[14] For each of the following equations,find all equilibria;• find general solutions;• solve the initial value problem with initial condition ₁ (0) = 2, x₂(0) = 1;• sketch the phase portrait, identify the type of each equilibrium, and determine thestability of each equilibrium.10 x1 11-3-4 963=(b)Q]=[4][B]+[B]x2-5 -73(a)

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Answered: [14] For each of the following…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section: Chapter Questions

Problem 18T

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Solve each of the following equations for y and graph the formula(s) on your graphing calculator. Which one of these equations represents y as a function of x? (A) x²+y² = 9 x’+1+ y* = 0 (C) y=±Vx-5 (B) 2.x = 5+ y? (E) ху -4у%3D7 (D)
C. Eliminate the arbitrary constants in each equation and express the final answers in the following form: a,n(x)y(n) + an-1(x)yn-1) + . .. + a1(x)y' + ao(x)y – g(x) = 0 . 1. r* – y² = cy 2. y = cje" + cze²" + c3e*r
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1. Convert the following difference equation into a first-order form: Yt = Yt-1 + 2yt-2(Yt-3 – 1)
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16. The equation of motion of a particle is =t-2t + t-t, where s is in meters and t is in %3D seconds. (a) Find the velocity and acceleration as functions of t. (b) Find the acceleration after 1 s. (c) Graph the position, velocity, and acceleration functions on the same screen.
A cell site is a site where electronic communications equipment is placed in a cellular network for the use of mobile phones. The numbers y of cell sites from 1985 through 2014 can be modeled by y = 320.110/1+377e-0.257t 320,110 1 + 377e−0.257t where t represents the year, with t = 5 corresponding to 1985. (a) Use the model to find the numbers of cell sites in the years 1998, 2003, and 2006. (Round your answers to the nearest whole number.) 1998 y = cell sites 2003 y = cell sites 2006 y = cell sites (b) Use a graphing utility to graph the function. (c) Use the graph to determine the year in which the number of cell sites reached 280,000. The number of cell sites reached 280,000 in . (d) Confirm your answer to part (c) algebraically. The number of cell sites reached 280,000 in .
Consider the following. x² + y2 : = 16 (a) Find two explicit functions by solving the equation for y in terms of x. Y = (positive function) Y2 = (negative function) (b) Sketch the graph of the equation and label the parts given by the corresponding explicit functions. y y 5 X -5 -5 y y 5 5 -5 -5 (c) Differentiate the explicit functions. dy/dx = + (d) Find dy/dx through implicit differentiation. dy/dx = y Is the result equivalent to that of part (c)? Yes No O O
B. NONHOMOGENEOUS EQUATIONS: UNDETERMINED COEFFICIENTS 2. (D² + D – 2)y = 2x – 40cos2x 3. (D² + 1)y = sinx

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