For geotrophic flows in the atmosphere of the Earth, the following first order system of ODE is formulated. X' = AX where 1 0 0 X2 and x= A = 1 X4 The solution vector X relates to the velocities and accelerations of two perpendicular components of airflows tangential to the surface of the Earth. The symbols u and a represent the kinematic viscosity of air and the Coriolis constant; and both of them can be assumed as constants. (i) Find the eigenvalues of the matrix;

A tire company has found that the quantity demanded x, in thousands of units per week, of their best-selling tire is related to the unit price p by the equation (see image). A.) Use differentials to find an approximate change in the quantity of tires demanded per week if the unit price of the tires is increased from $119 to $122 per tire. B.) Use your calculator to find the actual demand for tires when the price is set at $119 and $122 per tire. Then find the difference in demand. C.) Explain why the answers to parts A and B are not the same.

Question 4 of 16 - 3.7 Homewor X Compute the derivative of the function y using derivative rules. y = (11x² + 5)³ (Express numbers in exact form. Use symbolic notation and fractions where needed.) dy 132x³ (11x² + 5)2 Incorrect II Question 2 of 14 - 3.6 Homewor X Weighma Material Resources 90°F S TIME: 11.56

Use logarithmic differentiation to find the derivative of y.. 14) у %3D1 х - 3 1 A) B) (Inx In(x - 3)) X - 3 x X- 3 1 3 D) 2 x - 3 X - 3