Question

Suppose you are climbing a hill whose shape is given by the equation z = 1400-0.005x-0.01, where x, y, and z are measured in meters, and you are standing at a point with coordinates (60, 40, 1366). 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 descend At what rate? vertical meters per horizontal meter (b) If you walk northwest, will you start to ascend or descend? Oascend Odescend 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.

Answer 1

The solutio m is given beiou Нее given equatiori Z 1400 -0.0o5 0.01 where in measyred qnd poirit mete-2s qnd stamding at You aure with coodinates (60,40, 1366) (а) нече to dizeetion is south Stat nit The vecto is Poiut South South VZ = sao-0ahl(hei (2y)j -0.01 (2x)i -0.01 io.0 2 0.00S j o.0,-0.02y 0.01 (60)0.0 2 (40) Z60,0, 1366) = -0.6 ,-0.8 Dyf -0.6,-0.8 o,-1) o.8 So, you Uk due South wil yoy sdat

O.8 qScemd at the 2cte (b) Nou worlk mothuest you the unitvecto the n Point Northn ue st is Nth west 0.6,-0-8 1 Duf O.8 0. 6 0.14.14 - - 0. 2 wi you walk nohwest FI Start 0:2 -.1414 to descend at cte slope is lo2gest (c) Now the gadiet o.6 ,-0.8 direc tion ot in the dieetion of ascent The 2ate is NEO.60.8) z(60,40,1366 ate ot ohange is The

Now the angte hoeizonta the above does the that diection begin jn PCr Path tan -0.8 o.6 tem (1.3333 S3. 13 es in the the vecto (-0.6 , ) thid ucdrant dikeetion of the Szadie nt is S3. 13 180 233.13 which is eguiked solution,