1.explain how you would graph the inequality y<2/3x+1 on a coordinate plane. Be very specific and describe all your steps ple
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To solve this problem you must apply the proccedure shown below:
1. You have the following equation of a parabola, given in the problem above:
x<span>=1/16y^2
2. Then, based on the graph attached, you have:
p=y^2/4x
p=8^2/(4)(4)
p=64/16
p=4
3. The directrix is:
directrix=h-p
directrix=0-4
directrix=-4
The answer is:-4</span>
1. You have the following equation of a parabola, given in the problem above:
x<span>=1/16y^2
2. Then, based on the graph attached, you have:
p=y^2/4x
p=8^2/(4)(4)
p=64/16
p=4
3. The directrix is:
directrix=h-p
directrix=0-4
directrix=-4
The answer is:-4</span>
We want to find such that
. This means
Integrating both sides of the latter equation with respect to tells us
and differentiating with respect to gives
Integrating both sides with respect to gives
Then
and differentiating both sides with respect to gives
So the scalar potential function is
By the fundamental theorem of calculus, the work done by along any path depends only on the endpoints of that path. In particular, the work done over the line segment (call it
) in part (a) is
and does the same amount of work over both of the other paths.
In part (b), I don't know what is meant by "df/dt for F"...
In part (c), you're asked to find the work over the 2 parts (call them and
) of the given path. Using the fundamental theorem makes this trivial: