5%.Consider the discrete-time dynamical system xt+1 = 5xt(1-xt).If xt = 4/5, xt +1 = _____Is x1 = 4/5 an equilibrium for this system? ______Write the updating function rule as f(x) = 5x(1-x).Compute the derivative: f'(x) = ______Evaluate the derivative at the equilibrium: ___________Is the equilibrium stable, unstable or neither? ________The revenue per month earned by the Couture clothing chain at timetisR(t) =N(t)S(t),whereN(t) is the number of stores andS(t) is the average revenue per store per month. Couturereleases a statement to their investors saying that currently they have 50 stores with a total revenueof$7,500,000 and expect to increase the number of stores by about 2 stores per month and increasetotal revenue by about$250,000 per month. What does this statement imply about the current rateof change of the average revenue per store per month?
- How might the competitive-hunter model be validated? Include adiscussion of how the various constants a, b, m, and n might beestimated. How could state conservation authorities use the modelto ensure the survival of both species?Assume the stock price follows a geometric Brownian motion, where current price S0=50, expected return µ=0.02 and volatility σ=0.80. The risk-free interest rate r=0.05 p.a. Using the Black-Scholes formula, what is the current value c0 of an European call option written on the stock with a strike of K=50 and a maturity of 3 months?What is the stability of equilibrium points of A and B? Is the energy of B higher than A?