Consider the linear DE system æ' = Aæ with -14 -90 and A = 2 14 If the initial conditions are given by x (0) find the the functions #1 (t) and x2(t). Enter your answer as a 2x1 column vector, i.e x2 (t).

au Find : U(x1, x2) = 2X1 X2 дх2 O X1X2 2x1 2 2x2

The path of flight (trajectory) of a football thrown by a quarterback is described by the +0) ². x² following function: y(x) = - where y = vertical position of football relative to the ground Linear model yo = vertical launch position of football relative to the ground horizontal position of football relative to launch position g=magnitude of gravitational acceleration vo = launch speed = launch angle relative to horizontal Which type of mathematical model is used here to describe the football's trajectory? Nonlinear model g 2v² cos² e Exponential model + (tan)x + yo Trigonometric model

What does it mean for the differentiability of a function if the Cauchy-Reimann equations (Ux = Vy and Vx = -Uy) do not hold?

Find xy² Una -dA, R= [0,4] × [-2, 2] x² + 1

Differentiate the function. r(t) = (3t². + 8)i + r'(t) = (6t)i + +(12²) ₁ r'(t) = = (1²2); - 15 i + (6t)j r'(t) = (6t)i - r'(t) = (6)i + 15 25

Suppose that f(x) = x² – 5x + 7 has roots a and B. Use symmetric functions to find a + B, aß, a² + B², and a³ + B³.

Find an orthogonal change of variables, x = Py, that transforms the quadratic form q(x) = x² + x²+2x1x2 − 2x2x3 into a quadratic form no cross-product form. Write the new quadratic form.

Find two linearly independent solutions of y" + 1xy = 0 of the form Y1 1+ azx³ + a6x® + · ... Y2 = x + b4x4 + b7x + . ... Enter the first few coefficients: Az = -5/6 help (numbers) a6 help (numbers) b4 help (numbers) b7 help (numbers) I| ||

find domaine and image