) 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)

Suppose you are climbing a hill whose shape is given by the equation z = 1200 – 0.005x? - 0.01y2, where x, y, and z are measured in meters, and you are standing at a point with coordinates (60, 40, 1166). The positive x-axis points east and the positive y-axis points north. (a) If you walk due south, will you start to ascend or descend? O ascend descend At what rate? vertical meters per horizontal meter (b) If you walk northwest, will you start to ascend or descend? O ascend O descend At what rate? (Round your answer to two decimal places.) vertical meters per horizontal meter (c) In which direction is the slope largest? What is the rate of ascent in that direction? vertical meters per horizontal meter At what angle above the horizontal does the path in that direction begin? (Round your answer to two decimal places.)

Solve the following equation for y

What is the value of x when y = 9 in the equation y = 2x² + 1? O x = -5 Ox=0 Ox=2 Ox=2, -2 Ox= 3,5