
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:


Answer:
fraction:1/6 decimal:0.166666 repeated percent:16.6 repeated
Step-by-step explanation:
EXPLANATION:
-To formulate an equation, you must first know what data the exercise gives us to locate them correctly.
data:
-6 that must be added to a number.
-four times a number that is equal to 4x
-a result that is equal to 50
Now with these data we formulate the equation:

if we solve the equation we have: