Question

1. A car is driving northwest at vv mph across a sloping plain whose height, in feet above sea level, at a point NN miles north and EE miles east of a city is given by

h(N,E)=3250+125N+75E.h(N,E)=3250+125N+75E.

**(a)** At what rate is the height above sea level
changing with respect to distance in the direction the car is
driving?

**(b)** Express the rate of change of the height of
the car with respect to time in terms of vv.

2. Suppose that you are climbing a hill whose shape is given by z=993−0.05x2−0.07y2z=993−0.05x2−0.07y2, and that you are at the point (70,80,300).(70,80,300).

a) In which direction should you proceed initially in order to reach the top of the hill fastest?

b) If you climb in that direction, at what angle above the horizontal will you be climbing initially (radian measure)?

3. Consider a function f(x,y)f(x,y) at the point
(6,6)(6,6).

At that point the function has directional derivatives:

385√385 in the direction (parallel to) 〈7,6〉〈7,6〉, and

685√685 in the direction (parallel to) 〈6,7〉〈6,7〉.

The gradient of ff at the point (6,6)(6,6) is

4. Consider the surface x=3y2+5z2−126x=3y2+5z2−126.

a) Find an equation of the tangent plane to the surface at the point (2,6,2)(2,6,2).

b) Find a vector equation of the normal line to the surface at
(2,6,2)(2,6,2)

r(t)r(t) =

Answer #1

ch 6
1:
It is generally a good idea to gain an understanding of the
"size" of units. Consider the objects and calculate the kinetic
energy of each one.
A ladybug weighing 37.3 mg
flies by your head at 3.83 km/h
.
×10
J
A 7.15 kg
bowling ball slides (not rolls) down an alley at 17.5 km/h
.
J
A car weighing 1260 kg
moves at a speed of 49.5 km/h.
5:
The graph shows the ?-directed force
??...

What tools could AA leaders have used to increase their
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???ALASKA AIRLINES: NAVIGATING CHANGE
In the autumn of 2007, Alaska Airlines executives adjourned at
the end of a long and stressful day in the
midst of a multi-day strategic planning session. Most headed
outside to relax, unwind and enjoy a bonfire
on the shore of Semiahmoo Spit, outside the meeting venue in
Blaine, a seaport town in northwest
Washington state.
Meanwhile, several members of...

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