1) Suppose that you are climbing a hill whose shape is given by z = 321 ? 0.03 x
ID: 2834479 • Letter: 1
Question
1) Suppose that you are climbing a hill whose shape is given by z=321?0.03x2?0.01y2 , and that you are at the point (20, 30, 300).
In which direction (unit vector) should you proceed initially in order to reach the top of the hill fastest?
( , )
If you climb in that direction, at what angle above the horizontal will you be climbing initially (radian measure)
2) Find the points on the surface 4x^2 + 3y^2 + z^2=1 at which the tangent plane is parallel to the plane -5x+2y-z=3
( , , )
( , , )
3) You are standing above the point (5,1) on the surface z=10-(3x^2+y^2)
a) In which direction should you walk to descend fastest (Give answer as two unit vector) direction=
b) If you start to move in this direction, what is the slope of your path?
Suppose that you are climbing a hill whose shape is given by z=321?0.03x 2 ?0.01y 2 , and that you are at the point (20, 30, 300). In which direction (unit vector) should you proceed initially in order to reach the top of the hill fastest? If you climb in that direction, at what angle above the horizontal will you be climbing initially (radian measure) Find the points on the surface 4x^2 + 3y^2 + z^2=1 at which the tangent plane is parallel to the plane -5x+2y-z=3 ( , , ) ( , , ) You are standing above the point (5,1) on the surface z=10-(3x^2+y^2) In which direction should you walk to descend fastest (Give answer as two unit vector) direction= If you start to move in this direction, what is the slope of your path?Explanation / Answer
1) [21*k - 20*i - 30*j]/41.72 = -0.48*i -0.72*j + 0.503*k
3)
a) [-5*i - j]/5.1 = -0.98*i -0.196*j
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