Linear equations with constant coefficients, find the general solution, y, of the follow а. у" — 6у" + 9у %3D 0, b. y" — Зу' + 2у %3D0 с. у" + 16у %3D 0 d. y" - бу" + 25у' %3D 0 е. у" — 16у%3D 0 f. y" - бу' + 25у %3D 0 y(0) = -3, y'(0) = –1 - %3D

The equation in the form Ax + By = C (-6,3) and (0,-2)

Suppose you are climbing a hill whose shape is given by the equation z = 1300- 0.005x² - 0.01y², where x, y, and z are measured in meters, and you are standing at a point with coordinates (60, 40, 1266). 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? Ⓒascend O descend At what rate? 1.6 X descend (b) If you walk northwest, will you start to ascend or descend? O ascend vertical meters per horizontal meter At what rate? (Round your answer to two decimal places.) .57 vertical meters per horizontal meter X (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.) 60.81

Determine the y coordinate of the point on the line 27 8-8-4 -2 +t-3 -2 closest to the point (1, -2,-2). 81/14 O-25/14 O-13/7 26/7 O27/14 -2