Refer to page 313 for a nonlinear differential equation and its linear approximation. Instructions: • Linearize the given nonlinear system around the equilibrium points. • Analyze the stability of each equilibrium using the Jacobian matrix and its eigenvalues. • Discuss the limitations of linearization for determining global behavior. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440 AZF/view?usp=sharing]

Write out the design matrix 1. Polynomial regression : 2. Data transformation: X and find its rank for the following Y₁ = Bot fixi + B₂X²³² + ... + B₂-, X; log7; = B₁ + B₁ (-log D₁) + E; P-1 > +E; " i=1.- `n models. n>p. i=1...n

what is wrong with the python code? Trying to plot phase portraits for the linearized systems for each equilibrium point of a non-linear system of differential equations, but command line 7 defining the system -- [z,p]=y --- gives me the error: too many values to unpack (expected 2)

Suppose that in a certain chemical process the reaction time y (hr) is related to the temperature (°F) in the chamber in which the reaction takes place according to the simple linear regression model with equation y = 4.10 - 0.01x and o = 0.07. n USE SALT (a) What is the expected change in reaction time for a 1°F increase in temperature? For a 9°F increase in temperature? 1°F increase hr g°F increase hr (b) What is the expected reaction time when temperature is 190°F? When temperature is 260°F? 190°F hr 260°F hr (c) Suppose five observations are made independently on reaction time, each one for a temperature of 260°F. What is the probability that all five times are between 1.39 and 1.61 hours? (Round your answer to four decimal places.) (d) What is the probability that two independently observed reaction times for temperatures 1° apart are such that the time at the higher temperature exceeds the time at the lower temperature? (Round your answer to four decimal places.)

Please assist to solve quesions #1-#6 from the attached image. Need to use matrix to solve Ordinary Least Squares (OLS) RegressionThanks!

Find sin(A), A^5, and expm(A) using (1) Cayley-Hamilton theorem and (2) Jordan decompositiongiven the following matrices: A = [-3 1;        0 -2] A = [2 3;        0 2] Solve by hand, but you can verify it using software afterwards. Optional: plot the phase plane of the above systems xdot=A*x using any software.

Suppose that in a certain chemical process the reaction time y (hr) is related to the temperature (°F) in the chamber in which the reaction takes place according to the simple linear regression model with equation y = 5.50 – 0.01x and o = 0.07. n USE SALT (a) What is the expected change in reaction time for a 1°F increase in temperature? For an 8°F increase in temperature? 1°F increase -0.01 hr 8°F increase -0.08 hr (b) What is the expected reaction time when temperature is 220°F? When temperature is 260°F? 220°F 3.3 hr 260°F 2.9 hr (c) Suppose five observations are made independently on reaction time, each one for a temperature of 260°F. What is the probability that all five times are between 2.78 and 3.02 hours? (Round your answer to four decimal places.) (d) What is the probability that two independently observed reaction times for temperatures 1° apart are such that the time at the higher temperature exceeds the time at the lower temperature? (Round your answer to four decimal…

Suppose that in a certain chemical process the reaction time y (hr) is related to the temperature (°F) in the chamber in which the reaction takes place according to the simple linear regression model with equation y = 5.10 0.01x and a = 0.085. USE SALT (a) What is the expected change in reaction time for a 1°F increase in temperature? For a 9°F increase in temperature? 1°F increase hr hr 9°F increase (b) What is the expected reaction time when temperature is 220°F? When temperature is 260°F? 220°F hr ✓hr 260°F 2.5 (c) Suppose five observations are made independently on reaction time, each one for a temperature of 260°F. What is the probability that all five times are between 2.37 and 2.63 hours? (Round your answer to four decimal places.) (d) What is the probability that two independently observed reaction times for temperatures 1° apart are such that the time at the higher temperature exceeds the time at the lower temperature? (Round your answer to four decimal places.) 0.4602 X You…

Model the situation with a dynamical system. Use your model to answer the question. 12) You take a 259-mg dose of an antibiotic every 5 hours. Your body eliminates 44% of the drug in a 5-hour period. How much antibiotic will be in your bloodstream after two doses? A) Dn+1 = 56Dn + 259, n = 0, 1, 2, .., where Do = 0; 14,763.00 mg B) Dn+1 = 0.56 D n + 259, n = 0, 1, 2, .., where Do = 259; 663.04 mg C) Dn+1 = 0.56D + 259, n = 0, 1, 2, ..., where Do = 0; 404.04 mg %3D %3D %3D %3D %3D %3D %3! D) Dn+1 = 0.44Dn + 259, n = 0, 1, 2, .., where Do = 0; 372.96 mg %3D %3!

not use ai please