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(∞) =
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- y = (4 + x)-¹/2, Find the Linearization L(x) = = a = 5 at x = a.SOLVE STEP BY STEP IN DIGITAL FORMAT Given the transfer function H(s): Find y(t) when x(t)=8(t) = s+2 (s + 1)² + 4The 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.)
- (3) The approximate enrollment, in millions between the years 2009 and 2018 is provided by a linear model Y3D0.2309x+18.35 Where x-0 corresponds to 2009, x=1 to 2010, and so on, and y is in millions of students. Use the model determine projected enrollment for the year 2014. 近Solve b(a) Determine if the following sets of functions are linearly dependent or linearly independent on IR. -x¸ -2e2a + 5e¬ª -x (ii) x|x|, x? (b) Consider of the solutions is W (y1, Y2) = e². Find p(x) and q(x) and write the DE. Y1 and Y2 as two solutions for the following DE where y1 = x-1 and the Wronskian y" + p(x) y' + q(x) y = 0
- Determine which of the following pairs of functions are linearly independent.Let z = 8x2 + 7y2, and suppose that (x, y) changes from (2, -1) to (2.01, -0.98). (a) Compute Az. Az = (b) Compute dz. dz = (c) Compare the values of Az and dz. O dz is a good approximation of Az. O dz is not a good approximation of Az.(15) Determine whether or not the functions y₁ 4x³, y2 = π, y3 = 12x², and y4 = 24x are linearly independent on any interval. Show all work to support your answer.
- Determine which of the following pairs of functions are linearly independent. 1. f(x) = x² g(x) = 4|x|² NO_ANSWER NO_ANSWER NO_ANSWER NO_ANSWER " ✓ 2. f(x) = e4x ✓ 3. f(0) = cos(30) ✓ 4. f(t) = 3t, g(t) = |t| " g(x) = 4(x-3) 2 g(0) = 4 cos³ (0) - 4 cos(0)The temperature of the air in Boise is given by the function f(t,h) = 0.01ht² - 0.12ht - 0.6h t² + 12t + 60 Where f is the temperature in degrees Fahrenheit, t is measured in hours (with t = 0 corresponding to 9 a.m.), and h is the height above sea level, measured in thousands of feet. Find all four second order partial derivatives: a. ft(t,h) = b. fth(t,h) = c. fht(t,h) = d. fnn(t,h) =