) Suppose that a fourth order differential equation has a solution y = 3e2xx sin(x). (a) Find such a differential equation, assuming it is homogeneous and has constant coefficients. help (equations) (b) Find the general solution to this differential equation. In your answer, use C₁, C₂, C3 and C4 to denote arbitrary constants and x the independent variable. Enter c₁ as c1, c₂ as c2, etc. help

Give an equation for the cylinder passing through (0, 2, 4) with the vertical line through (1,0,0) as its central axis. (Express numbers in exact form. Use symbolic notation and fractions where needed.) equation: (x-1) + (v)² = 2/5

Suppose you are climbing a hill whose shape is given by the equation below, where x, y, and z are measured in meters, and you are standing at a point with coordinates (180, 120, 1194). The positive x-axis points east and the positive y-axis points north. 2 = 1500 -0.005.x² -0.01y² (a) If you walk due south, will you start to ascend or descend? ascend O descend At what rate? (b) If you walk northwest, will you start to ascend or descend? ascend descend At what rate? (Round the answer to two decimal places.) (c) In which direction is the slope largest? O(-1.8, -2.4)

8. A snow plow has a maximum speed of 30 miles per hour on a dry highway. Its maximum speed decreases by 0.5 mile per hour for every inch of snow on the highway. a) Determine the independent and dependent variable. b) Write the equation that describes this situation in the form y=mx+b. c) At what snow depth will the plow be unable to move? 9. If you deposit $1,000 in an account that earns an APR of 5% compounded once per year a) How long will it take for an initial deposit to triple? b) How much will you have after 20 months?